(************** Content-type: application/mathematica ************** CreatedBy='Mathematica 5.0' Mathematica-Compatible Notebook This notebook can be used with any Mathematica-compatible application, such as Mathematica, MathReader or Publicon. The data for the notebook starts with the line containing stars above. To get the notebook into a Mathematica-compatible application, do one of the following: * Save the data starting with the line of stars above into a file with a name ending in .nb, then open the file inside the application; * Copy the data starting with the line of stars above to the clipboard, then use the Paste menu command inside the application. Data for notebooks contains only printable 7-bit ASCII and can be sent directly in email or through ftp in text mode. Newlines can be CR, LF or CRLF (Unix, Macintosh or MS-DOS style). 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For more information on notebooks and Mathematica-compatible applications, contact Wolfram Research: web: http://www.wolfram.com email: info@wolfram.com phone: +1-217-398-0700 (U.S.) Notebook reader applications are available free of charge from Wolfram Research. *******************************************************************) (*CacheID: 232*) (*NotebookFileLineBreakTest NotebookFileLineBreakTest*) (*NotebookOptionsPosition[ 1746318, 25760]*) (*NotebookOutlinePosition[ 1746952, 25782]*) (* CellTagsIndexPosition[ 1746908, 25778]*) (*WindowFrame->Normal*) Notebook[{ Cell[CellGroupData[{ Cell["Finiteness for Relative Equilibria of the Four-Body Problem", "Title"], Cell[CellGroupData[{ Cell["Introduction", "Section"], Cell["\<\ This notebook contains computational algorithms and results which support the \ paper \"Finiteness of relative equilibria of the four-body problem\" by \ Marshall Hampton and Richard Moeckel. The notebook is divided into sections \ explaining the different kinds of computations used to verify the results in \ the paper. The reader can go through the notebook section by section, \ executing the cells in order to check the computations. Some computations were done with the other programs such as Porta, Macaulay2, \ lrs and Mixvol. As explained below, these results have simply been copied \ into this notebook so that further computations based on them can be \ illustrated.\ \>", "Text"] }, Open ]], Cell[CellGroupData[{ Cell["Equations for Relative Equilibria", "Section"], Cell["\<\ First we define some functions to automatically construct the \ Albouy-Chenciner equations for central configurations. For the four-body \ problem, there are six equations for the six mutual distances.\ \>", "Text"], Cell[BoxData[{ \( (*\ Define\ mutual\ distances\ and\ normalized\ variables\ Sij\ *) \ \[IndentingNewLine]r[i_, i_] := 0\), "\[IndentingNewLine]", \(r[i_, j_] := r[j, i] /; j < i\), "\[IndentingNewLine]", \(S[i_, i_] := \ 0\), "\[IndentingNewLine]", \(S[i_, j_]\ := \(\(1/r[i, j]^3 - 1\)\(\[IndentingNewLine]\)\(\[IndentingNewLine]\)\( (*\ Carry\ out\ the\ sum\ in\ equation\ \((10)\)\ of\ section\ 2.1\ *) \)\ \)\), "\[IndentingNewLine]", \(\(\(P[i_, j_, n_]\ := Plus @@ Table[ m[k]*\((S[i, k]*\((r[j, k]^2 - r[i, k]^2 - r[i, j]^2)\) + S[j, k]*\((r[i, k]^2 - r[j, k]^2 - r[i, j]^2)\))\), {k, 1, n}]\)\(\[IndentingNewLine]\)\(\[IndentingNewLine]\)\) (*\ Make\ a\ table\ of\ all\ of\ the\ Albouy - Chenciner\ equations\ and\ clear\ the\ denominators\ *) \ \), "\ \[IndentingNewLine]", \(ACeqs[ n_]\ := \ \(\(Table[P[i, j, n], {j, 2, n}, {i, 1, j - 1}] // Flatten\) // Factor\) // Numerator\)}], "Input"], Cell["\<\ Here are the equations written out with the array variables replaced by \ ordinary ones. \ \>", "Text"], Cell[CellGroupData[{ Cell[BoxData[{ \(\(varsub\ = \ {r[1, 2] \[Rule] r12, r[1, 3] \[Rule] r13, r[2, 3] \[Rule] r23, r[1, 4] \[Rule] r14, r[2, 4] \[Rule] r24, r[3, 4] \[Rule] r34, m[1] \[Rule] m1, m[2] \[Rule] m2, m[3] \[Rule] m3, m[4] \[Rule] m4};\)\[IndentingNewLine]\), "\[IndentingNewLine]", \(aceqs\ = \ ACeqs[4] /. varsub\)}], "Input"], Cell[BoxData[ \({\(-m4\)\ r12\^3\ r13\^3\ r14\^3\ r23\^3 + m4\ r12\ r13\^3\ r14\^5\ r23\^3 - m4\ r12\ r13\^3\ r14\^3\ r23\^3\ r24\^2 - m3\ r12\^3\ r13\^3\ r14\^3\ r24\^3 + m3\ r12\ r13\^5\ r14\^3\ r24\^3 - m3\ r12\ r13\^3\ r14\^3\ r23\^2\ r24\^3 - m4\ r12\^3\ r13\^3\ r23\^3\ r24\^3 - m4\ r12\ r13\^3\ r14\^2\ r23\^3\ r24\^3 - m3\ r12\^3\ r14\^3\ r23\^3\ r24\^3 - m3\ r12\ r13\^2\ r14\^3\ r23\^3\ r24\^3 - 2\ m1\ r13\^3\ r14\^3\ r23\^3\ r24\^3 - 2\ m2\ r13\^3\ r14\^3\ r23\^3\ r24\^3 + 2\ m1\ r12\^3\ r13\^3\ r14\^3\ r23\^3\ r24\^3 + 2\ m2\ r12\^3\ r13\^3\ r14\^3\ r23\^3\ r24\^3 + 2\ m3\ r12\^3\ r13\^3\ r14\^3\ r23\^3\ r24\^3 + 2\ m4\ r12\^3\ r13\^3\ r14\^3\ r23\^3\ r24\^3 + m3\ r12\ r14\^3\ r23\^5\ r24\^3 + m4\ r12\ r13\^3\ r23\^3\ r24\^5, \(-m4\)\ r12\^3\ r13\^3\ r14\^3\ r23\ \^3 + m4\ r12\^3\ r13\ r14\^5\ r23\^3 - m4\ r12\^3\ r13\ r14\^3\ r23\^3\ r34\^2 + m2\ r12\^5\ r13\ r14\^3\ r34\^3 - m2\ r12\^3\ r13\^3\ r14\^3\ r34\^3 - m2\ r12\^3\ r13\ r14\^3\ r23\^2\ r34\^3 - m4\ r12\^3\ r13\^3\ r23\^3\ r34\^3 - m4\ r12\^3\ r13\ r14\^2\ r23\^3\ r34\^3 - 2\ m1\ r12\^3\ r14\^3\ r23\^3\ r34\^3 - 2\ m3\ r12\^3\ r14\^3\ r23\^3\ r34\^3 - m2\ r12\^2\ r13\ r14\^3\ r23\^3\ r34\^3 - m2\ r13\^3\ r14\^3\ r23\^3\ r34\^3 + 2\ m1\ r12\^3\ r13\^3\ r14\^3\ r23\^3\ r34\^3 + 2\ m2\ r12\^3\ r13\^3\ r14\^3\ r23\^3\ r34\^3 + 2\ m3\ r12\^3\ r13\^3\ r14\^3\ r23\^3\ r34\^3 + 2\ m4\ r12\^3\ r13\^3\ r14\^3\ r23\^3\ r34\^3 + m2\ r13\ r14\^3\ r23\^5\ r34\^3 + m4\ r12\^3\ r13\ r23\^3\ r34\^5, \(-m4\)\ r12\^3\ r13\^3\ r23\^3\ r24\ \^3 + m4\ r12\^3\ r13\^3\ r23\ r24\^5 - m4\ r12\^3\ r13\^3\ r23\ r24\^3\ r34\^2 - m4\ r12\^3\ r13\^3\ r23\^3\ r34\^3 - m4\ r12\^3\ r13\^3\ r23\ r24\^2\ r34\^3 - 2\ m2\ r12\^3\ r13\^3\ r24\^3\ r34\^3 - 2\ m3\ r12\^3\ r13\^3\ r24\^3\ r34\^3 + m1\ r12\^5\ r23\ r24\^3\ r34\^3 - m1\ r12\^3\ r13\^2\ r23\ r24\^3\ r34\^3 - m1\ r12\^2\ r13\^3\ r23\ r24\^3\ r34\^3 + m1\ r13\^5\ r23\ r24\^3\ r34\^3 - m1\ r12\^3\ r23\^3\ r24\^3\ r34\^3 - m1\ r13\^3\ r23\^3\ r24\^3\ r34\^3 + 2\ m1\ r12\^3\ r13\^3\ r23\^3\ r24\^3\ r34\^3 + 2\ m2\ r12\^3\ r13\^3\ r23\^3\ r24\^3\ r34\^3 + 2\ m3\ r12\^3\ r13\^3\ r23\^3\ r24\^3\ r34\^3 + 2\ m4\ r12\^3\ r13\^3\ r23\^3\ r24\^3\ r34\^3 + m4\ r12\^3\ r13\^3\ r23\ r34\^5, m3\ r12\^3\ r13\^5\ r14\ r24\^3 - m3\ r12\^3\ r13\^3\ r14\^3\ r24\^3 - m3\ r12\^3\ r13\^3\ r14\ r24\^3\ r34\^2 + m2\ r12\^5\ r13\^3\ r14\ r34\^3 - m2\ r12\^3\ r13\^3\ r14\^3\ r34\^3 - m2\ r12\^3\ r13\^3\ r14\ r24\^2\ r34\^3 - 2\ m1\ r12\^3\ r13\^3\ r24\^3\ r34\^3 - 2\ m4\ r12\^3\ r13\^3\ r24\^3\ r34\^3 - m3\ r12\^3\ r13\^2\ r14\ r24\^3\ r34\^3 - m2\ r12\^2\ r13\^3\ r14\ r24\^3\ r34\^3 - m3\ r12\^3\ r14\^3\ r24\^3\ r34\^3 - m2\ r13\^3\ r14\^3\ r24\^3\ r34\^3 + 2\ m1\ r12\^3\ r13\^3\ r14\^3\ r24\^3\ r34\^3 + 2\ m2\ r12\^3\ r13\^3\ r14\^3\ r24\^3\ r34\^3 + 2\ m3\ r12\^3\ r13\^3\ r14\^3\ r24\^3\ r34\^3 + 2\ m4\ r12\^3\ r13\^3\ r14\^3\ r24\^3\ r34\^3 + m2\ r13\^3\ r14\ r24\^5\ r34\^3 + m3\ r12\^3\ r14\ r24\^3\ r34\^5, m3\ r12\^3\ r14\^3\ r23\^5\ r24 - m3\ r12\^3\ r14\^3\ r23\^3\ r24\^3 - m3\ r12\^3\ r14\^3\ r23\^3\ r24\ r34\^2 - 2\ m2\ r12\^3\ r14\^3\ r23\^3\ r34\^3 - 2\ m4\ r12\^3\ r14\^3\ r23\^3\ r34\^3 - m3\ r12\^3\ r14\^3\ r23\^2\ r24\ r34\^3 + m1\ r12\^5\ r23\^3\ r24\ r34\^3 - m1\ r12\^3\ r14\^2\ r23\^3\ r24\ r34\^3 - m1\ r12\^2\ r14\^3\ r23\^3\ r24\ r34\^3 + m1\ r14\^5\ r23\^3\ r24\ r34\^3 - m3\ r12\^3\ r14\^3\ r24\^3\ r34\^3 - m1\ r12\^3\ r23\^3\ r24\^3\ r34\^3 - m1\ r14\^3\ r23\^3\ r24\^3\ r34\^3 + 2\ m1\ r12\^3\ r14\^3\ r23\^3\ r24\^3\ r34\^3 + 2\ m2\ r12\^3\ r14\^3\ r23\^3\ r24\^3\ r34\^3 + 2\ m3\ r12\^3\ r14\^3\ r23\^3\ r24\^3\ r34\^3 + 2\ m4\ r12\^3\ r14\^3\ r23\^3\ r24\^3\ r34\^3 + m3\ r12\^3\ r14\^3\ r24\ r34\^5, \(-2\)\ m3\ r13\^3\ r14\^3\ r23\^3\ \ r24\^3 - 2\ m4\ r13\^3\ r14\^3\ r23\^3\ r24\^3 + m2\ r13\^3\ r14\^3\ r23\^5\ r34 - m2\ r13\^3\ r14\^3\ r23\^3\ r24\^2\ r34 - m2\ r13\^3\ r14\^3\ r23\^2\ r24\^3\ r34 + m1\ r13\^5\ r23\^3\ r24\^3\ r34 - m1\ r13\^3\ r14\^2\ r23\^3\ r24\^3\ r34 - m1\ r13\^2\ r14\^3\ r23\^3\ r24\^3\ r34 + m1\ r14\^5\ r23\^3\ r24\^3\ r34 + m2\ r13\^3\ r14\^3\ r24\^5\ r34 - m2\ r13\^3\ r14\^3\ r23\^3\ r34\^3 - m2\ r13\^3\ r14\^3\ r24\^3\ r34\^3 - m1\ r13\^3\ r23\^3\ r24\^3\ r34\^3 - m1\ r14\^3\ r23\^3\ r24\^3\ r34\^3 + 2\ m1\ r13\^3\ r14\^3\ r23\^3\ r24\^3\ r34\^3 + 2\ m2\ r13\^3\ r14\^3\ r23\^3\ r24\^3\ r34\^3 + 2\ m3\ r13\^3\ r14\^3\ r23\^3\ r24\^3\ r34\^3 + 2\ m4\ r13\^3\ r14\^3\ r23\^3\ r24\^3\ r34\^3}\)], "Output"] }, Open ]], Cell["Next we enter in the three Dziobek equations.", "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(\(\( (*\ Equations\ \((12)\)\ from\ section\ 2.2\ \ *) \)\(\[IndentingNewLine]\)\(dzeqs\ = \ \({S[1, 2] S[3, 4] - S[1, 4] S[2, 3], S[1, 2] S[3, 4] - S[1, 3] S[2, 4], S[1, 3] S[2, 4] - S[1, 4] S[2, 3]} /. varsub // Factor\) // Numerator\)\)\)], "Input"], Cell[BoxData[ \({r14\^3\ r23\^3 - r12\^3\ r14\^3\ r23\^3 - r12\^3\ r34\^3 + r12\^3\ r14\^3\ r34\^3 + r12\^3\ r23\^3\ r34\^3 - r14\^3\ r23\^3\ r34\^3, r13\^3\ r24\^3 - r12\^3\ r13\^3\ r24\^3 - r12\^3\ r34\^3 + r12\^3\ r13\^3\ r34\^3 + r12\^3\ r24\^3\ r34\^3 - r13\^3\ r24\^3\ r34\^3, r14\^3\ r23\^3 - r13\^3\ r14\^3\ r23\^3 - r13\^3\ r24\^3 + r13\^3\ r14\^3\ r24\^3 + r13\^3\ r23\^3\ r24\^3 - r14\^3\ r23\^3\ r24\^3}\)], "Output"] }, Open ]], Cell["\<\ Our main system consists of these nine equations for the six mutual \ distances. \ \>", "Text"], Cell[BoxData[ \(\(acdzeqs\ = \ aceqs~Join~dzeqs;\)\)], "Input"], Cell["\<\ For constructing the upper bound we also use another system of 10 equations \ and 10 unknowns. We begin by entering the system of 11 equations and \ unknowns (13) from section 2.2 The first five are geometrical equations \ arising from the \"Cayley-Menger\" matrix of squared mutual distances. \ \>", "Text"], Cell[CellGroupData[{ Cell[BoxData[{ \(\(CM = \ {{0, 1, 1, 1, 1}, \[IndentingNewLine]{1, 0, r12^2, r13^2, r14^2}, \[IndentingNewLine]{1, r12^2, 0, r23^2, r24^2}, \[IndentingNewLine]{1, r13^2, r23^2, 0, r34^2}, \[IndentingNewLine]{1, r14^2, r24^2, r34^2, 0}};\)\), "\[IndentingNewLine]", \(geomeqs\ = \ CM . {k, m1*z1, m2*z2, m3*z3, m4*z4}\)}], "Input"], Cell[BoxData[ \({m1\ z1 + m2\ z2 + m3\ z3 + m4\ z4, k + m2\ r12\^2\ z2 + m3\ r13\^2\ z3 + m4\ r14\^2\ z4, k + m1\ r12\^2\ z1 + m3\ r23\^2\ z3 + m4\ r24\^2\ z4, k + m1\ r13\^2\ z1 + m2\ r23\^2\ z2 + m4\ r34\^2\ z4, k + m1\ r14\^2\ z1 + m2\ r24\^2\ z2 + m3\ r34\^2\ z3}\)], "Output"] }, Open ]], Cell["The other six are essentially due to Dziobek.", "Text"], Cell[CellGroupData[{ Cell[BoxData[{ \(\(moredzeqs\ = \ \(\(Table[ S[i, j] - z[i]*z[j], {j, 2, 4}, {i, 1, j - 1}] // Flatten\) // Factor\) // Numerator;\)\), "\[IndentingNewLine]", \(\(varsub2\ = \ {z[1] \[Rule] z1, z[2] \[Rule] z2, z[3] \[Rule] z3, z[4] \[Rule] z4};\)\), "\[IndentingNewLine]", \(moredzeqs\ = \ \(moredzeqs /. varsub\) /. varsub2\)}], "Input"], Cell[BoxData[ \({1 - r12\^3 - r12\^3\ z1\ z2, 1 - r13\^3 - r13\^3\ z1\ z3, 1 - r23\^3 - r23\^3\ z2\ z3, 1 - r14\^3 - r14\^3\ z1\ z4, 1 - r24\^3 - r24\^3\ z2\ z4, 1 - r34\^3 - r34\^3\ z3\ z4}\)], "Output"] }, Open ]], Cell["\<\ The system of 10 equations and ten unknowns is obtained by eliminating k. \ \>", "Text"], Cell[CellGroupData[{ Cell[BoxData[{ \(\(geomeqsnok\ = \ {geomeqs[\([1]\)], geomeqs[\([2]\)] - geomeqs[\([5]\)], geomeqs[\([3]\)] - geomeqs[\([5]\)], geomeqs[\([4]\)] - geomeqs[\([5]\)]};\)\), "\[IndentingNewLine]", \(teneqs\ = \ geomeqsnok~Join~moredzeqs\)}], "Input"], Cell[BoxData[ \({m1\ z1 + m2\ z2 + m3\ z3 + m4\ z4, \(-m1\)\ r14\^2\ z1 + m2\ r12\^2\ z2 - m2\ r24\^2\ z2 + m3\ r13\^2\ z3 - m3\ r34\^2\ z3 + m4\ r14\^2\ z4, m1\ r12\^2\ z1 - m1\ r14\^2\ z1 - m2\ r24\^2\ z2 + m3\ r23\^2\ z3 - m3\ r34\^2\ z3 + m4\ r24\^2\ z4, m1\ r13\^2\ z1 - m1\ r14\^2\ z1 + m2\ r23\^2\ z2 - m2\ r24\^2\ z2 - m3\ r34\^2\ z3 + m4\ r34\^2\ z4, 1 - r12\^3 - r12\^3\ z1\ z2, 1 - r13\^3 - r13\^3\ z1\ z3, 1 - r23\^3 - r23\^3\ z2\ z3, 1 - r14\^3 - r14\^3\ z1\ z4, 1 - r24\^3 - r24\^3\ z2\ z4, 1 - r34\^3 - r34\^3\ z3\ z4}\)], "Output"] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell["Newton Polytopes", "Section"], Cell[TextData[{ "In this section we find show the ", StyleBox["Mathematica", FontSlant->"Italic"], " functions used to compute the Newton polytopes of our equations and their \ Minkowski sums. The ", StyleBox["Mathematica", FontSlant->"Italic"], " part just involves reading off all the exponent vectors and adding them. \ For the real work of finding the convex hulls we used Porta 1.3.2. The \ final result was verified using lrs 4.1." }], "Text"], Cell[CellGroupData[{ Cell["Exponent Lists", "Subsection"], Cell[TextData[{ "First we have some simple functions based on ", StyleBox["Mathematica's ", FontSlant->"Italic"], StyleBox["built-in Exponent command. Essentially a polynomial which has \ been completely expanded is represented in ", FontVariations->{"CompatibilityType"->0}], StyleBox["Mathematica", FontSlant->"Italic", FontVariations->{"CompatibilityType"->0}], StyleBox[" as a list of its terms (with a \"Head\" of \"Plus\" in front). \ We also make use of a list of the variables whose exponents we want to read \ off. The first function below is intended to act on a single term of a \ polynomials. It applies ", FontVariations->{"CompatibilityType"->0}], StyleBox["Mathematica", FontSlant->"Italic", FontVariations->{"CompatibilityType"->0}], StyleBox["'s Exponent command to the monomial for each variable in the \ variable list thereby producing a list of the exponents for all the \ variables. For a polynomial, we just to this for every term to get a list of \ lists of exponents. The Union command eliminates redundancies arising from \ terms which involve the same powers of the variables with different \ coefficients.", FontVariations->{"CompatibilityType"->0}] }], "Text"], Cell[BoxData[{ \(GetExponents[mon_, vars_]\ := \ Map[Exponent[mon, #] &, vars]\), "\[IndentingNewLine]", \(GetAllExponents[poly_, vars_] := \[IndentingNewLine]Table[ GetExponents[poly[\([i]\)], vars], {i, 1, Length[poly]}] // Union\)}], "Input"], Cell["\<\ Here is the exponent list for the Albouy-Chenciner-Dziobek system. \ \>", "Text"], Cell[CellGroupData[{ Cell[BoxData[{ \(\(vars4bp\ = \ {r12, r13, r14, r23, r24, r34};\)\), "\[IndentingNewLine]", \(explist9\ = \ Map[GetAllExponents[#, vars4bp] &, acdzeqs]\)}], "Input"], Cell[BoxData[ \({{{0, 3, 3, 3, 3, 0}, {1, 0, 3, 5, 3, 0}, {1, 2, 3, 3, 3, 0}, {1, 3, 0, 3, 5, 0}, {1, 3, 2, 3, 3, 0}, {1, 3, 3, 2, 3, 0}, {1, 3, 3, 3, 2, 0}, {1, 3, 5, 3, 0, 0}, {1, 5, 3, 0, 3, 0}, {3, 0, 3, 3, 3, 0}, {3, 3, 0, 3, 3, 0}, {3, 3, 3, 0, 3, 0}, {3, 3, 3, 3, 0, 0}, {3, 3, 3, 3, 3, 0}}, {{0, 1, 3, 5, 0, 3}, {0, 3, 3, 3, 0, 3}, {2, 1, 3, 3, 0, 3}, {3, 0, 3, 3, 0, 3}, {3, 1, 0, 3, 0, 5}, {3, 1, 2, 3, 0, 3}, {3, 1, 3, 2, 0, 3}, {3, 1, 3, 3, 0, 2}, {3, 1, 5, 3, 0, 0}, {3, 3, 0, 3, 0, 3}, {3, 3, 3, 0, 0, 3}, {3, 3, 3, 3, 0, 0}, {3, 3, 3, 3, 0, 3}, {5, 1, 3, 0, 0, 3}}, {{0, 3, 0, 3, 3, 3}, {0, 5, 0, 1, 3, 3}, {2, 3, 0, 1, 3, 3}, {3, 0, 0, 3, 3, 3}, {3, 2, 0, 1, 3, 3}, {3, 3, 0, 0, 3, 3}, {3, 3, 0, 1, 0, 5}, {3, 3, 0, 1, 2, 3}, {3, 3, 0, 1, 3, 2}, {3, 3, 0, 1, 5, 0}, {3, 3, 0, 3, 0, 3}, {3, 3, 0, 3, 3, 0}, {3, 3, 0, 3, 3, 3}, {5, 0, 0, 1, 3, 3}}, {{0, 3, 1, 0, 5, 3}, {0, 3, 3, 0, 3, 3}, {2, 3, 1, 0, 3, 3}, {3, 0, 1, 0, 3, 5}, {3, 0, 3, 0, 3, 3}, {3, 2, 1, 0, 3, 3}, {3, 3, 0, 0, 3, 3}, {3, 3, 1, 0, 2, 3}, {3, 3, 1, 0, 3, 2}, {3, 3, 3, 0, 0, 3}, {3, 3, 3, 0, 3, 0}, {3, 3, 3, 0, 3, 3}, {3, 5, 1, 0, 3, 0}, {5, 3, 1, 0, 0, 3}}, {{0, 0, 3, 3, 3, 3}, {0, 0, 5, 3, 1, 3}, {2, 0, 3, 3, 1, 3}, {3, 0, 0, 3, 3, 3}, {3, 0, 2, 3, 1, 3}, {3, 0, 3, 0, 1, 5}, {3, 0, 3, 0, 3, 3}, {3, 0, 3, 2, 1, 3}, {3, 0, 3, 3, 0, 3}, {3, 0, 3, 3, 1, 2}, {3, 0, 3, 3, 3, 0}, {3, 0, 3, 3, 3, 3}, {3, 0, 3, 5, 1, 0}, {5, 0, 0, 3, 1, 3}}, {{0, 0, 3, 3, 3, 3}, {0, 0, 5, 3, 3, 1}, {0, 2, 3, 3, 3, 1}, {0, 3, 0, 3, 3, 3}, {0, 3, 2, 3, 3, 1}, {0, 3, 3, 0, 3, 3}, {0, 3, 3, 0, 5, 1}, {0, 3, 3, 2, 3, 1}, {0, 3, 3, 3, 0, 3}, {0, 3, 3, 3, 2, 1}, {0, 3, 3, 3, 3, 0}, {0, 3, 3, 3, 3, 3}, {0, 3, 3, 5, 0, 1}, {0, 5, 0, 3, 3, 1}}, {{0, 0, 3, 3, 0, 0}, {0, 0, 3, 3, 0, 3}, {3, 0, 0, 0, 0, 3}, {3, 0, 0, 3, 0, 3}, {3, 0, 3, 0, 0, 3}, {3, 0, 3, 3, 0, 0}}, {{0, 3, 0, 0, 3, 0}, {0, 3, 0, 0, 3, 3}, {3, 0, 0, 0, 0, 3}, {3, 0, 0, 0, 3, 3}, {3, 3, 0, 0, 0, 3}, {3, 3, 0, 0, 3, 0}}, {{0, 0, 3, 3, 0, 0}, {0, 0, 3, 3, 3, 0}, {0, 3, 0, 0, 3, 0}, {0, 3, 0, 3, 3, 0}, {0, 3, 3, 0, 3, 0}, {0, 3, 3, 3, 0, 0}}}\)], "Output"] }, Open ]], Cell["\<\ The Albouy-Chenciner equations have 14 essentially different monomials and \ the Dziobek equations have 6. These will be the initial numbers of \ vertices in the initial Newton polytopes, but some of them may not be extreme \ points on the convex hull. \ \>", "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(Map[Length, explist9]\)], "Input"], Cell[BoxData[ \({14, 14, 14, 14, 14, 14, 6, 6, 6}\)], "Output"] }, Open ]], Cell["\<\ In a similar way, we compute the exponent vectors for the auxiliary system of \ 10 equations and 10 unknowns. \ \>", "Text"], Cell[CellGroupData[{ Cell[BoxData[{ \(\(tenvars\ = \ {r12, r13, r14, r23, r24, r34, z1, z2, z3, z4};\)\[IndentingNewLine]\), "\[IndentingNewLine]", \(explist10\ = \ Map[GetAllExponents[#, tenvars] &, teneqs]\[IndentingNewLine]\), "\[IndentingNewLine]", \(Map[Length, explist10]\)}], "Input"], Cell[BoxData[ \({{{0, 0, 0, 0, 0, 0, 0, 0, 0, 1}, {0, 0, 0, 0, 0, 0, 0, 0, 1, 0}, {0, 0, 0, 0, 0, 0, 0, 1, 0, 0}, {0, 0, 0, 0, 0, 0, 1, 0, 0, 0}}, {{0, 0, 0, 0, 0, 2, 0, 0, 1, 0}, {0, 0, 0, 0, 2, 0, 0, 1, 0, 0}, {0, 0, 2, 0, 0, 0, 0, 0, 0, 1}, {0, 0, 2, 0, 0, 0, 1, 0, 0, 0}, {0, 2, 0, 0, 0, 0, 0, 0, 1, 0}, {2, 0, 0, 0, 0, 0, 0, 1, 0, 0}}, {{0, 0, 0, 0, 0, 2, 0, 0, 1, 0}, {0, 0, 0, 0, 2, 0, 0, 0, 0, 1}, {0, 0, 0, 0, 2, 0, 0, 1, 0, 0}, {0, 0, 0, 2, 0, 0, 0, 0, 1, 0}, {0, 0, 2, 0, 0, 0, 1, 0, 0, 0}, {2, 0, 0, 0, 0, 0, 1, 0, 0, 0}}, {{0, 0, 0, 0, 0, 2, 0, 0, 0, 1}, {0, 0, 0, 0, 0, 2, 0, 0, 1, 0}, {0, 0, 0, 0, 2, 0, 0, 1, 0, 0}, {0, 0, 0, 2, 0, 0, 0, 1, 0, 0}, {0, 0, 2, 0, 0, 0, 1, 0, 0, 0}, {0, 2, 0, 0, 0, 0, 1, 0, 0, 0}}, {{0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {3, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {3, 0, 0, 0, 0, 0, 1, 1, 0, 0}}, {{0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 3, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 3, 0, 0, 0, 0, 1, 0, 1, 0}}, {{0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 3, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 3, 0, 0, 0, 1, 1, 0}}, {{0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 3, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 3, 0, 0, 0, 1, 0, 0, 1}}, {{0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 3, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 3, 0, 0, 1, 0, 1}}, {{0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 3, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 3, 0, 0, 1, 1}}}\)], "Output"], Cell[BoxData[ \({4, 6, 6, 6, 3, 3, 3, 3, 3, 3}\)], "Output"] }, Open ]], Cell["\<\ At this point the exponent list explist10 was put into a data file and edited \ to conform with the syntax requirements of the program Mixvol. The resulting \ file, called teneqs.sites was given as input to that program which \ computed the mixed volume of the 10 polytopes. The result was 25380 as \ reported in section 6 of the paper. After this we have no further need for \ the system of 10 equations or its exponent lists. \ \>", "Text"] }, Closed]], Cell[CellGroupData[{ Cell["Partial Minkowski Sums", "Subsection"], Cell["\<\ A key step in the method is to find the Minkowski sum of the 9 Newton \ polytopes of the Albouy-Chenciner-Dziobek system. The naive way to find a \ Minkowski sum is just to take all possible sums of nine vertices, one from \ each of the Newton polytopes. In practice, we had to go through cycles of \ taking Minkowski sums of a few of the 9 Newton polytopes, finding a more \ efficient representation of the convex hull using Porta and then adding in \ more of the Newton polytopes. In this way we could succeed in finding \ separate Minkowski sums for the six Albouy-Chenciner equations and for the \ three Dziobek equations. To add these two together required some tricks \ which will be handled in the next subsection. \ \>", "Text"], Cell["\<\ We begin with basic functios to add a single vertex to a list of vertices and \ to add two lists of vertices together. The second function is a primitive \ Minkowski sum for two polytopes but the vertex list will be unnecessarily \ long. One needs a program like Porta to find the true extreme points of the \ convex hull. \ \>", "Text"], Cell[BoxData[{ \(AddToAll[vect_, vlist_]\ := Map[\((\ vect + #)\) &, vlist]\), "\[IndentingNewLine]", \(MinkSum[vlist_, wlist_]\ := \ \(Map[AddToAll[#, wlist] &, vlist] // Flatten[#, 1] &\) // Union\)}], "Input"], Cell["\<\ Here is the primitive Minkowski sum for the three Dziobek equations. We get a \ list of 132 vertices. \ \>", "Text"], Cell[BoxData[{ \(dzmink\ = \ MinkSum[MinkSum[explist9[\([7]\)], explist9[\([8]\)]], explist9[\([9]\)]]\), "\[IndentingNewLine]", \(Length[dzmink]\)}], "Input"], Cell[TextData[{ "We put this list in a file named \"dzmink.poi\" and edited it to conform \ with the syntax of the program Porta 1.3.2. Running the command ", StyleBox["traf -l dzmink.poi ", FontWeight->"Bold"], "produces a file called \"dzmink.poi.ieq\" containing a minimal list of \ inequalities in six variables x1, ... , x6 defining the convex hull . \ Running the command ", StyleBox["traf -l dzmink.poi.ieq ", FontWeight->"Bold"], StyleBox["produces yet another file \"dzmink.poi.ieq.poi which contains the \ true vertices of the Minkowski sum polytope. To avoid having to deal with \ these files here, we will just copy the results, showing the commands in \ comments", FontVariations->{"CompatibilityType"->0}] }], "Text"], Cell[BoxData[{ \( (*\ Write\ the\ raw\ vertices\ to\ a\ file\ *) \[IndentingNewLine] (*\ Put[dzmink, "\"]\ *) \ \[IndentingNewLine]\[IndentingNewLine] (*\ Read\ in\ the\ results\ from\ porta, \ after\ editing\ the\ output\ files\ to\ Mathematica\ syntax\ *) \ \[IndentingNewLine] (*\ dzconv\ = \ ReadList["\", {Number, Number, Number, Number, Number, Number}]*) (*\ dzineq\ = \ ReadList["\", Expression]*) \[IndentingNewLine]\[IndentingNewLine]\(dzconv\ = \ \ {{3, 6, 0, 0, 6, 3}, {0, 3, 6, 6, 6, 0}, {3, 6, 0, 0, 6, 6}, {3, 6, 0, 6, 6, 6}, {6, 3, 0, 0, 6, 6}, {6, 3, 0, 6, 6, 6}, {0, 3, 6, 6, 3, 0}, {0, 6, 3, 3, 6, 0}, {0, 3, 6, 6, 6, 6}, {0, 6, 3, 6, 6, 0}, {0, 6, 3, 6, 6, 6}, {0, 6, 6, 3, 6, 0}, {0, 6, 6, 3, 6, 6}, {0, 6, 6, 6, 3, 0}, {6, 3, 6, 0, 6, 6}, {0, 3, 6, 6, 3, 6}, {0, 6, 3, 3, 6, 6}, {0, 6, 6, 6, 3, 6}, {6, 6, 0, 0, 3, 6}, {6, 6, 0, 6, 3, 6}, {6, 6, 6, 0, 3, 6}, {6, 0, 3, 3, 0, 6}, {6, 0, 3, 3, 6, 6}, {6, 0, 3, 6, 0, 6}, {6, 0, 3, 6, 6, 6}, {3, 0, 6, 6, 0, 3}, {3, 0, 6, 6, 6, 3}, {3, 0, 6, 6, 0, 6}, {3, 0, 6, 6, 6, 6}, {6, 0, 6, 3, 0, 6}, {6, 0, 6, 3, 6, 6}, {3, 6, 6, 6, 0, 3}, {3, 6, 6, 6, 0, 6}, {6, 6, 3, 3, 0, 6}, {6, 6, 3, 6, 0, 6}, {6, 6, 6, 3, 0, 6}, {6, 0, 6, 6, 0, 3}, {6, 0, 6, 6, 6, 3}, {6, 6, 0, 0, 6, 3}, {6, 6, 0, 6, 6, 3}, {6, 6, 6, 6, 0, 3}, {6, 3, 6, 6, 6, 0}, {6, 3, 6, 6, 3, 0}, {6, 6, 3, 3, 6, 0}, {3, 6, 6, 0, 6, 6}, {6, 6, 3, 6, 6, 0}, {6, 6, 6, 0, 6, 3}, {6, 6, 6, 3, 6, 0}, {3, 6, 0, 6, 6, 3}, {3, 6, 6, 0, 6, 3}, {6, 3, 0, 0, 3, 6}, {6, 3, 0, 6, 3, 6}, {6, 3, 6, 0, 3, 6}, {6, 6, 6, 6, 3, 0}};\)\[IndentingNewLine]\), "\[IndentingNewLine]", \(\(dzineq\ = \ {x1 + x2 + x5 + x6 \[LessEqual] 21, \(-x1\) - x2 - x3 \[LessEqual] \(-9\), \(-x1\) - x2 - x4 \[LessEqual] \(-9\), x3 \[LessEqual] 6, \(-x1\) - x4 - x5 \[LessEqual] \(-9\), x4 \[LessEqual] 6, \(-x1\) - x3 - x5 \[LessEqual] \(-9\), x6 \[LessEqual] 6, x5 \[LessEqual] 6, \(-x6\) \[LessEqual] 0, \(-x2\) - x3 - x6 \[LessEqual] \(-9\), \(-x2\) - x4 - x6 \[LessEqual] \(-9\), \(-x3\) - x5 - x6 \[LessEqual] \(-9\), \(-x4\) - x5 - x6 \[LessEqual] \(-9\), x2 + x3 + x4 + x5 \[LessEqual] 21, \(-x1\) \[LessEqual] 0, x2 \[LessEqual] 6, \(-x2\) \[LessEqual] 0, \(-x5\) \[LessEqual] 0, x1 + x3 + x4 + x6 \[LessEqual] 21, x1 \[LessEqual] 6, \(-x3\) \[LessEqual] 0, \(-x4\) \[LessEqual] 0, x1 + x2 + x3 + x4 + x5 + x6 \[LessEqual] 27};\)\)}], "Input"], Cell["\<\ This is the description of the polytope P2 in section 4.1 of the paper. It \ has 54 vertices and 24 facets. \ \>", "Text"], Cell[CellGroupData[{ Cell[BoxData[{ \(Length[dzconv]\), "\[IndentingNewLine]", \(Length[dzineq]\)}], "Input"], Cell[BoxData[ \(54\)], "Output"], Cell[BoxData[ \(24\)], "Output"] }, Open ]], Cell["\<\ A similar approach was used for the six Albouy-Chenciner equations. This \ time it is not possible to add all six at once. Instead we had to add three \ of the polytopes, reduce the number of hull vertices with Porta, add in the \ fourth, reduces the hull, etc. Here are the final results. To save space, \ this cell has been kept closed. Select it and open it to see the results. \ In any case, the cell should be selected and executed at this time before \ continuing. \ \>", "Text"], Cell[BoxData[{ \(\(acconv = {{0, 13, 13, 17, 17, 15}, {0, 13, 13, 19, 14, 13}, {0, 10, 15, 17, 17, 13}, {0, 10, 13, 17, 17, 15}, {0, 13, 17, 17, 13, 15}, {0, 13, 17, 19, 10, 13}, {0, 10, 19, 17, 13, 13}, {0, 10, 17, 17, 13, 15}, {0, 13, 17, 17, 10, 15}, {0, 13, 10, 17, 17, 15}, {0, 13, 13, 14, 19, 13}, {0, 13, 13, 17, 17, 12}, {0, 15, 10, 17, 17, 13}, {0, 17, 17, 13, 13, 15}, {0, 17, 17, 15, 10, 13}, {0, 14, 19, 13, 13, 13}, {0, 17, 17, 13, 10, 15}, {0, 17, 13, 13, 17, 15}, {0, 17, 10, 13, 17, 15}, {0, 17, 13, 10, 19, 13}, {0, 19, 10, 13, 17, 13}, {0, 17, 17, 10, 13, 15}, {0, 17, 13, 10, 17, 15}, {0, 17, 17, 10, 15, 13}, {0, 19, 14, 13, 13, 13}, {0, 17, 17, 13, 13, 12}, {0, 17, 13, 13, 17, 12}, {0, 13, 17, 17, 13, 12}, {1, 10, 13, 19, 17, 15}, {1, 10, 13, 21, 14, 13}, {1, 7, 15, 19, 17, 13}, {1, 7, 13, 19, 17, 15}, {1, 10, 17, 19, 13, 15}, {1, 10, 17, 21, 10, 13}, {1, 7, 19, 19, 13, 13}, {1, 7, 17, 19, 13, 15}, {1, 10, 17, 19, 10, 15}, {1, 10, 10, 19, 17, 15}, {1, 13, 10, 17, 19, 15}, {1, 10, 12, 17, 19, 13}, {1, 10, 10, 17, 19, 15}, {1, 13, 10, 14, 21, 13}, {1, 10, 13, 16, 19, 13}, {1, 13, 10, 17, 19, 12}, {1, 13, 7, 17, 19, 15}, {1, 10, 13, 19, 17, 12}, {1, 12, 10, 19, 17, 13}, {1, 15, 7, 17, 19, 13}, {1, 13, 19, 17, 10, 15}, {1, 13, 19, 19, 7, 13}, {1, 10, 21, 17, 10, 13}, {1, 10, 19, 17, 10, 15}, {1, 13, 19, 17, 7, 15}, {1, 10, 17, 19, 13, 12}, {1, 17, 10, 10, 21, 13}, {1, 17, 10, 13, 19, 15}, {1, 17, 7, 13, 19, 15}, {1, 17, 10, 10, 19, 15}, {1, 13, 10, 19, 16, 13}, {3, 13, 13, 15, 19, 12}, {3, 10, 15, 15, 19, 10}, {3, 13, 13, 12, 21, 10}, {3, 13, 13, 15, 19, 9}, {6, 13, 15, 13, 19, 6}, {4, 10, 13, 17, 19, 12}, {4, 7, 15, 17, 19, 10}, {4, 13, 10, 15, 21, 12}, {4, 10, 12, 15, 21, 10}, {4, 13, 10, 12, 23, 10}, {4, 13, 10, 15, 21, 9}, {4, 10, 13, 17, 19, 9}, {1, 17, 19, 13, 10, 15}, {1, 14, 21, 13, 10, 13}, {1, 17, 19, 13, 7, 15}, {1, 17, 19, 10, 10, 15}, {1, 17, 19, 15, 7, 13}, {1, 17, 19, 13, 10, 12}, {1, 13, 19, 17, 10, 12}, {1, 17, 19, 10, 12, 13}, {1, 19, 17, 10, 13, 15}, {1, 16, 19, 10, 13, 13}, {1, 19, 17, 7, 13, 15}, {1, 19, 17, 7, 15, 13}, {1, 19, 7, 13, 19, 13}, {1, 17, 10, 13, 19, 12}, {3, 13, 13, 19, 15, 12}, {3, 13, 13, 21, 12, 10}, {3, 13, 13, 19, 15, 9}, {3, 15, 10, 19, 15, 10}, {6, 15, 13, 19, 13, 6}, {4, 10, 13, 21, 15, 12}, {4, 10, 13, 23, 12, 10}, {4, 13, 10, 19, 17, 9}, {4, 13, 10, 19, 17, 12}, {4, 10, 13, 21, 15, 9}, {4, 12, 10, 21, 15, 10}, {4, 15, 7, 19, 17, 10}, {3, 15, 19, 13, 13, 12}, {3, 12, 21, 13, 13, 10}, {3, 15, 19, 10, 15, 10}, {3, 15, 19, 13, 13, 9}, {6, 13, 19, 13, 15, 6}, {4, 15, 21, 13, 10, 12}, {4, 12, 23, 13, 10, 10}, {4, 15, 21, 13, 10, 9}, {4, 15, 21, 10, 12, 10}, {4, 17, 19, 10, 13, 12}, {4, 17, 19, 7, 15, 10}, {1, 19, 13, 7, 17, 15}, {1, 21, 10, 10, 17, 13}, {1, 19, 13, 10, 17, 15}, {1, 19, 10, 10, 17, 15}, {1, 19, 13, 7, 19, 13}, {1, 19, 17, 12, 10, 13}, {1, 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15, 7, 10}, {21, 10, 7, 15, 4, 15}, {21, 10, 7, 13, 4, 17}, {23, 7, 10, 12, 7, 13}, {21, 7, 4, 10, 13, 17}, {21, 7, 10, 7, 15, 15}, {21, 7, 7, 7, 15, 15}, {21, 12, 7, 7, 15, 10}, {21, 12, 10, 7, 15, 10}, {21, 10, 12, 7, 15, 10}, {21, 7, 12, 7, 15, 10}, {21, 7, 15, 7, 10, 15}, {21, 4, 15, 7, 10, 15}, {21, 7, 15, 7, 7, 15}, {21, 10, 13, 7, 4, 17}, {21, 4, 13, 7, 10, 17}, {21, 7, 10, 4, 15, 15}, {21, 7, 10, 4, 13, 17}, {23, 7, 10, 7, 12, 13}, {23, 10, 7, 7, 12, 13}, {23, 10, 7, 12, 7, 13}, {21, 4, 15, 7, 12, 13}, {21, 7, 15, 12, 7, 10}, {21, 7, 15, 12, 10, 10}, {21, 7, 15, 10, 12, 10}, {21, 7, 15, 7, 12, 10}, {21, 7, 13, 10, 12, 9}, {21, 7, 13, 12, 10, 9}, {21, 7, 12, 4, 15, 13}, {21, 10, 12, 7, 13, 9}, {21, 12, 10, 7, 13, 9}, {21, 10, 12, 13, 7, 9}, {21, 12, 10, 13, 7, 9}, {21, 12, 7, 15, 4, 13}, {23, 7, 12, 10, 7, 13}, {23, 7, 12, 7, 10, 13}, {21, 13, 10, 4, 7, 17}, {21, 15, 7, 10, 7, 15}, {21, 15, 4, 10, 7, 15}, {21, 15, 7, 7, 7, 15}, {21, 13, 4, 10, 7, 17}, {21, 13, 7, 12, 10, 9}, {21, 15, 7, 7, 12, 10}, {21, 15, 7, 10, 12, 10}, {21, 13, 7, 10, 12, 9}, {21, 15, 7, 12, 10, 10}, {21, 15, 7, 12, 7, 10}, {23, 12, 7, 7, 10, 13}, {23, 12, 7, 10, 7, 13}, {21, 15, 4, 12, 7, 13}, {23, 12, 7, 10, 10, 13}};\)\[IndentingNewLine]\), "\[IndentingNewLine]", \(\(acineq\ = \ {\(-x1\) \[LessEqual] 0, x3\/45 + x5\/45 + x6\/45 \[LessEqual] 1, \(-\(x1\/72\)\) - x2\/72 - x3\/72 - x4\/72 - x5\/72 - x6\/72 \[LessEqual] \(-1\), \(-\(\(2\ x1\)\/35\)\) + \(2\ \ x3\)\/175 + x4\/35 + \(2\ x5\)\/175 + \(2\ x6\)\/175 \[LessEqual] 1, \(-\(x1\/16\)\) + x4\/32 + x6\/32 \[LessEqual] 1, \(-\(\(6\ x1\)\/85\)\) + \(3\ x4\)\/85 + \(2\ x5\)\/85 \ \[LessEqual] 1, \(-\(\(6\ x1\)\/385\)\) + \(4\ x2\)\/385 + \(6\ x3\)\/385 + \ \(9\ x4\)\/385 + \(6\ x5\)\/385 \[LessEqual] 1, \(-\(\(2\ x1\)\/49\)\) + x3\/49 + x4\/49 + x6\/49 \[LessEqual] 1, \(-\(\(6\ x1\)\/85\)\) + \(2\ x4\)\/85 + \(3\ x5\)\/85 \ \[LessEqual] 1, \(-\(x1\/16\)\) + x5\/32 + x6\/32 \[LessEqual] 1, \(-\(\(4\ x1\)\/175\)\) + \(2\ x3\)\/175 + \(2\ x4\)\/175 + x5\/35 + \(2\ x6\)\/175 \[LessEqual] 1, x3\/61 + \(3\ x5\)\/122 + \(3\ x6\)\/122 \[LessEqual] 1, \(-\(x1\/17\)\) + x4\/34 + x5\/34 \[LessEqual] 1, \(-\(x1\/16\)\) + x3\/32 + x6\/32 \[LessEqual] 1, \(3\ x3\)\/122 + x5\/61 + \(3\ x6\)\/122 \[LessEqual] 1, \(-\(\(6\ x1\)\/385\)\) + \(6\ x2\)\/385 + \(9\ x3\)\/385 + \ \(6\ x4\)\/385 + \(4\ x5\)\/385 \[LessEqual] 1, \(-\(\(2\ x1\)\/35\)\) + \(2\ x2\)\/175 + x3\/35 + \(2\ x4\)\/175 + \(2\ x6\)\/175 \[LessEqual] 1, x2\/77 + \(3\ x3\)\/154 + \(3\ x4\)\/154 + x5\/77 \[LessEqual] 1, \(-\(\(2\ x1\)\/35\)\) + \(2\ x2\)\/175 + \(2\ x4\)\/175 + x5\/35 + \(2\ x6\)\/175 \[LessEqual] 1, x2\/45 + x4\/45 + x6\/45 \[LessEqual] 1, x2\/61 + \(3\ x4\)\/122 + \(3\ x6\)\/122 \[LessEqual] 1, \(-\(\(4\ x1\)\/175\)\) + \(2\ x2\)\/175 + x4\/35 + \(2\ x5\)\/175 + \(2\ x6\)\/175 \[LessEqual] 1, \(-\(\(6\ x1\)\/385\)\) + \(6\ x2\)\/385 + \(4\ x3\)\/385 + \ \(6\ x4\)\/385 + \(9\ x5\)\/385 \[LessEqual] 1, \(-\(\(6\ x1\)\/85\)\) + \(2\ x2\)\/85 + \(3\ x3\)\/85 \ \[LessEqual] 1, \(-\(\(4\ x1\)\/175\)\) + \(2\ x2\)\/175 + x3\/35 + \(2\ x5\)\/175 + \(2\ x6\)\/175 \[LessEqual] 1, \(-\(\(2\ x1\)\/49\)\) + x2\/49 + x5\/49 + x6\/49 \[LessEqual] 1, \(-\(x1\/16\)\) + x2\/32 + x6\/32 \[LessEqual] 1, \(3\ x2\)\/122 + x4\/61 + \(3\ x6\)\/122 \[LessEqual] 1, \(-\(\(2\ x1\)\/35\)\) + x2\/35 + \(2\ x3\)\/175 + \(2\ x5\)\/175 + \(2\ x6\)\/175 \ \[LessEqual] 1, \(-\(\(6\ x1\)\/385\)\) + \(9\ x2\)\/385 + \(6\ x3\)\/385 + \ \(4\ x4\)\/385 + \(6\ x5\)\/385 \[LessEqual] 1, \(3\ x2\)\/154 + x3\/77 + x4\/77 + \(3\ x5\)\/154 \[LessEqual] 1, \(-\(\(6\ x1\)\/85\)\) + \(3\ x2\)\/85 + \(2\ x3\)\/85 \ \[LessEqual] 1, \(-\(x1\/17\)\) + x2\/34 + x3\/34 \[LessEqual] 1, \(-\(\(4\ x1\)\/175\)\) + x2\/35 + \(2\ x3\)\/175 + \(2\ x4\)\/175 + \(2\ x6\)\/175 \ \[LessEqual] 1, \(-\(\(2\ x1\)\/45\)\) + x6\/15 \[LessEqual] 1, \(-\(x1\/31\)\) + x4\/62 + \(3\ x6\)\/62 \[LessEqual] 1, \(-\(x1\/47\)\) + x4\/94 + x5\/94 + \(2\ x6\)\/47 \[LessEqual] 1, \(-\(x1\/47\)\) + x3\/94 + x4\/94 + \(2\ x6\)\/47 \[LessEqual] 1, \(-\(x1\/31\)\) + x5\/62 + \(3\ x6\)\/62 \[LessEqual] 1, \(-\(x1\/225\)\) + x2\/75 + x3\/50 + x4\/75 + x5\/50 \[LessEqual] 1, \(2\ x2\)\/167 + \(3\ x3\)\/167 + \(3\ x4\)\/167 + \(3\ \ x5\)\/167 \[LessEqual] 1, \(-\(\(2\ x1\)\/419\)\) + \(4\ x2\)\/419 + \(6\ x3\)\/419 + \ \(7\ x4\)\/419 + \(10\ x5\)\/419 \[LessEqual] 1, \(-\(\(18\ x1\)\/3335\)\) + \(32\ x2\)\/3335 + \(48\ \ x3\)\/3335 + \(54\ x4\)\/3335 + \(81\ x5\)\/3335 \[LessEqual] 1, \(-\(\(4\ x1\)\/945\)\) + \(8\ x2\)\/945 + \(2\ x3\)\/135 + \ \(2\ x4\)\/135 + \(23\ x5\)\/945 + \(2\ x6\)\/945 \[LessEqual] 1, \(-\(x1\/31\)\) + x3\/62 + \(3\ x6\)\/62 \[LessEqual] 1, \(-\(\(6\ x1\)\/1207\)\) + \(18\ x2\)\/1207 + \(27\ x3\)\/1207 \ + \(18\ x4\)\/1207 + \(16\ x5\)\/1207 \[LessEqual] 1, \(-\(\(18\ x1\)\/3335\)\) + \(54\ x2\)\/3335 + \(81\ \ x3\)\/3335 + \(32\ x4\)\/3335 + \(48\ x5\)\/3335 \[LessEqual] 1, \(-\(\(4\ x1\)\/945\)\) + \(2\ x2\)\/135 + \(23\ x3\)\/945 + \ \(8\ x4\)\/945 + \(2\ x5\)\/135 + \(2\ x6\)\/945 \[LessEqual] 1, \(-\(\(6\ x1\)\/1207\)\) + \(18\ x2\)\/1207 + \(16\ x3\)\/1207 \ + \(18\ x4\)\/1207 + \(27\ x5\)\/1207 \[LessEqual] 1, \(3\ x2\)\/167 + \(2\ x3\)\/167 + \(3\ x4\)\/167 + \(3\ \ x5\)\/167 \[LessEqual] 1, \(-\(x1\/225\)\) + x2\/50 + x3\/75 + x4\/50 + x5\/75 \[LessEqual] 1, \(-\(\(18\ x1\)\/3335\)\) + \(48\ x2\)\/3335 + \(32\ \ x3\)\/3335 + \(81\ x4\)\/3335 + \(54\ x5\)\/3335 \[LessEqual] 1, \(-\(\(6\ x1\)\/1207\)\) + \(16\ x2\)\/1207 + \(18\ x3\)\/1207 \ + \(27\ x4\)\/1207 + \(18\ x5\)\/1207 \[LessEqual] 1, \(-\(\(2\ x1\)\/419\)\) + \(6\ x2\)\/419 + \(4\ x3\)\/419 + \ \(10\ x4\)\/419 + \(7\ x5\)\/419 \[LessEqual] 1, x2\/60 + x3\/60 + x4\/60 + x5\/60 \[LessEqual] 1, x2\/77 + x3\/77 + \(3\ x4\)\/154 + \(3\ x5\)\/154 \[LessEqual] 1, \(-\(\(4\ x1\)\/945\)\) + \(2\ x2\)\/135 + \(8\ x3\)\/945 + \ \(23\ x4\)\/945 + \(2\ x5\)\/135 + \(2\ x6\)\/945 \[LessEqual] 1, \(3\ x2\)\/167 + \(3\ x3\)\/167 + \(3\ x4\)\/167 + \(2\ \ x5\)\/167 \[LessEqual] 1, \(-\(x1\/47\)\) + x2\/94 + x5\/94 + \(2\ x6\)\/47 \[LessEqual] 1, \(3\ x2\)\/167 + \(3\ x3\)\/167 + \(2\ x4\)\/167 + \(3\ \ x5\)\/167 \[LessEqual] 1, \(-\(x1\/47\)\) + x2\/94 + x3\/94 + \(2\ x6\)\/47 \[LessEqual] 1, \(-\(\(2\ x1\)\/419\)\) + \(7\ x2\)\/419 + \(10\ x3\)\/419 + \ \(4\ x4\)\/419 + \(6\ x5\)\/419 \[LessEqual] 1, \(-\(x1\/31\)\) + x2\/62 + \(3\ x6\)\/62 \[LessEqual] 1, \(-\(\(6\ x1\)\/1207\)\) + \(27\ x2\)\/1207 + \(18\ x3\)\/1207 \ + \(16\ x4\)\/1207 + \(18\ x5\)\/1207 \[LessEqual] 1, \(-\(\(2\ x1\)\/419\)\) + \(10\ x2\)\/419 + \(7\ x3\)\/419 + \ \(6\ x4\)\/419 + \(4\ x5\)\/419 \[LessEqual] 1, \(-\(\(18\ x1\)\/3335\)\) + \(81\ x2\)\/3335 + \(54\ \ x3\)\/3335 + \(48\ x4\)\/3335 + \(32\ x5\)\/3335 \[LessEqual] 1, \(3\ x2\)\/154 + \(3\ x3\)\/154 + x4\/77 + x5\/77 \[LessEqual] 1, \(-\(\(4\ x1\)\/945\)\) + \(23\ x2\)\/945 + \(2\ x3\)\/135 + \ \(2\ x4\)\/135 + \(8\ x5\)\/945 + \(2\ x6\)\/945 \[LessEqual] 1, \(2\ x3\)\/185 + x4\/37 + \(2\ x5\)\/185 + \(2\ x6\)\/185 \[LessEqual] 1, \(-\(x1\/50\)\) + \(3\ x4\)\/100 + \(3\ x6\)\/100 \[LessEqual] 1, \(2\ x3\)\/179 + \(2\ x4\)\/179 + \(5\ x5\)\/179 + \(2\ \ x6\)\/179 \[LessEqual] 1, x4\/36 + x5\/36 \[LessEqual] 1, x4\/51 + x5\/51 + x6\/51 \[LessEqual] 1, \(5\ x4\)\/159 + \(2\ x5\)\/159 + \(2\ x6\)\/159 \[LessEqual] 1, x3\/51 + x4\/51 + x6\/51 \[LessEqual] 1, \(-\(\(2\ x1\)\/271\)\) + \(9\ x4\)\/271 + \(6\ x5\)\/271 \ \[LessEqual] 1, \(-\(\(2\ x1\)\/389\)\) + \(4\ x2\)\/389 + \(6\ x3\)\/389 + \ \(9\ x4\)\/389 + \(6\ x5\)\/389 \[LessEqual] 1, \(-\(x1\/50\)\) + \(3\ x5\)\/100 + \(3\ x6\)\/100 \[LessEqual] 1, \(2\ x4\)\/159 + \(5\ x5\)\/159 + \(2\ x6\)\/159 \[LessEqual] 1, \(2\ x2\)\/179 + \(5\ x4\)\/179 + \(2\ x5\)\/179 + \(2\ \ x6\)\/179 \[LessEqual] 1, \(-\(\(2\ x1\)\/271\)\) + \(6\ x4\)\/271 + \(9\ x5\)\/271 \ \[LessEqual] 1, \(4\ x2\)\/391 + \(6\ x3\)\/391 + \(6\ x4\)\/391 + \(9\ \ x5\)\/391 \[LessEqual] 1, \(-\(x1\/50\)\) + \(3\ x3\)\/100 + \(3\ x6\)\/100 \[LessEqual] 1, \(2\ x2\)\/185 + x3\/37 + \(2\ x4\)\/185 + \(2\ x6\)\/185 \[LessEqual] 1, \(-\(\(2\ x1\)\/389\)\) + \(6\ x2\)\/389 + \(9\ x3\)\/389 + \ \(6\ x4\)\/389 + \(4\ x5\)\/389 \[LessEqual] 1, \(-\(\(2\ x1\)\/271\)\) + \(6\ x2\)\/271 + \(9\ x3\)\/271 \ \[LessEqual] 1, \(2\ x2\)\/179 + \(5\ x3\)\/179 + \(2\ x5\)\/179 + \(2\ \ x6\)\/179 \[LessEqual] 1, \(2\ x2\)\/159 + \(5\ x3\)\/159 + \(2\ x6\)\/159 \[LessEqual] 1, \(2\ x2\)\/185 + \(2\ x4\)\/185 + x5\/37 + \(2\ x6\)\/185 \[LessEqual] 1, \(-\(\(2\ x1\)\/389\)\) + \(6\ x2\)\/389 + \(4\ x3\)\/389 + \ \(6\ x4\)\/389 + \(9\ x5\)\/389 \[LessEqual] 1, \(6\ x2\)\/391 + \(4\ x3\)\/391 + \(9\ x4\)\/391 + \(6\ \ x5\)\/391 \[LessEqual] 1, \(6\ x2\)\/391 + \(9\ x3\)\/391 + \(4\ x4\)\/391 + \(6\ \ x5\)\/391 \[LessEqual] 1, x2\/51 + x5\/51 + x6\/51 \[LessEqual] 1, x2\/36 + x3\/36 \[LessEqual] 1, x2\/51 + x3\/51 + x6\/51 \[LessEqual] 1, \(5\ x2\)\/179 + \(2\ x3\)\/179 + \(2\ x4\)\/179 + \(2\ \ x6\)\/179 \[LessEqual] 1, \(-\(x1\/50\)\) + \(3\ x2\)\/100 + \(3\ x6\)\/100 \[LessEqual] 1, x2\/37 + \(2\ x3\)\/185 + \(2\ x5\)\/185 + \(2\ x6\)\/185 \ \[LessEqual] 1, \(5\ x2\)\/159 + \(2\ x3\)\/159 + \(2\ x6\)\/159 \[LessEqual] 1, \(-\(\(2\ x1\)\/389\)\) + \(9\ x2\)\/389 + \(6\ x3\)\/389 + \ \(4\ x4\)\/389 + \(6\ x5\)\/389 \[LessEqual] 1, \(-\(\(2\ x1\)\/271\)\) + \(9\ x2\)\/271 + \(6\ x3\)\/271 \ \[LessEqual] 1, \(9\ x2\)\/391 + \(6\ x3\)\/391 + \(6\ x4\)\/391 + \(4\ \ x5\)\/391 \[LessEqual] 1, \(-\(\(2\ x1\)\/79\)\) + x4\/79 + \(4\ x6\)\/79 \[LessEqual] 1, \(-\(\(2\ x1\)\/79\)\) + x5\/79 + \(4\ x6\)\/79 \[LessEqual] 1, \(-\(\(4\ x1\)\/265\)\) + \(2\ x3\)\/265 + \(2\ x4\)\/265 + \ \(2\ x5\)\/265 + \(11\ x6\)\/265 \[LessEqual] 1, \(-\(\(2\ x1\)\/79\)\) + x3\/79 + \(4\ x6\)\/79 \[LessEqual] 1, \(2\ x2\)\/139 + \(3\ x3\)\/139 + \(2\ x4\)\/139 + \(2\ \ x5\)\/139 \[LessEqual] 1, \(-\(\(4\ x1\)\/265\)\) + \(2\ x2\)\/265 + \(2\ x4\)\/265 + \ \(2\ x5\)\/265 + \(11\ x6\)\/265 \[LessEqual] 1, \(2\ x2\)\/139 + \(2\ x3\)\/139 + \(2\ x4\)\/139 + \(3\ \ x5\)\/139 \[LessEqual] 1, \(2\ x2\)\/139 + \(2\ x3\)\/139 + \(3\ x4\)\/139 + \(2\ \ x5\)\/139 \[LessEqual] 1, \(-\(\(4\ x1\)\/265\)\) + \(2\ x2\)\/265 + \(2\ x3\)\/265 + \ \(2\ x4\)\/265 + \(11\ x6\)\/265 \[LessEqual] 1, \(-\(\(2\ x1\)\/79\)\) + x2\/79 + \(4\ x6\)\/79 \[LessEqual] 1, \(-\(\(4\ x1\)\/265\)\) + \(2\ x2\)\/265 + \(2\ x3\)\/265 + \ \(2\ x5\)\/265 + \(11\ x6\)\/265 \[LessEqual] 1, \(3\ x2\)\/139 + \(2\ x3\)\/139 + \(2\ x4\)\/139 + \(2\ \ x5\)\/139 \[LessEqual] 1, x4\/36 + x6\/36 \[LessEqual] 1, \(2\ x3\)\/179 + \(2\ x4\)\/179 + \(2\ x5\)\/179 + \(5\ \ x6\)\/179 \[LessEqual] 1, \(-\(\(4\ x2\)\/265\)\) + \(2\ x3\)\/265 + \(2\ x4\)\/265 + \ \(11\ x5\)\/265 + \(2\ x6\)\/265 \[LessEqual] 1, \(-\(x2\/31\)\) + x4\/62 + \(3\ x5\)\/62 \[LessEqual] 1, \(-\(x2\/47\)\) + x4\/94 + \(2\ x5\)\/47 + x6\/94 \[LessEqual] 1, \(-\(\(2\ x2\)\/79\)\) + x4\/79 + \(4\ x5\)\/79 \[LessEqual] 1, x4\/31 + \(2\ x5\)\/93 \[LessEqual] 1, \(-\(x2\/50\)\) + \(3\ x4\)\/100 + \(3\ x5\)\/100 \[LessEqual] 1, \(3\ x3\)\/122 + \(3\ x5\)\/122 + x6\/61 \[LessEqual] 1, x3\/51 + x4\/51 + x5\/51 \[LessEqual] 1, \(-\(x2\/47\)\) + x3\/94 + x4\/94 + \(2\ x5\)\/47 \[LessEqual] 1, x5\/36 + x6\/36 \[LessEqual] 1, \(-\(\(4\ x2\)\/245\)\) + \(2\ x4\)\/245 + \(11\ x5\)\/245 + \ \(2\ x6\)\/245 \[LessEqual] 1, \(2\ x3\)\/109 + \(3\ x5\)\/109 + \(2\ x6\)\/109 \[LessEqual] 1, \(-\(\(4\ x2\)\/245\)\) + \(2\ x3\)\/245 + \(2\ x4\)\/245 + \ \(11\ x5\)\/245 \[LessEqual] 1, \(4\ x2\)\/655 + \(12\ x3\)\/655 + \(6\ x4\)\/655 + \(3\ \ x5\)\/131 + \(6\ x6\)\/655 \[LessEqual] 1, \(4\ x2\)\/565 + \(6\ x3\)\/565 + \(6\ x4\)\/565 + \(6\ \ x5\)\/565 + \(3\ x6\)\/113 \[LessEqual] 1, \(4\ x2\)\/307 + \(9\ x4\)\/307 + \(6\ x6\)\/307 \[LessEqual] 1, x4\/31 + \(2\ x6\)\/93 \[LessEqual] 1, \(2\ x3\)\/165 + x4\/33 + \(2\ x6\)\/165 \[LessEqual] 1, \(4\ x2\)\/397 + \(6\ x3\)\/397 + \(9\ x4\)\/397 + \(6\ \ x5\)\/397 \[LessEqual] 1, \(2\ x3\)\/165 + x4\/33 + \(2\ x5\)\/165 \[LessEqual] 1, x3\/36 + x6\/36 \[LessEqual] 1, \(3\ x3\)\/109 + \(2\ x5\)\/109 + \(2\ x6\)\/109 \[LessEqual] 1, x3\/38 + x4\/38 \[LessEqual] 1, \(2\ x4\)\/93 + x5\/31 \[LessEqual] 1, \(2\ x2\)\/265 - \(4\ x3\)\/265 + \(11\ x4\)\/265 + \(2\ \ x5\)\/265 + \(2\ x6\)\/265 \[LessEqual] 1, \(-\(\(4\ x3\)\/245\)\) + \(11\ x4\)\/245 + \(2\ x5\)\/245 + \ \(2\ x6\)\/245 \[LessEqual] 1, \(-\(\(2\ x3\)\/79\)\) + \(4\ x4\)\/79 + x5\/79 \[LessEqual] 1, \(-\(x3\/47\)\) + \(2\ x4\)\/47 + x5\/94 + x6\/94 \[LessEqual] 1, \(4\ x3\)\/307 + \(9\ x5\)\/307 + \(6\ x6\)\/307 \[LessEqual] 1, \(-\(\(4\ x2\)\/179\)\) + \(2\ x4\)\/179 + \(9\ x5\)\/179 \ \[LessEqual] 1, \(2\ x2\)\/109 + \(3\ x4\)\/109 + \(2\ x6\)\/109 \[LessEqual] 1, \(-\(\(4\ x3\)\/179\)\) + \(9\ x4\)\/179 + \(2\ x5\)\/179 \ \[LessEqual] 1, \(6\ x3\)\/307 + \(9\ x5\)\/307 + \(4\ x6\)\/307 \[LessEqual] 1, \(4\ x2\)\/629 + \(10\ x3\)\/629 + \(6\ x4\)\/629 + \(15\ x5\)\ \/629 + \(6\ x6\)\/629 \[LessEqual] 1, \(2\ x2\)\/131 + \(6\ x3\)\/655 + \(3\ x4\)\/131 + \(6\ \ x5\)\/655 + \(6\ x6\)\/655 \[LessEqual] 1, \(10\ x2\)\/629 + \(4\ x3\)\/629 + \(15\ x4\)\/629 + \(6\ x5\)\ \/629 + \(6\ x6\)\/629 \[LessEqual] 1, x4\/23 \[LessEqual] 1, \(6\ x2\)\/307 + \(9\ x4\)\/307 + \(4\ x6\)\/307 \[LessEqual] 1, \(2\ x2\)\/245 - \(4\ x3\)\/245 + \(11\ x4\)\/245 + \(2\ \ x5\)\/245 \[LessEqual] 1, \(9\ x3\)\/307 + \(4\ x5\)\/307 + \(6\ x6\)\/307 \[LessEqual] 1, x3\/33 + \(2\ x4\)\/165 + \(2\ x6\)\/165 \[LessEqual] 1, \(6\ x2\)\/655 + \(3\ x3\)\/131 + \(6\ x4\)\/655 + \(2\ \ x5\)\/131 + \(6\ x6\)\/655 \[LessEqual] 1, x3\/31 + \(2\ x6\)\/93 \[LessEqual] 1, \(2\ x2\)\/93 + x3\/31 \[LessEqual] 1, \(6\ x2\)\/397 + \(9\ x3\)\/397 + \(6\ x4\)\/397 + \(4\ \ x5\)\/397 \[LessEqual] 1, \(9\ x3\)\/307 + \(6\ x5\)\/307 + \(4\ x6\)\/307 \[LessEqual] 1, \(2\ x2\)\/265 + \(11\ x3\)\/265 - \(4\ x4\)\/265 + \(2\ \ x5\)\/265 + \(2\ x6\)\/265 \[LessEqual] 1, \(2\ x2\)\/245 + \(11\ x3\)\/245 - \(4\ x4\)\/245 + \(2\ \ x6\)\/245 \[LessEqual] 1, x3\/23 \[LessEqual] 1, \(2\ x2\)\/245 + \(11\ x3\)\/245 - \(4\ x4\)\/245 + \(2\ \ x5\)\/245 \[LessEqual] 1, \(2\ x2\)\/179 + \(9\ x3\)\/179 - \(4\ x4\)\/179 \[LessEqual] 1, \(2\ x2\)\/165 + x3\/33 + \(2\ x4\)\/165 \[LessEqual] 1, \(6\ x2\)\/629 + \(15\ x3\)\/629 + \(4\ x4\)\/629 + \(10\ x5\)\ \/629 + \(6\ x6\)\/629 \[LessEqual] 1, \(2\ x2\)\/179 + \(2\ x4\)\/179 + \(2\ x5\)\/179 + \(5\ \ x6\)\/179 \[LessEqual] 1, \(-\(x3\/50\)\) + \(3\ x4\)\/100 + \(3\ x5\)\/100 \[LessEqual] 1, \(-\(x3\/31\)\) + \(3\ x4\)\/62 + x5\/62 \[LessEqual] 1, \(3\ x2\)\/122 + \(3\ x4\)\/122 + x6\/61 \[LessEqual] 1, \(6\ x2\)\/397 + \(4\ x3\)\/397 + \(6\ x4\)\/397 + \(9\ \ x5\)\/397 \[LessEqual] 1, x5\/23 \[LessEqual] 1, \(2\ x2\)\/165 + \(2\ x4\)\/165 + x5\/33 \[LessEqual] 1, \(6\ x2\)\/655 + \(2\ x3\)\/131 + \(6\ x4\)\/655 + \(3\ \ x5\)\/131 + \(6\ x6\)\/655 \[LessEqual] 1, \(12\ x2\)\/655 + \(4\ x3\)\/655 + \(3\ x4\)\/131 + \(6\ \ x5\)\/655 + \(6\ x6\)\/655 \[LessEqual] 1, \(2\ x2\)\/179 + \(2\ x3\)\/179 + \(2\ x4\)\/179 + \(5\ \ x6\)\/179 \[LessEqual] 1, \(6\ x2\)\/565 + \(6\ x3\)\/565 + \(6\ x4\)\/565 + \(4\ \ x5\)\/565 + \(3\ x6\)\/113 \[LessEqual] 1, x2\/51 + x3\/51 + x4\/51 \[LessEqual] 1, \(6\ x2\)\/655 + \(3\ x3\)\/131 + \(4\ x4\)\/655 + \(12\ \ x5\)\/655 + \(6\ x6\)\/655 \[LessEqual] 1, x2\/51 + x4\/51 + x5\/51 \[LessEqual] 1, x5\/31 + \(2\ x6\)\/93 \[LessEqual] 1, \(2\ x2\)\/165 + x5\/33 + \(2\ x6\)\/165 \[LessEqual] 1, \(6\ x2\)\/565 + \(4\ x3\)\/565 + \(6\ x4\)\/565 + \(6\ \ x5\)\/565 + \(3\ x6\)\/113 \[LessEqual] 1, x2\/79 + \(4\ x3\)\/79 - \(2\ x4\)\/79 \[LessEqual] 1, x2\/94 - x3\/47 + \(2\ x4\)\/47 + x5\/94 \[LessEqual] 1, x2\/36 + x6\/36 \[LessEqual] 1, x2\/38 + x5\/38 \[LessEqual] 1, x2\/94 + \(2\ x3\)\/47 - x4\/47 + x6\/94 \[LessEqual] 1, x2\/51 + x3\/51 + x5\/51 \[LessEqual] 1, x2\/94 + \(2\ x3\)\/47 - x4\/47 + x5\/94 \[LessEqual] 1, \(11\ x2\)\/265 + \(2\ x3\)\/265 + \(2\ x4\)\/265 - \(4\ \ x5\)\/265 + \(2\ x6\)\/265 \[LessEqual] 1, \(3\ x2\)\/62 + x3\/62 - x5\/31 \[LessEqual] 1, \(2\ x2\)\/47 + x3\/94 - x5\/47 + x6\/94 \[LessEqual] 1, \(3\ x2\)\/100 + \(3\ x3\)\/100 - x5\/50 \[LessEqual] 1, \(4\ x2\)\/79 + x3\/79 - \(2\ x5\)\/79 \[LessEqual] 1, \(3\ x2\)\/131 + \(6\ x3\)\/655 + \(12\ x4\)\/655 + \(4\ \ x5\)\/655 + \(6\ x6\)\/655 \[LessEqual] 1, \(15\ x2\)\/629 + \(6\ x3\)\/629 + \(10\ x4\)\/629 + \(4\ x5\)\ \/629 + \(6\ x6\)\/629 \[LessEqual] 1, \(2\ x2\)\/47 + x3\/94 + x4\/94 - x5\/47 \[LessEqual] 1, \(3\ x2\)\/109 + \(2\ x4\)\/109 + \(2\ x6\)\/109 \[LessEqual] 1, \(2\ x2\)\/179 + \(2\ x3\)\/179 + \(2\ x5\)\/179 + \(5\ \ x6\)\/179 \[LessEqual] 1, \(6\ x2\)\/565 + \(6\ x3\)\/565 + \(4\ x4\)\/565 + \(6\ \ x5\)\/565 + \(3\ x6\)\/113 \[LessEqual] 1, \(3\ x2\)\/131 + \(6\ x3\)\/655 + \(2\ x4\)\/131 + \(6\ \ x5\)\/655 + \(6\ x6\)\/655 \[LessEqual] 1, x2\/62 + \(3\ x3\)\/62 - x4\/31 \[LessEqual] 1, \(11\ x2\)\/245 + \(2\ x3\)\/245 - \(4\ x5\)\/245 + \(2\ \ x6\)\/245 \[LessEqual] 1, \(11\ x2\)\/245 + \(2\ x3\)\/245 + \(2\ x4\)\/245 - \(4\ \ x5\)\/245 \[LessEqual] 1, \(9\ x2\)\/307 + \(4\ x4\)\/307 + \(6\ x6\)\/307 \[LessEqual] 1, x2\/33 + \(2\ x5\)\/165 + \(2\ x6\)\/165 \[LessEqual] 1, \(9\ x2\)\/307 + \(6\ x4\)\/307 + \(4\ x6\)\/307 \[LessEqual] 1, x2\/31 + \(2\ x3\)\/93 \[LessEqual] 1, \(3\ x2\)\/100 + \(3\ x3\)\/100 - x4\/50 \[LessEqual] 1, \(9\ x2\)\/397 + \(6\ x3\)\/397 + \(4\ x4\)\/397 + \(6\ \ x5\)\/397 \[LessEqual] 1, x2\/33 + \(2\ x3\)\/165 + \(2\ x5\)\/165 \[LessEqual] 1, \(9\ x2\)\/179 + \(2\ x3\)\/179 - \(4\ x5\)\/179 \[LessEqual] 1, x2\/31 + \(2\ x6\)\/93 \[LessEqual] 1, x2\/23 \[LessEqual] 1, \(-\(\(4\ x1\)\/245\)\) + \(2\ x4\)\/245 + \(2\ x5\)\/245 + \ \(11\ x6\)\/245 \[LessEqual] 1, \(-\(\(4\ x1\)\/245\)\) + \(2\ x3\)\/245 + \(2\ x4\)\/245 + \ \(11\ x6\)\/245 \[LessEqual] 1, \(2\ x3\)\/109 + \(2\ x5\)\/109 + \(3\ x6\)\/109 \[LessEqual] 1, \(2\ x2\)\/195 + \(2\ x3\)\/195 + \(2\ x4\)\/195 + \(2\ \ x5\)\/195 + x6\/39 \[LessEqual] 1, \(4\ x2\)\/545 + \(6\ x3\)\/545 + \(6\ x4\)\/545 + \(4\ \ x5\)\/545 + \(3\ x6\)\/109 \[LessEqual] 1, x2\/120 + x3\/48 + x4\/120 + x5\/48 + x6\/120 \[LessEqual] 1, x2\/77 + \(3\ x3\)\/154 + x4\/77 + \(3\ x5\)\/154 \[LessEqual] 1, \(-\(\(4\ x1\)\/245\)\) + \(2\ x2\)\/245 + \(2\ x5\)\/245 + \ \(11\ x6\)\/245 \[LessEqual] 1, \(-\(\(4\ x1\)\/245\)\) + \(2\ x2\)\/245 + \(2\ x3\)\/245 + \ \(11\ x6\)\/245 \[LessEqual] 1, \(2\ x2\)\/109 + \(2\ x4\)\/109 + \(3\ x6\)\/109 \[LessEqual] 1, x2\/48 + x3\/120 + x4\/48 + x5\/120 + x6\/120 \[LessEqual] 1, x2\/75 + x3\/75 + x4\/50 + x5\/50 - x6\/225 \[LessEqual] 1, \(6\ x2\)\/545 + \(4\ x3\)\/545 + \(4\ x4\)\/545 + \(6\ \ x5\)\/545 + \(3\ x6\)\/109 \[LessEqual] 1, \(3\ x2\)\/154 + x3\/77 + \(3\ x4\)\/154 + x5\/77 \[LessEqual] 1, x2\/50 + x3\/50 + x4\/75 + x5\/75 - x6\/225 \[LessEqual] 1, \(2\ x1\)\/167 + \(3\ x3\)\/167 + \(3\ x4\)\/167 + \(3\ \ x6\)\/167 \[LessEqual] 1, x1\/61 + \(3\ x4\)\/122 + \(3\ x5\)\/122 \[LessEqual] 1, \(-\(x2\/17\)\) + x4\/34 + x6\/34 \[LessEqual] 1, \(-\(\(4\ x2\)\/175\)\) + \(2\ x3\)\/175 + \(2\ x4\)\/175 + \ \(2\ x5\)\/175 + x6\/35 \[LessEqual] 1, \(8\ x1\)\/945 - \(4\ x2\)\/945 + \(2\ x3\)\/135 + \(2\ \ x4\)\/135 + \(2\ x5\)\/945 + \(23\ x6\)\/945 \[LessEqual] 1, \(4\ x1\)\/419 - \(2\ x2\)\/419 + \(6\ x3\)\/419 + \(7\ \ x4\)\/419 + \(10\ x6\)\/419 \[LessEqual] 1, \(4\ x1\)\/655 + \(12\ x3\)\/655 + \(6\ x4\)\/655 + \(6\ \ x5\)\/655 + \(3\ x6\)\/131 \[LessEqual] 1, \(-\(\(2\ x2\)\/35\)\) + \(2\ x3\)\/175 + x4\/35 + \(2\ x5\)\/175 + \(2\ x6\)\/175 \[LessEqual] 1, \(4\ x1\)\/307 + \(9\ x4\)\/307 + \(6\ x5\)\/307 \[LessEqual] 1, \(-\(\(2\ x2\)\/271\)\) + \(9\ x4\)\/271 + \(6\ x6\)\/271 \ \[LessEqual] 1, \(-\(x2\/16\)\) + x4\/32 + x5\/32 \[LessEqual] 1, \(4\ x1\)\/385 - \(6\ x2\)\/385 + \(6\ x3\)\/385 + \(9\ \ x4\)\/385 + \(6\ x6\)\/385 \[LessEqual] 1, \(4\ x1\)\/389 - \(2\ x2\)\/389 + \(6\ x3\)\/389 + \(9\ \ x4\)\/389 + \(6\ x6\)\/389 \[LessEqual] 1, \(-\(\(6\ x2\)\/85\)\) + \(3\ x4\)\/85 + \(2\ x6\)\/85 \ \[LessEqual] 1, x1\/77 + \(3\ x3\)\/154 + \(3\ x4\)\/154 + x6\/77 \[LessEqual] 1, \(-\(\(2\ x2\)\/49\)\) + x3\/49 + x4\/49 + x5\/49 \[LessEqual] 1, \(-\(\(2\ x2\)\/45\)\) + x5\/15 \[LessEqual] 1, \(4\ x1\)\/565 + \(6\ x3\)\/565 + \(6\ x4\)\/565 + \(3\ \ x5\)\/113 + \(6\ x6\)\/565 \[LessEqual] 1, \(2\ x4\)\/159 + \(2\ x5\)\/159 + \(5\ x6\)\/159 \[LessEqual] 1, \(4\ x1\)\/391 + \(6\ x3\)\/391 + \(6\ x4\)\/391 + \(9\ \ x6\)\/391 \[LessEqual] 1, \(4\ x1\)\/397 + \(6\ x3\)\/397 + \(9\ x4\)\/397 + \(6\ \ x6\)\/397 \[LessEqual] 1, \(4\ x1\)\/397 + \(9\ x3\)\/397 + \(6\ x4\)\/397 + \(6\ \ x6\)\/397 \[LessEqual] 1, \(-\(\(2\ x2\)\/79\)\) + \(4\ x5\)\/79 + x6\/79 \[LessEqual] 1, \(-\(\(2\ x2\)\/79\)\) + x3\/79 + \(4\ x5\)\/79 \[LessEqual] 1, \(4\ x1\)\/545 + \(4\ x3\)\/545 + \(6\ x4\)\/545 + \(3\ \ x5\)\/109 + \(6\ x6\)\/545 \[LessEqual] 1, \(-\(\(2\ x3\)\/79\)\) + \(4\ x4\)\/79 + x6\/79 \[LessEqual] 1, \(4\ x1\)\/777 + \(4\ x2\)\/777 + \(10\ x3\)\/777 + \(10\ x4\)\ \/777 + \(4\ x5\)\/777 + \(19\ x6\)\/777 \[LessEqual] 1, \(-\(\(4\ x3\)\/179\)\) + \(9\ x4\)\/179 + \(2\ x6\)\/179 \ \[LessEqual] 1, x3\/36 + x5\/36 \[LessEqual] 1, x1\/135 + x2\/135 + x3\/54 + x4\/54 + x5\/135 + x6\/135 \[LessEqual] 1, \(4\ x2\)\/397 + \(9\ x3\)\/397 + \(6\ x4\)\/397 + \(6\ \ x5\)\/397 \[LessEqual] 1, x3\/31 + \(2\ x5\)\/93 \[LessEqual] 1, x3\/33 + \(2\ x4\)\/165 + \(2\ x5\)\/165 \[LessEqual] 1, \(4\ x1\)\/307 + \(6\ x4\)\/307 + \(9\ x5\)\/307 \[LessEqual] 1, x1\/180 + x2\/180 + x3\/72 + x4\/72 + x5\/180 + x6\/45 \[LessEqual] 1, \(4\ x1\)\/1041 + \(4\ x2\)\/1041 + \(16\ x3\)\/1041 + \(10\ \ x4\)\/1041 + \(10\ x5\)\/1041 + \(25\ x6\)\/1041 \[LessEqual] 1, x1\/180 + x2\/180 + x3\/72 + x4\/72 + x5\/45 + x6\/180 \[LessEqual] 1, \(4\ x1\)\/777 + \(4\ x2\)\/777 + \(10\ x3\)\/777 + \(10\ x4\)\ \/777 + \(19\ x5\)\/777 + \(4\ x6\)\/777 \[LessEqual] 1, \(4\ x1\)\/545 + \(6\ x3\)\/545 + \(6\ x4\)\/545 + \(3\ \ x5\)\/109 + \(4\ x6\)\/545 \[LessEqual] 1, \(4\ x1\)\/1041 + \(4\ x2\)\/1041 + \(16\ x3\)\/1041 + \(10\ \ x4\)\/1041 + \(25\ x5\)\/1041 + \(10\ x6\)\/1041 \[LessEqual] 1, \(-\(\(2\ x3\)\/45\)\) + x4\/15 \[LessEqual] 1, \(4\ x1\)\/545 + \(4\ x2\)\/545 + \(3\ x4\)\/109 + \(6\ \ x5\)\/545 + \(6\ x6\)\/545 \[LessEqual] 1, \(4\ x1\)\/565 + \(6\ x2\)\/565 + \(3\ x4\)\/113 + \(6\ \ x5\)\/565 + \(6\ x6\)\/565 \[LessEqual] 1, \(2\ x2\)\/179 - \(4\ x3\)\/179 + \(9\ x4\)\/179 \[LessEqual] 1, \(2\ x3\)\/93 + x5\/31 \[LessEqual] 1, x1\/120 + x2\/120 + x3\/120 + x4\/48 + x5\/48 \[LessEqual] 1, \(4\ x1\)\/1015 + \(2\ x2\)\/145 + \(4\ x3\)\/1015 + \(5\ x4\)\ \/203 + \(2\ x5\)\/203 + \(2\ x6\)\/203 \[LessEqual] 1, \(4\ x1\)\/777 + \(10\ x2\)\/777 + \(4\ x3\)\/777 + \(19\ x4\)\ \/777 + \(10\ x5\)\/777 + \(4\ x6\)\/777 \[LessEqual] 1, \(6\ x2\)\/397 + \(6\ x3\)\/397 + \(9\ x4\)\/397 + \(4\ \ x5\)\/397 \[LessEqual] 1, \(2\ x2\)\/165 + \(2\ x3\)\/165 + x4\/33 \[LessEqual] 1, \(4\ x1\)\/307 + \(6\ x2\)\/307 + \(9\ x3\)\/307 \[LessEqual] 1, x3\/15 - \(2\ x4\)\/45 \[LessEqual] 1, \(9\ x3\)\/179 - \(4\ x4\)\/179 + \(2\ x6\)\/179 \[LessEqual] 1, \(9\ x3\)\/179 - \(4\ x4\)\/179 + \(2\ x5\)\/179 \[LessEqual] 1, \(4\ x1\)\/565 + \(6\ x2\)\/565 + \(3\ x3\)\/113 + \(6\ \ x5\)\/565 + \(6\ x6\)\/565 \[LessEqual] 1, \(4\ x1\)\/545 + \(6\ x2\)\/545 + \(3\ x3\)\/109 + \(4\ \ x5\)\/545 + \(6\ x6\)\/545 \[LessEqual] 1, \(4\ x1\)\/777 + \(10\ x2\)\/777 + \(19\ x3\)\/777 + \(4\ x4\)\ \/777 + \(10\ x5\)\/777 + \(4\ x6\)\/777 \[LessEqual] 1, \(4\ x1\)\/545 + \(6\ x2\)\/545 + \(3\ x3\)\/109 + \(6\ \ x5\)\/545 + \(4\ x6\)\/545 \[LessEqual] 1, \(4\ x1\)\/1015 + \(2\ x2\)\/203 + \(5\ x3\)\/203 + \(4\ \ x4\)\/1015 + \(2\ x5\)\/145 + \(2\ x6\)\/203 \[LessEqual] 1, \(-\(\(4\ x2\)\/179\)\) + \(9\ x5\)\/179 + \(2\ x6\)\/179 \ \[LessEqual] 1, \(-\(\(4\ x2\)\/179\)\) + \(2\ x3\)\/179 + \(9\ x5\)\/179 \ \[LessEqual] 1, \(4\ x1\)\/1015 + \(4\ x2\)\/1015 + \(2\ x3\)\/145 + \(2\ x4\)\ \/203 + \(5\ x5\)\/203 + \(2\ x6\)\/203 \[LessEqual] 1, \(2\ x1\)\/315 + \(2\ x2\)\/315 + \(2\ x3\)\/315 + x4\/63 + x5\/63 + x6\/63 \[LessEqual] 1, \(2\ x2\)\/93 + x4\/31 \[LessEqual] 1, \(4\ x1\)\/545 + \(6\ x2\)\/545 + \(3\ x4\)\/109 + \(6\ \ x5\)\/545 + \(4\ x6\)\/545 \[LessEqual] 1, \(4\ x1\)\/419 + \(7\ x3\)\/419 + \(6\ x4\)\/419 - \(2\ \ x5\)\/419 + \(10\ x6\)\/419 \[LessEqual] 1, \(8\ x1\)\/945 + \(2\ x2\)\/945 + \(2\ x3\)\/135 + \(2\ \ x4\)\/135 - \(4\ x5\)\/945 + \(23\ x6\)\/945 \[LessEqual] 1, \(4\ x1\)\/655 + \(6\ x2\)\/655 + \(6\ x3\)\/655 + \(12\ \ x4\)\/655 + \(3\ x6\)\/131 \[LessEqual] 1, \(4\ x1\)\/1041 + \(10\ x2\)\/1041 + \(10\ x3\)\/1041 + \(16\ \ x4\)\/1041 + \(4\ x5\)\/1041 + \(25\ x6\)\/1041 \[LessEqual] 1, \(4\ x3\)\/79 - \(2\ x4\)\/79 + x6\/79 \[LessEqual] 1, \(4\ x3\)\/79 - \(2\ x4\)\/79 + x5\/79 \[LessEqual] 1, \(4\ x1\)\/1041 + \(10\ x2\)\/1041 + \(25\ x3\)\/1041 + \(4\ \ x4\)\/1041 + \(16\ x5\)\/1041 + \(10\ x6\)\/1041 \[LessEqual] 1, \(9\ x3\)\/271 - \(2\ x5\)\/271 + \(6\ x6\)\/271 \[LessEqual] 1, \(4\ x1\)\/389 + \(9\ x3\)\/389 + \(6\ x4\)\/389 - \(2\ \ x5\)\/389 + \(6\ x6\)\/389 \[LessEqual] 1, \(2\ x1\)\/167 + \(3\ x2\)\/167 + \(3\ x5\)\/167 + \(3\ \ x6\)\/167 \[LessEqual] 1, \(-\(x3\/17\)\) + x5\/34 + x6\/34 \[LessEqual] 1, \(2\ x2\)\/175 - \(4\ x3\)\/175 + \(2\ x4\)\/175 + \(2\ \ x5\)\/175 + x6\/35 \[LessEqual] 1, \(2\ x2\)\/175 - \(2\ x3\)\/35 + \(2\ x4\)\/175 + x5\/35 + \(2\ x6\)\/175 \[LessEqual] 1, \(-\(\(2\ x3\)\/271\)\) + \(9\ x5\)\/271 + \(6\ x6\)\/271 \ \[LessEqual] 1, \(-\(x3\/16\)\) + x4\/32 + x5\/32 \[LessEqual] 1, \(-\(\(6\ x3\)\/85\)\) + \(3\ x5\)\/85 + \(2\ x6\)\/85 \ \[LessEqual] 1, \(4\ x1\)\/389 + \(6\ x2\)\/389 - \(2\ x3\)\/389 + \(9\ \ x5\)\/389 + \(6\ x6\)\/389 \[LessEqual] 1, \(4\ x1\)\/391 + \(6\ x2\)\/391 + \(6\ x5\)\/391 + \(9\ \ x6\)\/391 \[LessEqual] 1, \(4\ x1\)\/397 + \(6\ x2\)\/397 + \(9\ x5\)\/397 + \(6\ \ x6\)\/397 \[LessEqual] 1, \(4\ x1\)\/777 + \(10\ x2\)\/777 + \(4\ x3\)\/777 + \(4\ \ x4\)\/777 + \(10\ x5\)\/777 + \(19\ x6\)\/777 \[LessEqual] 1, \(6\ x2\)\/397 + \(6\ x3\)\/397 + \(4\ x4\)\/397 + \(9\ \ x5\)\/397 \[LessEqual] 1, \(2\ x2\)\/165 + \(2\ x3\)\/165 + x5\/33 \[LessEqual] 1, \(4\ x1\)\/1041 + \(16\ x2\)\/1041 + \(4\ x3\)\/1041 + \(25\ \ x4\)\/1041 + \(10\ x5\)\/1041 + \(10\ x6\)\/1041 \[LessEqual] 1, x1\/61 + \(3\ x2\)\/122 + \(3\ x3\)\/122 \[LessEqual] 1, x1\/120 + x2\/48 + x3\/48 + x4\/120 + x5\/120 \[LessEqual] 1, \(4\ x1\)\/385 + \(6\ x2\)\/385 - \(6\ x3\)\/385 + \(9\ \ x5\)\/385 + \(6\ x6\)\/385 \[LessEqual] 1, \(4\ x1\)\/419 + \(6\ x2\)\/419 - \(2\ x3\)\/419 + \(7\ \ x5\)\/419 + \(10\ x6\)\/419 \[LessEqual] 1, \(8\ x1\)\/945 + \(2\ x2\)\/135 - \(4\ x3\)\/945 + \(2\ \ x4\)\/945 + \(2\ x5\)\/135 + \(23\ x6\)\/945 \[LessEqual] 1, \(4\ x1\)\/655 + \(12\ x2\)\/655 + \(6\ x4\)\/655 + \(6\ \ x5\)\/655 + \(3\ x6\)\/131 \[LessEqual] 1, x1\/77 + \(3\ x2\)\/154 + \(3\ x5\)\/154 + x6\/77 \[LessEqual] 1, x2\/79 - \(2\ x3\)\/79 + \(4\ x4\)\/79 \[LessEqual] 1, x1\/180 + x2\/72 + x3\/180 + x4\/180 + x5\/72 + x6\/45 \[LessEqual] 1, \(4\ x1\)\/1041 + \(16\ x2\)\/1041 + \(4\ x3\)\/1041 + \(10\ \ x4\)\/1041 + \(10\ x5\)\/1041 + \(25\ x6\)\/1041 \[LessEqual] 1, x1\/135 + x2\/54 + x3\/135 + x4\/135 + x5\/54 + x6\/135 \[LessEqual] 1, x1\/180 + x2\/72 + x3\/180 + x4\/45 + x5\/72 + x6\/180 \[LessEqual] 1, x2\/36 + x4\/36 \[LessEqual] 1, \(2\ x2\)\/159 + \(2\ x3\)\/159 + \(5\ x6\)\/159 \[LessEqual] 1, x1\/180 + x2\/72 + x3\/45 + x4\/180 + x5\/72 + x6\/180 \[LessEqual] 1, \(2\ x2\)\/175 + x3\/35 + \(2\ x4\)\/175 - \(2\ x5\)\/35 + \(2\ x6\)\/175 \ \[LessEqual] 1, x3\/34 - x5\/17 + x6\/34 \[LessEqual] 1, \(2\ x2\)\/175 + \(2\ x3\)\/175 + \(2\ x4\)\/175 - \(4\ \ x5\)\/175 + x6\/35 \[LessEqual] 1, \(4\ x1\)\/385 + \(9\ x3\)\/385 + \(6\ x4\)\/385 - \(6\ \ x5\)\/385 + \(6\ x6\)\/385 \[LessEqual] 1, \(3\ x3\)\/85 - \(6\ x5\)\/85 + \(2\ x6\)\/85 \[LessEqual] 1, x2\/32 + x3\/32 - x5\/16 \[LessEqual] 1, x2\/49 + x3\/49 + x4\/49 - \(2\ x5\)\/49 \[LessEqual] 1, x2\/49 - \(2\ x3\)\/49 + x4\/49 + x5\/49 \[LessEqual] 1, \(8\ x1\)\/945 + \(2\ x2\)\/135 + \(2\ x3\)\/945 - \(4\ \ x4\)\/945 + \(2\ x5\)\/135 + \(23\ x6\)\/945 \[LessEqual] 1, \(4\ x1\)\/419 + \(7\ x2\)\/419 - \(2\ x4\)\/419 + \(6\ \ x5\)\/419 + \(10\ x6\)\/419 \[LessEqual] 1, \(4\ x1\)\/655 + \(6\ x2\)\/655 + \(6\ x3\)\/655 + \(12\ \ x5\)\/655 + \(3\ x6\)\/131 \[LessEqual] 1, \(4\ x1\)\/1041 + \(10\ x2\)\/1041 + \(10\ x3\)\/1041 + \(4\ \ x4\)\/1041 + \(16\ x5\)\/1041 + \(25\ x6\)\/1041 \[LessEqual] 1, x2\/15 - \(2\ x5\)\/45 \[LessEqual] 1, \(4\ x1\)\/565 + \(3\ x2\)\/113 + \(6\ x3\)\/565 + \(6\ \ x4\)\/565 + \(6\ x6\)\/565 \[LessEqual] 1, \(2\ x1\)\/315 + x2\/63 + x3\/63 + \(2\ x4\)\/315 + \(2\ x5\)\/315 + x6\/63 \[LessEqual] 1, x1\/180 + x2\/45 + x3\/72 + x4\/72 + x5\/180 + x6\/180 \[LessEqual] 1, \(4\ x1\)\/1041 + \(25\ x2\)\/1041 + \(10\ x3\)\/1041 + \(16\ \ x4\)\/1041 + \(4\ x5\)\/1041 + \(10\ x6\)\/1041 \[LessEqual] 1, \(4\ x1\)\/1015 + \(5\ x2\)\/203 + \(2\ x3\)\/203 + \(2\ \ x4\)\/145 + \(4\ x5\)\/1015 + \(2\ x6\)\/203 \[LessEqual] 1, \(2\ x2\)\/175 + \(2\ x3\)\/175 - \(4\ x4\)\/175 + \(2\ \ x5\)\/175 + x6\/35 \[LessEqual] 1, x2\/34 - x4\/17 + x6\/34 \[LessEqual] 1, x2\/49 + x3\/49 - \(2\ x4\)\/49 + x5\/49 \[LessEqual] 1, \(4\ x2\)\/79 - \(2\ x5\)\/79 + x6\/79 \[LessEqual] 1, \(4\ x1\)\/545 + \(3\ x2\)\/109 + \(6\ x3\)\/545 + \(4\ \ x4\)\/545 + \(6\ x6\)\/545 \[LessEqual] 1, \(4\ x1\)\/777 + \(19\ x2\)\/777 + \(10\ x3\)\/777 + \(10\ \ x4\)\/777 + \(4\ x5\)\/777 + \(4\ x6\)\/777 \[LessEqual] 1, \(4\ x2\)\/79 + x4\/79 - \(2\ x5\)\/79 \[LessEqual] 1, \(4\ x1\)\/545 + \(3\ x2\)\/109 + \(6\ x3\)\/545 + \(6\ \ x4\)\/545 + \(4\ x6\)\/545 \[LessEqual] 1, \(9\ x2\)\/397 + \(4\ x3\)\/397 + \(6\ x4\)\/397 + \(6\ \ x5\)\/397 \[LessEqual] 1, x2\/33 + \(2\ x4\)\/165 + \(2\ x5\)\/165 \[LessEqual] 1, x2\/31 + \(2\ x4\)\/93 \[LessEqual] 1, x2\/35 + \(2\ x3\)\/175 - \(2\ x4\)\/35 + \(2\ x5\)\/175 + \(2\ \ x6\)\/175 \[LessEqual] 1, \(9\ x2\)\/271 - \(2\ x4\)\/271 + \(6\ x6\)\/271 \[LessEqual] 1, \(4\ x1\)\/389 + \(9\ x2\)\/389 - \(2\ x4\)\/389 + \(6\ \ x5\)\/389 + \(6\ x6\)\/389 \[LessEqual] 1, x2\/32 + x3\/32 - x4\/16 \[LessEqual] 1, \(4\ x1\)\/307 + \(9\ x2\)\/307 + \(6\ x3\)\/307 \[LessEqual] 1, \(4\ x1\)\/385 + \(9\ x2\)\/385 - \(6\ x4\)\/385 + \(6\ \ x5\)\/385 + \(6\ x6\)\/385 \[LessEqual] 1, \(3\ x2\)\/85 - \(6\ x4\)\/85 + \(2\ x6\)\/85 \[LessEqual] 1, \(4\ x1\)\/397 + \(9\ x2\)\/397 + \(6\ x5\)\/397 + \(6\ \ x6\)\/397 \[LessEqual] 1, \(9\ x2\)\/179 - \(4\ x5\)\/179 + \(2\ x6\)\/179 \[LessEqual] 1, \(9\ x2\)\/179 + \(2\ x4\)\/179 - \(4\ x5\)\/179 \[LessEqual] 1, \(2\ x1\)\/179 + \(5\ x4\)\/179 + \(2\ x5\)\/179 + \(2\ \ x6\)\/179 \[LessEqual] 1, \(2\ x1\)\/139 + \(3\ x3\)\/139 + \(2\ x4\)\/139 + \(2\ \ x6\)\/139 \[LessEqual] 1, \(2\ x1\)\/265 - \(4\ x3\)\/265 + \(11\ x4\)\/265 + \(2\ \ x5\)\/265 + \(2\ x6\)\/265 \[LessEqual] 1, \(2\ x1\)\/185 + x3\/37 + \(2\ x4\)\/185 + \(2\ x5\)\/185 \[LessEqual] 1, \(2\ x1\)\/265 - \(4\ x2\)\/265 + \(2\ x4\)\/265 + \(11\ \ x5\)\/265 + \(2\ x6\)\/265 \[LessEqual] 1, \(6\ x1\)\/565 + \(4\ x3\)\/565 + \(6\ x4\)\/565 + \(3\ \ x5\)\/113 + \(6\ x6\)\/565 \[LessEqual] 1, \(2\ x1\)\/195 + \(2\ x3\)\/195 + \(2\ x4\)\/195 + x5\/39 + \(2\ x6\)\/195 \[LessEqual] 1, \(2\ x1\)\/265 - \(4\ x2\)\/265 + \(2\ x3\)\/265 + \(2\ \ x4\)\/265 + \(11\ x5\)\/265 \[LessEqual] 1, \(6\ x1\)\/565 + \(6\ x3\)\/565 + \(6\ x4\)\/565 + \(3\ \ x5\)\/113 + \(4\ x6\)\/565 \[LessEqual] 1, \(2\ x1\)\/179 + \(2\ x4\)\/179 + \(5\ x5\)\/179 + \(2\ \ x6\)\/179 \[LessEqual] 1, \(6\ x1\)\/565 + \(4\ x2\)\/565 + \(3\ x4\)\/113 + \(6\ \ x5\)\/565 + \(6\ x6\)\/565 \[LessEqual] 1, \(4\ x3\)\/307 + \(6\ x5\)\/307 + \(9\ x6\)\/307 \[LessEqual] 1, \(6\ x3\)\/307 + \(4\ x5\)\/307 + \(9\ x6\)\/307 \[LessEqual] 1, \(-\(\(4\ x1\)\/179\)\) + \(2\ x4\)\/179 + \(9\ x6\)\/179 \ \[LessEqual] 1, \(-\(\(4\ x1\)\/179\)\) + \(2\ x5\)\/179 + \(9\ x6\)\/179 \ \[LessEqual] 1, \(-\(\(4\ x1\)\/179\)\) + \(2\ x3\)\/179 + \(9\ x6\)\/179 \ \[LessEqual] 1, \(6\ x1\)\/391 + \(4\ x3\)\/391 + \(9\ x4\)\/391 + \(6\ \ x6\)\/391 \[LessEqual] 1, \(2\ x1\)\/139 + \(2\ x3\)\/139 + \(3\ x4\)\/139 + \(2\ \ x6\)\/139 \[LessEqual] 1, \(2\ x1\)\/245 - \(4\ x3\)\/245 + \(11\ x4\)\/245 + \(2\ \ x6\)\/245 \[LessEqual] 1, \(2\ x1\)\/245 + \(11\ x3\)\/245 - \(4\ x4\)\/245 + \(2\ \ x6\)\/245 \[LessEqual] 1, \(2\ x1\)\/245 + \(11\ x3\)\/245 - \(4\ x4\)\/245 + \(2\ \ x5\)\/245 \[LessEqual] 1, \(6\ x1\)\/391 + \(9\ x3\)\/391 + \(4\ x4\)\/391 + \(6\ \ x6\)\/391 \[LessEqual] 1, \(2\ x1\)\/159 + \(5\ x3\)\/159 + \(2\ x5\)\/159 \[LessEqual] 1, \(2\ x1\)\/195 + \(2\ x2\)\/195 + x4\/39 + \(2\ x5\)\/195 + \(2\ x6\)\/195 \[LessEqual] 1, \(6\ x2\)\/307 + \(4\ x4\)\/307 + \(9\ x6\)\/307 \[LessEqual] 1, \(4\ x2\)\/307 + \(6\ x4\)\/307 + \(9\ x6\)\/307 \[LessEqual] 1, \(-\(\(4\ x1\)\/179\)\) + \(2\ x2\)\/179 + \(9\ x6\)\/179 \ \[LessEqual] 1, \(2\ x1\)\/185 + \(2\ x2\)\/185 + \(2\ x3\)\/185 + x4\/37 \[LessEqual] 1, \(2\ x1\)\/179 + \(2\ x3\)\/179 + \(2\ x4\)\/179 + \(5\ \ x5\)\/179 \[LessEqual] 1, \(4\ x2\)\/419 + \(7\ x3\)\/419 + \(6\ x4\)\/419 + \(10\ \ x5\)\/419 - \(2\ x6\)\/419 \[LessEqual] 1, \(2\ x1\)\/265 + \(2\ x2\)\/265 + \(11\ x3\)\/265 - \(4\ \ x4\)\/265 + \(2\ x6\)\/265 \[LessEqual] 1, \(2\ x1\)\/195 + \(2\ x2\)\/195 + x3\/39 + \(2\ x5\)\/195 + \(2\ x6\)\/195 \[LessEqual] 1, \(6\ x1\)\/565 + \(6\ x2\)\/565 + \(3\ x3\)\/113 + \(4\ \ x5\)\/565 + \(6\ x6\)\/565 \[LessEqual] 1, \(2\ x1\)\/265 + \(2\ x2\)\/265 + \(11\ x3\)\/265 - \(4\ \ x4\)\/265 + \(2\ x5\)\/265 \[LessEqual] 1, \(6\ x1\)\/565 + \(6\ x2\)\/565 + \(3\ x3\)\/113 + \(6\ \ x5\)\/565 + \(4\ x6\)\/565 \[LessEqual] 1, \(2\ x1\)\/179 + \(2\ x2\)\/179 + \(5\ x3\)\/179 + \(2\ \ x6\)\/179 \[LessEqual] 1, \(48\ x2\)\/3335 + \(81\ x3\)\/3335 + \(32\ x4\)\/3335 + \(54\ \ x5\)\/3335 - \(18\ x6\)\/3335 \[LessEqual] 1, \(6\ x2\)\/419 + \(10\ x3\)\/419 + \(4\ x4\)\/419 + \(7\ \ x5\)\/419 - \(2\ x6\)\/419 \[LessEqual] 1, \(16\ x2\)\/1207 + \(27\ x3\)\/1207 + \(18\ x4\)\/1207 + \(18\ \ x5\)\/1207 - \(6\ x6\)\/1207 \[LessEqual] 1, \(4\ x2\)\/389 + \(9\ x3\)\/389 + \(6\ x4\)\/389 + \(6\ \ x5\)\/389 - \(2\ x6\)\/389 \[LessEqual] 1, \(9\ x3\)\/271 + \(6\ x5\)\/271 - \(2\ x6\)\/271 \[LessEqual] 1, \(2\ x1\)\/179 + \(2\ x2\)\/179 + \(5\ x3\)\/179 + \(2\ \ x5\)\/179 \[LessEqual] 1, \(6\ x1\)\/391 + \(4\ x2\)\/391 + \(9\ x5\)\/391 + \(6\ \ x6\)\/391 \[LessEqual] 1, \(2\ x1\)\/139 + \(2\ x2\)\/139 + \(3\ x5\)\/139 + \(2\ \ x6\)\/139 \[LessEqual] 1, \(2\ x1\)\/245 - \(4\ x2\)\/245 + \(11\ x5\)\/245 + \(2\ \ x6\)\/245 \[LessEqual] 1, \(2\ x1\)\/245 + \(2\ x2\)\/245 - \(4\ x3\)\/245 + \(11\ \ x4\)\/245 \[LessEqual] 1, \(2\ x1\)\/265 + \(2\ x2\)\/265 - \(4\ x3\)\/265 + \(11\ \ x4\)\/265 + \(2\ x5\)\/265 \[LessEqual] 1, \(6\ x1\)\/565 + \(6\ x2\)\/565 + \(3\ x4\)\/113 + \(6\ \ x5\)\/565 + \(4\ x6\)\/565 \[LessEqual] 1, \(2\ x1\)\/245 - \(4\ x2\)\/245 + \(2\ x3\)\/245 + \(11\ \ x5\)\/245 \[LessEqual] 1, \(2\ x1\)\/185 + \(2\ x2\)\/185 + \(2\ x3\)\/185 + x5\/37 \[LessEqual] 1, \(2\ x1\)\/159 + \(2\ x3\)\/159 + \(5\ x5\)\/159 \[LessEqual] 1, \(32\ x2\)\/3335 + \(54\ x3\)\/3335 + \(48\ x4\)\/3335 + \(81\ \ x5\)\/3335 - \(18\ x6\)\/3335 \[LessEqual] 1, \(18\ x2\)\/1207 + \(18\ x3\)\/1207 + \(16\ x4\)\/1207 + \(27\ \ x5\)\/1207 - \(6\ x6\)\/1207 \[LessEqual] 1, \(6\ x3\)\/271 + \(9\ x5\)\/271 - \(2\ x6\)\/271 \[LessEqual] 1, \(6\ x2\)\/389 + \(6\ x3\)\/389 + \(4\ x4\)\/389 + \(9\ \ x5\)\/389 - \(2\ x6\)\/389 \[LessEqual] 1, \(18\ x2\)\/1207 + \(18\ x3\)\/1207 + \(27\ x4\)\/1207 + \(16\ \ x5\)\/1207 - \(6\ x6\)\/1207 \[LessEqual] 1, \(6\ x2\)\/389 + \(6\ x3\)\/389 + \(9\ x4\)\/389 + \(4\ \ x5\)\/389 - \(2\ x6\)\/389 \[LessEqual] 1, \(2\ x1\)\/159 + \(2\ x2\)\/159 + \(5\ x4\)\/159 \[LessEqual] 1, \(2\ x1\)\/179 + \(2\ x2\)\/179 + \(5\ x4\)\/179 + \(2\ \ x5\)\/179 \[LessEqual] 1, \(7\ x2\)\/419 + \(4\ x3\)\/419 + \(10\ x4\)\/419 + \(6\ \ x5\)\/419 - \(2\ x6\)\/419 \[LessEqual] 1, \(54\ x2\)\/3335 + \(32\ x3\)\/3335 + \(81\ x4\)\/3335 + \(48\ \ x5\)\/3335 - \(18\ x6\)\/3335 \[LessEqual] 1, \(6\ x2\)\/271 + \(9\ x4\)\/271 - \(2\ x6\)\/271 \[LessEqual] 1, \(2\ x1\)\/195 + x2\/39 + \(2\ x3\)\/195 + \(2\ x4\)\/195 + \(2\ x6\)\/195 \ \[LessEqual] 1, \(2\ x1\)\/179 + \(5\ x2\)\/179 + \(2\ x3\)\/179 + \(2\ \ x6\)\/179 \[LessEqual] 1, \(2\ x1\)\/265 + \(11\ x2\)\/265 + \(2\ x3\)\/265 - \(4\ \ x5\)\/265 + \(2\ x6\)\/265 \[LessEqual] 1, \(6\ x1\)\/565 + \(3\ x2\)\/113 + \(6\ x3\)\/565 + \(4\ \ x4\)\/565 + \(6\ x6\)\/565 \[LessEqual] 1, \(27\ x2\)\/1207 + \(16\ x3\)\/1207 + \(18\ x4\)\/1207 + \(18\ \ x5\)\/1207 - \(6\ x6\)\/1207 \[LessEqual] 1, \(2\ x1\)\/265 + \(11\ x2\)\/265 + \(2\ x3\)\/265 + \(2\ \ x4\)\/265 - \(4\ x5\)\/265 \[LessEqual] 1, \(6\ x1\)\/565 + \(3\ x2\)\/113 + \(6\ x3\)\/565 + \(6\ \ x4\)\/565 + \(4\ x6\)\/565 \[LessEqual] 1, \(10\ x2\)\/419 + \(6\ x3\)\/419 + \(7\ x4\)\/419 + \(4\ \ x5\)\/419 - \(2\ x6\)\/419 \[LessEqual] 1, \(81\ x2\)\/3335 + \(48\ x3\)\/3335 + \(54\ x4\)\/3335 + \(32\ \ x5\)\/3335 - \(18\ x6\)\/3335 \[LessEqual] 1, \(2\ x1\)\/179 + \(5\ x2\)\/179 + \(2\ x3\)\/179 + \(2\ \ x4\)\/179 \[LessEqual] 1, \(2\ x1\)\/139 + \(3\ x2\)\/139 + \(2\ x5\)\/139 + \(2\ \ x6\)\/139 \[LessEqual] 1, \(2\ x1\)\/185 + x2\/37 + \(2\ x4\)\/185 + \(2\ x5\)\/185 \[LessEqual] 1, \(6\ x1\)\/391 + \(9\ x2\)\/391 + \(4\ x5\)\/391 + \(6\ \ x6\)\/391 \[LessEqual] 1, \(9\ x2\)\/389 + \(4\ x3\)\/389 + \(6\ x4\)\/389 + \(6\ \ x5\)\/389 - \(2\ x6\)\/389 \[LessEqual] 1, \(9\ x2\)\/271 + \(6\ x4\)\/271 - \(2\ x6\)\/271 \[LessEqual] 1, \(2\ x1\)\/159 + \(5\ x2\)\/159 + \(2\ x4\)\/159 \[LessEqual] 1, \(2\ x1\)\/245 + \(11\ x2\)\/245 - \(4\ x5\)\/245 + \(2\ \ x6\)\/245 \[LessEqual] 1, \(2\ x1\)\/245 + \(11\ x2\)\/245 + \(2\ x4\)\/245 - \(4\ \ x5\)\/245 \[LessEqual] 1, \(16\ x1\)\/1207 - \(6\ x2\)\/1207 + \(18\ x3\)\/1207 + \(27\ \ x4\)\/1207 + \(18\ x6\)\/1207 \[LessEqual] 1, \(48\ x1\)\/3335 - \(18\ x2\)\/3335 + \(32\ x3\)\/3335 + \(81\ \ x4\)\/3335 + \(54\ x6\)\/3335 \[LessEqual] 1, \(-\(\(6\ x2\)\/85\)\) + \(2\ x4\)\/85 + \(3\ x6\)\/85 \ \[LessEqual] 1, \(-x2\) \[LessEqual] 0, x1\/75 - x2\/225 + x3\/50 + x4\/75 + x6\/50 \[LessEqual] 1, \(32\ x1\)\/3335 - \(18\ x2\)\/3335 + \(48\ x3\)\/3335 + \(54\ \ x4\)\/3335 + \(81\ x6\)\/3335 \[LessEqual] 1, x1\/120 + x3\/48 + x4\/120 + x5\/120 + x6\/48 \[LessEqual] 1, \(2\ x1\)\/131 + \(6\ x3\)\/655 + \(3\ x4\)\/131 + \(6\ \ x5\)\/655 + \(6\ x6\)\/655 \[LessEqual] 1, \(2\ x1\)\/109 + \(3\ x4\)\/109 + \(2\ x5\)\/109 \[LessEqual] 1, \(18\ x1\)\/1207 - \(6\ x2\)\/1207 + \(27\ x3\)\/1207 + \(18\ \ x4\)\/1207 + \(16\ x6\)\/1207 \[LessEqual] 1, \(6\ x1\)\/655 + \(3\ x3\)\/131 + \(6\ x4\)\/655 + \(6\ \ x5\)\/655 + \(2\ x6\)\/131 \[LessEqual] 1, \(2\ x1\)\/175 - \(4\ x2\)\/175 + x4\/35 + \(2\ x5\)\/175 + \(2\ x6\)\/175 \[LessEqual] 1, \(4\ x1\)\/629 + \(10\ x3\)\/629 + \(6\ x4\)\/629 + \(6\ \ x5\)\/629 + \(15\ x6\)\/629 \[LessEqual] 1, x1\/77 + x3\/77 + \(3\ x4\)\/154 + \(3\ x6\)\/154 \[LessEqual] 1, \(6\ x1\)\/419 - \(2\ x2\)\/419 + \(4\ x3\)\/419 + \(10\ \ x4\)\/419 + \(7\ x6\)\/419 \[LessEqual] 1, \(-\(\(2\ x2\)\/271\)\) + \(6\ x4\)\/271 + \(9\ x6\)\/271 \ \[LessEqual] 1, \(2\ x1\)\/135 - \(4\ x2\)\/945 + \(8\ x3\)\/945 + \(23\ \ x4\)\/945 + \(2\ x5\)\/945 + \(2\ x6\)\/135 \[LessEqual] 1, \(10\ x1\)\/629 + \(4\ x3\)\/629 + \(15\ x4\)\/629 + \(6\ x5\)\ \/629 + \(6\ x6\)\/629 \[LessEqual] 1, \(-\(x2\/50\)\) + \(3\ x3\)\/100 + \(3\ x5\)\/100 \[LessEqual] 1, \(6\ x1\)\/389 - \(2\ x2\)\/389 + \(9\ x3\)\/389 + \(6\ \ x4\)\/389 + \(4\ x6\)\/389 \[LessEqual] 1, \(6\ x1\)\/307 + \(9\ x4\)\/307 + \(4\ x5\)\/307 \[LessEqual] 1, x6\/23 \[LessEqual] 1, \(2\ x4\)\/93 + x6\/31 \[LessEqual] 1, \(2\ x1\)\/165 + \(2\ x3\)\/165 + x4\/33 \[LessEqual] 1, \(6\ x1\)\/397 + \(6\ x3\)\/397 + \(9\ x4\)\/397 + \(4\ \ x6\)\/397 \[LessEqual] 1, \(2\ x1\)\/165 + x3\/33 + \(2\ x4\)\/165 \[LessEqual] 1, \(6\ x1\)\/397 + \(9\ x3\)\/397 + \(6\ x4\)\/397 + \(4\ \ x6\)\/397 \[LessEqual] 1, \(2\ x1\)\/109 + \(2\ x4\)\/109 + \(3\ x5\)\/109 \[LessEqual] 1, x1\/77 + \(3\ x3\)\/154 + x4\/77 + \(3\ x6\)\/154 \[LessEqual] 1, \(2\ x5\)\/93 + x6\/31 \[LessEqual] 1, \(2\ x1\)\/179 - \(4\ x3\)\/179 + \(9\ x4\)\/179 \[LessEqual] 1, \(4\ x2\)\/545 + \(4\ x3\)\/545 + \(6\ x4\)\/545 + \(6\ \ x5\)\/545 + \(3\ x6\)\/109 \[LessEqual] 1, \(10\ x1\)\/777 + \(4\ x2\)\/777 + \(4\ x3\)\/777 + \(19\ x4\)\ \/777 + \(4\ x5\)\/777 + \(10\ x6\)\/777 \[LessEqual] 1, \(6\ x1\)\/545 + \(4\ x2\)\/545 + \(3\ x4\)\/109 + \(4\ \ x5\)\/545 + \(6\ x6\)\/545 \[LessEqual] 1, \(2\ x3\)\/93 + x6\/31 \[LessEqual] 1, \(2\ x1\)\/945 + \(8\ x2\)\/945 + \(2\ x3\)\/135 + \(2\ \ x4\)\/135 + \(23\ x5\)\/945 - \(4\ x6\)\/945 \[LessEqual] 1, \(6\ x1\)\/655 + \(4\ x2\)\/655 + \(6\ x3\)\/655 + \(12\ \ x4\)\/655 + \(3\ x5\)\/131 \[LessEqual] 1, \(10\ x1\)\/1041 + \(4\ x2\)\/1041 + \(10\ x3\)\/1041 + \(16\ \ x4\)\/1041 + \(25\ x5\)\/1041 + \(4\ x6\)\/1041 \[LessEqual] 1, \(2\ x1\)\/265 + \(11\ x3\)\/265 - \(4\ x4\)\/265 + \(2\ \ x5\)\/265 + \(2\ x6\)\/265 \[LessEqual] 1, \(2\ x1\)\/179 + \(9\ x3\)\/179 - \(4\ x4\)\/179 \[LessEqual] 1, \(6\ x1\)\/307 + \(4\ x4\)\/307 + \(9\ x5\)\/307 \[LessEqual] 1, \(2\ x1\)\/179 - \(4\ x2\)\/179 + \(9\ x5\)\/179 \[LessEqual] 1, \(2\ x1\)\/265 - \(4\ x2\)\/265 + \(2\ x3\)\/265 + \(11\ \ x5\)\/265 + \(2\ x6\)\/265 \[LessEqual] 1, \(6\ x1\)\/545 + \(4\ x3\)\/545 + \(4\ x4\)\/545 + \(3\ \ x5\)\/109 + \(6\ x6\)\/545 \[LessEqual] 1, \(6\ x1\)\/565 + \(6\ x3\)\/565 + \(4\ x4\)\/565 + \(3\ \ x5\)\/113 + \(6\ x6\)\/565 \[LessEqual] 1, \(6\ x1\)\/545 + \(6\ x3\)\/545 + \(4\ x4\)\/545 + \(3\ \ x5\)\/109 + \(4\ x6\)\/545 \[LessEqual] 1, \(4\ x1\)\/1015 + \(4\ x2\)\/1015 + \(2\ x3\)\/145 + \(2\ x4\)\ \/203 + \(2\ x5\)\/203 + \(5\ x6\)\/203 \[LessEqual] 1, x1\/75 + x3\/75 + x4\/50 - x5\/225 + x6\/50 \[LessEqual] 1, x1\/120 + x2\/120 + x3\/120 + x4\/48 + x6\/48 \[LessEqual] 1, \(2\ x1\)\/145 + \(4\ x2\)\/1015 + \(4\ x3\)\/1015 + \(5\ x4\)\ \/203 + \(2\ x5\)\/203 + \(2\ x6\)\/203 \[LessEqual] 1, \(48\ x1\)\/3335 + \(81\ x3\)\/3335 + \(32\ x4\)\/3335 - \(18\ \ x5\)\/3335 + \(54\ x6\)\/3335 \[LessEqual] 1, \(6\ x1\)\/419 + \(10\ x3\)\/419 + \(4\ x4\)\/419 - \(2\ \ x5\)\/419 + \(7\ x6\)\/419 \[LessEqual] 1, \(16\ x1\)\/1207 + \(27\ x3\)\/1207 + \(18\ x4\)\/1207 - \(6\ \ x5\)\/1207 + \(18\ x6\)\/1207 \[LessEqual] 1, \(2\ x1\)\/175 - \(4\ x3\)\/175 + \(2\ x4\)\/175 + x5\/35 + \(2\ x6\)\/175 \[LessEqual] 1, \(-\(\(2\ x3\)\/271\)\) + \(6\ x5\)\/271 + \(9\ x6\)\/271 \ \[LessEqual] 1, \(-\(\(6\ x3\)\/85\)\) + \(2\ x5\)\/85 + \(3\ x6\)\/85 \ \[LessEqual] 1, \(32\ x1\)\/3335 + \(48\ x2\)\/3335 - \(18\ x3\)\/3335 + \(54\ \ x5\)\/3335 + \(81\ x6\)\/3335 \[LessEqual] 1, \(10\ x1\)\/777 + \(4\ x2\)\/777 + \(4\ x3\)\/777 + \(4\ \ x4\)\/777 + \(19\ x5\)\/777 + \(10\ x6\)\/777 \[LessEqual] 1, \(2\ x1\)\/265 + \(2\ x2\)\/265 - \(4\ x3\)\/265 + \(11\ \ x4\)\/265 + \(2\ x6\)\/265 \[LessEqual] 1, \(6\ x1\)\/565 + \(6\ x2\)\/565 + \(3\ x4\)\/113 + \(4\ \ x5\)\/565 + \(6\ x6\)\/565 \[LessEqual] 1, \(4\ x1\)\/629 + \(6\ x2\)\/629 + \(6\ x3\)\/629 + \(10\ \ x4\)\/629 + \(15\ x6\)\/629 \[LessEqual] 1, \(4\ x1\)\/1015 + \(2\ x2\)\/203 + \(2\ x3\)\/203 + \(2\ \ x4\)\/145 + \(4\ x5\)\/1015 + \(5\ x6\)\/203 \[LessEqual] 1, \(6\ x1\)\/629 + \(4\ x2\)\/629 + \(6\ x3\)\/629 + \(10\ \ x4\)\/629 + \(15\ x5\)\/629 \[LessEqual] 1, \(2\ x1\)\/203 + \(4\ x2\)\/1015 + \(2\ x3\)\/203 + \(2\ \ x4\)\/145 + \(5\ x5\)\/203 + \(4\ x6\)\/1015 \[LessEqual] 1, \(6\ x1\)\/655 + \(6\ x2\)\/655 + \(6\ x3\)\/655 + \(3\ \ x4\)\/131 + \(2\ x5\)\/131 \[LessEqual] 1, \(6\ x1\)\/307 + \(4\ x2\)\/307 + \(9\ x3\)\/307 \[LessEqual] 1, \(2\ x1\)\/109 + \(2\ x2\)\/109 + \(3\ x3\)\/109 \[LessEqual] 1, \(6\ x1\)\/565 + \(4\ x2\)\/565 + \(3\ x3\)\/113 + \(6\ \ x5\)\/565 + \(6\ x6\)\/565 \[LessEqual] 1, \(6\ x1\)\/545 + \(4\ x2\)\/545 + \(3\ x3\)\/109 + \(4\ \ x5\)\/545 + \(6\ x6\)\/545 \[LessEqual] 1, \(6\ x1\)\/545 + \(4\ x2\)\/545 + \(3\ x3\)\/109 + \(6\ \ x5\)\/545 + \(4\ x6\)\/545 \[LessEqual] 1, \(10\ x1\)\/777 + \(4\ x2\)\/777 + \(19\ x3\)\/777 + \(4\ x4\)\ \/777 + \(4\ x5\)\/777 + \(10\ x6\)\/777 \[LessEqual] 1, \(2\ x1\)\/131 + \(6\ x2\)\/655 + \(3\ x3\)\/131 + \(6\ \ x4\)\/655 + \(6\ x6\)\/655 \[LessEqual] 1, \(10\ x1\)\/629 + \(6\ x2\)\/629 + \(15\ x3\)\/629 + \(4\ x4\)\ \/629 + \(6\ x6\)\/629 \[LessEqual] 1, \(2\ x1\)\/135 + \(2\ x2\)\/945 + \(23\ x3\)\/945 + \(8\ \ x4\)\/945 - \(4\ x5\)\/945 + \(2\ x6\)\/135 \[LessEqual] 1, \(2\ x1\)\/145 + \(2\ x2\)\/203 + \(5\ x3\)\/203 + \(4\ \ x4\)\/1015 + \(4\ x5\)\/1015 + \(2\ x6\)\/203 \[LessEqual] 1, \(2\ x1\)\/945 + \(2\ x2\)\/135 + \(23\ x3\)\/945 + \(8\ \ x4\)\/945 + \(2\ x5\)\/135 - \(4\ x6\)\/945 \[LessEqual] 1, \(6\ x1\)\/629 + \(10\ x2\)\/629 + \(15\ x3\)\/629 + \(4\ x4\)\ \/629 + \(6\ x5\)\/629 \[LessEqual] 1, \(6\ x1\)\/655 + \(2\ x2\)\/131 + \(3\ x3\)\/131 + \(6\ \ x4\)\/655 + \(6\ x5\)\/655 \[LessEqual] 1, \(2\ x1\)\/203 + \(2\ x2\)\/145 + \(5\ x3\)\/203 + \(4\ \ x4\)\/1015 + \(2\ x5\)\/203 + \(4\ x6\)\/1015 \[LessEqual] 1, \(2\ x1\)\/203 + \(4\ x2\)\/1015 + \(5\ x3\)\/203 + \(4\ \ x4\)\/1015 + \(2\ x5\)\/203 + \(2\ x6\)\/145 \[LessEqual] 1, \(6\ x1\)\/545 + \(6\ x2\)\/545 + \(3\ x4\)\/109 + \(4\ \ x5\)\/545 + \(4\ x6\)\/545 \[LessEqual] 1, \(4\ x1\)\/629 + \(6\ x2\)\/629 + \(6\ x3\)\/629 + \(10\ \ x5\)\/629 + \(15\ x6\)\/629 \[LessEqual] 1, \(4\ x1\)\/1015 + \(2\ x2\)\/203 + \(2\ x3\)\/203 + \(4\ \ x4\)\/1015 + \(2\ x5\)\/145 + \(5\ x6\)\/203 \[LessEqual] 1, \(6\ x3\)\/271 - \(2\ x5\)\/271 + \(9\ x6\)\/271 \[LessEqual] 1, \(32\ x1\)\/3335 + \(54\ x3\)\/3335 + \(48\ x4\)\/3335 - \(18\ \ x5\)\/3335 + \(81\ x6\)\/3335 \[LessEqual] 1, \(6\ x2\)\/545 + \(6\ x3\)\/545 + \(4\ x4\)\/545 + \(4\ \ x5\)\/545 + \(3\ x6\)\/109 \[LessEqual] 1, \(18\ x1\)\/1207 + \(18\ x3\)\/1207 + \(27\ x4\)\/1207 - \(6\ \ x5\)\/1207 + \(16\ x6\)\/1207 \[LessEqual] 1, \(6\ x1\)\/655 + \(6\ x2\)\/655 + \(6\ x3\)\/655 + \(3\ \ x4\)\/131 + \(2\ x6\)\/131 \[LessEqual] 1, \(10\ x1\)\/1041 + \(10\ x2\)\/1041 + \(4\ x3\)\/1041 + \(25\ \ x4\)\/1041 + \(4\ x5\)\/1041 + \(16\ x6\)\/1041 \[LessEqual] 1, \(2\ x1\)\/203 + \(2\ x2\)\/203 + \(4\ x3\)\/1015 + \(5\ \ x4\)\/203 + \(4\ x5\)\/1015 + \(2\ x6\)\/145 \[LessEqual] 1, \(2\ x1\)\/203 + \(2\ x2\)\/203 + \(4\ x3\)\/1015 + \(5\ \ x4\)\/203 + \(2\ x5\)\/145 + \(4\ x6\)\/1015 \[LessEqual] 1, \(10\ x1\)\/1041 + \(10\ x2\)\/1041 + \(4\ x3\)\/1041 + \(25\ \ x4\)\/1041 + \(16\ x5\)\/1041 + \(4\ x6\)\/1041 \[LessEqual] 1, \(6\ x1\)\/389 + \(6\ x3\)\/389 + \(9\ x4\)\/389 - \(2\ \ x5\)\/389 + \(4\ x6\)\/389 \[LessEqual] 1, \(10\ x1\)\/1041 + \(4\ x2\)\/1041 + \(25\ x3\)\/1041 + \(4\ \ x4\)\/1041 + \(10\ x5\)\/1041 + \(16\ x6\)\/1041 \[LessEqual] 1, \(48\ x1\)\/3335 + \(32\ x2\)\/3335 - \(18\ x3\)\/3335 + \(81\ \ x5\)\/3335 + \(54\ x6\)\/3335 \[LessEqual] 1, x1\/77 + x2\/77 + \(3\ x5\)\/154 + \(3\ x6\)\/154 \[LessEqual] 1, \(6\ x1\)\/419 + \(4\ x2\)\/419 - \(2\ x3\)\/419 + \(10\ \ x5\)\/419 + \(7\ x6\)\/419 \[LessEqual] 1, \(16\ x1\)\/1207 + \(18\ x2\)\/1207 - \(6\ x3\)\/1207 + \(27\ \ x5\)\/1207 + \(18\ x6\)\/1207 \[LessEqual] 1, \(4\ x1\)\/629 + \(10\ x2\)\/629 + \(6\ x4\)\/629 + \(6\ \ x5\)\/629 + \(15\ x6\)\/629 \[LessEqual] 1, \(2\ x1\)\/131 + \(6\ x2\)\/655 + \(6\ x4\)\/655 + \(3\ \ x5\)\/131 + \(6\ x6\)\/655 \[LessEqual] 1, \(10\ x1\)\/629 + \(4\ x2\)\/629 + \(6\ x4\)\/629 + \(15\ x5\)\ \/629 + \(6\ x6\)\/629 \[LessEqual] 1, \(2\ x1\)\/135 + \(8\ x2\)\/945 - \(4\ x3\)\/945 + \(2\ \ x4\)\/945 + \(23\ x5\)\/945 + \(2\ x6\)\/135 \[LessEqual] 1, \(-x3\) \[LessEqual] 0, x1\/75 + x2\/50 - x3\/225 + x5\/75 + x6\/50 \[LessEqual] 1, x1\/120 + x2\/48 + x4\/120 + x5\/120 + x6\/48 \[LessEqual] 1, x1\/75 + x2\/75 - x4\/225 + x5\/50 + x6\/50 \[LessEqual] 1, x1\/120 + x2\/120 + x3\/120 + x5\/48 + x6\/48 \[LessEqual] 1, \(4\ x1\)\/1015 + \(2\ x2\)\/145 + \(4\ x3\)\/1015 + \(2\ x4\)\ \/203 + \(2\ x5\)\/203 + \(5\ x6\)\/203 \[LessEqual] 1, \(2\ x1\)\/145 + \(4\ x2\)\/1015 + \(4\ x3\)\/1015 + \(2\ x4\)\ \/203 + \(5\ x5\)\/203 + \(2\ x6\)\/203 \[LessEqual] 1, \(6\ x1\)\/655 + \(6\ x2\)\/655 + \(6\ x3\)\/655 + \(2\ \ x4\)\/131 + \(3\ x5\)\/131 \[LessEqual] 1, \(6\ x1\)\/655 + \(12\ x2\)\/655 + \(3\ x3\)\/131 + \(4\ \ x4\)\/655 + \(6\ x5\)\/655 \[LessEqual] 1, \(10\ x1\)\/1041 + \(16\ x2\)\/1041 + \(25\ x3\)\/1041 + \(4\ \ x4\)\/1041 + \(10\ x5\)\/1041 + \(4\ x6\)\/1041 \[LessEqual] 1, \(2\ x1\)\/175 + \(2\ x2\)\/175 + x3\/35 - \(4\ x5\)\/175 + \(2\ x6\)\/175 \[LessEqual] 1, \(2\ x1\)\/945 + \(2\ x2\)\/135 + \(8\ x3\)\/945 + \(23\ \ x4\)\/945 + \(2\ x5\)\/135 - \(4\ x6\)\/945 \[LessEqual] 1, \(6\ x1\)\/629 + \(6\ x2\)\/629 + \(4\ x3\)\/629 + \(15\ \ x4\)\/629 + \(10\ x5\)\/629 \[LessEqual] 1, \(6\ x1\)\/655 + \(6\ x2\)\/655 + \(4\ x3\)\/655 + \(3\ \ x4\)\/131 + \(12\ x5\)\/655 \[LessEqual] 1, x1\/77 + \(3\ x2\)\/154 + x5\/77 + \(3\ x6\)\/154 \[LessEqual] 1, \(2\ x2\)\/93 + x6\/31 \[LessEqual] 1, \(32\ x1\)\/3335 + \(54\ x2\)\/3335 - \(18\ x4\)\/3335 + \(48\ \ x5\)\/3335 + \(81\ x6\)\/3335 \[LessEqual] 1, \(18\ x1\)\/1207 + \(18\ x2\)\/1207 - \(6\ x4\)\/1207 + \(27\ \ x5\)\/1207 + \(16\ x6\)\/1207 \[LessEqual] 1, \(6\ x1\)\/655 + \(6\ x2\)\/655 + \(6\ x3\)\/655 + \(3\ \ x5\)\/131 + \(2\ x6\)\/131 \[LessEqual] 1, \(6\ x2\)\/271 - \(2\ x4\)\/271 + \(9\ x6\)\/271 \[LessEqual] 1, \(2\ x1\)\/203 + \(4\ x2\)\/1015 + \(2\ x3\)\/203 + \(4\ \ x4\)\/1015 + \(5\ x5\)\/203 + \(2\ x6\)\/145 \[LessEqual] 1, \(10\ x1\)\/1041 + \(4\ x2\)\/1041 + \(10\ x3\)\/1041 + \(4\ \ x4\)\/1041 + \(25\ x5\)\/1041 + \(16\ x6\)\/1041 \[LessEqual] 1, \(3\ x3\)\/100 - x4\/50 + \(3\ x5\)\/100 \[LessEqual] 1, \(2\ x3\)\/85 - \(6\ x5\)\/85 + \(3\ x6\)\/85 \[LessEqual] 1, \(-x5\) \[LessEqual] 0, \(3\ x2\)\/100 + \(3\ x4\)\/100 - x5\/50 \[LessEqual] 1, \(18\ x1\)\/1207 + \(27\ x2\)\/1207 - \(6\ x3\)\/1207 + \(18\ \ x5\)\/1207 + \(16\ x6\)\/1207 \[LessEqual] 1, \(6\ x1\)\/655 + \(3\ x2\)\/131 + \(6\ x4\)\/655 + \(6\ \ x5\)\/655 + \(2\ x6\)\/131 \[LessEqual] 1, \(2\ x1\)\/165 + \(2\ x2\)\/165 + x5\/33 \[LessEqual] 1, \(6\ x1\)\/397 + \(6\ x2\)\/397 + \(9\ x5\)\/397 + \(4\ \ x6\)\/397 \[LessEqual] 1, \(6\ x1\)\/389 + \(6\ x2\)\/389 - \(2\ x4\)\/389 + \(9\ \ x5\)\/389 + \(4\ x6\)\/389 \[LessEqual] 1, \(16\ x1\)\/1207 + \(27\ x2\)\/1207 - \(6\ x4\)\/1207 + \(18\ \ x5\)\/1207 + \(18\ x6\)\/1207 \[LessEqual] 1, \(48\ x1\)\/3335 + \(81\ x2\)\/3335 - \(18\ x4\)\/3335 + \(32\ \ x5\)\/3335 + \(54\ x6\)\/3335 \[LessEqual] 1, \(6\ x1\)\/419 + \(10\ x2\)\/419 - \(2\ x4\)\/419 + \(4\ \ x5\)\/419 + \(7\ x6\)\/419 \[LessEqual] 1, \(-x4\) \[LessEqual] 0, \(2\ x2\)\/85 - \(6\ x4\)\/85 + \(3\ x6\)\/85 \[LessEqual] 1, \(2\ x1\)\/131 + \(3\ x2\)\/131 + \(6\ x3\)\/655 + \(6\ \ x5\)\/655 + \(6\ x6\)\/655 \[LessEqual] 1, \(2\ x1\)\/175 + x2\/35 + \(2\ x3\)\/175 - \(4\ x4\)\/175 + \(2\ x6\)\/175 \ \[LessEqual] 1, \(2\ x1\)\/135 + \(23\ x2\)\/945 + \(2\ x3\)\/945 - \(4\ \ x4\)\/945 + \(8\ x5\)\/945 + \(2\ x6\)\/135 \[LessEqual] 1, \(10\ x1\)\/629 + \(15\ x2\)\/629 + \(6\ x3\)\/629 + \(4\ x5\)\ \/629 + \(6\ x6\)\/629 \[LessEqual] 1, \(2\ x1\)\/145 + \(5\ x2\)\/203 + \(2\ x3\)\/203 + \(4\ \ x4\)\/1015 + \(4\ x5\)\/1015 + \(2\ x6\)\/203 \[LessEqual] 1, \(10\ x1\)\/1041 + \(25\ x2\)\/1041 + \(16\ x3\)\/1041 + \(10\ \ x4\)\/1041 + \(4\ x5\)\/1041 + \(4\ x6\)\/1041 \[LessEqual] 1, \(2\ x1\)\/945 + \(23\ x2\)\/945 + \(2\ x3\)\/135 + \(2\ \ x4\)\/135 + \(8\ x5\)\/945 - \(4\ x6\)\/945 \[LessEqual] 1, \(6\ x1\)\/655 + \(3\ x2\)\/131 + \(12\ x3\)\/655 + \(6\ \ x4\)\/655 + \(4\ x5\)\/655 \[LessEqual] 1, \(6\ x1\)\/389 + \(9\ x2\)\/389 - \(2\ x3\)\/389 + \(6\ \ x5\)\/389 + \(4\ x6\)\/389 \[LessEqual] 1, \(3\ x2\)\/100 - x3\/50 + \(3\ x4\)\/100 \[LessEqual] 1, \(10\ x1\)\/777 + \(19\ x2\)\/777 + \(4\ x3\)\/777 + \(4\ x4\)\ \/777 + \(4\ x5\)\/777 + \(10\ x6\)\/777 \[LessEqual] 1, \(10\ x1\)\/1041 + \(25\ x2\)\/1041 + \(4\ x3\)\/1041 + \(10\ \ x4\)\/1041 + \(4\ x5\)\/1041 + \(16\ x6\)\/1041 \[LessEqual] 1, \(2\ x1\)\/203 + \(5\ x2\)\/203 + \(4\ x3\)\/1015 + \(2\ \ x4\)\/203 + \(4\ x5\)\/1015 + \(2\ x6\)\/145 \[LessEqual] 1, \(2\ x1\)\/109 + \(3\ x2\)\/109 + \(2\ x3\)\/109 \[LessEqual] 1, \(6\ x1\)\/655 + \(3\ x2\)\/131 + \(2\ x3\)\/131 + \(6\ \ x4\)\/655 + \(6\ x5\)\/655 \[LessEqual] 1, \(2\ x1\)\/203 + \(5\ x2\)\/203 + \(2\ x3\)\/145 + \(2\ \ x4\)\/203 + \(4\ x5\)\/1015 + \(4\ x6\)\/1015 \[LessEqual] 1, \(6\ x1\)\/629 + \(15\ x2\)\/629 + \(10\ x3\)\/629 + \(6\ x4\)\ \/629 + \(4\ x5\)\/629 \[LessEqual] 1, \(2\ x1\)\/165 + x2\/33 + \(2\ x5\)\/165 \[LessEqual] 1, \(6\ x1\)\/397 + \(9\ x2\)\/397 + \(6\ x5\)\/397 + \(4\ \ x6\)\/397 \[LessEqual] 1, \(2\ x1\)\/265 + \(11\ x2\)\/265 + \(2\ x4\)\/265 - \(4\ \ x5\)\/265 + \(2\ x6\)\/265 \[LessEqual] 1, \(2\ x1\)\/179 + \(9\ x2\)\/179 - \(4\ x5\)\/179 \[LessEqual] 1, \(6\ x1\)\/307 + \(9\ x2\)\/307 + \(4\ x3\)\/307 \[LessEqual] 1, \(6\ x1\)\/545 + \(3\ x2\)\/109 + \(4\ x3\)\/545 + \(4\ \ x4\)\/545 + \(6\ x6\)\/545 \[LessEqual] 1, \(6\ x1\)\/565 + \(3\ x2\)\/113 + \(4\ x3\)\/565 + \(6\ \ x4\)\/565 + \(6\ x6\)\/565 \[LessEqual] 1, \(6\ x1\)\/545 + \(3\ x2\)\/109 + \(4\ x3\)\/545 + \(6\ \ x4\)\/545 + \(4\ x6\)\/545 \[LessEqual] 1, \(6\ x1\)\/385 - \(6\ x2\)\/385 + \(9\ x3\)\/385 + \(6\ \ x4\)\/385 + \(4\ x6\)\/385 \[LessEqual] 1, \(-\(x2\/16\)\) + x3\/32 + x5\/32 \[LessEqual] 1, \(2\ x1\)\/175 - \(2\ x2\)\/35 + x3\/35 + \(2\ x4\)\/175 + \(2\ x5\)\/175 \[LessEqual] 1, \(2\ x1\)\/175 + \(2\ x2\)\/175 + \(2\ x3\)\/175 - \(2\ \ x4\)\/35 + x5\/35 \[LessEqual] 1, \(6\ x1\)\/385 + \(6\ x2\)\/385 - \(6\ x4\)\/385 + \(9\ \ x5\)\/385 + \(4\ x6\)\/385 \[LessEqual] 1, x3\/32 - x4\/16 + x5\/32 \[LessEqual] 1, \(6\ x1\)\/385 + \(6\ x3\)\/385 + \(9\ x4\)\/385 - \(6\ \ x5\)\/385 + \(4\ x6\)\/385 \[LessEqual] 1, \(2\ x1\)\/175 + \(2\ x2\)\/175 + \(2\ x3\)\/175 + x4\/35 - \(2\ x5\)\/35 \[LessEqual] 1, x2\/32 + x4\/32 - x5\/16 \[LessEqual] 1, \(2\ x1\)\/175 + x2\/35 - \(2\ x3\)\/35 + \(2\ x4\)\/175 + \(2\ x5\)\/175 \ \[LessEqual] 1, \(6\ x1\)\/385 + \(9\ x2\)\/385 - \(6\ x3\)\/385 + \(6\ \ x5\)\/385 + \(4\ x6\)\/385 \[LessEqual] 1, x2\/32 - x3\/16 + x4\/32 \[LessEqual] 1, \(3\ x1\)\/122 + \(3\ x4\)\/122 + x5\/61 \[LessEqual] 1, x1\/48 + x3\/120 + x4\/48 + x5\/120 + x6\/120 \[LessEqual] 1, \(12\ x1\)\/655 + \(4\ x3\)\/655 + \(3\ x4\)\/131 + \(6\ \ x5\)\/655 + \(6\ x6\)\/655 \[LessEqual] 1, x1\/45 + x4\/45 + x5\/45 \[LessEqual] 1, x1\/50 - x2\/225 + x3\/75 + x4\/50 + x6\/75 \[LessEqual] 1, \(3\ x1\)\/167 + \(2\ x3\)\/167 + \(3\ x4\)\/167 + \(3\ \ x6\)\/167 \[LessEqual] 1, \(2\ x1\)\/185 + \(2\ x4\)\/185 + \(2\ x5\)\/185 + x6\/37 \[LessEqual] 1, \(-\(x2\/31\)\) + \(3\ x5\)\/62 + x6\/62 \[LessEqual] 1, \(3\ x1\)\/122 + x4\/61 + \(3\ x5\)\/122 \[LessEqual] 1, \(6\ x1\)\/655 + \(2\ x3\)\/131 + \(6\ x4\)\/655 + \(6\ \ x5\)\/655 + \(3\ x6\)\/131 \[LessEqual] 1, \(18\ x1\)\/1207 - \(6\ x2\)\/1207 + \(16\ x3\)\/1207 + \(18\ \ x4\)\/1207 + \(27\ x6\)\/1207 \[LessEqual] 1, \(2\ x1\)\/139 + \(2\ x3\)\/139 + \(2\ x4\)\/139 + \(3\ \ x6\)\/139 \[LessEqual] 1, \(3\ x1\)\/167 + \(3\ x3\)\/167 + \(2\ x4\)\/167 + \(3\ \ x6\)\/167 \[LessEqual] 1, x1\/60 + x3\/60 + x4\/60 + x6\/60 \[LessEqual] 1, \(3\ x1\)\/167 + \(3\ x3\)\/167 + \(3\ x4\)\/167 + \(2\ \ x6\)\/167 \[LessEqual] 1, \(-\(x2\/31\)\) + x3\/62 + \(3\ x5\)\/62 \[LessEqual] 1, \(2\ x1\)\/135 - \(4\ x2\)\/945 + \(23\ x3\)\/945 + \(8\ \ x4\)\/945 + \(2\ x5\)\/945 + \(2\ x6\)\/135 \[LessEqual] 1, \(54\ x1\)\/3335 - \(18\ x2\)\/3335 + \(81\ x3\)\/3335 + \(32\ \ x4\)\/3335 + \(48\ x6\)\/3335 \[LessEqual] 1, \(6\ x1\)\/655 + \(3\ x3\)\/131 + \(4\ x4\)\/655 + \(6\ \ x5\)\/655 + \(12\ x6\)\/655 \[LessEqual] 1, \(6\ x1\)\/629 + \(15\ x3\)\/629 + \(4\ x4\)\/629 + \(6\ \ x5\)\/629 + \(10\ x6\)\/629 \[LessEqual] 1, \(-\(x2\/50\)\) + \(3\ x5\)\/100 + \(3\ x6\)\/100 \[LessEqual] 1, \(-\(x3\/31\)\) + \(3\ x4\)\/62 + x6\/62 \[LessEqual] 1, \(-\(x3\/50\)\) + \(3\ x4\)\/100 + \(3\ x6\)\/100 \[LessEqual] 1, \(6\ x1\)\/397 + \(4\ x3\)\/397 + \(6\ x4\)\/397 + \(9\ \ x6\)\/397 \[LessEqual] 1, \(2\ x1\)\/165 + \(2\ x5\)\/165 + x6\/33 \[LessEqual] 1, \(2\ x1\)\/165 + \(2\ x4\)\/165 + x6\/33 \[LessEqual] 1, \(6\ x1\)\/389 - \(2\ x2\)\/389 + \(4\ x3\)\/389 + \(6\ \ x4\)\/389 + \(9\ x6\)\/389 \[LessEqual] 1, x1\/51 + x3\/51 + x4\/51 \[LessEqual] 1, \(2\ x1\)\/179 + \(5\ x3\)\/179 + \(2\ x5\)\/179 + \(2\ \ x6\)\/179 \[LessEqual] 1, \(2\ x1\)\/93 + x3\/31 \[LessEqual] 1, \(6\ x1\)\/271 - \(2\ x2\)\/271 + \(9\ x3\)\/271 \[LessEqual] 1, x1\/50 + x3\/50 + x4\/75 - x5\/225 + x6\/75 \[LessEqual] 1, \(3\ x1\)\/167 + \(2\ x2\)\/167 + \(3\ x5\)\/167 + \(3\ \ x6\)\/167 \[LessEqual] 1, \(12\ x1\)\/655 + \(4\ x2\)\/655 + \(6\ x4\)\/655 + \(3\ \ x5\)\/131 + \(6\ x6\)\/655 \[LessEqual] 1, \(16\ x1\)\/1041 + \(4\ x2\)\/1041 + \(4\ x3\)\/1041 + \(10\ \ x4\)\/1041 + \(25\ x5\)\/1041 + \(10\ x6\)\/1041 \[LessEqual] 1, \(16\ x1\)\/1041 + \(4\ x2\)\/1041 + \(4\ x3\)\/1041 + \(25\ \ x4\)\/1041 + \(10\ x5\)\/1041 + \(10\ x6\)\/1041 \[LessEqual] 1, x1\/79 - \(2\ x3\)\/79 + \(4\ x4\)\/79 \[LessEqual] 1, \(2\ x1\)\/93 + x4\/31 \[LessEqual] 1, \(2\ x1\)\/165 + \(2\ x3\)\/165 + x6\/33 \[LessEqual] 1, \(6\ x1\)\/397 + \(6\ x3\)\/397 + \(4\ x4\)\/397 + \(9\ \ x6\)\/397 \[LessEqual] 1, x1\/79 + \(4\ x3\)\/79 - \(2\ x4\)\/79 \[LessEqual] 1, \(3\ x1\)\/122 + x2\/61 + \(3\ x3\)\/122 \[LessEqual] 1, x1\/48 + x2\/120 + x3\/48 + x4\/120 + x6\/120 \[LessEqual] 1, \(18\ x1\)\/1207 + \(18\ x3\)\/1207 + \(16\ x4\)\/1207 - \(6\ \ x5\)\/1207 + \(27\ x6\)\/1207 \[LessEqual] 1, x1\/48 + x2\/120 + x4\/120 + x5\/48 + x6\/120 \[LessEqual] 1, x1\/50 + x2\/75 - x3\/225 + x5\/50 + x6\/75 \[LessEqual] 1, \(18\ x1\)\/1207 + \(16\ x2\)\/1207 - \(6\ x3\)\/1207 + \(18\ \ x5\)\/1207 + \(27\ x6\)\/1207 \[LessEqual] 1, \(2\ x1\)\/139 + \(2\ x2\)\/139 + \(2\ x5\)\/139 + \(3\ \ x6\)\/139 \[LessEqual] 1, \(6\ x1\)\/389 + \(4\ x2\)\/389 - \(2\ x3\)\/389 + \(6\ \ x5\)\/389 + \(9\ x6\)\/389 \[LessEqual] 1, \(6\ x1\)\/397 + \(4\ x2\)\/397 + \(6\ x5\)\/397 + \(9\ \ x6\)\/397 \[LessEqual] 1, \(6\ x1\)\/655 + \(2\ x2\)\/131 + \(6\ x4\)\/655 + \(6\ \ x5\)\/655 + \(3\ x6\)\/131 \[LessEqual] 1, x1\/79 - \(2\ x2\)\/79 + \(4\ x5\)\/79 \[LessEqual] 1, \(18\ x1\)\/1207 + \(18\ x2\)\/1207 - \(6\ x4\)\/1207 + \(16\ \ x5\)\/1207 + \(27\ x6\)\/1207 \[LessEqual] 1, \(6\ x1\)\/655 + \(6\ x2\)\/655 + \(6\ x3\)\/655 + \(2\ \ x5\)\/131 + \(3\ x6\)\/131 \[LessEqual] 1, \(2\ x1\)\/185 + \(2\ x2\)\/185 + \(2\ x3\)\/185 + x6\/37 \[LessEqual] 1, \(2\ x1\)\/179 + \(2\ x3\)\/179 + \(5\ x5\)\/179 + \(2\ \ x6\)\/179 \[LessEqual] 1, x1\/72 + x2\/180 + x3\/180 + x4\/180 + x5\/45 + x6\/72 \[LessEqual] 1, \(6\ x1\)\/655 + \(6\ x2\)\/655 + \(6\ x3\)\/655 + \(2\ \ x4\)\/131 + \(3\ x6\)\/131 \[LessEqual] 1, x1\/72 + x2\/180 + x3\/180 + x4\/45 + x5\/180 + x6\/72 \[LessEqual] 1, \(2\ x1\)\/179 + \(2\ x2\)\/179 + \(5\ x4\)\/179 + \(2\ \ x6\)\/179 \[LessEqual] 1, \(3\ x3\)\/100 - x4\/50 + \(3\ x6\)\/100 \[LessEqual] 1, \(6\ x1\)\/389 + \(6\ x3\)\/389 + \(4\ x4\)\/389 - \(2\ \ x5\)\/389 + \(9\ x6\)\/389 \[LessEqual] 1, \(3\ x3\)\/62 - x4\/31 + x6\/62 \[LessEqual] 1, \(3\ x3\)\/62 - x4\/31 + x5\/62 \[LessEqual] 1, \(12\ x1\)\/655 + \(6\ x2\)\/655 + \(3\ x3\)\/131 + \(4\ \ x4\)\/655 + \(6\ x6\)\/655 \[LessEqual] 1, x1\/72 + x2\/180 + x3\/45 + x4\/180 + x5\/180 + x6\/72 \[LessEqual] 1, \(16\ x1\)\/1041 + \(10\ x2\)\/1041 + \(25\ x3\)\/1041 + \(4\ \ x4\)\/1041 + \(4\ x5\)\/1041 + \(10\ x6\)\/1041 \[LessEqual] 1, x3\/34 + x5\/34 - x6\/17 \[LessEqual] 1, \(2\ x1\)\/175 + \(2\ x3\)\/175 + \(2\ x4\)\/175 + x5\/35 - \(4\ x6\)\/175 \[LessEqual] 1, \(4\ x2\)\/385 + \(9\ x3\)\/385 + \(6\ x4\)\/385 + \(6\ \ x5\)\/385 - \(6\ x6\)\/385 \[LessEqual] 1, \(2\ x1\)\/175 + x3\/35 + \(2\ x4\)\/175 + \(2\ x5\)\/175 - \(2\ x6\)\/35 \ \[LessEqual] 1, \(3\ x3\)\/85 + \(2\ x5\)\/85 - \(6\ x6\)\/85 \[LessEqual] 1, \(2\ x1\)\/175 + \(2\ x2\)\/175 + x3\/35 + \(2\ x5\)\/175 - \(4\ x6\)\/175 \[LessEqual] 1, \(3\ x1\)\/100 + \(3\ x3\)\/100 - x6\/50 \[LessEqual] 1, x1\/32 + x3\/32 - x6\/16 \[LessEqual] 1, x1\/49 + x3\/49 + x4\/49 - \(2\ x6\)\/49 \[LessEqual] 1, \(2\ x1\)\/135 + \(2\ x2\)\/945 + \(8\ x3\)\/945 + \(23\ \ x4\)\/945 - \(4\ x5\)\/945 + \(2\ x6\)\/135 \[LessEqual] 1, \(54\ x1\)\/3335 + \(32\ x3\)\/3335 + \(81\ x4\)\/3335 - \(18\ \ x5\)\/3335 + \(48\ x6\)\/3335 \[LessEqual] 1, \(6\ x1\)\/655 + \(6\ x2\)\/655 + \(4\ x3\)\/655 + \(3\ \ x4\)\/131 + \(12\ x6\)\/655 \[LessEqual] 1, \(6\ x1\)\/629 + \(6\ x2\)\/629 + \(4\ x3\)\/629 + \(15\ \ x4\)\/629 + \(10\ x6\)\/629 \[LessEqual] 1, \(6\ x1\)\/271 + \(9\ x4\)\/271 - \(2\ x5\)\/271 \[LessEqual] 1, x1\/60 + x2\/60 + x5\/60 + x6\/60 \[LessEqual] 1, \(3\ x1\)\/167 + \(3\ x2\)\/167 + \(2\ x5\)\/167 + \(3\ \ x6\)\/167 \[LessEqual] 1, \(3\ x1\)\/167 + \(3\ x2\)\/167 + \(3\ x5\)\/167 + \(2\ \ x6\)\/167 \[LessEqual] 1, \(2\ x1\)\/93 + x5\/31 \[LessEqual] 1, \(2\ x1\)\/135 + \(8\ x2\)\/945 + \(2\ x3\)\/945 - \(4\ \ x4\)\/945 + \(23\ x5\)\/945 + \(2\ x6\)\/135 \[LessEqual] 1, \(54\ x1\)\/3335 + \(32\ x2\)\/3335 - \(18\ x4\)\/3335 + \(81\ \ x5\)\/3335 + \(48\ x6\)\/3335 \[LessEqual] 1, \(6\ x1\)\/655 + \(4\ x2\)\/655 + \(6\ x3\)\/655 + \(3\ \ x5\)\/131 + \(12\ x6\)\/655 \[LessEqual] 1, \(6\ x1\)\/629 + \(4\ x2\)\/629 + \(6\ x3\)\/629 + \(15\ \ x5\)\/629 + \(10\ x6\)\/629 \[LessEqual] 1, \(6\ x1\)\/271 - \(2\ x4\)\/271 + \(9\ x5\)\/271 \[LessEqual] 1, x1\/45 + x2\/45 + x3\/45 \[LessEqual] 1, \(6\ x2\)\/385 + \(6\ x3\)\/385 + \(4\ x4\)\/385 + \(9\ \ x5\)\/385 - \(6\ x6\)\/385 \[LessEqual] 1, \(2\ x3\)\/85 + \(3\ x5\)\/85 - \(6\ x6\)\/85 \[LessEqual] 1, \(2\ x1\)\/175 + \(2\ x2\)\/175 + \(2\ x3\)\/175 + x5\/35 - \(2\ x6\)\/35 \[LessEqual] 1, x1\/32 + x5\/32 - x6\/16 \[LessEqual] 1, \(3\ x1\)\/100 + \(3\ x5\)\/100 - x6\/50 \[LessEqual] 1, \(-x6\) \[LessEqual] 0, x1\/32 + x4\/32 - x6\/16 \[LessEqual] 1, \(6\ x2\)\/385 + \(6\ x3\)\/385 + \(9\ x4\)\/385 + \(4\ \ x5\)\/385 - \(6\ x6\)\/385 \[LessEqual] 1, \(2\ x1\)\/175 + \(2\ x2\)\/175 + \(2\ x3\)\/175 + x4\/35 - \(2\ x6\)\/35 \[LessEqual] 1, \(3\ x1\)\/100 + \(3\ x4\)\/100 - x6\/50 \[LessEqual] 1, \(2\ x1\)\/165 + \(2\ x2\)\/165 + x6\/33 \[LessEqual] 1, \(6\ x1\)\/397 + \(6\ x2\)\/397 + \(4\ x5\)\/397 + \(9\ \ x6\)\/397 \[LessEqual] 1, x1\/51 + x2\/51 + x5\/51 \[LessEqual] 1, \(6\ x1\)\/389 + \(6\ x2\)\/389 - \(2\ x4\)\/389 + \(4\ \ x5\)\/389 + \(9\ x6\)\/389 \[LessEqual] 1, \(3\ x2\)\/100 - x5\/50 + \(3\ x6\)\/100 \[LessEqual] 1, x1\/48 + x2\/48 + x3\/120 + x5\/120 + x6\/120 \[LessEqual] 1, x2\/62 - x3\/31 + \(3\ x4\)\/62 \[LessEqual] 1, x1\/50 + x2\/50 - x4\/225 + x5\/75 + x6\/75 \[LessEqual] 1, \(3\ x2\)\/62 - x5\/31 + x6\/62 \[LessEqual] 1, \(3\ x2\)\/62 + x4\/62 - x5\/31 \[LessEqual] 1, \(12\ x1\)\/655 + \(3\ x2\)\/131 + \(6\ x3\)\/655 + \(4\ \ x5\)\/655 + \(6\ x6\)\/655 \[LessEqual] 1, \(3\ x1\)\/122 + \(3\ x2\)\/122 + x3\/61 \[LessEqual] 1, x1\/72 + x2\/45 + x3\/180 + x4\/180 + x5\/180 + x6\/72 \[LessEqual] 1, \(16\ x1\)\/1041 + \(25\ x2\)\/1041 + \(10\ x3\)\/1041 + \(4\ \ x4\)\/1041 + \(4\ x5\)\/1041 + \(10\ x6\)\/1041 \[LessEqual] 1, x1\/49 + x2\/49 + x5\/49 - \(2\ x6\)\/49 \[LessEqual] 1, \(9\ x2\)\/385 + \(4\ x3\)\/385 + \(6\ x4\)\/385 + \(6\ \ x5\)\/385 - \(6\ x6\)\/385 \[LessEqual] 1, \(2\ x1\)\/175 + x2\/35 + \(2\ x4\)\/175 + \(2\ x5\)\/175 - \(2\ x6\)\/35 \ \[LessEqual] 1, x1\/32 + x2\/32 - x6\/16 \[LessEqual] 1, \(2\ x2\)\/85 + \(3\ x4\)\/85 - \(6\ x6\)\/85 \[LessEqual] 1, \(3\ x2\)\/85 + \(2\ x4\)\/85 - \(6\ x6\)\/85 \[LessEqual] 1, x2\/34 + x4\/34 - x6\/17 \[LessEqual] 1, \(2\ x1\)\/175 + \(2\ x2\)\/175 + x4\/35 + \(2\ x5\)\/175 - \(4\ x6\)\/175 \[LessEqual] 1, \(2\ x1\)\/175 + x2\/35 + \(2\ x3\)\/175 + \(2\ x4\)\/175 - \(4\ x6\)\/175 \ \[LessEqual] 1, \(2\ x1\)\/135 + \(23\ x2\)\/945 - \(4\ x3\)\/945 + \(2\ \ x4\)\/945 + \(8\ x5\)\/945 + \(2\ x6\)\/135 \[LessEqual] 1, \(54\ x1\)\/3335 + \(81\ x2\)\/3335 - \(18\ x3\)\/3335 + \(32\ \ x5\)\/3335 + \(48\ x6\)\/3335 \[LessEqual] 1, \(6\ x1\)\/655 + \(3\ x2\)\/131 + \(6\ x4\)\/655 + \(4\ \ x5\)\/655 + \(12\ x6\)\/655 \[LessEqual] 1, \(6\ x1\)\/629 + \(15\ x2\)\/629 + \(6\ x4\)\/629 + \(4\ \ x5\)\/629 + \(10\ x6\)\/629 \[LessEqual] 1, \(2\ x1\)\/179 + \(5\ x2\)\/179 + \(2\ x4\)\/179 + \(2\ \ x6\)\/179 \[LessEqual] 1, x1\/79 + \(4\ x2\)\/79 - \(2\ x5\)\/79 \[LessEqual] 1, \(2\ x1\)\/93 + x2\/31 \[LessEqual] 1, \(6\ x1\)\/271 + \(9\ x2\)\/271 - \(2\ x3\)\/271 \[LessEqual] 1, \(3\ x1\)\/100 + \(3\ x2\)\/100 - x6\/50 \[LessEqual] 1, x1\/94 - x2\/47 + \(2\ x5\)\/47 + x6\/94 \[LessEqual] 1, \(-\(x2\/16\)\) + x5\/32 + x6\/32 \[LessEqual] 1, \(2\ x1\)\/175 - \(2\ x2\)\/35 + \(2\ x4\)\/175 + \(2\ \ x5\)\/175 + x6\/35 \[LessEqual] 1, \(3\ x1\)\/154 + x3\/77 + x4\/77 + \(3\ x6\)\/154 \[LessEqual] 1, \(6\ x1\)\/385 - \(6\ x2\)\/385 + \(4\ x3\)\/385 + \(6\ \ x4\)\/385 + \(9\ x6\)\/385 \[LessEqual] 1, x1\/94 - x2\/47 + x3\/94 + \(2\ x5\)\/47 \[LessEqual] 1, \(2\ x1\)\/175 - \(4\ x2\)\/175 + x3\/35 + \(2\ x5\)\/175 + \(2\ x6\)\/175 \[LessEqual] 1, \(2\ x1\)\/85 - \(6\ x2\)\/85 + \(3\ x3\)\/85 \[LessEqual] 1, x1\/51 + x5\/51 + x6\/51 \[LessEqual] 1, x1\/38 + x6\/38 \[LessEqual] 1, x1\/36 + x3\/36 \[LessEqual] 1, x1\/51 + x3\/51 + x5\/51 \[LessEqual] 1, x1\/51 + x4\/51 + x6\/51 \[LessEqual] 1, x1\/51 + x3\/51 + x6\/51 \[LessEqual] 1, x1\/94 + \(2\ x3\)\/47 - x4\/47 + x6\/94 \[LessEqual] 1, \(7\ x1\)\/419 - \(2\ x2\)\/419 + \(10\ x3\)\/419 + \(4\ \ x4\)\/419 + \(6\ x6\)\/419 \[LessEqual] 1, x1\/94 + \(2\ x3\)\/47 - x4\/47 + x5\/94 \[LessEqual] 1, \(3\ x1\)\/154 + \(3\ x3\)\/154 + x4\/77 + x6\/77 \[LessEqual] 1, \(2\ x1\)\/47 + x3\/94 + x5\/94 - x6\/47 \[LessEqual] 1, \(3\ x1\)\/62 + x3\/62 - x6\/31 \[LessEqual] 1, \(2\ x1\)\/47 + x3\/94 + x4\/94 - x6\/47 \[LessEqual] 1, x1\/36 + x4\/36 \[LessEqual] 1, x1\/94 - x3\/47 + \(2\ x4\)\/47 + x6\/94 \[LessEqual] 1, \(-\(x3\/16\)\) + x4\/32 + x6\/32 \[LessEqual] 1, \(2\ x1\)\/175 - \(2\ x3\)\/35 + \(2\ x4\)\/175 + \(2\ \ x5\)\/175 + x6\/35 \[LessEqual] 1, \(3\ x1\)\/154 + x2\/77 + x5\/77 + \(3\ x6\)\/154 \[LessEqual] 1, x1\/36 + x5\/36 \[LessEqual] 1, x1\/54 + x2\/135 + x3\/135 + x4\/135 + x5\/135 + x6\/54 \[LessEqual] 1, x1\/15 - \(2\ x6\)\/45 \[LessEqual] 1, x1\/63 + \(2\ x2\)\/315 + x3\/63 + \(2\ x4\)\/315 + x5\/63 + \(2\ x6\)\/315 \[LessEqual] 1, x1\/45 + x2\/180 + x3\/72 + x4\/72 + x5\/180 + x6\/180 \[LessEqual] 1, \(6\ x1\)\/385 + \(4\ x2\)\/385 - \(6\ x3\)\/385 + \(6\ \ x5\)\/385 + \(9\ x6\)\/385 \[LessEqual] 1, x3\/32 - x4\/16 + x6\/32 \[LessEqual] 1, \(6\ x1\)\/385 + \(6\ x2\)\/385 - \(6\ x4\)\/385 + \(4\ \ x5\)\/385 + \(9\ x6\)\/385 \[LessEqual] 1, \(2\ x1\)\/175 + \(2\ x2\)\/175 + \(2\ x3\)\/175 - \(2\ \ x4\)\/35 + x6\/35 \[LessEqual] 1, \(7\ x1\)\/419 + \(4\ x2\)\/419 - \(2\ x4\)\/419 + \(10\ \ x5\)\/419 + \(6\ x6\)\/419 \[LessEqual] 1, \(3\ x1\)\/62 + x5\/62 - x6\/31 \[LessEqual] 1, \(3\ x1\)\/62 + x4\/62 - x6\/31 \[LessEqual] 1, \(6\ x1\)\/385 + \(6\ x3\)\/385 + \(4\ x4\)\/385 - \(6\ \ x5\)\/385 + \(9\ x6\)\/385 \[LessEqual] 1, \(7\ x1\)\/419 + \(4\ x3\)\/419 + \(10\ x4\)\/419 - \(2\ \ x5\)\/419 + \(6\ x6\)\/419 \[LessEqual] 1, \(3\ x1\)\/154 + x3\/77 + \(3\ x4\)\/154 + x6\/77 \[LessEqual] 1, x1\/51 + x2\/51 + x6\/51 \[LessEqual] 1, x2\/32 - x5\/16 + x6\/32 \[LessEqual] 1, \(2\ x1\)\/175 + \(2\ x2\)\/175 + \(2\ x3\)\/175 - \(2\ \ x5\)\/35 + x6\/35 \[LessEqual] 1, \(3\ x1\)\/154 + x2\/77 + \(3\ x5\)\/154 + x6\/77 \[LessEqual] 1, \(2\ x1\)\/175 + \(2\ x3\)\/175 - \(4\ x4\)\/175 + x5\/35 + \(2\ x6\)\/175 \[LessEqual] 1, \(2\ x1\)\/85 - \(6\ x4\)\/85 + \(3\ x5\)\/85 \[LessEqual] 1, x1\/45 + x2\/72 + x3\/180 + x4\/180 + x5\/72 + x6\/180 \[LessEqual] 1, x1\/39 + \(2\ x2\)\/195 + \(2\ x3\)\/195 + \(2\ x4\)\/195 + \ \(2\ x5\)\/195 \[LessEqual] 1, x1\/94 + x2\/94 - x3\/47 + \(2\ x4\)\/47 \[LessEqual] 1, x1\/51 + x2\/51 + x4\/51 \[LessEqual] 1, \(2\ x1\)\/47 + x2\/94 + x5\/94 - x6\/47 \[LessEqual] 1, x1\/94 + \(2\ x2\)\/47 - x5\/47 + x6\/94 \[LessEqual] 1, x1\/94 + \(2\ x2\)\/47 + x4\/94 - x5\/47 \[LessEqual] 1, \(2\ x1\)\/47 + x2\/94 + x4\/94 - x6\/47 \[LessEqual] 1, x1\/63 + x2\/63 + \(2\ x3\)\/315 + x4\/63 + \(2\ x5\)\/315 + \(2\ x6\)\/315 \[LessEqual] 1, \(2\ x1\)\/85 + \(3\ x4\)\/85 - \(6\ x5\)\/85 \[LessEqual] 1, \(2\ x1\)\/175 + \(2\ x2\)\/175 + x4\/35 - \(4\ x5\)\/175 + \(2\ x6\)\/175 \[LessEqual] 1, \(2\ x1\)\/85 + \(3\ x2\)\/85 - \(6\ x3\)\/85 \[LessEqual] 1, \(2\ x1\)\/175 + x2\/35 - \(4\ x3\)\/175 + \(2\ x4\)\/175 + \(2\ x6\)\/175 \ \[LessEqual] 1, \(3\ x1\)\/62 + x2\/62 - x6\/31 \[LessEqual] 1, x1\/36 + x2\/36 \[LessEqual] 1, \(3\ x1\)\/154 + \(3\ x2\)\/154 + x5\/77 + x6\/77 \[LessEqual] 1, \(7\ x1\)\/419 + \(10\ x2\)\/419 - \(2\ x3\)\/419 + \(4\ \ x5\)\/419 + \(6\ x6\)\/419 \[LessEqual] 1, x1\/49 - \(2\ x2\)\/49 + x5\/49 + x6\/49 \[LessEqual] 1, x1\/62 - x2\/31 + \(3\ x5\)\/62 \[LessEqual] 1, x1\/32 - x2\/16 + x5\/32 \[LessEqual] 1, \(9\ x1\)\/385 - \(6\ x2\)\/385 + \(6\ x3\)\/385 + \(4\ \ x4\)\/385 + \(6\ x6\)\/385 \[LessEqual] 1, x1\/35 - \(2\ x2\)\/35 + \(2\ x3\)\/175 + \(2\ x5\)\/175 + \(2\ \ x6\)\/175 \[LessEqual] 1, \(3\ x1\)\/85 - \(6\ x2\)\/85 + \(2\ x3\)\/85 \[LessEqual] 1, x1\/34 - x2\/17 + x3\/34 \[LessEqual] 1, x1\/35 - \(4\ x2\)\/175 + \(2\ x3\)\/175 + \(2\ x4\)\/175 + \(2\ x5\ \)\/175 \[LessEqual] 1, \(5\ x1\)\/179 + \(2\ x3\)\/179 + \(2\ x4\)\/179 + \(2\ \ x5\)\/179 \[LessEqual] 1, \(27\ x1\)\/1207 - \(6\ x2\)\/1207 + \(18\ x3\)\/1207 + \(16\ \ x4\)\/1207 + \(18\ x6\)\/1207 \[LessEqual] 1, \(3\ x1\)\/131 + \(6\ x3\)\/655 + \(2\ x4\)\/131 + \(6\ \ x5\)\/655 + \(6\ x6\)\/655 \[LessEqual] 1, \(81\ x1\)\/3335 - \(18\ x2\)\/3335 + \(54\ x3\)\/3335 + \(48\ \ x4\)\/3335 + \(32\ x6\)\/3335 \[LessEqual] 1, \(10\ x1\)\/419 - \(2\ x2\)\/419 + \(7\ x3\)\/419 + \(6\ \ x4\)\/419 + \(4\ x6\)\/419 \[LessEqual] 1, \(3\ x1\)\/131 + \(6\ x3\)\/655 + \(12\ x4\)\/655 + \(6\ \ x5\)\/655 + \(4\ x6\)\/655 \[LessEqual] 1, \(15\ x1\)\/629 + \(6\ x3\)\/629 + \(10\ x4\)\/629 + \(6\ x5\)\ \/629 + \(4\ x6\)\/629 \[LessEqual] 1, \(23\ x1\)\/945 - \(4\ x2\)\/945 + \(2\ x3\)\/135 + \(2\ \ x4\)\/135 + \(2\ x5\)\/945 + \(8\ x6\)\/945 \[LessEqual] 1, x1\/62 + \(3\ x3\)\/62 - x4\/31 \[LessEqual] 1, \(11\ x1\)\/265 + \(2\ x3\)\/265 + \(2\ x4\)\/265 + \(2\ \ x5\)\/265 - \(4\ x6\)\/265 \[LessEqual] 1, \(4\ x1\)\/79 + x3\/79 - \(2\ x6\)\/79 \[LessEqual] 1, x1\/49 - \(2\ x3\)\/49 + x4\/49 + x6\/49 \[LessEqual] 1, x1\/49 + x3\/49 - \(2\ x4\)\/49 + x6\/49 \[LessEqual] 1, x1\/34 - x4\/17 + x5\/34 \[LessEqual] 1, \(4\ x1\)\/79 + x5\/79 - \(2\ x6\)\/79 \[LessEqual] 1, \(4\ x1\)\/79 + x4\/79 - \(2\ x6\)\/79 \[LessEqual] 1, \(3\ x1\)\/113 + \(4\ x2\)\/565 + \(6\ x3\)\/565 + \(6\ \ x4\)\/565 + \(6\ x5\)\/565 \[LessEqual] 1, \(25\ x1\)\/1041 + \(4\ x2\)\/1041 + \(10\ x3\)\/1041 + \(16\ \ x4\)\/1041 + \(10\ x5\)\/1041 + \(4\ x6\)\/1041 \[LessEqual] 1, \(5\ x1\)\/203 + \(4\ x2\)\/1015 + \(2\ x3\)\/203 + \(2\ \ x4\)\/145 + \(2\ x5\)\/203 + \(4\ x6\)\/1015 \[LessEqual] 1, x1\/62 - x3\/31 + \(3\ x4\)\/62 \[LessEqual] 1, x1\/32 - x3\/16 + x4\/32 \[LessEqual] 1, \(10\ x1\)\/419 + \(6\ x3\)\/419 + \(7\ x4\)\/419 - \(2\ \ x5\)\/419 + \(4\ x6\)\/419 \[LessEqual] 1, x1\/34 + x4\/34 - x5\/17 \[LessEqual] 1, \(9\ x1\)\/385 + \(6\ x2\)\/385 - \(6\ x3\)\/385 + \(4\ \ x5\)\/385 + \(6\ x6\)\/385 \[LessEqual] 1, x1\/35 + \(2\ x2\)\/175 - \(2\ x3\)\/35 + \(2\ x4\)\/175 + \(2\ \ x6\)\/175 \[LessEqual] 1, \(27\ x1\)\/1207 + \(18\ x2\)\/1207 - \(6\ x3\)\/1207 + \(16\ \ x5\)\/1207 + \(18\ x6\)\/1207 \[LessEqual] 1, \(3\ x1\)\/131 + \(6\ x2\)\/655 + \(6\ x4\)\/655 + \(2\ \ x5\)\/131 + \(6\ x6\)\/655 \[LessEqual] 1, x1\/49 + x2\/49 - \(2\ x5\)\/49 + x6\/49 \[LessEqual] 1, \(10\ x1\)\/419 + \(6\ x2\)\/419 - \(2\ x4\)\/419 + \(7\ \ x5\)\/419 + \(4\ x6\)\/419 \[LessEqual] 1, \(25\ x1\)\/1041 + \(10\ x2\)\/1041 + \(4\ x3\)\/1041 + \(10\ \ x4\)\/1041 + \(16\ x5\)\/1041 + \(4\ x6\)\/1041 \[LessEqual] 1, x1\/35 + \(2\ x3\)\/175 - \(2\ x4\)\/35 + \(2\ x5\)\/175 + \(2\ \ x6\)\/175 \[LessEqual] 1, \(27\ x1\)\/1207 + \(16\ x2\)\/1207 - \(6\ x4\)\/1207 + \(18\ \ x5\)\/1207 + \(18\ x6\)\/1207 \[LessEqual] 1, \(3\ x1\)\/131 + \(2\ x2\)\/131 + \(6\ x3\)\/655 + \(6\ \ x5\)\/655 + \(6\ x6\)\/655 \[LessEqual] 1, \(9\ x1\)\/385 + \(4\ x2\)\/385 - \(6\ x4\)\/385 + \(6\ \ x5\)\/385 + \(6\ x6\)\/385 \[LessEqual] 1, x1\/32 + x3\/32 - x4\/16 \[LessEqual] 1, \(3\ x1\)\/131 + \(12\ x2\)\/655 + \(6\ x3\)\/655 + \(6\ \ x5\)\/655 + \(4\ x6\)\/655 \[LessEqual] 1, \(15\ x1\)\/629 + \(10\ x2\)\/629 + \(6\ x3\)\/629 + \(6\ x5\)\ \/629 + \(4\ x6\)\/629 \[LessEqual] 1, \(3\ x1\)\/85 - \(6\ x4\)\/85 + \(2\ x5\)\/85 \[LessEqual] 1, x1\/35 + \(2\ x2\)\/175 + \(2\ x3\)\/175 - \(4\ x4\)\/175 + \(2\ x5\ \)\/175 \[LessEqual] 1, \(23\ x1\)\/945 + \(2\ x2\)\/135 + \(2\ x3\)\/945 - \(4\ \ x4\)\/945 + \(2\ x5\)\/135 + \(8\ x6\)\/945 \[LessEqual] 1, \(81\ x1\)\/3335 + \(48\ x2\)\/3335 - \(18\ x4\)\/3335 + \(54\ \ x5\)\/3335 + \(32\ x6\)\/3335 \[LessEqual] 1, \(5\ x1\)\/179 + \(2\ x2\)\/179 + \(2\ x3\)\/179 + \(2\ \ x5\)\/179 \[LessEqual] 1, \(11\ x1\)\/265 + \(2\ x2\)\/265 + \(2\ x3\)\/265 + \(2\ \ x5\)\/265 - \(4\ x6\)\/265 \[LessEqual] 1, \(3\ x1\)\/113 + \(6\ x2\)\/565 + \(6\ x3\)\/565 + \(4\ \ x4\)\/565 + \(6\ x5\)\/565 \[LessEqual] 1, \(5\ x1\)\/203 + \(2\ x2\)\/145 + \(2\ x3\)\/203 + \(4\ \ x4\)\/1015 + \(2\ x5\)\/203 + \(4\ x6\)\/1015 \[LessEqual] 1, \(25\ x1\)\/1041 + \(16\ x2\)\/1041 + \(10\ x3\)\/1041 + \(4\ \ x4\)\/1041 + \(10\ x5\)\/1041 + \(4\ x6\)\/1041 \[LessEqual] 1, x1\/35 + \(2\ x2\)\/175 + \(2\ x4\)\/175 - \(2\ x5\)\/35 + \(2\ \ x6\)\/175 \[LessEqual] 1, \(9\ x1\)\/385 + \(4\ x3\)\/385 + \(6\ x4\)\/385 - \(6\ \ x5\)\/385 + \(6\ x6\)\/385 \[LessEqual] 1, \(27\ x1\)\/1207 + \(16\ x3\)\/1207 + \(18\ x4\)\/1207 - \(6\ \ x5\)\/1207 + \(18\ x6\)\/1207 \[LessEqual] 1, \(25\ x1\)\/1041 + \(10\ x2\)\/1041 + \(16\ x3\)\/1041 + \(10\ \ x4\)\/1041 + \(4\ x5\)\/1041 + \(4\ x6\)\/1041 \[LessEqual] 1, \(3\ x1\)\/131 + \(6\ x2\)\/655 + \(12\ x3\)\/655 + \(6\ \ x4\)\/655 + \(4\ x6\)\/655 \[LessEqual] 1, \(81\ x1\)\/3335 + \(48\ x3\)\/3335 + \(54\ x4\)\/3335 - \(18\ \ x5\)\/3335 + \(32\ x6\)\/3335 \[LessEqual] 1, \(23\ x1\)\/945 + \(2\ x2\)\/945 + \(2\ x3\)\/135 + \(2\ \ x4\)\/135 - \(4\ x5\)\/945 + \(8\ x6\)\/945 \[LessEqual] 1, \(3\ x1\)\/85 + \(2\ x4\)\/85 - \(6\ x5\)\/85 \[LessEqual] 1, x1\/35 + \(2\ x2\)\/175 + \(2\ x3\)\/175 + \(2\ x4\)\/175 - \(4\ x5\ \)\/175 \[LessEqual] 1, \(11\ x1\)\/265 + \(2\ x2\)\/265 + \(2\ x3\)\/265 + \(2\ \ x4\)\/265 - \(4\ x6\)\/265 \[LessEqual] 1, \(3\ x1\)\/113 + \(6\ x2\)\/565 + \(6\ x3\)\/565 + \(6\ \ x4\)\/565 + \(4\ x5\)\/565 \[LessEqual] 1, \(5\ x1\)\/179 + \(2\ x2\)\/179 + \(2\ x3\)\/179 + \(2\ \ x4\)\/179 \[LessEqual] 1, \(3\ x1\)\/131 + \(6\ x2\)\/655 + \(6\ x4\)\/655 + \(12\ \ x5\)\/655 + \(4\ x6\)\/655 \[LessEqual] 1, \(11\ x1\)\/265 + \(2\ x2\)\/265 + \(2\ x4\)\/265 + \(2\ \ x5\)\/265 - \(4\ x6\)\/265 \[LessEqual] 1, \(4\ x1\)\/79 + x2\/79 - \(2\ x6\)\/79 \[LessEqual] 1, x1\/62 + \(3\ x2\)\/62 - x5\/31 \[LessEqual] 1, x1\/32 + x2\/32 - x5\/16 \[LessEqual] 1, \(3\ x1\)\/113 + \(6\ x2\)\/565 + \(4\ x3\)\/565 + \(6\ \ x4\)\/565 + \(6\ x5\)\/565 \[LessEqual] 1, \(3\ x1\)\/131 + \(6\ x2\)\/655 + \(2\ x3\)\/131 + \(6\ \ x4\)\/655 + \(6\ x6\)\/655 \[LessEqual] 1, \(5\ x1\)\/203 + \(2\ x2\)\/203 + \(4\ x3\)\/1015 + \(2\ \ x4\)\/203 + \(2\ x5\)\/145 + \(4\ x6\)\/1015 \[LessEqual] 1, \(5\ x1\)\/203 + \(2\ x2\)\/203 + \(2\ x3\)\/145 + \(2\ \ x4\)\/203 + \(4\ x5\)\/1015 + \(4\ x6\)\/1015 \[LessEqual] 1, \(15\ x1\)\/629 + \(6\ x2\)\/629 + \(10\ x3\)\/629 + \(6\ x4\)\ \/629 + \(4\ x6\)\/629 \[LessEqual] 1, \(3\ x1\)\/85 + \(2\ x2\)\/85 - \(6\ x3\)\/85 \[LessEqual] 1, \(81\ x1\)\/3335 + \(54\ x2\)\/3335 - \(18\ x3\)\/3335 + \(48\ \ x5\)\/3335 + \(32\ x6\)\/3335 \[LessEqual] 1, \(10\ x1\)\/419 + \(7\ x2\)\/419 - \(2\ x3\)\/419 + \(6\ \ x5\)\/419 + \(4\ x6\)\/419 \[LessEqual] 1, x1\/34 + x2\/34 - x3\/17 \[LessEqual] 1, x1\/35 + \(2\ x2\)\/175 - \(4\ x3\)\/175 + \(2\ x4\)\/175 + \(2\ x5\ \)\/175 \[LessEqual] 1, \(5\ x1\)\/179 + \(2\ x2\)\/179 + \(2\ x4\)\/179 + \(2\ \ x5\)\/179 \[LessEqual] 1, \(23\ x1\)\/945 + \(2\ x2\)\/135 - \(4\ x3\)\/945 + \(2\ \ x4\)\/945 + \(2\ x5\)\/135 + \(8\ x6\)\/945 \[LessEqual] 1, \(15\ x1\)\/629 + \(6\ x2\)\/629 + \(6\ x4\)\/629 + \(10\ x5\)\ \/629 + \(4\ x6\)\/629 \[LessEqual] 1, x1\/37 + \(2\ x3\)\/185 + \(2\ x5\)\/185 + \(2\ x6\)\/185 \ \[LessEqual] 1, \(3\ x1\)\/100 - x2\/50 + \(3\ x5\)\/100 \[LessEqual] 1, \(5\ x1\)\/159 + \(2\ x3\)\/159 + \(2\ x5\)\/159 \[LessEqual] 1, \(3\ x1\)\/109 + \(2\ x4\)\/109 + \(2\ x5\)\/109 \[LessEqual] 1, \(3\ x1\)\/139 + \(2\ x3\)\/139 + \(2\ x4\)\/139 + \(2\ \ x6\)\/139 \[LessEqual] 1, \(9\ x1\)\/391 + \(6\ x3\)\/391 + \(6\ x4\)\/391 + \(4\ \ x6\)\/391 \[LessEqual] 1, \(9\ x1\)\/389 - \(2\ x2\)\/389 + \(6\ x3\)\/389 + \(4\ \ x4\)\/389 + \(6\ x6\)\/389 \[LessEqual] 1, \(11\ x1\)\/245 + \(2\ x3\)\/245 + \(2\ x5\)\/245 - \(4\ \ x6\)\/245 \[LessEqual] 1, \(11\ x1\)\/245 + \(2\ x3\)\/245 + \(2\ x4\)\/245 - \(4\ \ x6\)\/245 \[LessEqual] 1, \(9\ x1\)\/271 - \(2\ x2\)\/271 + \(6\ x3\)\/271 \[LessEqual] 1, \(19\ x1\)\/777 + \(4\ x2\)\/777 + \(10\ x3\)\/777 + \(10\ \ x4\)\/777 + \(4\ x5\)\/777 + \(4\ x6\)\/777 \[LessEqual] 1, \(3\ x1\)\/100 + \(3\ x3\)\/100 - x4\/50 \[LessEqual] 1, \(3\ x1\)\/109 + \(4\ x2\)\/545 + \(6\ x3\)\/545 + \(4\ \ x4\)\/545 + \(6\ x5\)\/545 \[LessEqual] 1, \(3\ x1\)\/109 + \(4\ x2\)\/545 + \(6\ x3\)\/545 + \(6\ \ x4\)\/545 + \(4\ x5\)\/545 \[LessEqual] 1, x1\/37 + \(2\ x2\)\/185 + \(2\ x4\)\/185 + \(2\ x6\)\/185 \ \[LessEqual] 1, \(3\ x1\)\/100 - x3\/50 + \(3\ x4\)\/100 \[LessEqual] 1, \(3\ x1\)\/139 + \(2\ x2\)\/139 + \(2\ x5\)\/139 + \(2\ \ x6\)\/139 \[LessEqual] 1, \(9\ x1\)\/391 + \(6\ x2\)\/391 + \(6\ x5\)\/391 + \(4\ \ x6\)\/391 \[LessEqual] 1, \(19\ x1\)\/777 + \(10\ x2\)\/777 + \(4\ x3\)\/777 + \(4\ x4\)\ \/777 + \(10\ x5\)\/777 + \(4\ x6\)\/777 \[LessEqual] 1, \(9\ x1\)\/389 + \(4\ x2\)\/389 - \(2\ x4\)\/389 + \(6\ \ x5\)\/389 + \(6\ x6\)\/389 \[LessEqual] 1, \(9\ x1\)\/271 - \(2\ x4\)\/271 + \(6\ x5\)\/271 \[LessEqual] 1, \(5\ x1\)\/159 + \(2\ x2\)\/159 + \(2\ x4\)\/159 \[LessEqual] 1, \(11\ x1\)\/245 + \(2\ x2\)\/245 + \(2\ x5\)\/245 - \(4\ \ x6\)\/245 \[LessEqual] 1, \(11\ x1\)\/245 + \(2\ x2\)\/245 + \(2\ x4\)\/245 - \(4\ \ x6\)\/245 \[LessEqual] 1, \(9\ x1\)\/389 + \(6\ x2\)\/389 - \(2\ x3\)\/389 + \(4\ \ x5\)\/389 + \(6\ x6\)\/389 \[LessEqual] 1, \(3\ x1\)\/109 + \(2\ x2\)\/109 + \(2\ x3\)\/109 \[LessEqual] 1, \(3\ x1\)\/109 + \(6\ x2\)\/545 + \(4\ x3\)\/545 + \(4\ \ x4\)\/545 + \(6\ x5\)\/545 \[LessEqual] 1, \(9\ x1\)\/389 + \(4\ x3\)\/389 + \(6\ x4\)\/389 - \(2\ \ x5\)\/389 + \(6\ x6\)\/389 \[LessEqual] 1, \(3\ x1\)\/100 + \(3\ x2\)\/100 - x5\/50 \[LessEqual] 1, \(3\ x1\)\/109 + \(6\ x2\)\/545 + \(4\ x3\)\/545 + \(6\ \ x4\)\/545 + \(4\ x5\)\/545 \[LessEqual] 1, \(9\ x1\)\/271 + \(6\ x4\)\/271 - \(2\ x5\)\/271 \[LessEqual] 1, \(9\ x1\)\/271 + \(6\ x2\)\/271 - \(2\ x3\)\/271 \[LessEqual] 1, \(9\ x1\)\/307 + \(6\ x4\)\/307 + \(4\ x5\)\/307 \[LessEqual] 1, \(9\ x1\)\/397 + \(4\ x3\)\/397 + \(6\ x4\)\/397 + \(6\ \ x6\)\/397 \[LessEqual] 1, \(9\ x1\)\/307 + \(4\ x4\)\/307 + \(6\ x5\)\/307 \[LessEqual] 1, \(9\ x1\)\/397 + \(6\ x3\)\/397 + \(4\ x4\)\/397 + \(6\ \ x6\)\/397 \[LessEqual] 1, x1\/33 + \(2\ x5\)\/165 + \(2\ x6\)\/165 \[LessEqual] 1, x1\/33 + \(2\ x4\)\/165 + \(2\ x6\)\/165 \[LessEqual] 1, x1\/33 + \(2\ x3\)\/165 + \(2\ x6\)\/165 \[LessEqual] 1, x1\/31 + \(2\ x3\)\/93 \[LessEqual] 1, \(9\ x1\)\/179 + \(2\ x3\)\/179 - \(4\ x6\)\/179 \[LessEqual] 1, x1\/31 + \(2\ x5\)\/93 \[LessEqual] 1, \(9\ x1\)\/179 + \(2\ x5\)\/179 - \(4\ x6\)\/179 \[LessEqual] 1, \(9\ x1\)\/179 + \(2\ x4\)\/179 - \(4\ x6\)\/179 \[LessEqual] 1, x1\/23 \[LessEqual] 1, x1\/31 + \(2\ x4\)\/93 \[LessEqual] 1, \(9\ x1\)\/307 + \(4\ x2\)\/307 + \(6\ x3\)\/307 \[LessEqual] 1, \(9\ x1\)\/397 + \(4\ x2\)\/397 + \(6\ x5\)\/397 + \(6\ \ x6\)\/397 \[LessEqual] 1, \(9\ x1\)\/397 + \(6\ x2\)\/397 + \(4\ x5\)\/397 + \(6\ \ x6\)\/397 \[LessEqual] 1, x1\/33 + \(2\ x2\)\/165 + \(2\ x6\)\/165 \[LessEqual] 1, \(9\ x1\)\/179 + \(2\ x2\)\/179 - \(4\ x6\)\/179 \[LessEqual] 1, \(9\ x1\)\/307 + \(6\ x2\)\/307 + \(4\ x3\)\/307 \[LessEqual] 1, x1\/31 + \(2\ x2\)\/93 \[LessEqual] 1};\)\)}], "Input", CellOpen->False], Cell["\<\ This is the polytope P1 of section 4.1 and it has 2881 vertices and 964 \ facets. \ \>", "Text"], Cell[CellGroupData[{ Cell[BoxData[{ \(Length[acconv]\), "\[IndentingNewLine]", \(Length[acineq]\)}], "Input"], Cell[BoxData[ \(2881\)], "Output"], Cell[BoxData[ \(964\)], "Output"] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell["The Big Minkowski", "Subsection"], Cell["\<\ In this subsection we find the Minkowski sum P = P1 + P2. Many of the \ computations in this section may take up to 30 minutes or so depending on the \ hardware used. Some are also quite memory intensive. However, the final \ results are contained in the last two cells of the subsection which can be \ executed independently. \ \>", "Text"], Cell["\<\ As described in section 4.1, we will exploit the fact that each facet Fi of P \ can be written as a sum of faces from P1 and P2, i.e. Fi = gi + hi. For our \ purposes it suffices to consider sums where dim(gi) + dim(hi) = 5. We will \ also exploit the S4 symmetry of P1 and P2 by only considering a \ representative gi from each orbit of the S4 action. We will need some \ functions which can compute face lattices of polytopes. The first step is \ computing the facet-vertex relations: \ \>", "Text"], Cell[BoxData[{ \(\(VerticesOfFaces[normals_, mins_, vertices_] := Module[{i = 1, j = 1, inclist = Table[{}, {k, 1, Length[normals]}]}, \[IndentingNewLine]While[ i < Length[normals] + 1, \[IndentingNewLine]j = 1; \[IndentingNewLine]While[ j < Length[vertices] + 1, \[IndentingNewLine]If[ Dot[vertices[\([j]\)], normals[\([i]\)]] \[Equal] mins[\([i]\)], inclist[\([i]\)] = Append[inclist[\([i]\)], j], Null]; \[IndentingNewLine]j = j + 1]; \[IndentingNewLine]i = i + 1;\[IndentingNewLine]]; \[IndentingNewLine]inclist];\)\ \), \ "\[IndentingNewLine]", \(\(FacesOfVertices[inclist_] := Module[{NormalIndices = Table[j, {j, 1, Length[inclist]}]}, Table[Select[NormalIndices, Intersection[inclist[\([#]\)], {i}] \[NotEqual] {} &], {i, 1, Max[Flatten[inclist]]}]];\)\), "\[IndentingNewLine]", \(\(P1normals = \(-Table[{Coefficient[acineq[\([i, 1]\)], x1], Coefficient[acineq[\([i, 1]\)], x2], Coefficient[acineq[\([i, 1]\)], x3], Coefficient[acineq[\([i, 1]\)], x4], Coefficient[acineq[\([i, 1]\)], x5], Coefficient[acineq[\([i, 1]\)], x6]}, {i, 1, Length[acineq]}]\);\)\), "\[IndentingNewLine]", \(\(P1mins = \(-acineq[\([All, 2]\)]\);\)\), "\[IndentingNewLine]", \(\(P2normals = \(-Table[{Coefficient[dzineq[\([i, 1]\)], x1], Coefficient[dzineq[\([i, 1]\)], x2], Coefficient[dzineq[\([i, 1]\)], x3], Coefficient[dzineq[\([i, 1]\)], x4], Coefficient[dzineq[\([i, 1]\)], x5], Coefficient[dzineq[\([i, 1]\)], x6]}, {i, 1, Length[dzineq]}]\);\)\), "\[IndentingNewLine]", \(\(P2mins = \(-dzineq[\([All, 2]\)]\);\)\)}], "Input"], Cell[BoxData[{ \(\(P1voff = VerticesOfFaces[P1normals, P1mins, acconv];\)\), "\[IndentingNewLine]", \(\(P1fofv = FacesOfVertices[P1voff];\)\), "\[IndentingNewLine]", \(\(P2voff = VerticesOfFaces[P2normals, P2mins, dzconv];\)\), "\[IndentingNewLine]", \(\(P2fofv = FacesOfVertices[P2voff];\)\)}], "Input"], Cell[BoxData[{ \(\(P1VIndex = Table[i, {i, 1, Length[P1fofv]}];\)\), "\[IndentingNewLine]", \(\(P1FIndex = Table[i, {i, 1, Length[P1voff]}];\)\), "\[IndentingNewLine]", \(\(P1vlist = Table[{i}, {i, 1, Length[P1fofv]}];\)\), "\[IndentingNewLine]", \(\(P2VIndex = Table[i, {i, 1, Length[P2fofv]}];\)\), "\[IndentingNewLine]", \(\(P2FIndex = Table[i, {i, 1, Length[P2voff]}];\)\), "\[IndentingNewLine]", \(\(P2vlist = Table[{i}, {i, 1, Length[P2fofv]}];\)\)}], "Input"], Cell["We now find the orbit representatives for the vertices of P1", "Text"], Cell[BoxData[{ \(\(s4orbits = {{1, 2, 3, 4, 5, 6}, {1, 3, 2, 5, 4, 6}, {2, 1, 3, 4, 6, 5}, {2, 3, 1, 6, 4, 5}, {3, 1, 2, 5, 6, 4}, {3, 2, 1, 6, 5, 4}, {1, 4, 5, 2, 3, 6}, {1, 5, 4, 3, 2, 6}, {4, 1, 5, 2, 6, 3}, {4, 5, 1, 6, 2, 3}, {5, 1, 4, 3, 6, 2}, {5, 4, 1, 6, 3, 2}, {2, 4, 6, 1, 3, 5}, {2, 6, 4, 3, 1, 5}, {4, 2, 6, 1, 5, 3}, {4, 6, 2, 5, 1, 3}, {6, 2, 4, 3, 5, 1}, {6, 4, 2, 5, 3, 1}, {3, 5, 6, 1, 2, 4}, {3, 6, 5, 2, 1, 4}, {5, 3, 6, 1, 4, 2}, {5, 6, 3, 4, 1, 2}, {6, 3, 5, 2, 4, 1}, {6, 5, 3, 4, 2, 1}};\)\), "\[IndentingNewLine]", \(PermuteAList[alist_, perm_] := Table[alist[\([perm[\([i]\)]]\)], {i, 1, Length[alist]}]; MakePermIndex[alist_] := Table[\(Position[alist, PermuteAList[alist[\([i]\)], s4orbits[\([j]\)]]]\)[\([1, 1]\)], {i, 1, Length[alist]}, {j, 1, Length[s4orbits]}];\)}], "Input"], Cell["\<\ The following evaluation may take a considerable amount of time. \ \>", "Text"], Cell[BoxData[{ \(\(P1perms = MakePermIndex[acconv];\)\), "\[IndentingNewLine]", \(\(P1vreps = GetIndexReps[P1vlist, P1perms];\)\)}], "Input"], Cell[BoxData[{ \(\(PermuteAnIndex[indexlist_, permindex_, permnumber_] := Map[permindex[\([#, permnumber]\)] &, indexlist];\)\), "\[IndentingNewLine]", \(\(IndexOrbit[alist_, pindex_] := Union[Sort[ Map[Sort, Map[PermuteAnIndex[alist, pindex, #] &, Table[i, {i, 1, Length[s4orbits]}]]]]];\)\), "\[IndentingNewLine]", \(\(GetIndexReps[alist_, pindex_] := Module[{replist = {}, remainder = Sort[alist]}, \[IndentingNewLine]While[ remainder \[NotEqual] {}, \[IndentingNewLine]replist = Join[replist, {remainder[\([1]\)]}]; \ \[IndentingNewLine]remainder = Complement[remainder, IndexOrbit[remainder[\([1]\)], pindex]];\[IndentingNewLine]]; \[IndentingNewLine]replist\ \[IndentingNewLine]];\)\)}], "Input"], Cell[BoxData[ \(\(P1VertexReps = GetIndexReps[P1vlist, P1perms];\)\)], "Input"], Cell["\<\ With the vertex representatives in hand, we will use the functions below to \ find representatives of the edges, and so on. To do this we consider every \ pair consisting of a representative face and any other face. The set of all \ facets which contain both faces is computed, and then the common vertices of \ those facets are found. The minimal sets under inclusion are the vertex sets \ of faces of the next higher dimension. \ \>", "Text"], Cell[BoxData[{ \(\(Closure[vertices_, voff_, fofv_] := Module[{vs, fs}, \[IndentingNewLine]fs = Fold[Intersection, fofv[\([vertices[\([1]\)]]\)], Map[fofv[\([#]\)] &, vertices]]; \[IndentingNewLine]If[ fs \[NotEqual] {}, vs = Fold[Intersection, voff[\([fs[\([1]\)]]\)], Map[voff[\([#]\)] &, fs]], vs = {}]; \[IndentingNewLine]vs\[IndentingNewLine]];\)\ \ \n\ \ \[IndentingNewLine]\), "\n", \(AddOn[subfacevertices_, vertlist_] := Map[Union[subfacevertices, {#}] &, Complement[vertlist, subfacevertices]]; MinInclusiveSort[alist_, vertlist_] := Module[{mins = {}, \ remainder = alist}, \[IndentingNewLine]remainder = Sort[Complement[alist, {{}}]]; \[IndentingNewLine]While[ remainder \[NotEqual] {}, \[IndentingNewLine]mins = Join[mins, {remainder[\([1]\)]}]; \[IndentingNewLine]remainder = Sort[Select[remainder, Length[Intersection[#, remainder[\([1]\)]]] != Length[remainder[\([1]\)]] &]];\[IndentingNewLine]]; \ \[IndentingNewLine]mins\[IndentingNewLine]];\), "\[IndentingNewLine]", \(\(LatticeStep[subfaces_, vertices_, voff_, fofv_] := Module[{candids, closedcandids}, \[IndentingNewLine]candids = Union[Flatten[Map[AddOn[#, vertices] &, subfaces], 1]]; \[IndentingNewLine]closedcandids = Union[Map[Closure[#, voff, fofv] &, candids]]; \[IndentingNewLine]MinInclusiveSort[closedcandids, verticesvertices]\[IndentingNewLine]];\)\)}], "Input"], Cell[BoxData[{ \(\(P1EdgeRepsWithExtras = LatticeStep[P1VertexReps, P1VIndex, P1voff, P1fofv];\)\), "\[IndentingNewLine]", \(\(P1EdgeReps = GetIndexReps[P1EdgeRepsWithExtras, P1perms];\)\), "\[IndentingNewLine]", \(Dimensions[P1EdgeReps]\)}], "Input"], Cell["\<\ For the higher dimenionsal faces of P1, we split the computation into pieces \ to avoid excessive memory usage. \ \>", "Text"], Cell[BoxData[{ \(\(P1EdgeRepsTablePartA = Partition[P1EdgeReps, 100];\)\), "\[IndentingNewLine]", \(\(P1EdgeRepsTable = Join[P1EdgeRepsTablePartA, {Complement[P1EdgeReps, Flatten[P1EdgeRepsTablePartA, 1]]}];\)\), "\[IndentingNewLine]", \(\(P1dim2RepsWithExtrasTable = Map[LatticeStep[#, P1VIndex, P1voff, P1fofv] &, P1EdgeRepsTable];\)\), "\[IndentingNewLine]", \(\(P1dim2RepsWithExtras = Union[Flatten[P1dim2RepsWithExtrasTable, 1]];\)\), "\[IndentingNewLine]", \(\(P1dim2Reps = GetIndexReps[P1dim2RepsWithExtras, P1perms];\)\), "\[IndentingNewLine]", \(Dimensions[P1dim2Reps]\)}], "Input"], Cell[BoxData[{ \(\(P1dim2RepsTablePartA = Partition[P1dim2Reps, 100];\)\), "\[IndentingNewLine]", \(\(P1dim2RepsTable = Join[P1dim2RepsTablePartA, {Complement[P1dim2Reps, Flatten[P1dim2RepsTablePartA, 1]]}];\)\), "\[IndentingNewLine]", \(\(P1dim3RepsWithExtrasTable = Map[LatticeStep[#, P1VIndex, P1voff, P1fofv] &, P1dim2RepsTable];\)\), "\[IndentingNewLine]", \(\(P1dim3RepsWithExtras = Union[Flatten[P1dim3RepsWithExtrasTable, 1]];\)\), "\[IndentingNewLine]", \(\(P1dim3Reps = GetIndexReps[P1dim3RepsWithExtras, P1perms];\)\), "\[IndentingNewLine]", \(Dimensions[P1dim3Reps]\)}], "Input"], Cell[BoxData[{ \(\(P1dim3RepsTablePartA = Partition[P1dim3Reps, 100];\)\), "\[IndentingNewLine]", \(\(P1dim3RepsTable = Join[P1dim3RepsTablePartA, {Complement[P1dim3Reps, Flatten[P1dim3RepsTablePartA, 1]]}];\)\), "\[IndentingNewLine]", \(\(P1dim4RepsWithExtrasTable = Map[LatticeStep[#, P1VIndex, P1voff, P1fofv] &, P1dim3RepsTable];\)\), "\[IndentingNewLine]", \(\(P1dim4RepsWithExtras = Union[Flatten[P1dim4RepsWithExtrasTable, 1]];\)\), "\[IndentingNewLine]", \(\(P1dim4Reps = GetIndexReps[P1dim4RepsWithExtras, P1perms];\)\), "\[IndentingNewLine]", \(Dimensions[P1dim4Reps]\)}], "Input"], Cell["\<\ Although unnecessary, its a nice check of our calculations to compute the \ facets of P1 from \"below\" and compare to the Porta output: \ \>", "Text"], Cell[BoxData[{ \(\(P1dim4RepsTablePartA = Partition[P1dim4Reps, 100];\)\), "\[IndentingNewLine]", \(\(P1dim4RepsTable = Join[P1dim4RepsTablePartA, {Complement[P1dim4Reps, Flatten[P1dim4RepsTablePartA, 1]]}];\)\), "\[IndentingNewLine]", \(\(P1dim5RepsWithExtrasTable = Map[LatticeStep[#, P1VIndex, P1voff, P1fofv] &, P1dim4RepsTable];\)\), "\[IndentingNewLine]", \(\(P1dim5RepsWithExtras = Union[Flatten[P1dim5RepsWithExtrasTable, 1]];\)\), "\[IndentingNewLine]", \(\(P1dim5Reps = GetIndexReps[P1dim5RepsWithExtras, P1perms];\)\), "\[IndentingNewLine]", \(Dimensions[P1dim5Reps]\)}], "Input"], Cell[BoxData[{ \(\(P1dim5Faces = Union[Flatten[Map[IndexOrbit[#, P1perms] &, P1dim5Reps], 1]];\)\), "\[IndentingNewLine]", \(Dimensions[P1dim5Faces]\)}], "Input"], Cell["Next we find all the faces of P2.", "Text"], Cell[BoxData[{ \(\(dzEdges = LatticeStep[P2vlist, P2VIndex, P2voff, P2fofv];\)\), "\[IndentingNewLine]", \(\(dzEdges = Union[dzEdges];\)\), "\[IndentingNewLine]", \(Dimensions[dzEdges]\)}], "Input"], Cell[BoxData[{ \(\(dz2dims = LatticeStep[dzEdges, P2VIndex, P2voff, P2fofv];\)\), "\[IndentingNewLine]", \(\(dz2dims = Union[dz2dims];\)\), "\[IndentingNewLine]", \(Dimensions[dz2dims]\)}], "Input"], Cell[BoxData[{ \(\(dz3dims = LatticeStep[dz2dims, P2VIndex, P2voff, P2fofv];\)\), "\[IndentingNewLine]", \(\(dz3dims = Union[dz3dims];\)\), "\[IndentingNewLine]", \(Dimensions[dz3dims]\)}], "Input"], Cell[BoxData[{ \(\(dz4dims = LatticeStep[dz3dims, P2VIndex, P2voff, P2fofv];\)\), "\[IndentingNewLine]", \(\(dz4dims = Union[dz4dims];\)\), "\[IndentingNewLine]", \(Dimensions[dz4dims]\)}], "Input"], Cell[BoxData[{ \(\(dz5dims = LatticeStep[dz4dims, P2VIndex, P2voff, P2fofv];\)\), "\[IndentingNewLine]", \(\(dz5dims = Union[dz5dims];\)\), "\[IndentingNewLine]", \(Dimensions[dz5dims]\)}], "Input"], Cell["\<\ Now we compute the normals to combinations of faces from polytopes P1 and P2. \ \>", "Text"], Cell[BoxData[ \(GetVectors[indexlist_, vertices_] := Map[vertices[\([#]\)] - vertices[\([indexlist[\([1]\)]]\)] &, Rest[indexlist]]; Normals[vect1_, vect2_] := NullSpace[Union[vect1, vect2]]; NewNormals[list1_, vertices1_, list2_, vertices2_, fofv1_] := \[IndentingNewLine]Module[{vectlist1, vectlist2, newnormlist = {}, tempnorm}, \[IndentingNewLine]For[i = 1, i < Length[list1] + 1, i = i + 1, \[IndentingNewLine]vectlist1 = GetVectors[list1[\([i]\)], vertices1]; \[IndentingNewLine]For[ j = 1, j < Length[list2] + 1, j = j + 1, \[IndentingNewLine]vectlist2 = GetVectors[list2[\([j]\)], vertices2]; \[IndentingNewLine]tempnorm = Normals[vectlist1, vectlist2]; \[IndentingNewLine]If[ Length[tempnorm] \[Equal] 1, \[IndentingNewLine]\(newnormlist = Join[newnormlist, tempnorm];\)\[IndentingNewLine]];\[IndentingNewLine]];\ \[IndentingNewLine]]; \[IndentingNewLine]newnormlist\[IndentingNewLine]];\)], \ "Input"], Cell[BoxData[{ \(\(Pdim3Anddim2 = Union[NewNormals[P1dim3Reps, acconv, dz2dims, dzconv, P1fofv]];\)\), "\[IndentingNewLine]", \(Dimensions[Pdim3Anddim2]\)}], "Input"], Cell[BoxData[{ \(\(Pdim2Anddim3 = Union[NewNormals[P1dim2Reps, acconv, dz3dims, dzconv, P1fofv]];\)\), "\[IndentingNewLine]", \(Dimensions[Pdim2Anddim3]\)}], "Input"], Cell[BoxData[{ \(\(Pdim1Anddim4 = Union[NewNormals[P1EdgeReps, acconv, dz4dims, dzconv, P1fofv]];\)\), "\[IndentingNewLine]", \(Dimensions[Pdim1Anddim4]\)}], "Input"], Cell[BoxData[{ \(\(Pdim4Anddim1 = Union[NewNormals[P1dim4Reps, acconv, dzEdges, dzconv, P1fofv]];\)\), "\[IndentingNewLine]", \(Dimensions[Pdim4Anddim1]\)}], "Input"], Cell["\<\ Now we have a large list of candidate normals. Again we exploit the symmetry \ of P by doing most of our calculations on representatives from each orbit. \ \>", "Text"], Cell[BoxData[ \(\(GetReps[alist_] := Module[{newlist = {}, complist = alist, temp, temporbit}, \[IndentingNewLine]While[ complist \[NotEqual] {}, \[IndentingNewLine]temporbit = Sort[Flatten[ Table[Map[ PermuteAList[#, s4orbits[\([i]\)]] &, {complist[\([1]\)]}], {i, 1, Length[s4orbits]}], 1]]; \[IndentingNewLine]temp = temporbit[\([1]\)]; \[IndentingNewLine]complist = Complement[complist, temporbit]; \[IndentingNewLine]newlist = Join[newlist, {temp}];\[IndentingNewLine]]; \ \[IndentingNewLine]newlist];\)\)], "Input"], Cell["\<\ Our construction does not detect whether the computed normal is outward or \ inward pointing so we add in the negatives of each candidate. \ \>", "Text"], Cell[BoxData[{ \(\(NewNormalCandidates = Union[Pdim3Anddim2, Pdim2Anddim3, Pdim1Anddim4, Pdim4Anddim1];\)\), "\[IndentingNewLine]", \(\(NewNormalCandidateReps = GetReps[NewNormalCandidates];\)\), "\[IndentingNewLine]", \(\(NewNormalCandidateReps = Union[NewNormalCandidateReps, \(-NewNormalCandidateReps\)];\)\ \), "\ \[IndentingNewLine]", \(Dimensions[NewNormalCandidateReps]\)}], "Input"], Cell["\<\ Now we need to determine the true normals of facets from our candidate list. \ To do this we need the vertices of P. \ \>", "Text"], Cell[CellGroupData[{ Cell[BoxData[{ \(\(PVertexCandidates = MinkSum[acconv, dzconv];\)\), "\[IndentingNewLine]", \(Dimensions[PVertexCandidates]\)}], "Input"], Cell[BoxData[ \({134784, 6}\)], "Output"] }, Open ]], Cell["\<\ To cut down on the size of the vertices under consideration, we computed the \ convex hulls of other partial Minkowski sums. For example, we could compute \ P = P1' + P2' where P1' is the convex hull of the Minkowski sum of the first 5 Albouy-Chenciner equations and P2' is the convex hull of the Minkowski sum \ of the 3 Dziobek equations plus the remaining Albouy-Chenciner equation. Any \ candidate vertices of P computed in this way which are lacking a full orbit \ under the S4 action must be spurious and can be deleted. Intersecting \ various such candidate lists whittles down the list considerably. After a \ few such iterations we arrive at the list in the cell below, which is not \ open due to its size. \ \>", "Text"], Cell[BoxData[ \(\(PVertexCandidates2 = {{0, 13, 19, 23, 20, 15}, {0, 13, 19, 23, 20, 21}, {0, 13, 19, 23, 23, 15}, {0, 13, 19, 23, 23, 21}, {0, 13, 21, 23, 20, 13}, {0, 13, 21, 23, 20, 19}, {0, 13, 21, 23, 23, 13}, {0, 13, 21, 23, 23, 19}, {0, 13, 23, 23, 16, 15}, {0, 13, 23, 23, 16, 21}, {0, 13, 23, 23, 19, 15}, {0, 13, 23, 23, 19, 21}, {0, 13, 25, 23, 16, 13}, {0, 13, 25, 23, 16, 19}, {0, 13, 25, 23, 19, 13}, {0, 13, 25, 23, 19, 19}, {0, 16, 16, 20, 23, 15}, {0, 16, 16, 20, 23, 21}, {0, 16, 16, 23, 20, 15}, {0, 16, 16, 23, 20, 21}, {0, 16, 18, 20, 23, 13}, {0, 16, 18, 20, 23, 19}, {0, 16, 19, 20, 25, 13}, {0, 16, 19, 20, 25, 19}, {0, 16, 19, 23, 20, 12}, {0, 16, 19, 23, 20, 15}, {0, 16, 19, 23, 20, 18}, {0, 16, 19, 23, 23, 12}, {0, 16, 19, 23, 23, 15}, {0, 16, 19, 23, 23, 18}, {0, 16, 19, 23, 23, 21}, {0, 16, 19, 25, 17, 13}, {0, 16, 19, 25, 17, 19}, {0, 16, 19, 25, 20, 13}, {0, 16, 19, 25, 20, 19}, {0, 16, 23, 23, 13, 15}, {0, 16, 23, 23, 13, 21}, {0, 16, 23, 23, 16, 12}, {0, 16, 23, 23, 16, 15}, {0, 16, 23, 23, 16, 18}, {0, 16, 23, 23, 19, 12}, {0, 16, 23, 23, 19, 15}, {0, 16, 23, 23, 19, 18}, {0, 16, 23, 23, 19, 21}, {0, 16, 23, 25, 13, 13}, {0, 16, 23, 25, 13, 19}, {0, 16, 23, 25, 16, 13}, {0, 16, 23, 25, 16, 19}, {0, 16, 25, 23, 16, 13}, {0, 16, 25, 23, 16, 19}, {0, 17, 25, 19, 16, 13}, {0, 17, 25, 19, 16, 19}, {0, 18, 16, 23, 20, 13}, {0, 18, 16, 23, 20, 19}, {0, 19, 13, 20, 23, 15}, {0, 19, 13, 20, 23, 21}, {0, 19, 13, 23, 23, 15}, {0, 19, 13, 23, 23, 21}, {0, 19, 16, 17, 25, 13}, {0, 19, 16, 17, 25, 19}, {0, 19, 16, 20, 23, 12}, {0, 19, 16, 20, 23, 15}, {0, 19, 16, 20, 23, 18}, {0, 19, 16, 20, 25, 13}, {0, 19, 16, 20, 25, 19}, {0, 19, 16, 23, 23, 12}, {0, 19, 16, 23, 23, 15}, {0, 19, 16, 23, 23, 18}, {0, 19, 16, 23, 23, 21}, {0, 19, 16, 25, 20, 13}, {0, 19, 16, 25, 20, 19}, {0, 19, 23, 23, 13, 15}, {0, 19, 23, 23, 13, 21}, {0, 19, 23, 23, 16, 12}, {0, 19, 23, 23, 16, 15}, {0, 19, 23, 23, 16, 18}, {0, 19, 23, 23, 16, 21}, {0, 19, 23, 25, 13, 13}, {0, 19, 23, 25, 13, 19}, {0, 20, 23, 16, 16, 15}, {0, 20, 23, 16, 16, 21}, {0, 20, 23, 16, 18, 13}, {0, 20, 23, 16, 18, 19}, {0, 20, 23, 19, 13, 15}, {0, 20, 23, 19, 13, 21}, {0, 20, 23, 19, 16, 12}, {0, 20, 23, 19, 16, 15}, {0, 20, 23, 19, 16, 18}, {0, 20, 23, 21, 13, 13}, {0, 20, 23, 21, 13, 19}, {0, 20, 25, 16, 19, 13}, {0, 20, 25, 16, 19, 19}, {0, 20, 25, 19, 16, 13}, {0, 20, 25, 19, 16, 19}, {0, 21, 13, 20, 23, 13}, {0, 21, 13, 20, 23, 19}, {0, 21, 13, 23, 23, 13}, {0, 21, 13, 23, 23, 19}, {0, 23, 13, 16, 23, 15}, {0, 23, 13, 16, 23, 21}, {0, 23, 13, 19, 23, 15}, {0, 23, 13, 19, 23, 21}, {0, 23, 16, 13, 23, 15}, {0, 23, 16, 13, 23, 21}, {0, 23, 16, 13, 25, 13}, {0, 23, 16, 13, 25, 19}, {0, 23, 16, 16, 23, 12}, {0, 23, 16, 16, 23, 15}, {0, 23, 16, 16, 23, 18}, {0, 23, 16, 16, 25, 13}, {0, 23, 16, 16, 25, 19}, {0, 23, 16, 19, 23, 12}, {0, 23, 16, 19, 23, 15}, {0, 23, 16, 19, 23, 18}, {0, 23, 16, 19, 23, 21}, {0, 23, 19, 13, 23, 15}, {0, 23, 19, 13, 23, 21}, {0, 23, 19, 13, 25, 13}, {0, 23, 19, 13, 25, 19}, {0, 23, 19, 16, 23, 12}, {0, 23, 19, 16, 23, 15}, {0, 23, 19, 16, 23, 18}, {0, 23, 19, 16, 23, 21}, {0, 23, 20, 13, 19, 15}, {0, 23, 20, 13, 19, 21}, {0, 23, 20, 13, 21, 13}, {0, 23, 20, 13, 21, 19}, {0, 23, 20, 16, 16, 15}, {0, 23, 20, 16, 16, 21}, {0, 23, 20, 16, 19, 12}, {0, 23, 20, 16, 19, 15}, {0, 23, 20, 16, 19, 18}, {0, 23, 20, 18, 16, 13}, {0, 23, 20, 18, 16, 19}, {0, 23, 23, 13, 19, 15}, {0, 23, 23, 13, 19, 21}, {0, 23, 23, 13, 21, 13}, {0, 23, 23, 13, 21, 19}, {0, 23, 23, 16, 19, 12}, {0, 23, 23, 16, 19, 15}, {0, 23, 23, 16, 19, 18}, {0, 23, 23, 16, 19, 21}, {0, 23, 23, 19, 13, 15}, {0, 23, 23, 19, 13, 21}, {0, 23, 23, 19, 16, 12}, {0, 23, 23, 19, 16, 15}, {0, 23, 23, 19, 16, 18}, {0, 23, 23, 19, 16, 21}, {0, 23, 23, 21, 13, 13}, {0, 23, 23, 21, 13, 19}, {0, 25, 13, 16, 23, 13}, {0, 25, 13, 16, 23, 19}, {0, 25, 13, 19, 23, 13}, {0, 25, 13, 19, 23, 19}, {0, 25, 16, 16, 23, 13}, {0, 25, 16, 16, 23, 19}, {0, 25, 17, 16, 19, 13}, {0, 25, 17, 16, 19, 19}, {0, 25, 20, 16, 19, 13}, {0, 25, 20, 16, 19, 19}, {0, 25, 20, 19, 16, 13}, {0, 25, 20, 19, 16, 19}, {1, 10, 19, 25, 20, 15}, {1, 10, 19, 25, 20, 21}, {1, 10, 19, 25, 23, 15}, {1, 10, 19, 25, 23, 21}, {1, 10, 21, 25, 20, 13}, {1, 10, 21, 25, 20, 19}, {1, 10, 21, 25, 23, 13}, {1, 10, 21, 25, 23, 19}, {1, 10, 23, 25, 16, 15}, {1, 10, 23, 25, 16, 21}, {1, 10, 23, 25, 19, 15}, {1, 10, 23, 25, 19, 21}, {1, 10, 25, 25, 16, 13}, {1, 10, 25, 25, 16, 19}, {1, 10, 25, 25, 19, 13}, {1, 10, 25, 25, 19, 19}, {1, 13, 16, 22, 23, 15}, {1, 13, 16, 22, 23, 21}, {1, 13, 16, 23, 25, 15}, {1, 13, 16, 23, 25, 21}, {1, 13, 16, 25, 20, 15}, {1, 13, 16, 25, 20, 21}, {1, 13, 18, 22, 23, 13}, {1, 13, 18, 22, 23, 19}, {1, 13, 18, 23, 25, 13}, {1, 13, 18, 23, 25, 19}, {1, 13, 19, 22, 25, 13}, {1, 13, 19, 22, 25, 19}, {1, 13, 19, 25, 20, 12}, {1, 13, 19, 25, 20, 15}, {1, 13, 19, 25, 20, 18}, {1, 13, 19, 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19}, {29, 18, 7, 16, 16, 13}, {29, 18, 7, 16, 16, 16}, {29, 18, 10, 10, 10, 19}, {29, 18, 10, 10, 13, 19}, {29, 18, 10, 10, 16, 13}, {29, 18, 10, 10, 16, 16}, {29, 18, 10, 13, 7, 19}, {29, 18, 10, 13, 10, 19}, {29, 18, 10, 13, 13, 13}, {29, 18, 10, 16, 7, 19}, {29, 18, 10, 16, 10, 16}, {29, 18, 10, 16, 10, 19}, {29, 18, 10, 16, 16, 13}, {29, 18, 13, 7, 13, 19}, {29, 18, 13, 7, 16, 16}, {29, 18, 13, 10, 13, 16}, {29, 18, 13, 10, 13, 19}, {29, 18, 13, 10, 16, 13}, {29, 18, 13, 10, 16, 16}, {29, 18, 13, 13, 7, 19}, {29, 18, 13, 13, 10, 16}, {29, 18, 13, 13, 10, 19}, {29, 18, 13, 13, 16, 13}, {29, 18, 13, 16, 7, 16}, {29, 18, 13, 16, 10, 13}, {29, 18, 13, 16, 10, 16}, {29, 18, 13, 16, 13, 13}};\)\)], "Input", CellOpen->False], Cell[CellGroupData[{ Cell[BoxData[ \(Dimensions[PVertexCandidates2]\)], "Input"], Cell[BoxData[ \({25356, 6}\)], "Output"] }, Open ]], Cell["\<\ Now we find the minimal values of the candidate normals on P, thinking of the \ normal as a linear function. \ \>", "Text"], Cell[BoxData[ \(FindMinForNormal[normal_, vertexlist_] := Module[{vals}, vals = Map[Dot[normal, #] &, vertexlist]; Min[vals]]; MinsForNormals[normallist_, vertexlist_] := Module[{minlist = {}, i}, \[IndentingNewLine]For[i = 1, i < Length[normallist] + 1, i = i + 1, \[IndentingNewLine]\(minlist = Join[minlist, {FindMinForNormal[normallist[\([i]\)], vertexlist]}];\)\[IndentingNewLine]]; \ \[IndentingNewLine]minlist\[IndentingNewLine]];\)], "Input"], Cell[BoxData[ \(\(MinList = MinsForNormals[NewNormalCandidateReps, PVertexCandidates2];\)\)], "Input"], Cell["The vertices for each candidate facet are computed:", "Text"], Cell[BoxData[ \(\(FaceCandidates = Table[Select[PVertexCandidates2, Dot[#, NewNormalCandidateReps[\([i]\)]] \[Equal] MinList[\([i]\)] &], {i, 1, Length[NewNormalCandidateReps]}];\)\)], "Input"], Cell["\<\ We can throw out any facet candidates which have fewer than 6 vertices, since \ then they could not be 5-dimensional. \ \>", "Text"], Cell[BoxData[{ \(\(NormalIndex = Table[i, {i, 1, Length[NewNormalCandidateReps]}];\)\), "\[IndentingNewLine]", \(\(NewNormalCandidateReps2 = Select[NormalIndex, Length[FaceCandidates[\([#]\)]] > 5 &];\)\), "\[IndentingNewLine]", \(Dimensions[NewNormalCandidateReps2]\)}], "Input"], Cell["\<\ Now we weed out the remainder by requiring the vertex sets of each candidate \ facet to be strictly 5-dimensional. \ \>", "Text"], Cell[BoxData[{ \(\(GetVectors2[vertlist_] := Map[vertlist[\([1]\)] - # &, Rest[vertlist]];\)\), "\[IndentingNewLine]", \(\(TrueFaces[verts_] := Module[{vertlist = {}, i}, \[IndentingNewLine]For[i = 1, i < Length[verts] + 1, i = i + 1, \[IndentingNewLine]\(If[ Length[NullSpace[GetVectors2[verts[\([i]\)]]]] \[Equal] 1, vertlist = Join[vertlist, {verts[\([i]\)]}]];\)\[IndentingNewLine]]; \ \[IndentingNewLine]vertlist\[IndentingNewLine]];\)\)}], "Input"], Cell[BoxData[{ \(\(FaceCandidates2 = Map[FaceCandidates[\([#]\)] &, NewNormalCandidateReps2];\)\), "\[IndentingNewLine]", \(\(TrueFaceVertices = TrueFaces[FaceCandidates2];\)\), "\[IndentingNewLine]", \(Dimensions[TrueFaceVertices]\)}], "Input"], Cell[BoxData[{ \(\(FaceIndex = Map[Position[FaceCandidates, #] &, TrueFaceVertices];\)\), "\[IndentingNewLine]", \(\(FaceIndex = FaceIndex[\([All, 1, 1]\)];\)\), "\[IndentingNewLine]", \(\(TrueNormalReps = Map[NewNormalCandidateReps[\([#]\)] &, FaceIndex];\)\), "\[IndentingNewLine]", \(Dimensions[TrueNormalReps]\)}], "Input"], Cell["\<\ For completeness and to verify our results with Porta, we recover the full \ set of new normals by computing the orbits of the representatives that we \ have found. \ \>", "Text"], Cell[BoxData[ \(\(Orbit[alist_] := Map[PermuteAList[alist, #] &, s4orbits];\)\)], "Input"], Cell[BoxData[{ \(\(AllNewNormals = Union[Flatten[Map[Union[Orbit[#]] &, TrueNormalReps], 1]];\)\), "\[IndentingNewLine]", \(Dimensions[AllNewNormals]\)}], "Input"], Cell["\<\ So far we have not added in the facet normals from polytopes P1 and P2. In \ order to eliminate redundancies from the combination, we convert all our \ rational normals to integer normals. It turns out that the new normals contained the facet normals of P1 and P2. \ \>", "Text"], Cell[BoxData[{ \(\(lcmlist[list_] := Fold[LCM, 1, list];\)\), "\[IndentingNewLine]", \(\(CleanNormal[list_] := Module[{denom = lcmlist[Denominator[list]]}, denom*list];\)\), "\[IndentingNewLine]", \(\(AllNormals = Union[Map[CleanNormal[#] &, Union[AllNewNormals, P1normals, P2normals]]];\)\), "\[IndentingNewLine]", \(Dimensions[AllNormals]\)}], "Input"], Cell["\<\ Now we compute the true vertices of the convex hull of P1 + P2, which are \ useful for verification. First we weed out any vertices which do not lie on \ at least 6 supporting hyperplanes. \ \>", "Text"], Cell[BoxData[ \(\(TrueFaceMinList = MinsForNormals[AllNormals, PVertexCandidates2];\)\)], "Input"], Cell[BoxData[ \(\(Pvoff = VerticesOfFaces[AllNormals, TrueFaceMinList, PVertexCandidates2];\)\)], "Input"], Cell[BoxData[{ \(\(Pfofv = FacesOfVertices[Pvoff];\)\), "\[IndentingNewLine]", \(\(PVIndex = Range[Length[Pfofv]];\)\), "\[IndentingNewLine]", \(\(VertexIndex2 = Select[PVIndex, Length[Pfofv[\([#]\)]] > 5 &];\)\)}], "Input"], Cell[CellGroupData[{ Cell[BoxData[{ \(\(Pvertices = Map[PVertexCandidates2[\([#]\)] &, VertexIndex2];\)\), "\[IndentingNewLine]", \(Dimensions[Pvertices]\)}], "Input"], Cell[BoxData[ \({13836, 6}\)], "Output"] }, Open ]], Cell["\<\ Finally we weed out vertices which are not extreme points by checking the \ dimension of the span of the facet normals. \ \>", "Text"], Cell[BoxData[ \(\(KernelDimensions = Table[Length[ NullSpace[ Map[AllNormals[\([#]\)] &, Pfofv[\([VertexIndex2[\([i]\)]]\)]]]], {i, 1, Length[VertexIndex2]}];\)\)], "Input"], Cell[BoxData[ \(\(KernelDimIndex = Select[Range[Length[KernelDimensions]], KernelDimensions[\([#]\)] \[Equal] 0 &];\)\)], "Input"], Cell[CellGroupData[{ Cell[BoxData[{ \(\(Pvertices2 = Map[Pvertices[\([#]\)] &, KernelDimIndex];\)\), "\[IndentingNewLine]", \(Dimensions[Pvertices2]\)}], "Input"], Cell[BoxData[ \({12828, 6}\)], "Output"] }, Open ]], Cell[TextData[{ "\nThe final results for the big Minkowski sum are contained in the \ following closed cell, which should be executed before continuing. The \ vertices are stored in the variable ", StyleBox["acdzconv", FontWeight->"Bold"], " and the facet inequalities are in ", StyleBox["acdzineq", FontWeight->"Bold"], ".\n" }], "Text"], Cell[BoxData[{ \(\(acdzconv\ = {{6, 13, 13, 17, 20, 21}, {3, 16, 13, 17, 23, 18}, {0, 16, 16, 20, 23, 15}, {0, 13, 19, 23, 20, 15}, {0, 13, 23, 23, 16, 15}, {0, 16, 19, 25, 20, 13}, {0, 16, 18, 20, 23, 13}, {0, 13, 21, 23, 20, 13}, {9, 13, 27, 21, 16, 4}, {12, 13, 25, 23, 16, 1}, {3, 13, 21, 21, 22, 10}, {1, 13, 18, 22, 23, 13}, {1, 10, 21, 25, 20, 13}, {4, 7, 21, 25, 20, 13}, {7, 4, 23, 25, 18, 13}, {10, 4, 25, 23, 18, 10}, {4, 10, 21, 23, 22, 10}, {4, 10, 21, 27, 18, 10}, {1, 13, 19, 25, 20, 12}, {4, 13, 19, 27, 18, 9}, {4, 13, 19, 23, 22, 9}, {4, 10, 18, 22, 23, 13}, {7, 9, 18, 20, 23, 13}, {10, 6, 20, 20, 21, 13}, {17, 6, 20, 13, 21, 13}, {17, 3, 23, 16, 18, 13}, {15, 9, 20, 13, 23, 10}, {10, 3, 23, 23, 18, 13}, {7, 12, 18, 18, 25, 10}, {10, 9, 20, 18, 23, 10}, {4, 13, 18, 20, 25, 10}, {3, 16, 18, 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25, 23, 15}, {16, 19, 15, 25, 21, 12}, {16, 19, 15, 23, 23, 15}, {13, 16, 16, 23, 25, 15}, {16, 15, 19, 23, 23, 15}, {16, 15, 19, 21, 25, 12}, {13, 13, 16, 21, 27, 15}, {16, 18, 16, 21, 25, 15}, {13, 7, 13, 23, 25, 21}, {13, 13, 13, 23, 25, 21}, {13, 16, 10, 23, 25, 21}, {13, 13, 16, 23, 25, 18}, {16, 10, 10, 19, 27, 20}, {16, 13, 10, 19, 27, 20}, {16, 16, 7, 19, 27, 20}, {16, 15, 13, 19, 27, 18}, {16, 15, 16, 19, 27, 15}, {19, 15, 18, 18, 23, 21}, {16, 18, 10, 19, 27, 18}, {16, 7, 7, 21, 25, 23}, {16, 13, 1, 21, 25, 23}, {18, 13, 1, 19, 25, 23}, {16, 16, 1, 21, 25, 23}, {16, 16, 7, 21, 25, 23}, {16, 7, 10, 21, 25, 23}, {16, 13, 10, 21, 25, 23}, {16, 9, 21, 21, 25, 13}, {16, 12, 19, 21, 25, 15}, {16, 9, 21, 23, 23, 16}, {16, 12, 19, 23, 23, 18}, {16, 15, 13, 21, 25, 21}, {16, 18, 10, 21, 25, 21}, {16, 15, 16, 21, 25, 18}, {16, 12, 16, 23, 23, 21}, {10, 7, 16, 23, 25, 21}, {10, 18, 16, 21, 25, 21}, {4, 13, 16, 21, 27, 18}, {7, 10, 16, 21, 27, 18}, {10, 10, 16, 21, 27, 18}, {4, 19, 10, 21, 27, 18}, {10, 19, 4, 21, 27, 18}, {10, 13, 16, 21, 27, 18}, {4, 19, 13, 21, 27, 18}, {7, 19, 13, 21, 27, 18}, {4, 16, 16, 21, 27, 18}, {7, 16, 16, 21, 27, 18}, {1, 16, 16, 23, 25, 21}, {7, 16, 16, 23, 25, 21}, {10, 13, 16, 23, 25, 21}, {4, 13, 13, 21, 25, 23}, {10, 7, 13, 21, 25, 23}, {10, 6, 16, 21, 25, 21}, {10, 9, 16, 19, 27, 18}, {10, 9, 18, 19, 27, 16}, {13, 3, 16, 21, 23, 23}, {21, 3, 16, 13, 23, 23}, {21, 6, 16, 10, 25, 21}, {13, 6, 16, 21, 25, 21}, {13, 9, 16, 19, 27, 18}, {13, 9, 18, 19, 27, 16}, {16, 3, 16, 21, 23, 23}, {21, 3, 16, 16, 23, 23}, {21, 6, 16, 13, 25, 21}, {7, 10, 13, 21, 23, 25}, {13, 4, 13, 21, 23, 25}, {10, 10, 13, 18, 21, 27}, {16, 4, 13, 18, 21, 27}, {21, 4, 13, 13, 21, 27}, {21, 4, 13, 13, 23, 25}, {21, 7, 13, 10, 25, 23}, {21, 7, 13, 13, 25, 23}, {21, 7, 13, 16, 23, 25}, {19, 10, 13, 18, 23, 25}, {19, 10, 13, 15, 25, 23}, {23, 7, 16, 7, 25, 21}, {23, 10, 16, 4, 25, 21}, {23, 13, 19, 1, 25, 18}, {23, 10, 16, 7, 25, 21}, {23, 7, 16, 10, 25, 21}, {23, 10, 18, 10, 25, 19}, {21, 4, 13, 16, 23, 25}, {23, 1, 16, 13, 21, 25}, {21, 7, 13, 13, 21, 27}, {10, 18, 13, 10, 21, 27}, {13, 18, 13, 7, 21, 27}, {16, 16, 13, 6, 21, 27}, {19, 13, 13, 6, 21, 27}, {19, 13, 13, 6, 25, 23}, {19, 13, 13, 12, 25, 23}, {19, 13, 13, 15, 23, 25}, {19, 15, 16, 15, 23, 23}, {21, 13, 16, 9, 25, 21}, {19, 15, 16, 12, 25, 21}, {21, 13, 16, 3, 25, 21}, {21, 10, 13, 7, 21, 27}, {21, 10, 13, 7, 25, 23}, {21, 10, 13, 10, 25, 23}, {21, 10, 13, 13, 23, 25}, {21, 10, 13, 10, 21, 27}, {19, 13, 13, 12, 21, 27}, {16, 16, 13, 12, 21, 27}, {13, 18, 13, 10, 21, 27}, {10, 18, 13, 13, 21, 27}, {13, 16, 13, 15, 21, 27}, {23, 1, 16, 13, 19, 27}, {23, 10, 16, 4, 19, 27}, {23, 7, 16, 13, 19, 27}, {21, 10, 16, 15, 19, 27}, {23, 10, 16, 10, 19, 27}, {21, 13, 16, 12, 19, 27}, {23, 10, 16, 13, 21, 25}, {21, 13, 16, 15, 21, 25}, {23, 7, 16, 16, 21, 25}, {21, 10, 16, 18, 21, 25}, {23, 1, 16, 16, 21, 25}, {18, 16, 16, 15, 21, 25}, {16, 4, 13, 21, 23, 25}, {19, 4, 10, 18, 21, 27}, {19, 10, 4, 18, 21, 27}, {19, 10, 10, 18, 21, 27}, {10, 13, 13, 18, 21, 27}, {13, 13, 13, 18, 21, 27}, {16, 10, 13, 18, 21, 27}, {19, 10, 13, 15, 21, 27}, {10, 16, 7, 18, 21, 27}, {13, 16, 4, 18, 21, 27}, {10, 16, 10, 18, 21, 27}, {13, 16, 10, 18, 21, 27}, {7, 13, 13, 21, 23, 25}, {13, 13, 13, 21, 23, 25}, {16, 10, 13, 21, 23, 25}, {4, 16, 13, 18, 27, 21}, {10, 10, 13, 18, 27, 21}, {18, 10, 13, 10, 27, 21}, {18, 10, 13, 13, 27, 21}, {16, 13, 13, 15, 27, 21}, {4, 21, 13, 13, 27, 21}, {7, 21, 13, 13, 27, 21}, {4, 21, 13, 13, 25, 23}, {7, 21, 13, 10, 23, 25}, {10, 21, 13, 7, 23, 25}, {10, 21, 13, 7, 27, 21}, {13, 19, 13, 6, 27, 21}, {16, 16, 13, 6, 27, 21}, {18, 13, 13, 7, 27, 21}, {18, 13, 13, 10, 27, 21}, {16, 16, 13, 12, 27, 21}, {13, 19, 13, 12, 27, 21}, {16, 18, 16, 15, 25, 21}, {10, 21, 13, 10, 27, 21}, {13, 19, 13, 6, 23, 25}, {13, 19, 13, 12, 23, 25}, {13, 19, 13, 15, 25, 23}, {16, 16, 13, 15, 25, 23}, {16, 16, 13, 15, 23, 25}, {13, 21, 16, 9, 21, 25}, {15, 19, 16, 15, 23, 23}, {15, 19, 16, 12, 21, 25}, {13, 21, 16, 3, 21, 25}, {10, 21, 13, 10, 23, 25}, {10, 21, 13, 13, 25, 23}, {7, 21, 13, 13, 23, 25}, {7, 21, 13, 16, 25, 23}, {10, 19, 13, 18, 25, 23}, {13, 16, 13, 18, 23, 25}, {10, 19, 13, 15, 23, 25}, {4, 21, 13, 16, 25, 23}, {7, 23, 16, 7, 21, 25}, {10, 23, 16, 4, 21, 25}, {13, 23, 19, 1, 18, 25}, {10, 23, 16, 7, 21, 25}, {7, 23, 16, 10, 21, 25}, {10, 23, 18, 10, 19, 25}, {13, 7, 13, 21, 25, 23}, {13, 12, 18, 19, 27, 16}, {16, 12, 16, 21, 23, 23}, {13, 10, 13, 18, 27, 21}, {16, 10, 7, 18, 27, 21}, {16, 13, 4, 18, 27, 21}, {16, 10, 10, 18, 27, 21}, {16, 13, 10, 18, 27, 21}, {10, 16, 13, 18, 27, 21}, {13, 13, 13, 18, 27, 21}, {10, 19, 13, 15, 27, 21}, {4, 19, 10, 18, 27, 21}, {10, 19, 4, 18, 27, 21}, {10, 19, 10, 18, 27, 21}, {4, 16, 13, 21, 25, 23}, {10, 16, 13, 21, 25, 23}, {13, 13, 13, 21, 25, 23}, {16, 13, 13, 18, 25, 23}, {10, 10, 16, 20, 19, 27}, {13, 10, 16, 20, 19, 27}, {16, 7, 16, 20, 19, 27}, {3, 13, 16, 21, 23, 23}, {3, 21, 16, 13, 23, 23}, {6, 21, 16, 10, 21, 25}, {6, 10, 16, 21, 21, 25}, {3, 16, 16, 21, 23, 23}, {3, 21, 16, 16, 23, 23}, {6, 21, 16, 13, 21, 25}, {9, 21, 16, 13, 21, 25}, {12, 19, 16, 15, 21, 25}, {9, 21, 16, 16, 23, 23}, {12, 19, 16, 18, 23, 23}, {6, 13, 16, 21, 21, 25}, {15, 13, 16, 21, 21, 25}, {18, 10, 16, 21, 21, 25}, {15, 16, 16, 18, 21, 25}, {9, 16, 13, 18, 19, 27}, {9, 13, 16, 19, 18, 27}};\)\[IndentingNewLine]\), "\[IndentingNewLine]", \(\(acdzineq\ = \ {5\ x1 + 2\ x2 + 2\ x3 + 2\ x4 - 4\ x5 \[LessEqual] 241, 5\ x1 + 2\ x2 + 2\ x3 - 4\ x4 + 2\ x5 \[LessEqual] 241, 5\ x1 + 2\ x2 - 4\ x3 + 2\ x4 + 2\ x5 \[LessEqual] 241, 5\ x1 - 4\ x2 + 2\ x3 + 2\ x4 + 2\ x5 \[LessEqual] 241, 2\ x1 + 5\ x2 + 2\ x3 + 2\ x4 - 4\ x6 \[LessEqual] 241, 2\ x1 + 5\ x2 + 2\ x3 - 4\ x4 + 2\ x6 \[LessEqual] 241, 2\ x1 + 5\ x2 - 4\ x3 + 2\ x4 + 2\ x6 \[LessEqual] 241, 2\ x1 + 2\ x2 + 5\ x3 + 2\ x5 - 4\ x6 \[LessEqual] 241, 2\ x1 + 2\ x2 + 5\ x3 - 4\ x5 + 2\ x6 \[LessEqual] 241, 2\ x1 + 2\ x2 + 5\ x4 + 2\ x5 - 4\ x6 \[LessEqual] 241, 2\ x1 + 2\ x2 + 5\ x4 - 4\ x5 + 2\ x6 \[LessEqual] 241, 2\ x1 + 2\ x3 + 2\ x4 + 5\ x5 - 4\ x6 \[LessEqual] 241, 2\ x1 + 2\ x3 - 4\ x4 + 5\ x5 + 2\ x6 \[LessEqual] 241, 2\ x1 - 4\ x3 + 2\ x4 + 5\ x5 + 2\ x6 \[LessEqual] 241, 2\ x1 - 4\ x2 + 5\ x3 + 2\ x5 + 2\ x6 \[LessEqual] 241, 2\ x1 - 4\ x2 + 5\ x4 + 2\ x5 + 2\ x6 \[LessEqual] 241, 2\ x2 + 2\ x3 + 2\ x4 - 4\ x5 + 5\ x6 \[LessEqual] 241, 2\ x2 + 2\ x3 - 4\ x4 + 2\ x5 + 5\ x6 \[LessEqual] 241, 2\ x2 - 4\ x3 + 2\ x4 + 2\ x5 + 5\ x6 \[LessEqual] 241, \(-4\)\ x2 + 2\ x3 + 2\ x4 + 2\ x5 + 5\ x6 \[LessEqual] 241, \(-4\)\ x1 + 5\ x2 + 2\ x3 + 2\ x4 + 2\ x6 \[LessEqual] 241, \(-4\)\ x1 + 2\ x2 + 5\ x3 + 2\ x5 + 2\ x6 \[LessEqual] 241, \(-4\)\ x1 + 2\ x2 + 5\ x4 + 2\ x5 + 2\ x6 \[LessEqual] 241, \(-4\)\ x1 + 2\ x3 + 2\ x4 + 5\ x5 + 2\ x6 \[LessEqual] 241, 5\ x1 + 2\ x2 + 2\ x4 - 10\ x5 + 2\ x6 \[LessEqual] 241, 5\ x1 + 2\ x2 - 10\ x3 + 2\ x4 + 2\ x6 \[LessEqual] 241, 5\ x1 + 2\ x3 - 10\ x4 + 2\ x5 + 2\ x6 \[LessEqual] 241, 5\ x1 - 10\ x2 + 2\ x3 + 2\ x5 + 2\ x6 \[LessEqual] 241, 2\ x1 + 5\ x2 + 2\ x4 + 2\ x5 - 10\ x6 \[LessEqual] 241, 2\ x1 + 5\ x2 - 10\ x3 + 2\ x4 + 2\ x5 \[LessEqual] 241, 2\ x1 + 2\ x2 + 2\ x3 + 5\ x4 - 10\ x6 \[LessEqual] 241, 2\ x1 + 2\ x2 + 2\ x3 + 5\ x4 - 10\ x5 \[LessEqual] 241, 2\ x1 + 2\ x2 + 2\ x3 + 5\ x5 - 10\ x6 \[LessEqual] 241, 2\ x1 + 2\ x2 + 2\ x3 - 10\ x5 + 5\ x6 \[LessEqual] 241, 2\ x1 + 2\ x2 + 2\ x3 - 10\ x4 + 5\ x5 \[LessEqual] 241, 2\ x1 + 2\ x2 + 2\ x3 - 10\ x4 + 5\ x6 \[LessEqual] 241, 2\ x1 + 5\ x3 + 2\ x4 + 2\ x5 - 10\ x6 \[LessEqual] 241, 2\ x1 - 10\ x3 + 2\ x4 + 2\ x5 + 5\ x6 \[LessEqual] 241, 2\ x1 - 10\ x2 + 5\ x3 + 2\ x4 + 2\ x5 \[LessEqual] 241, 2\ x1 - 10\ x2 + 2\ x4 + 2\ x5 + 5\ x6 \[LessEqual] 241, 5\ x2 + 2\ x3 - 10\ x4 + 2\ x5 + 2\ x6 \[LessEqual] 241, 2\ x2 + 5\ x3 + 2\ x4 - 10\ x5 + 2\ x6 \[LessEqual] 241, 2\ x2 - 10\ x3 + 2\ x4 + 5\ x5 + 2\ x6 \[LessEqual] 241, \(-10\)\ x2 + 2\ x3 + 5\ x4 + 2\ x5 + 2\ x6 \[LessEqual] 241, \(-10\)\ x1 + 5\ x2 + 2\ x3 + 2\ x5 + 2\ x6 \[LessEqual] 241, \(-10\)\ x1 + 2\ x2 + 5\ x3 + 2\ x4 + 2\ x6 \[LessEqual] 241, \(-10\)\ x1 + 2\ x2 + 2\ x4 + 5\ x5 + 2\ x6 \[LessEqual] 241, \(-10\)\ x1 + 2\ x3 + 5\ x4 + 2\ x5 + 2\ x6 \[LessEqual] 241, x1 - 2\ x2 - 2\ x3 - 2\ x4 - 8\ x5 - 4\ x6 \[LessEqual] \(-143\), x1 - 2\ x2 - 2\ x3 - 8\ x4 - 2\ x5 - 4\ x6 \[LessEqual] \(-143\), x1 - 2\ x2 - 8\ x3 - 2\ x4 - 2\ x5 - 4\ x6 \[LessEqual] \(-143\), x1 - 8\ x2 - 2\ x3 - 2\ x4 - 2\ x5 - 4\ x6 \[LessEqual] \(-143\), \(-2\)\ x1 + x2 - 2\ x3 - 2\ x4 - 4\ x5 - 8\ x6 \[LessEqual] \(-143\), \(-2\)\ x1 + x2 - 2\ x3 - 8\ x4 - 4\ x5 - 2\ x6 \[LessEqual] \(-143\), \(-2\)\ x1 + x2 - 8\ x3 - 2\ x4 - 4\ x5 - 2\ x6 \[LessEqual] \(-143\), \(-2\)\ x1 - 2\ x2 + x3 - 4\ x4 - 2\ x5 - 8\ x6 \[LessEqual] \(-143\), \(-2\)\ x1 - 2\ x2 + x3 - 4\ x4 - 8\ x5 - 2\ x6 \[LessEqual] \(-143\), \(-2\)\ x1 - 2\ x2 - 4\ x3 + x4 - 2\ x5 - 8\ x6 \[LessEqual] \(-143\), \(-2\)\ x1 - 2\ x2 - 4\ x3 + x4 - 8\ x5 - 2\ x6 \[LessEqual] \(-143\), \(-2\)\ x1 - 4\ x2 - 2\ x3 - 2\ x4 + x5 - 8\ x6 \[LessEqual] \(-143\), \(-2\)\ x1 - 4\ x2 - 2\ x3 - 8\ x4 + x5 - 2\ x6 \[LessEqual] \(-143\), \(-2\)\ x1 - 4\ x2 - 8\ x3 - 2\ x4 + x5 - 2\ x6 \[LessEqual] \(-143\), \(-2\)\ x1 - 8\ x2 + x3 - 4\ x4 - 2\ x5 - 2\ x6 \[LessEqual] \(-143\), \(-2\)\ x1 - 8\ x2 - 4\ x3 + x4 - 2\ x5 - 2\ x6 \[LessEqual] \(-143\), \(-4\)\ x1 - 2\ x2 - 2\ x3 - 2\ x4 - 8\ x5 + x6 \[LessEqual] \(-143\), \(-4\)\ x1 - 2\ x2 - 2\ x3 - 8\ x4 - 2\ x5 + x6 \[LessEqual] \(-143\), \(-4\)\ x1 - 2\ x2 - 8\ x3 - 2\ x4 - 2\ x5 + x6 \[LessEqual] \(-143\), \(-4\)\ x1 - 8\ x2 - 2\ x3 - 2\ x4 - 2\ x5 + x6 \[LessEqual] \(-143\), \(-8\)\ x1 + x2 - 2\ x3 - 2\ x4 - 4\ x5 - 2\ x6 \[LessEqual] \(-143\), \(-8\)\ x1 - 2\ x2 + x3 - 4\ x4 - 2\ x5 - 2\ x6 \[LessEqual] \(-143\), \(-8\)\ x1 - 2\ x2 - 4\ x3 + x4 - 2\ x5 - 2\ x6 \[LessEqual] \(-143\), \(-8\)\ x1 - 4\ x2 - 2\ x3 - 2\ x4 + x5 - 2\ x6 \[LessEqual] \(-143\), 3\ x1 - 6\ x5 - 2\ x6 \[LessEqual] 43, 3\ x1 - 6\ x4 - 2\ x6 \[LessEqual] 43, 3\ x1 - 6\ x3 - 2\ x6 \[LessEqual] 43, 3\ x1 - 6\ x2 - 2\ x6 \[LessEqual] 43, 3\ x2 - 2\ x5 - 6\ x6 \[LessEqual] 43, 3\ x2 - 6\ x4 - 2\ x5 \[LessEqual] 43, 3\ x2 - 6\ x3 - 2\ x5 \[LessEqual] 43, 3\ x3 - 2\ x4 - 6\ x6 \[LessEqual] 43, 3\ x3 - 2\ x4 - 6\ x5 \[LessEqual] 43, \(-2\)\ x3 + 3\ x4 - 6\ x6 \[LessEqual] 43, \(-2\)\ x3 + 3\ x4 - 6\ x5 \[LessEqual] 43, \(-2\)\ x2 + 3\ x5 - 6\ x6 \[LessEqual] 43, \(-2\)\ x2 - 6\ x4 + 3\ x5 \[LessEqual] 43, \(-2\)\ x2 - 6\ x3 + 3\ x5 \[LessEqual] 43, \(-6\)\ x2 + 3\ x3 - 2\ x4 \[LessEqual] 43, \(-6\)\ x2 - 2\ x3 + 3\ x4 \[LessEqual] 43, \(-2\)\ x1 - 6\ x5 + 3\ x6 \[LessEqual] 43, \(-2\)\ x1 - 6\ x4 + 3\ x6 \[LessEqual] 43, \(-2\)\ x1 - 6\ x3 + 3\ x6 \[LessEqual] 43, \(-2\)\ x1 - 6\ x2 + 3\ x6 \[LessEqual] 43, \(-6\)\ x1 + 3\ x2 - 2\ x5 \[LessEqual] 43, \(-6\)\ x1 + 3\ x3 - 2\ x4 \[LessEqual] 43, \(-6\)\ x1 - 2\ x3 + 3\ x4 \[LessEqual] 43, \(-6\)\ x1 - 2\ x2 + 3\ x5 \[LessEqual] 43, 23\ x1 + 14\ x2 + 2\ x3 - 4\ x4 + 14\ x5 + 8\ x6 \[LessEqual] 1287, 23\ x1 + 14\ x2 - 4\ x3 + 2\ x4 + 14\ x5 + 8\ x6 \[LessEqual] 1287, 23\ x1 + 2\ x2 + 14\ x3 + 14\ x4 - 4\ x5 + 8\ x6 \[LessEqual] 1287, 23\ x1 - 4\ x2 + 14\ x3 + 14\ x4 + 2\ x5 + 8\ x6 \[LessEqual] 1287, 14\ x1 + 23\ x2 + 2\ x3 - 4\ x4 + 8\ x5 + 14\ x6 \[LessEqual] 1287, 14\ x1 + 23\ x2 - 4\ x3 + 2\ x4 + 8\ x5 + 14\ x6 \[LessEqual] 1287, 14\ x1 + 8\ x2 + 2\ x3 - 4\ x4 + 23\ x5 + 14\ x6 \[LessEqual] 1287, 14\ x1 + 8\ x2 - 4\ x3 + 2\ x4 + 23\ x5 + 14\ x6 \[LessEqual] 1287, 14\ x1 + 2\ x2 + 23\ x3 + 8\ x4 - 4\ x5 + 14\ x6 \[LessEqual] 1287, 14\ x1 + 2\ x2 + 8\ x3 + 23\ x4 - 4\ x5 + 14\ x6 \[LessEqual] 1287, 14\ x1 - 4\ x2 + 23\ x3 + 8\ x4 + 2\ x5 + 14\ x6 \[LessEqual] 1287, 14\ x1 - 4\ x2 + 8\ x3 + 23\ x4 + 2\ x5 + 14\ x6 \[LessEqual] 1287, 8\ x1 + 14\ x2 + 2\ x3 - 4\ x4 + 14\ x5 + 23\ x6 \[LessEqual] 1287, 8\ x1 + 14\ x2 - 4\ x3 + 2\ x4 + 14\ x5 + 23\ x6 \[LessEqual] 1287, 8\ x1 + 2\ x2 + 14\ x3 + 14\ x4 - 4\ x5 + 23\ x6 \[LessEqual] 1287, 8\ x1 - 4\ x2 + 14\ x3 + 14\ x4 + 2\ x5 + 23\ x6 \[LessEqual] 1287, 2\ x1 + 23\ x2 + 14\ x3 + 14\ x4 + 8\ x5 - 4\ x6 \[LessEqual] 1287, 2\ x1 + 14\ x2 + 23\ x3 + 8\ x4 + 14\ x5 - 4\ x6 \[LessEqual] 1287, 2\ x1 + 14\ x2 + 8\ x3 + 23\ x4 + 14\ x5 - 4\ x6 \[LessEqual] 1287, 2\ x1 + 8\ x2 + 14\ x3 + 14\ x4 + 23\ x5 - 4\ x6 \[LessEqual] 1287, \(-4\)\ x1 + 23\ x2 + 14\ x3 + 14\ x4 + 8\ x5 + 2\ x6 \[LessEqual] 1287, \(-4\)\ x1 + 14\ x2 + 23\ x3 + 8\ x4 + 14\ x5 + 2\ x6 \[LessEqual] 1287, \(-4\)\ x1 + 14\ x2 + 8\ x3 + 23\ x4 + 14\ x5 + 2\ x6 \[LessEqual] 1287, \(-4\)\ x1 + 8\ x2 + 14\ x3 + 14\ x4 + 23\ x5 + 2\ x6 \[LessEqual] 1287, \(-x3\) - x4 - 3\ x6 \[LessEqual] \(-29\), \(-x3\) - x4 - 3\ x5 \[LessEqual] \(-29\), \(-x2\) - x5 - 3\ x6 \[LessEqual] \(-29\), \(-x2\) - 3\ x4 - x5 \[LessEqual] \(-29\), \(-x2\) - 3\ x3 - x5 \[LessEqual] \(-29\), \(-3\)\ x2 - x3 - x4 \[LessEqual] \(-29\), \(-x1\) - 3\ x5 - x6 \[LessEqual] \(-29\), \(-x1\) - 3\ x4 - x6 \[LessEqual] \(-29\), \(-x1\) - 3\ x3 - x6 \[LessEqual] \(-29\), \(-x1\) - 3\ x2 - x6 \[LessEqual] \(-29\), \(-3\)\ x1 - x3 - x4 \[LessEqual] \(-29\), \(-3\)\ x1 - x2 - x5 \[LessEqual] \(-29\), x1 + x2 + x3 + x4 + x5 + x6 \[LessEqual] 117, \(-x3\) - x4 - x5 - 3\ x6 \[LessEqual] \(-52\), \(-x3\) - x4 - 3\ x5 - x6 \[LessEqual] \(-52\), \(-x2\) - x4 - x5 - 3\ x6 \[LessEqual] \(-52\), \(-x2\) - 3\ x4 - x5 - x6 \[LessEqual] \(-52\), \(-x2\) - x3 - x5 - 3\ x6 \[LessEqual] \(-52\), \(-x2\) - x3 - x4 - 3\ x6 \[LessEqual] \(-52\), \(-x2\) - 3\ x3 - x5 - x6 \[LessEqual] \(-52\), \(-3\)\ x2 - x3 - x4 - x6 \[LessEqual] \(-52\), \(-x1\) - x4 - 3\ x5 - x6 \[LessEqual] \(-52\), \(-x1\) - 3\ x4 - x5 - x6 \[LessEqual] \(-52\), \(-x1\) - x3 - 3\ x5 - x6 \[LessEqual] \(-52\), \(-x1\) - x3 - x4 - 3\ x5 \[LessEqual] \(-52\), \(-x1\) - 3\ x3 - x5 - x6 \[LessEqual] \(-52\), \(-x1\) - x2 - 3\ x4 - x6 \[LessEqual] \(-52\), \(-x1\) - x2 - 3\ x4 - x5 \[LessEqual] \(-52\), \(-x1\) - x2 - 3\ x3 - x6 \[LessEqual] \(-52\), \(-x1\) - x2 - 3\ x3 - x5 \[LessEqual] \(-52\), \(-x1\) - 3\ x2 - x4 - x6 \[LessEqual] \(-52\), \(-x1\) - 3\ x2 - x3 - x6 \[LessEqual] \(-52\), \(-x1\) - 3\ x2 - x3 - x4 \[LessEqual] \(-52\), \(-3\)\ x1 - x3 - x4 - x5 \[LessEqual] \(-52\), \(-3\)\ x1 - x2 - x4 - x5 \[LessEqual] \(-52\), \(-3\)\ x1 - x2 - x3 - x5 \[LessEqual] \(-52\), \(-3\)\ x1 - x2 - x3 - x4 \[LessEqual] \(-52\), \(-2\)\ x3 - 4\ x4 - 3\ x5 - 6\ x6 \[LessEqual] \(-153\), \(-2\)\ x3 - 4\ x4 - 6\ x5 - 3\ x6 \[LessEqual] \(-153\), \(-2\)\ x2 - 3\ x4 - 4\ x5 - 6\ x6 \[LessEqual] \(-153\), \(-2\)\ x2 - 6\ x4 - 4\ x5 - 3\ x6 \[LessEqual] \(-153\), \(-3\)\ x2 - 4\ x3 - 2\ x4 - 6\ x6 \[LessEqual] \(-153\), \(-4\)\ x2 - 3\ x3 - 2\ x5 - 6\ x6 \[LessEqual] \(-153\), \(-4\)\ x2 - 6\ x3 - 2\ x5 - 3\ x6 \[LessEqual] \(-153\), \(-6\)\ x2 - 4\ x3 - 2\ x4 - 3\ x6 \[LessEqual] \(-153\), \(-2\)\ x1 - 3\ x4 - 6\ x5 - 4\ x6 \[LessEqual] \(-153\), \(-2\)\ x1 - 6\ x4 - 3\ x5 - 4\ x6 \[LessEqual] \(-153\), \(-2\)\ x1 - 3\ x2 - 6\ x3 - 4\ x6 \[LessEqual] \(-153\), \(-2\)\ x1 - 6\ x2 - 3\ x3 - 4\ x6 \[LessEqual] \(-153\), \(-3\)\ x1 - 4\ x3 - 2\ x4 - 6\ x5 \[LessEqual] \(-153\), \(-3\)\ x1 - 2\ x2 - 6\ x3 - 4\ x5 \[LessEqual] \(-153\), \(-3\)\ x1 - 4\ x2 - 6\ x4 - 2\ x5 \[LessEqual] \(-153\), \(-3\)\ x1 - 6\ x2 - 2\ x3 - 4\ x4 \[LessEqual] \(-153\), \(-4\)\ x1 - 3\ x3 - 6\ x5 - 2\ x6 \[LessEqual] \(-153\), \(-4\)\ x1 - 6\ x3 - 3\ x5 - 2\ x6 \[LessEqual] \(-153\), \(-4\)\ x1 - 3\ x2 - 6\ x4 - 2\ x6 \[LessEqual] \(-153\), \(-4\)\ x1 - 6\ x2 - 3\ x4 - 2\ x6 \[LessEqual] \(-153\), \(-6\)\ x1 - 4\ x3 - 2\ x4 - 3\ x5 \[LessEqual] \(-153\), \(-6\)\ x1 - 2\ x2 - 3\ x3 - 4\ x5 \[LessEqual] \(-153\), \(-6\)\ x1 - 3\ x2 - 2\ x3 - 4\ x4 \[LessEqual] \(-153\), \(-6\)\ x1 - 4\ x2 - 3\ x4 - 2\ x5 \[LessEqual] \(-153\), 10\ x1 + 7\ x2 + 4\ x3 + 2\ x4 + 4\ x5 + 2\ x6 \[LessEqual] 591, 10\ x1 + 4\ x2 + 7\ x3 + 4\ x4 + 2\ x5 + 2\ x6 \[LessEqual] 591, 10\ x1 + 4\ x2 + 2\ x3 + 4\ x4 + 7\ x5 + 2\ x6 \[LessEqual] 591, 10\ x1 + 2\ x2 + 4\ x3 + 7\ x4 + 4\ x5 + 2\ x6 \[LessEqual] 591, 7\ x1 + 10\ x2 + 4\ x3 + 2\ x4 + 2\ x5 + 4\ x6 \[LessEqual] 591, 7\ x1 + 4\ x2 + 10\ x3 + 2\ x4 + 2\ x5 + 4\ x6 \[LessEqual] 591, 7\ x1 + 2\ x2 + 2\ x3 + 10\ x4 + 4\ x5 + 4\ x6 \[LessEqual] 591, 7\ x1 + 2\ x2 + 2\ x3 + 4\ x4 + 10\ x5 + 4\ x6 \[LessEqual] 591, 4\ x1 + 10\ x2 + 7\ x3 + 4\ x4 + 2\ x5 + 2\ x6 \[LessEqual] 591, 4\ x1 + 10\ x2 + 2\ x3 + 4\ x4 + 2\ x5 + 7\ x6 \[LessEqual] 591, 4\ x1 + 7\ x2 + 10\ x3 + 2\ x4 + 4\ x5 + 2\ x6 \[LessEqual] 591, 4\ x1 + 4\ x2 + 2\ x3 + 10\ x4 + 7\ x5 + 2\ x6 \[LessEqual] 591, 4\ x1 + 4\ x2 + 2\ x3 + 10\ x4 + 2\ x5 + 7\ x6 \[LessEqual] 591, 4\ x1 + 2\ x2 + 10\ x3 + 2\ x4 + 4\ x5 + 7\ x6 \[LessEqual] 591, 4\ x1 + 2\ x2 + 4\ x3 + 7\ x4 + 10\ x5 + 2\ x6 \[LessEqual] 591, 4\ x1 + 2\ x2 + 4\ x3 + 2\ x4 + 10\ x5 + 7\ x6 \[LessEqual] 591, 2\ x1 + 10\ x2 + 4\ x3 + 7\ x4 + 2\ x5 + 4\ x6 \[LessEqual] 591, 2\ x1 + 7\ x2 + 2\ x3 + 10\ x4 + 4\ x5 + 4\ x6 \[LessEqual] 591, 2\ x1 + 7\ x2 + 2\ x3 + 4\ x4 + 4\ x5 + 10\ x6 \[LessEqual] 591, 2\ x1 + 4\ x2 + 10\ x3 + 2\ x4 + 7\ x5 + 4\ x6 \[LessEqual] 591, 2\ x1 + 4\ x2 + 4\ x3 + 7\ x4 + 2\ x5 + 10\ x6 \[LessEqual] 591, 2\ x1 + 4\ x2 + 4\ x3 + 2\ x4 + 7\ x5 + 10\ x6 \[LessEqual] 591, 2\ x1 + 2\ x2 + 7\ x3 + 4\ x4 + 10\ x5 + 4\ x6 \[LessEqual] 591, 2\ x1 + 2\ x2 + 7\ x3 + 4\ x4 + 4\ x5 + 10\ x6 \[LessEqual] 591, \(-x2\) - 2\ x3 - 2\ x4 - x5 - 4\ x6 \[LessEqual] \(-104\), \(-2\)\ x2 - x3 - x4 - 2\ x5 - 4\ x6 \[LessEqual] \(-104\), \(-x1\) - 2\ x3 - 2\ x4 - 4\ x5 - x6 \[LessEqual] \(-104\), \(-x1\) - 2\ x2 - 4\ x4 - 2\ x5 - x6 \[LessEqual] \(-104\), \(-x1\) - 2\ x2 - 4\ x3 - 2\ x5 - x6 \[LessEqual] \(-104\), \(-x1\) - 4\ x2 - 2\ x3 - 2\ x4 - x6 \[LessEqual] \(-104\), \(-2\)\ x1 - x3 - x4 - 4\ x5 - 2\ x6 \[LessEqual] \(-104\), \(-2\)\ x1 - x2 - 4\ x4 - x5 - 2\ x6 \[LessEqual] \(-104\), \(-2\)\ x1 - x2 - 4\ x3 - x5 - 2\ x6 \[LessEqual] \(-104\), \(-2\)\ x1 - 4\ x2 - x3 - x4 - 2\ x6 \[LessEqual] \(-104\), \(-4\)\ x1 - x2 - 2\ x3 - 2\ x4 - x5 \[LessEqual] \(-104\), \(-4\)\ x1 - 2\ x2 - x3 - x4 - 2\ x5 \[LessEqual] \(-104\), \(-x3\) - x4 - x5 - 2\ x6 \[LessEqual] \(-51\), \(-x3\) - x4 - 2\ x5 - x6 \[LessEqual] \(-51\), \(-x2\) - x4 - x5 - 2\ x6 \[LessEqual] \(-51\), \(-x2\) - 2\ x4 - x5 - x6 \[LessEqual] \(-51\), \(-x2\) - x3 - x5 - 2\ x6 \[LessEqual] \(-51\), \(-x2\) - x3 - x4 - 2\ x6 \[LessEqual] \(-51\), \(-x2\) - 2\ x3 - x5 - x6 \[LessEqual] \(-51\), \(-2\)\ x2 - x3 - x4 - x6 \[LessEqual] \(-51\), \(-x1\) - x4 - 2\ x5 - x6 \[LessEqual] \(-51\), \(-x1\) - 2\ x4 - x5 - x6 \[LessEqual] \(-51\), \(-x1\) - x3 - 2\ x5 - x6 \[LessEqual] \(-51\), \(-x1\) - x3 - x4 - 2\ x5 \[LessEqual] \(-51\), \(-x1\) - 2\ x3 - x5 - x6 \[LessEqual] \(-51\), \(-x1\) - x2 - 2\ x4 - x6 \[LessEqual] \(-51\), \(-x1\) - x2 - 2\ x4 - x5 \[LessEqual] \(-51\), \(-x1\) - x2 - 2\ x3 - x6 \[LessEqual] \(-51\), \(-x1\) - x2 - 2\ x3 - x5 \[LessEqual] \(-51\), \(-x1\) - 2\ x2 - x4 - x6 \[LessEqual] \(-51\), \(-x1\) - 2\ x2 - x3 - x6 \[LessEqual] \(-51\), \(-x1\) - 2\ x2 - x3 - x4 \[LessEqual] \(-51\), \(-2\)\ x1 - x3 - x4 - x5 \[LessEqual] \(-51\), \(-2\)\ x1 - x2 - x4 - x5 \[LessEqual] \(-51\), \(-2\)\ x1 - x2 - x3 - x5 \[LessEqual] \(-51\), \(-2\)\ x1 - x2 - x3 - x4 \[LessEqual] \(-51\), \(-3\)\ x3 - 3\ x4 - 3\ x5 - 5\ x6 \[LessEqual] \(-149\), \(-3\)\ x3 - 3\ x4 - 5\ x5 - 3\ x6 \[LessEqual] \(-149\), \(-3\)\ x2 - 3\ x4 - 3\ x5 - 5\ x6 \[LessEqual] \(-149\), \(-3\)\ x2 - 5\ x4 - 3\ x5 - 3\ x6 \[LessEqual] \(-149\), \(-3\)\ x2 - 3\ x3 - 3\ x5 - 5\ x6 \[LessEqual] \(-149\), \(-3\)\ x2 - 3\ x3 - 3\ x4 - 5\ x6 \[LessEqual] \(-149\), \(-3\)\ x2 - 5\ x3 - 3\ x5 - 3\ x6 \[LessEqual] \(-149\), \(-5\)\ x2 - 3\ x3 - 3\ x4 - 3\ x6 \[LessEqual] \(-149\), \(-3\)\ x1 - 3\ x4 - 5\ x5 - 3\ x6 \[LessEqual] \(-149\), \(-3\)\ x1 - 5\ x4 - 3\ x5 - 3\ x6 \[LessEqual] \(-149\), \(-3\)\ x1 - 3\ x3 - 5\ x5 - 3\ x6 \[LessEqual] \(-149\), \(-3\)\ x1 - 3\ x3 - 3\ x4 - 5\ x5 \[LessEqual] \(-149\), \(-3\)\ x1 - 5\ x3 - 3\ x5 - 3\ x6 \[LessEqual] \(-149\), \(-3\)\ x1 - 3\ x2 - 5\ x4 - 3\ x6 \[LessEqual] \(-149\), \(-3\)\ x1 - 3\ x2 - 5\ x4 - 3\ x5 \[LessEqual] \(-149\), \(-3\)\ x1 - 3\ x2 - 5\ x3 - 3\ x6 \[LessEqual] \(-149\), \(-3\)\ x1 - 3\ x2 - 5\ x3 - 3\ x5 \[LessEqual] \(-149\), \(-3\)\ x1 - 5\ x2 - 3\ x4 - 3\ x6 \[LessEqual] \(-149\), \(-3\)\ x1 - 5\ x2 - 3\ x3 - 3\ x6 \[LessEqual] \(-149\), \(-3\)\ x1 - 5\ x2 - 3\ x3 - 3\ x4 \[LessEqual] \(-149\), \(-5\)\ x1 - 3\ x3 - 3\ x4 - 3\ x5 \[LessEqual] \(-149\), \(-5\)\ x1 - 3\ x2 - 3\ x4 - 3\ x5 \[LessEqual] \(-149\), \(-5\)\ x1 - 3\ x2 - 3\ x3 - 3\ x5 \[LessEqual] \(-149\), \(-5\)\ x1 - 3\ x2 - 3\ x3 - 3\ x4 \[LessEqual] \(-149\), x1 + x2 - 2\ x3 - 2\ x4 - 2\ x5 - 4\ x6 \[LessEqual] \(-56\), x1 + x2 - 2\ x3 - 2\ x4 - 4\ x5 - 2\ x6 \[LessEqual] \(-56\), x1 - 2\ x2 + x3 - 2\ x4 - 2\ x5 - 4\ x6 \[LessEqual] \(-56\), x1 - 2\ x2 + x3 - 4\ x4 - 2\ x5 - 2\ x6 \[LessEqual] \(-56\), x1 - 2\ x2 - 2\ x3 + x4 - 2\ x5 - 4\ x6 \[LessEqual] \(-56\), x1 - 2\ x2 - 2\ x3 - 2\ x4 + x5 - 4\ x6 \[LessEqual] \(-56\), x1 - 2\ x2 - 4\ x3 + x4 - 2\ x5 - 2\ x6 \[LessEqual] \(-56\), x1 - 4\ x2 - 2\ x3 - 2\ x4 + x5 - 2\ x6 \[LessEqual] \(-56\), \(-2\)\ x1 + x2 + x3 - 2\ x4 - 4\ x5 - 2\ x6 \[LessEqual] \(-56\), \(-2\)\ x1 + x2 + x3 - 4\ x4 - 2\ x5 - 2\ x6 \[LessEqual] \(-56\), \(-2\)\ x1 + x2 - 2\ x3 + x4 - 4\ x5 - 2\ x6 \[LessEqual] \(-56\), \(-2\)\ x1 + x2 - 2\ x3 - 2\ x4 - 4\ x5 + x6 \[LessEqual] \(-56\), \(-2\)\ x1 + x2 - 4\ x3 + x4 - 2\ x5 - 2\ x6 \[LessEqual] \(-56\), \(-2\)\ x1 - 2\ x2 + x3 - 4\ x4 + x5 - 2\ x6 \[LessEqual] \(-56\), \(-2\)\ x1 - 2\ x2 + x3 - 4\ x4 - 2\ x5 + x6 \[LessEqual] \(-56\), \(-2\)\ x1 - 2\ x2 - 4\ x3 + x4 + x5 - 2\ x6 \[LessEqual] \(-56\), \(-2\)\ x1 - 2\ x2 - 4\ x3 + x4 - 2\ x5 + x6 \[LessEqual] \(-56\), \(-2\)\ x1 - 4\ x2 + x3 - 2\ x4 + x5 - 2\ x6 \[LessEqual] \(-56\), \(-2\)\ x1 - 4\ x2 - 2\ x3 + x4 + x5 - 2\ x6 \[LessEqual] \(-56\), \(-2\)\ x1 - 4\ x2 - 2\ x3 - 2\ x4 + x5 + x6 \[LessEqual] \(-56\), \(-4\)\ x1 + x2 - 2\ x3 - 2\ x4 - 2\ x5 + x6 \[LessEqual] \(-56\), \(-4\)\ x1 - 2\ x2 + x3 - 2\ x4 - 2\ x5 + x6 \[LessEqual] \(-56\), \(-4\)\ x1 - 2\ x2 - 2\ x3 + x4 - 2\ x5 + x6 \[LessEqual] \(-56\), \(-4\)\ x1 - 2\ x2 - 2\ x3 - 2\ x4 + x5 + x6 \[LessEqual] \(-56\), 3\ x1 - 2\ x3 - 6\ x4 - 12\ x5 - 8\ x6 \[LessEqual] \(-211\), 3\ x1 - 2\ x2 - 12\ x4 - 6\ x5 - 8\ x6 \[LessEqual] \(-211\), 3\ x1 - 6\ x2 - 12\ x3 - 2\ x5 - 8\ x6 \[LessEqual] \(-211\), 3\ x1 - 12\ x2 - 6\ x3 - 2\ x4 - 8\ x6 \[LessEqual] \(-211\), 3\ x2 - 2\ x3 - 6\ x4 - 8\ x5 - 12\ x6 \[LessEqual] \(-211\), \(-2\)\ x2 + 3\ x3 - 8\ x4 - 6\ x5 - 12\ x6 \[LessEqual] \(-211\), \(-6\)\ x2 - 8\ x3 + 3\ x4 - 2\ x5 - 12\ x6 \[LessEqual] \(-211\), \(-8\)\ x2 - 6\ x3 - 2\ x4 + 3\ x5 - 12\ x6 \[LessEqual] \(-211\), \(-2\)\ x1 + 3\ x2 - 12\ x4 - 8\ x5 - 6\ x6 \[LessEqual] \(-211\), \(-2\)\ x1 + 3\ x3 - 8\ x4 - 12\ x5 - 6\ x6 \[LessEqual] \(-211\), \(-2\)\ x1 - 8\ x2 - 12\ x3 + 3\ x5 - 6\ x6 \[LessEqual] \(-211\), \(-2\)\ x1 - 12\ x2 - 8\ x3 + 3\ x4 - 6\ x6 \[LessEqual] \(-211\), \(-6\)\ x1 + 3\ x2 - 12\ x3 - 8\ x5 - 2\ x6 \[LessEqual] \(-211\), \(-6\)\ x1 - 8\ x3 + 3\ x4 - 12\ x5 - 2\ x6 \[LessEqual] \(-211\), \(-6\)\ x1 - 8\ x2 - 12\ x4 + 3\ x5 - 2\ x6 \[LessEqual] \(-211\), \(-6\)\ x1 - 12\ x2 + 3\ x3 - 8\ x4 - 2\ x6 \[LessEqual] \(-211\), \(-8\)\ x1 - 6\ x3 - 2\ x4 - 12\ x5 + 3\ x6 \[LessEqual] \(-211\), \(-8\)\ x1 - 2\ x2 - 12\ x3 - 6\ x5 + 3\ x6 \[LessEqual] \(-211\), \(-8\)\ x1 - 6\ x2 - 12\ x4 - 2\ x5 + 3\ x6 \[LessEqual] \(-211\), \(-8\)\ x1 - 12\ x2 - 2\ x3 - 6\ x4 + 3\ x6 \[LessEqual] \(-211\), \(-12\)\ x1 + 3\ x2 - 6\ x3 - 2\ x4 - 8\ x5 \[LessEqual] \(-211\), \(-12\)\ x1 - 2\ x2 - 8\ x3 + 3\ x4 - 6\ x5 \[LessEqual] \(-211\), \(-12\)\ x1 - 6\ x2 + 3\ x3 - 8\ x4 - 2\ x5 \[LessEqual] \(-211\), \(-12\)\ x1 - 8\ x2 - 2\ x3 - 6\ x4 + 3\ x5 \[LessEqual] \(-211\), 15\ x1 + 12\ x2 + 6\ x3 + 6\ x5 + 4\ x6 \[LessEqual] 901, 15\ x1 + 6\ x2 + 12\ x3 + 6\ x4 + 4\ x6 \[LessEqual] 901, 15\ x1 + 6\ x2 + 6\ x4 + 12\ x5 + 4\ x6 \[LessEqual] 901, 15\ x1 + 6\ x3 + 12\ x4 + 6\ x5 + 4\ x6 \[LessEqual] 901, 12\ x1 + 15\ x2 + 6\ x3 + 4\ x5 + 6\ x6 \[LessEqual] 901, 12\ x1 + 6\ x2 + 15\ x3 + 4\ x4 + 6\ x6 \[LessEqual] 901, 12\ x1 + 4\ x2 + 6\ x4 + 15\ x5 + 6\ x6 \[LessEqual] 901, 12\ x1 + 4\ x3 + 15\ x4 + 6\ x5 + 6\ x6 \[LessEqual] 901, 6\ x1 + 15\ x2 + 12\ x3 + 6\ x4 + 4\ x5 \[LessEqual] 901, 6\ x1 + 15\ x2 + 6\ x4 + 4\ x5 + 12\ x6 \[LessEqual] 901, 6\ x1 + 12\ x2 + 15\ x3 + 4\ x4 + 6\ x5 \[LessEqual] 901, 6\ x1 + 6\ x2 + 4\ x3 + 15\ x4 + 12\ x5 \[LessEqual] 901, 6\ x1 + 6\ x2 + 4\ x3 + 15\ x4 + 12\ x6 \[LessEqual] 901, 6\ x1 + 4\ x2 + 6\ x3 + 12\ x4 + 15\ x5 \[LessEqual] 901, 6\ x1 + 4\ x2 + 6\ x3 + 15\ x5 + 12\ x6 \[LessEqual] 901, 6\ x1 + 15\ x3 + 4\ x4 + 6\ x5 + 12\ x6 \[LessEqual] 901, 4\ x1 + 12\ x2 + 6\ x4 + 6\ x5 + 15\ x6 \[LessEqual] 901, 4\ x1 + 6\ x2 + 6\ x3 + 12\ x4 + 15\ x6 \[LessEqual] 901, 4\ x1 + 6\ x2 + 6\ x3 + 12\ x5 + 15\ x6 \[LessEqual] 901, 4\ x1 + 12\ x3 + 6\ x4 + 6\ x5 + 15\ x6 \[LessEqual] 901, 15\ x2 + 6\ x3 + 12\ x4 + 4\ x5 + 6\ x6 \[LessEqual] 901, 12\ x2 + 4\ x3 + 15\ x4 + 6\ x5 + 6\ x6 \[LessEqual] 901, 6\ x2 + 15\ x3 + 4\ x4 + 12\ x5 + 6\ x6 \[LessEqual] 901, 4\ x2 + 12\ x3 + 6\ x4 + 15\ x5 + 6\ x6 \[LessEqual] 901, 15\ x1 + 10\ x2 + 6\ x3 + 6\ x5 + 4\ x6 \[LessEqual] 863, 15\ x1 + 6\ x2 + 10\ x3 + 6\ x4 + 4\ x6 \[LessEqual] 863, 15\ x1 + 6\ x2 + 6\ x4 + 10\ x5 + 4\ x6 \[LessEqual] 863, 15\ x1 + 6\ x3 + 10\ x4 + 6\ x5 + 4\ x6 \[LessEqual] 863, 10\ x1 + 15\ x2 + 6\ x3 + 4\ x5 + 6\ x6 \[LessEqual] 863, 10\ x1 + 6\ x2 + 15\ x3 + 4\ x4 + 6\ x6 \[LessEqual] 863, 10\ x1 + 4\ x2 + 6\ x4 + 15\ x5 + 6\ x6 \[LessEqual] 863, 10\ x1 + 4\ x3 + 15\ x4 + 6\ x5 + 6\ x6 \[LessEqual] 863, 6\ x1 + 15\ x2 + 10\ x3 + 6\ x4 + 4\ x5 \[LessEqual] 863, 6\ x1 + 15\ x2 + 6\ x4 + 4\ x5 + 10\ x6 \[LessEqual] 863, 6\ x1 + 10\ x2 + 15\ x3 + 4\ x4 + 6\ x5 \[LessEqual] 863, 6\ x1 + 6\ x2 + 4\ x3 + 15\ x4 + 10\ x5 \[LessEqual] 863, 6\ x1 + 6\ x2 + 4\ x3 + 15\ x4 + 10\ x6 \[LessEqual] 863, 6\ x1 + 4\ x2 + 6\ x3 + 10\ x4 + 15\ x5 \[LessEqual] 863, 6\ x1 + 4\ x2 + 6\ x3 + 15\ x5 + 10\ x6 \[LessEqual] 863, 6\ x1 + 15\ x3 + 4\ x4 + 6\ x5 + 10\ x6 \[LessEqual] 863, 4\ x1 + 10\ x2 + 6\ x4 + 6\ x5 + 15\ x6 \[LessEqual] 863, 4\ x1 + 6\ x2 + 6\ x3 + 10\ x4 + 15\ x6 \[LessEqual] 863, 4\ x1 + 6\ x2 + 6\ x3 + 10\ x5 + 15\ x6 \[LessEqual] 863, 4\ x1 + 10\ x3 + 6\ x4 + 6\ x5 + 15\ x6 \[LessEqual] 863, 15\ x2 + 6\ x3 + 10\ x4 + 4\ x5 + 6\ x6 \[LessEqual] 863, 10\ x2 + 4\ x3 + 15\ x4 + 6\ x5 + 6\ x6 \[LessEqual] 863, 6\ x2 + 15\ x3 + 4\ x4 + 10\ x5 + 6\ x6 \[LessEqual] 863, 4\ x2 + 10\ x3 + 6\ x4 + 15\ x5 + 6\ x6 \[LessEqual] 863, x1 - 2\ x2 - 6\ x3 - 8\ x4 - 2\ x5 - 4\ x6 \[LessEqual] \(-195\), x1 - 2\ x2 - 8\ x3 - 6\ x4 - 2\ x5 - 4\ x6 \[LessEqual] \(-195\), x1 - 6\ x2 - 2\ x3 - 2\ x4 - 8\ x5 - 4\ x6 \[LessEqual] \(-195\), x1 - 8\ x2 - 2\ x3 - 2\ x4 - 6\ x5 - 4\ x6 \[LessEqual] \(-195\), \(-2\)\ x1 + x2 - 6\ x3 - 8\ x4 - 4\ x5 - 2\ x6 \[LessEqual] \(-195\), \(-2\)\ x1 + x2 - 8\ x3 - 6\ x4 - 4\ x5 - 2\ x6 \[LessEqual] \(-195\), \(-2\)\ x1 - 4\ x2 - 6\ x3 - 8\ x4 + x5 - 2\ x6 \[LessEqual] \(-195\), \(-2\)\ x1 - 4\ x2 - 8\ x3 - 6\ x4 + x5 - 2\ x6 \[LessEqual] \(-195\), \(-2\)\ x1 - 6\ x2 + x3 - 4\ x4 - 8\ x5 - 2\ x6 \[LessEqual] \(-195\), \(-2\)\ x1 - 6\ x2 - 4\ x3 + x4 - 8\ x5 - 2\ x6 \[LessEqual] \(-195\), \(-2\)\ x1 - 8\ x2 + x3 - 4\ x4 - 6\ x5 - 2\ x6 \[LessEqual] \(-195\), \(-2\)\ x1 - 8\ x2 - 4\ x3 + x4 - 6\ x5 - 2\ x6 \[LessEqual] \(-195\), \(-4\)\ x1 - 2\ x2 - 6\ x3 - 8\ x4 - 2\ x5 + x6 \[LessEqual] \(-195\), \(-4\)\ x1 - 2\ x2 - 8\ x3 - 6\ x4 - 2\ x5 + x6 \[LessEqual] \(-195\), \(-4\)\ x1 - 6\ x2 - 2\ x3 - 2\ x4 - 8\ x5 + x6 \[LessEqual] \(-195\), \(-4\)\ x1 - 8\ x2 - 2\ x3 - 2\ x4 - 6\ x5 + x6 \[LessEqual] \(-195\), \(-6\)\ x1 + x2 - 2\ x3 - 2\ x4 - 4\ x5 - 8\ x6 \[LessEqual] \(-195\), \(-6\)\ x1 - 2\ x2 + x3 - 4\ x4 - 2\ x5 - 8\ x6 \[LessEqual] \(-195\), \(-6\)\ x1 - 2\ x2 - 4\ x3 + x4 - 2\ x5 - 8\ x6 \[LessEqual] \(-195\), \(-6\)\ x1 - 4\ x2 - 2\ x3 - 2\ x4 + x5 - 8\ x6 \[LessEqual] \(-195\), \(-8\)\ x1 + x2 - 2\ x3 - 2\ x4 - 4\ x5 - 6\ x6 \[LessEqual] \(-195\), \(-8\)\ x1 - 2\ x2 + x3 - 4\ x4 - 2\ x5 - 6\ x6 \[LessEqual] \(-195\), \(-8\)\ x1 - 2\ x2 - 4\ x3 + x4 - 2\ x5 - 6\ x6 \[LessEqual] \(-195\), \(-8\)\ x1 - 4\ x2 - 2\ x3 - 2\ x4 + x5 - 6\ x6 \[LessEqual] \(-195\), 7\ x1 + 4\ x2 - 2\ x4 + 4\ x5 + 2\ x6 \[LessEqual] 363, 7\ x1 + 4\ x2 - 2\ x3 + 4\ x5 + 2\ x6 \[LessEqual] 363, 7\ x1 + 4\ x3 + 4\ x4 - 2\ x5 + 2\ x6 \[LessEqual] 363, 7\ x1 - 2\ x2 + 4\ x3 + 4\ x4 + 2\ x6 \[LessEqual] 363, 4\ x1 + 7\ x2 - 2\ x4 + 2\ x5 + 4\ x6 \[LessEqual] 363, 4\ x1 + 7\ x2 - 2\ x3 + 2\ x5 + 4\ x6 \[LessEqual] 363, 4\ x1 + 2\ x2 - 2\ x4 + 7\ x5 + 4\ x6 \[LessEqual] 363, 4\ x1 + 2\ x2 - 2\ x3 + 7\ x5 + 4\ x6 \[LessEqual] 363, 4\ x1 + 7\ x3 + 2\ x4 - 2\ x5 + 4\ x6 \[LessEqual] 363, 4\ x1 + 2\ x3 + 7\ x4 - 2\ x5 + 4\ x6 \[LessEqual] 363, 4\ x1 - 2\ x2 + 7\ x3 + 2\ x4 + 4\ x6 \[LessEqual] 363, 4\ x1 - 2\ x2 + 2\ x3 + 7\ x4 + 4\ x6 \[LessEqual] 363, 2\ x1 + 4\ x2 - 2\ x4 + 4\ x5 + 7\ x6 \[LessEqual] 363, 2\ x1 + 4\ x2 - 2\ x3 + 4\ x5 + 7\ x6 \[LessEqual] 363, 2\ x1 + 4\ x3 + 4\ x4 - 2\ x5 + 7\ x6 \[LessEqual] 363, 2\ x1 - 2\ x2 + 4\ x3 + 4\ x4 + 7\ x6 \[LessEqual] 363, 7\ x2 + 4\ x3 + 4\ x4 + 2\ x5 - 2\ x6 \[LessEqual] 363, 4\ x2 + 7\ x3 + 2\ x4 + 4\ x5 - 2\ x6 \[LessEqual] 363, 4\ x2 + 2\ x3 + 7\ x4 + 4\ x5 - 2\ x6 \[LessEqual] 363, 2\ x2 + 4\ x3 + 4\ x4 + 7\ x5 - 2\ x6 \[LessEqual] 363, \(-2\)\ x1 + 7\ x2 + 4\ x3 + 4\ x4 + 2\ x5 \[LessEqual] 363, \(-2\)\ x1 + 4\ x2 + 7\ x3 + 2\ x4 + 4\ x5 \[LessEqual] 363, \(-2\)\ x1 + 4\ x2 + 2\ x3 + 7\ x4 + 4\ x5 \[LessEqual] 363, \(-2\)\ x1 + 2\ x2 + 4\ x3 + 4\ x4 + 7\ x5 \[LessEqual] 363, 3\ x1 - 6\ x3 - 18\ x4 - 24\ x5 - 20\ x6 \[LessEqual] \(-707\), 3\ x1 - 6\ x2 - 24\ x4 - 18\ x5 - 20\ x6 \[LessEqual] \(-707\), 3\ x1 - 18\ x2 - 24\ x3 - 6\ x5 - 20\ x6 \[LessEqual] \(-707\), 3\ x1 - 24\ x2 - 18\ x3 - 6\ x4 - 20\ x6 \[LessEqual] \(-707\), 3\ x2 - 6\ x3 - 18\ x4 - 20\ x5 - 24\ x6 \[LessEqual] \(-707\), \(-6\)\ x2 + 3\ x3 - 20\ x4 - 18\ x5 - 24\ x6 \[LessEqual] \(-707\), \(-18\)\ x2 - 20\ x3 + 3\ x4 - 6\ x5 - 24\ x6 \[LessEqual] \(-707\), \(-20\)\ x2 - 18\ x3 - 6\ x4 + 3\ x5 - 24\ x6 \[LessEqual] \(-707\), \(-6\)\ x1 + 3\ x2 - 24\ x4 - 20\ x5 - 18\ x6 \[LessEqual] \(-707\), \(-6\)\ x1 + 3\ x3 - 20\ x4 - 24\ x5 - 18\ x6 \[LessEqual] \(-707\), \(-6\)\ x1 - 20\ x2 - 24\ x3 + 3\ x5 - 18\ x6 \[LessEqual] \(-707\), \(-6\)\ x1 - 24\ x2 - 20\ x3 + 3\ x4 - 18\ x6 \[LessEqual] \(-707\), \(-18\)\ x1 + 3\ x2 - 24\ x3 - 20\ x5 - 6\ x6 \[LessEqual] \(-707\), \(-18\)\ x1 - 20\ x3 + 3\ x4 - 24\ x5 - 6\ x6 \[LessEqual] \(-707\), \(-18\)\ x1 - 20\ x2 - 24\ x4 + 3\ x5 - 6\ x6 \[LessEqual] \(-707\), \(-18\)\ x1 - 24\ x2 + 3\ x3 - 20\ x4 - 6\ x6 \[LessEqual] \(-707\), \(-20\)\ x1 - 18\ x3 - 6\ x4 - 24\ x5 + 3\ x6 \[LessEqual] \(-707\), \(-20\)\ x1 - 6\ x2 - 24\ x3 - 18\ x5 + 3\ x6 \[LessEqual] \(-707\), \(-20\)\ x1 - 18\ x2 - 24\ x4 - 6\ x5 + 3\ x6 \[LessEqual] \(-707\), \(-20\)\ x1 - 24\ x2 - 6\ x3 - 18\ x4 + 3\ x6 \[LessEqual] \(-707\), \(-24\)\ x1 + 3\ x2 - 18\ x3 - 6\ x4 - 20\ x5 \[LessEqual] \(-707\), \(-24\)\ x1 - 6\ x2 - 20\ x3 + 3\ x4 - 18\ x5 \[LessEqual] \(-707\), \(-24\)\ x1 - 18\ x2 + 3\ x3 - 20\ x4 - 6\ x5 \[LessEqual] \(-707\), \(-24\)\ x1 - 20\ x2 - 6\ x3 - 18\ x4 + 3\ x5 \[LessEqual] \(-707\), 9\ x1 - 2\ x3 - 6\ x4 - 8\ x5 - 12\ x6 \[LessEqual] \(-85\), 9\ x1 - 2\ x2 - 8\ x4 - 6\ x5 - 12\ x6 \[LessEqual] \(-85\), 9\ x1 - 6\ x2 - 8\ x3 - 2\ x5 - 12\ x6 \[LessEqual] \(-85\), 9\ x1 - 8\ x2 - 6\ x3 - 2\ x4 - 12\ x6 \[LessEqual] \(-85\), 9\ x2 - 2\ x3 - 6\ x4 - 12\ x5 - 8\ x6 \[LessEqual] \(-85\), \(-2\)\ x2 + 9\ x3 - 12\ x4 - 6\ x5 - 8\ x6 \[LessEqual] \(-85\), \(-6\)\ x2 - 12\ x3 + 9\ x4 - 2\ x5 - 8\ x6 \[LessEqual] \(-85\), \(-12\)\ x2 - 6\ x3 - 2\ x4 + 9\ x5 - 8\ x6 \[LessEqual] \(-85\), \(-2\)\ x1 + 9\ x2 - 8\ x4 - 12\ x5 - 6\ x6 \[LessEqual] \(-85\), \(-2\)\ x1 + 9\ x3 - 12\ x4 - 8\ x5 - 6\ x6 \[LessEqual] \(-85\), \(-2\)\ x1 - 8\ x2 - 12\ x3 + 9\ x4 - 6\ x6 \[LessEqual] \(-85\), \(-2\)\ x1 - 12\ x2 - 8\ x3 + 9\ x5 - 6\ x6 \[LessEqual] \(-85\), \(-6\)\ x1 + 9\ x2 - 8\ x3 - 12\ x5 - 2\ x6 \[LessEqual] \(-85\), \(-6\)\ x1 - 12\ x3 + 9\ x4 - 8\ x5 - 2\ x6 \[LessEqual] \(-85\), \(-6\)\ x1 - 8\ x2 + 9\ x3 - 12\ x4 - 2\ x6 \[LessEqual] \(-85\), \(-6\)\ x1 - 12\ x2 - 8\ x4 + 9\ x5 - 2\ x6 \[LessEqual] \(-85\), \(-8\)\ x1 + 9\ x2 - 6\ x3 - 2\ x4 - 12\ x5 \[LessEqual] \(-85\), \(-8\)\ x1 - 2\ x2 - 12\ x3 + 9\ x4 - 6\ x5 \[LessEqual] \(-85\), \(-8\)\ x1 - 6\ x2 + 9\ x3 - 12\ x4 - 2\ x5 \[LessEqual] \(-85\), \(-8\)\ x1 - 12\ x2 - 2\ x3 - 6\ x4 + 9\ x5 \[LessEqual] \(-85\), \(-12\)\ x1 - 6\ x3 - 2\ x4 - 8\ x5 + 9\ x6 \[LessEqual] \(-85\), \(-12\)\ x1 - 2\ x2 - 8\ x3 - 6\ x5 + 9\ x6 \[LessEqual] \(-85\), \(-12\)\ x1 - 6\ x2 - 8\ x4 - 2\ x5 + 9\ x6 \[LessEqual] \(-85\), \(-12\)\ x1 - 8\ x2 - 2\ x3 - 6\ x4 + 9\ x6 \[LessEqual] \(-85\), 9\ x1 - 24\ x3 - 18\ x4 - 2\ x5 - 2\ x6 \[LessEqual] \(-79\), 9\ x1 - 2\ x2 - 18\ x3 - 24\ x4 - 2\ x6 \[LessEqual] \(-79\), 9\ x1 - 18\ x2 - 2\ x3 - 24\ x5 - 2\ x6 \[LessEqual] \(-79\), 9\ x1 - 24\ x2 - 2\ x4 - 18\ x5 - 2\ x6 \[LessEqual] \(-79\), 9\ x2 - 24\ x3 - 18\ x4 - 2\ x5 - 2\ x6 \[LessEqual] \(-79\), \(-2\)\ x2 - 18\ x3 - 24\ x4 + 9\ x5 - 2\ x6 \[LessEqual] \(-79\), \(-18\)\ x2 - 2\ x3 + 9\ x4 - 24\ x5 - 2\ x6 \[LessEqual] \(-79\), \(-24\)\ x2 + 9\ x3 - 2\ x4 - 18\ x5 - 2\ x6 \[LessEqual] \(-79\), \(-2\)\ x1 + 9\ x2 - 18\ x3 - 24\ x4 - 2\ x5 \[LessEqual] \(-79\), \(-2\)\ x1 - 18\ x3 - 24\ x4 - 2\ x5 + 9\ x6 \[LessEqual] \(-79\), \(-2\)\ x1 - 2\ x2 - 24\ x3 - 18\ x4 + 9\ x5 \[LessEqual] \(-79\), \(-2\)\ x1 - 2\ x2 - 24\ x3 - 18\ x4 + 9\ x6 \[LessEqual] \(-79\), \(-2\)\ x1 - 18\ x2 + 9\ x3 - 2\ x4 - 24\ x5 \[LessEqual] \(-79\), \(-2\)\ x1 - 18\ x2 - 2\ x4 - 24\ x5 + 9\ x6 \[LessEqual] \(-79\), \(-2\)\ x1 - 24\ x2 - 2\ x3 + 9\ x4 - 18\ x5 \[LessEqual] \(-79\), \(-2\)\ x1 - 24\ x2 - 2\ x3 - 18\ x5 + 9\ x6 \[LessEqual] \(-79\), \(-18\)\ x1 + 9\ x2 - 2\ x3 - 2\ x5 - 24\ x6 \[LessEqual] \(-79\), \(-18\)\ x1 - 2\ x3 + 9\ x4 - 2\ x5 - 24\ x6 \[LessEqual] \(-79\), \(-18\)\ x1 - 2\ x2 + 9\ x3 - 2\ x4 - 24\ x6 \[LessEqual] \(-79\), \(-18\)\ x1 - 2\ x2 - 2\ x4 + 9\ x5 - 24\ x6 \[LessEqual] \(-79\), \(-24\)\ x1 + 9\ x2 - 2\ x4 - 2\ x5 - 18\ x6 \[LessEqual] \(-79\), \(-24\)\ x1 + 9\ x3 - 2\ x4 - 2\ x5 - 18\ x6 \[LessEqual] \(-79\), \(-24\)\ x1 - 2\ x2 - 2\ x3 + 9\ x4 - 18\ x6 \[LessEqual] \(-79\), \(-24\)\ x1 - 2\ x2 - 2\ x3 + 9\ x5 - 18\ x6 \[LessEqual] \(-79\), 11\ x1 - 16\ x2 - 88\ x3 - 70\ x4 - 22\ x5 - 38\ x6 \[LessEqual] \(-1981\), 11\ x1 - 22\ x2 - 70\ x3 - 88\ x4 - 16\ x5 - 38\ x6 \[LessEqual] \(-1981\), 11\ x1 - 70\ x2 - 22\ x3 - 16\ x4 - 88\ x5 - 38\ x6 \[LessEqual] \(-1981\), 11\ x1 - 88\ x2 - 16\ x3 - 22\ x4 - 70\ x5 - 38\ x6 \[LessEqual] \(-1981\), \(-16\)\ x1 + 11\ x2 - 88\ x3 - 70\ x4 - 38\ x5 - 22\ x6 \[LessEqual] \(-1981\), \(-16\)\ x1 - 38\ x2 - 70\ x3 - 88\ x4 + 11\ x5 - 22\ x6 \[LessEqual] \(-1981\), \(-16\)\ x1 - 70\ x2 - 38\ x3 + 11\ x4 - 88\ x5 - 22\ x6 \[LessEqual] \(-1981\), \(-16\)\ x1 - 88\ x2 + 11\ x3 - 38\ x4 - 70\ x5 - 22\ x6 \[LessEqual] \(-1981\), \(-22\)\ x1 + 11\ x2 - 70\ x3 - 88\ x4 - 38\ x5 - 16\ x6 \[LessEqual] \(-1981\), \(-22\)\ x1 - 38\ x2 - 88\ x3 - 70\ x4 + 11\ x5 - 16\ x6 \[LessEqual] \(-1981\), \(-22\)\ x1 - 70\ x2 + 11\ x3 - 38\ x4 - 88\ x5 - 16\ x6 \[LessEqual] \(-1981\), \(-22\)\ x1 - 88\ x2 - 38\ x3 + 11\ x4 - 70\ x5 - 16\ x6 \[LessEqual] \(-1981\), \(-38\)\ x1 - 16\ x2 - 70\ x3 - 88\ x4 - 22\ x5 + 11\ x6 \[LessEqual] \(-1981\), \(-38\)\ x1 - 22\ x2 - 88\ x3 - 70\ x4 - 16\ x5 + 11\ x6 \[LessEqual] \(-1981\), \(-38\)\ x1 - 70\ x2 - 16\ x3 - 22\ x4 - 88\ x5 + 11\ x6 \[LessEqual] \(-1981\), \(-38\)\ x1 - 88\ x2 - 22\ x3 - 16\ x4 - 70\ x5 + 11\ x6 \[LessEqual] \(-1981\), \(-70\)\ x1 + 11\ x2 - 22\ x3 - 16\ x4 - 38\ x5 - 88\ x6 \[LessEqual] \(-1981\), \(-70\)\ x1 - 16\ x2 - 38\ x3 + 11\ x4 - 22\ x5 - 88\ x6 \[LessEqual] \(-1981\), \(-70\)\ x1 - 22\ x2 + 11\ x3 - 38\ x4 - 16\ x5 - 88\ x6 \[LessEqual] \(-1981\), \(-70\)\ x1 - 38\ x2 - 16\ x3 - 22\ x4 + 11\ x5 - 88\ x6 \[LessEqual] \(-1981\), \(-88\)\ x1 + 11\ x2 - 16\ x3 - 22\ x4 - 38\ x5 - 70\ x6 \[LessEqual] \(-1981\), \(-88\)\ x1 - 16\ x2 + 11\ x3 - 38\ x4 - 22\ x5 - 70\ x6 \[LessEqual] \(-1981\), \(-88\)\ x1 - 22\ x2 - 38\ x3 + 11\ x4 - 16\ x5 - 70\ x6 \[LessEqual] \(-1981\), \(-88\)\ x1 - 38\ x2 - 22\ x3 - 16\ x4 + 11\ x5 - 70\ x6 \[LessEqual] \(-1981\), \(-3\)\ x2 - 15\ x3 - 13\ x4 - 4\ x5 - 7\ x6 \[LessEqual] \(-413\), \(-4\)\ x2 - 13\ x3 - 15\ x4 - 3\ x5 - 7\ x6 \[LessEqual] \(-413\), \(-13\)\ x2 - 4\ x3 - 3\ x4 - 15\ x5 - 7\ x6 \[LessEqual] \(-413\), \(-15\)\ x2 - 3\ x3 - 4\ x4 - 13\ x5 - 7\ x6 \[LessEqual] \(-413\), \(-3\)\ x1 - 15\ x3 - 13\ x4 - 7\ x5 - 4\ x6 \[LessEqual] \(-413\), \(-3\)\ x1 - 7\ x2 - 13\ x3 - 15\ x4 - 4\ x6 \[LessEqual] \(-413\), \(-3\)\ x1 - 13\ x2 - 7\ x3 - 15\ x5 - 4\ x6 \[LessEqual] \(-413\), \(-3\)\ x1 - 15\ x2 - 7\ x4 - 13\ x5 - 4\ x6 \[LessEqual] \(-413\), \(-4\)\ x1 - 13\ x3 - 15\ x4 - 7\ x5 - 3\ x6 \[LessEqual] \(-413\), \(-4\)\ x1 - 7\ x2 - 15\ x3 - 13\ x4 - 3\ x6 \[LessEqual] \(-413\), \(-4\)\ x1 - 13\ x2 - 7\ x4 - 15\ x5 - 3\ x6 \[LessEqual] \(-413\), \(-4\)\ x1 - 15\ x2 - 7\ x3 - 13\ x5 - 3\ x6 \[LessEqual] \(-413\), \(-7\)\ x1 - 3\ x2 - 13\ x3 - 15\ x4 - 4\ x5 \[LessEqual] \(-413\), \(-7\)\ x1 - 4\ x2 - 15\ x3 - 13\ x4 - 3\ x5 \[LessEqual] \(-413\), \(-7\)\ x1 - 13\ x2 - 3\ x3 - 4\ x4 - 15\ x5 \[LessEqual] \(-413\), \(-7\)\ x1 - 15\ x2 - 4\ x3 - 3\ x4 - 13\ x5 \[LessEqual] \(-413\), \(-13\)\ x1 - 4\ x3 - 3\ x4 - 7\ x5 - 15\ x6 \[LessEqual] \(-413\), \(-13\)\ x1 - 3\ x2 - 7\ x3 - 4\ x5 - 15\ x6 \[LessEqual] \(-413\), \(-13\)\ x1 - 4\ x2 - 7\ x4 - 3\ x5 - 15\ x6 \[LessEqual] \(-413\), \(-13\)\ x1 - 7\ x2 - 3\ x3 - 4\ x4 - 15\ x6 \[LessEqual] \(-413\), \(-15\)\ x1 - 3\ x3 - 4\ x4 - 7\ x5 - 13\ x6 \[LessEqual] \(-413\), \(-15\)\ x1 - 3\ x2 - 7\ x4 - 4\ x5 - 13\ x6 \[LessEqual] \(-413\), \(-15\)\ x1 - 4\ x2 - 7\ x3 - 3\ x5 - 13\ x6 \[LessEqual] \(-413\), \(-15\)\ x1 - 7\ x2 - 4\ x3 - 3\ x4 - 13\ x6 \[LessEqual] \(-413\), x1 - 2\ x2 - 11\ x3 - 9\ x4 - 3\ x5 - 5\ x6 \[LessEqual] \(-268\), x1 - 3\ x2 - 9\ x3 - 11\ x4 - 2\ x5 - 5\ x6 \[LessEqual] \(-268\), x1 - 9\ x2 - 3\ x3 - 2\ x4 - 11\ x5 - 5\ x6 \[LessEqual] \(-268\), x1 - 11\ x2 - 2\ x3 - 3\ x4 - 9\ x5 - 5\ x6 \[LessEqual] \(-268\), \(-2\)\ x1 + x2 - 11\ x3 - 9\ x4 - 5\ x5 - 3\ x6 \[LessEqual] \(-268\), \(-2\)\ x1 - 5\ x2 - 9\ x3 - 11\ x4 + x5 - 3\ x6 \[LessEqual] \(-268\), \(-2\)\ x1 - 9\ x2 - 5\ x3 + x4 - 11\ x5 - 3\ x6 \[LessEqual] \(-268\), \(-2\)\ x1 - 11\ x2 + x3 - 5\ x4 - 9\ x5 - 3\ x6 \[LessEqual] \(-268\), \(-3\)\ x1 + x2 - 9\ x3 - 11\ x4 - 5\ x5 - 2\ x6 \[LessEqual] \(-268\), \(-3\)\ x1 - 5\ x2 - 11\ x3 - 9\ x4 + x5 - 2\ x6 \[LessEqual] \(-268\), \(-3\)\ x1 - 9\ x2 + x3 - 5\ x4 - 11\ x5 - 2\ x6 \[LessEqual] \(-268\), \(-3\)\ x1 - 11\ x2 - 5\ x3 + x4 - 9\ x5 - 2\ x6 \[LessEqual] \(-268\), \(-5\)\ x1 - 2\ x2 - 9\ x3 - 11\ x4 - 3\ x5 + x6 \[LessEqual] \(-268\), \(-5\)\ x1 - 3\ x2 - 11\ x3 - 9\ x4 - 2\ x5 + x6 \[LessEqual] \(-268\), \(-5\)\ x1 - 9\ x2 - 2\ x3 - 3\ x4 - 11\ x5 + x6 \[LessEqual] \(-268\), \(-5\)\ x1 - 11\ x2 - 3\ x3 - 2\ x4 - 9\ x5 + x6 \[LessEqual] \(-268\), \(-9\)\ x1 + x2 - 3\ x3 - 2\ x4 - 5\ x5 - 11\ x6 \[LessEqual] \(-268\), \(-9\)\ x1 - 2\ x2 - 5\ x3 + x4 - 3\ x5 - 11\ x6 \[LessEqual] \(-268\), \(-9\)\ x1 - 3\ x2 + x3 - 5\ x4 - 2\ x5 - 11\ x6 \[LessEqual] \(-268\), \(-9\)\ x1 - 5\ x2 - 2\ x3 - 3\ x4 + x5 - 11\ x6 \[LessEqual] \(-268\), \(-11\)\ x1 + x2 - 2\ x3 - 3\ x4 - 5\ x5 - 9\ x6 \[LessEqual] \(-268\), \(-11\)\ x1 - 2\ x2 + x3 - 5\ x4 - 3\ x5 - 9\ x6 \[LessEqual] \(-268\), \(-11\)\ x1 - 3\ x2 - 5\ x3 + x4 - 2\ x5 - 9\ x6 \[LessEqual] \(-268\), \(-11\)\ x1 - 5\ x2 - 3\ x3 - 2\ x4 + x5 - 9\ x6 \[LessEqual] \(-268\), 3\ x1 - 12\ x3 - 6\ x4 - 2\ x5 \[LessEqual] \(-35\), 3\ x1 - 2\ x2 - 6\ x3 - 12\ x4 \[LessEqual] \(-35\), 3\ x1 - 6\ x2 - 2\ x3 - 12\ x5 \[LessEqual] \(-35\), 3\ x1 - 12\ x2 - 2\ x4 - 6\ x5 \[LessEqual] \(-35\), 3\ x2 - 12\ x3 - 6\ x4 - 2\ x6 \[LessEqual] \(-35\), \(-6\)\ x3 - 12\ x4 + 3\ x5 - 2\ x6 \[LessEqual] \(-35\), \(-6\)\ x3 - 12\ x4 - 2\ x5 + 3\ x6 \[LessEqual] \(-35\), \(-2\)\ x2 - 12\ x3 - 6\ x4 + 3\ x6 \[LessEqual] \(-35\), \(-6\)\ x2 + 3\ x4 - 12\ x5 - 2\ x6 \[LessEqual] \(-35\), \(-6\)\ x2 - 2\ x4 - 12\ x5 + 3\ x6 \[LessEqual] \(-35\), \(-12\)\ x2 + 3\ x3 - 6\ x5 - 2\ x6 \[LessEqual] \(-35\), \(-12\)\ x2 - 2\ x3 - 6\ x5 + 3\ x6 \[LessEqual] \(-35\), \(-2\)\ x1 + 3\ x2 - 6\ x3 - 12\ x4 \[LessEqual] \(-35\), \(-2\)\ x1 - 12\ x3 - 6\ x4 + 3\ x5 \[LessEqual] \(-35\), \(-2\)\ x1 - 6\ x2 + 3\ x3 - 12\ x5 \[LessEqual] \(-35\), \(-2\)\ x1 - 12\ x2 + 3\ x4 - 6\ x5 \[LessEqual] \(-35\), \(-6\)\ x1 + 3\ x2 - 2\ x3 - 12\ x6 \[LessEqual] \(-35\), \(-6\)\ x1 + 3\ x4 - 2\ x5 - 12\ x6 \[LessEqual] \(-35\), \(-6\)\ x1 - 2\ x4 + 3\ x5 - 12\ x6 \[LessEqual] \(-35\), \(-6\)\ x1 - 2\ x2 + 3\ x3 - 12\ x6 \[LessEqual] \(-35\), \(-12\)\ x1 + 3\ x2 - 2\ x4 - 6\ x6 \[LessEqual] \(-35\), \(-12\)\ x1 + 3\ x3 - 2\ x5 - 6\ x6 \[LessEqual] \(-35\), \(-12\)\ x1 - 2\ x3 + 3\ x5 - 6\ x6 \[LessEqual] \(-35\), \(-12\)\ x1 - 2\ x2 + 3\ x4 - 6\ x6 \[LessEqual] \(-35\), 3\ x1 - 8\ x3 - 6\ x4 - 2\ x5 \[LessEqual] \(-31\), 3\ x1 - 2\ x2 - 6\ x3 - 8\ x4 \[LessEqual] \(-31\), 3\ x1 - 6\ x2 - 2\ x3 - 8\ x5 \[LessEqual] \(-31\), 3\ x1 - 8\ x2 - 2\ x4 - 6\ x5 \[LessEqual] \(-31\), 3\ x2 - 8\ x3 - 6\ x4 - 2\ x6 \[LessEqual] \(-31\), \(-6\)\ x3 - 8\ x4 + 3\ x5 - 2\ x6 \[LessEqual] \(-31\), \(-6\)\ x3 - 8\ x4 - 2\ x5 + 3\ x6 \[LessEqual] \(-31\), \(-2\)\ x2 - 8\ x3 - 6\ x4 + 3\ x6 \[LessEqual] \(-31\), \(-6\)\ x2 + 3\ x4 - 8\ x5 - 2\ x6 \[LessEqual] \(-31\), \(-6\)\ x2 - 2\ x4 - 8\ x5 + 3\ x6 \[LessEqual] \(-31\), \(-8\)\ x2 + 3\ x3 - 6\ x5 - 2\ x6 \[LessEqual] \(-31\), \(-8\)\ x2 - 2\ x3 - 6\ x5 + 3\ x6 \[LessEqual] \(-31\), \(-2\)\ x1 + 3\ x2 - 6\ x3 - 8\ x4 \[LessEqual] \(-31\), \(-2\)\ x1 - 8\ x3 - 6\ x4 + 3\ x5 \[LessEqual] \(-31\), \(-2\)\ x1 - 6\ x2 + 3\ x3 - 8\ x5 \[LessEqual] \(-31\), \(-2\)\ x1 - 8\ x2 + 3\ x4 - 6\ x5 \[LessEqual] \(-31\), \(-6\)\ x1 + 3\ x2 - 2\ x3 - 8\ x6 \[LessEqual] \(-31\), \(-6\)\ x1 + 3\ x4 - 2\ x5 - 8\ x6 \[LessEqual] \(-31\), \(-6\)\ x1 - 2\ x4 + 3\ x5 - 8\ x6 \[LessEqual] \(-31\), \(-6\)\ x1 - 2\ x2 + 3\ x3 - 8\ x6 \[LessEqual] \(-31\), \(-8\)\ x1 + 3\ x2 - 2\ x4 - 6\ x6 \[LessEqual] \(-31\), \(-8\)\ x1 + 3\ x3 - 2\ x5 - 6\ x6 \[LessEqual] \(-31\), \(-8\)\ x1 - 2\ x3 + 3\ x5 - 6\ x6 \[LessEqual] \(-31\), \(-8\)\ x1 - 2\ x2 + 3\ x4 - 6\ x6 \[LessEqual] \(-31\), 3\ x1 - 2\ x3 - 2\ x4 - 2\ x5 \[LessEqual] 33, 3\ x1 - 2\ x2 - 2\ x4 - 2\ x5 \[LessEqual] 33, 3\ x1 - 2\ x2 - 2\ x3 - 2\ x5 \[LessEqual] 33, 3\ x1 - 2\ x2 - 2\ x3 - 2\ x4 \[LessEqual] 33, 3\ x2 - 2\ x3 - 2\ x4 - 2\ x6 \[LessEqual] 33, \(-2\)\ x3 - 2\ x4 + 3\ x5 - 2\ x6 \[LessEqual] 33, \(-2\)\ x3 - 2\ x4 - 2\ x5 + 3\ x6 \[LessEqual] 33, \(-2\)\ x2 + 3\ x3 - 2\ x5 - 2\ x6 \[LessEqual] 33, \(-2\)\ x2 + 3\ x4 - 2\ x5 - 2\ x6 \[LessEqual] 33, \(-2\)\ x2 - 2\ x4 - 2\ x5 + 3\ x6 \[LessEqual] 33, \(-2\)\ x2 - 2\ x3 - 2\ x5 + 3\ x6 \[LessEqual] 33, \(-2\)\ x2 - 2\ x3 - 2\ x4 + 3\ x6 \[LessEqual] 33, \(-2\)\ x1 + 3\ x2 - 2\ x4 - 2\ x6 \[LessEqual] 33, \(-2\)\ x1 + 3\ x2 - 2\ x3 - 2\ x6 \[LessEqual] 33, \(-2\)\ x1 + 3\ x2 - 2\ x3 - 2\ x4 \[LessEqual] 33, \(-2\)\ x1 + 3\ x3 - 2\ x5 - 2\ x6 \[LessEqual] 33, \(-2\)\ x1 + 3\ x4 - 2\ x5 - 2\ x6 \[LessEqual] 33, \(-2\)\ x1 - 2\ x4 + 3\ x5 - 2\ x6 \[LessEqual] 33, \(-2\)\ x1 - 2\ x3 + 3\ x5 - 2\ x6 \[LessEqual] 33, \(-2\)\ x1 - 2\ x3 - 2\ x4 + 3\ x5 \[LessEqual] 33, \(-2\)\ x1 - 2\ x2 + 3\ x3 - 2\ x6 \[LessEqual] 33, \(-2\)\ x1 - 2\ x2 + 3\ x3 - 2\ x5 \[LessEqual] 33, \(-2\)\ x1 - 2\ x2 + 3\ x4 - 2\ x6 \[LessEqual] 33, \(-2\)\ x1 - 2\ x2 + 3\ x4 - 2\ x5 \[LessEqual] 33, 14\ x1 + 8\ x2 + 2\ x3 + 2\ x4 + 2\ x5 + 5\ x6 \[LessEqual] 717, 14\ x1 + 2\ x2 + 8\ x3 + 2\ x4 + 2\ x5 + 5\ x6 \[LessEqual] 717, 14\ x1 + 2\ x2 + 2\ x3 + 8\ x4 + 2\ x5 + 5\ x6 \[LessEqual] 717, 14\ x1 + 2\ x2 + 2\ x3 + 2\ x4 + 8\ x5 + 5\ x6 \[LessEqual] 717, 8\ x1 + 14\ x2 + 2\ x3 + 2\ x4 + 5\ x5 + 2\ x6 \[LessEqual] 717, 8\ x1 + 5\ x2 + 2\ x3 + 2\ x4 + 14\ x5 + 2\ x6 \[LessEqual] 717, 8\ x1 + 2\ x2 + 14\ x3 + 5\ x4 + 2\ x5 + 2\ x6 \[LessEqual] 717, 8\ x1 + 2\ x2 + 5\ x3 + 14\ x4 + 2\ x5 + 2\ x6 \[LessEqual] 717, 5\ x1 + 8\ x2 + 2\ x3 + 2\ x4 + 2\ x5 + 14\ x6 \[LessEqual] 717, 5\ x1 + 2\ x2 + 8\ x3 + 2\ x4 + 2\ x5 + 14\ x6 \[LessEqual] 717, 5\ x1 + 2\ x2 + 2\ x3 + 8\ x4 + 2\ x5 + 14\ x6 \[LessEqual] 717, 5\ x1 + 2\ x2 + 2\ x3 + 2\ x4 + 8\ x5 + 14\ x6 \[LessEqual] 717, 2\ x1 + 14\ x2 + 8\ x3 + 2\ x4 + 5\ x5 + 2\ x6 \[LessEqual] 717, 2\ x1 + 14\ x2 + 2\ x3 + 8\ x4 + 5\ x5 + 2\ x6 \[LessEqual] 717, 2\ x1 + 14\ x2 + 2\ x3 + 2\ x4 + 5\ x5 + 8\ x6 \[LessEqual] 717, 2\ x1 + 8\ x2 + 14\ x3 + 5\ x4 + 2\ x5 + 2\ x6 \[LessEqual] 717, 2\ x1 + 8\ x2 + 5\ x3 + 14\ x4 + 2\ x5 + 2\ x6 \[LessEqual] 717, 2\ x1 + 5\ x2 + 8\ x3 + 2\ x4 + 14\ x5 + 2\ x6 \[LessEqual] 717, 2\ x1 + 5\ x2 + 2\ x3 + 8\ x4 + 14\ x5 + 2\ x6 \[LessEqual] 717, 2\ x1 + 5\ x2 + 2\ x3 + 2\ x4 + 14\ x5 + 8\ x6 \[LessEqual] 717, 2\ x1 + 2\ x2 + 14\ x3 + 5\ x4 + 8\ x5 + 2\ x6 \[LessEqual] 717, 2\ x1 + 2\ x2 + 14\ x3 + 5\ x4 + 2\ x5 + 8\ x6 \[LessEqual] 717, 2\ x1 + 2\ x2 + 5\ x3 + 14\ x4 + 8\ x5 + 2\ x6 \[LessEqual] 717, 2\ x1 + 2\ x2 + 5\ x3 + 14\ x4 + 2\ x5 + 8\ x6 \[LessEqual] 717, 3\ x1 - 6\ x3 - 6\ x4 - 2\ x5 \[LessEqual] \(-23\), 3\ x1 - 2\ x2 - 6\ x3 - 6\ x4 \[LessEqual] \(-23\), 3\ x1 - 6\ x2 - 2\ x4 - 6\ x5 \[LessEqual] \(-23\), 3\ x1 - 6\ x2 - 2\ x3 - 6\ x5 \[LessEqual] \(-23\), 3\ x2 - 6\ x3 - 6\ x4 - 2\ x6 \[LessEqual] \(-23\), \(-6\)\ x3 - 6\ x4 + 3\ x5 - 2\ x6 \[LessEqual] \(-23\), \(-6\)\ x3 - 6\ x4 - 2\ x5 + 3\ x6 \[LessEqual] \(-23\), \(-2\)\ x2 - 6\ x3 - 6\ x4 + 3\ x6 \[LessEqual] \(-23\), \(-6\)\ x2 + 3\ x3 - 6\ x5 - 2\ x6 \[LessEqual] \(-23\), \(-6\)\ x2 + 3\ x4 - 6\ x5 - 2\ x6 \[LessEqual] \(-23\), \(-6\)\ x2 - 2\ x4 - 6\ x5 + 3\ x6 \[LessEqual] \(-23\), \(-6\)\ x2 - 2\ x3 - 6\ x5 + 3\ x6 \[LessEqual] \(-23\), \(-2\)\ x1 + 3\ x2 - 6\ x3 - 6\ x4 \[LessEqual] \(-23\), \(-2\)\ x1 - 6\ x3 - 6\ x4 + 3\ x5 \[LessEqual] \(-23\), \(-2\)\ x1 - 6\ x2 + 3\ x3 - 6\ x5 \[LessEqual] \(-23\), \(-2\)\ x1 - 6\ x2 + 3\ x4 - 6\ x5 \[LessEqual] \(-23\), \(-6\)\ x1 + 3\ x2 - 2\ x4 - 6\ x6 \[LessEqual] \(-23\), \(-6\)\ x1 + 3\ x2 - 2\ x3 - 6\ x6 \[LessEqual] \(-23\), \(-6\)\ x1 + 3\ x3 - 2\ x5 - 6\ x6 \[LessEqual] \(-23\), \(-6\)\ x1 + 3\ x4 - 2\ x5 - 6\ x6 \[LessEqual] \(-23\), \(-6\)\ x1 - 2\ x4 + 3\ x5 - 6\ x6 \[LessEqual] \(-23\), \(-6\)\ x1 - 2\ x3 + 3\ x5 - 6\ x6 \[LessEqual] \(-23\), \(-6\)\ x1 - 2\ x2 + 3\ x3 - 6\ x6 \[LessEqual] \(-23\), \(-6\)\ x1 - 2\ x2 + 3\ x4 - 6\ x6 \[LessEqual] \(-23\), 15\ x1 + 6\ x2 - 4\ x5 \[LessEqual] 515, 15\ x1 + 6\ x3 - 4\ x4 \[LessEqual] 515, 15\ x1 - 4\ x3 + 6\ x4 \[LessEqual] 515, 15\ x1 - 4\ x2 + 6\ x5 \[LessEqual] 515, 6\ x1 + 15\ x2 - 4\ x6 \[LessEqual] 515, 6\ x1 + 15\ x3 - 4\ x6 \[LessEqual] 515, 6\ x1 + 15\ x4 - 4\ x6 \[LessEqual] 515, 6\ x1 + 15\ x5 - 4\ x6 \[LessEqual] 515, 15\ x2 + 6\ x3 - 4\ x4 \[LessEqual] 515, 15\ x2 - 4\ x3 + 6\ x4 \[LessEqual] 515, 6\ x2 + 15\ x3 - 4\ x5 \[LessEqual] 515, 6\ x2 + 15\ x4 - 4\ x5 \[LessEqual] 515, 6\ x2 - 4\ x5 + 15\ x6 \[LessEqual] 515, 6\ x3 - 4\ x4 + 15\ x5 \[LessEqual] 515, 6\ x3 - 4\ x4 + 15\ x6 \[LessEqual] 515, \(-4\)\ x3 + 6\ x4 + 15\ x5 \[LessEqual] 515, \(-4\)\ x3 + 6\ x4 + 15\ x6 \[LessEqual] 515, \(-4\)\ x2 + 15\ x3 + 6\ x5 \[LessEqual] 515, \(-4\)\ x2 + 15\ x4 + 6\ x5 \[LessEqual] 515, \(-4\)\ x2 + 6\ x5 + 15\ x6 \[LessEqual] 515, \(-4\)\ x1 + 15\ x2 + 6\ x6 \[LessEqual] 515, \(-4\)\ x1 + 15\ x3 + 6\ x6 \[LessEqual] 515, \(-4\)\ x1 + 15\ x4 + 6\ x6 \[LessEqual] 515, \(-4\)\ x1 + 15\ x5 + 6\ x6 \[LessEqual] 515, 3\ x1 - 4\ x2 - 6\ x3 - 6\ x4 - 6\ x5 - 10\ x6 \[LessEqual] \(-325\), 3\ x1 - 6\ x2 - 4\ x3 - 6\ x4 - 6\ x5 - 10\ x6 \[LessEqual] \(-325\), 3\ x1 - 6\ x2 - 6\ x3 - 4\ x4 - 6\ x5 - 10\ x6 \[LessEqual] \(-325\), 3\ x1 - 6\ x2 - 6\ x3 - 6\ x4 - 4\ x5 - 10\ x6 \[LessEqual] \(-325\), \(-4\)\ x1 + 3\ x2 - 6\ x3 - 6\ x4 - 10\ x5 - 6\ x6 \[LessEqual] \(-325\), \(-4\)\ x1 - 6\ x2 + 3\ x3 - 10\ x4 - 6\ x5 - 6\ x6 \[LessEqual] \(-325\), \(-4\)\ x1 - 6\ x2 - 10\ x3 + 3\ x4 - 6\ x5 - 6\ x6 \[LessEqual] \(-325\), \(-4\)\ x1 - 10\ x2 - 6\ x3 - 6\ x4 + 3\ x5 - 6\ x6 \[LessEqual] \(-325\), \(-6\)\ x1 + 3\ x2 - 4\ x3 - 6\ x4 - 10\ x5 - 6\ x6 \[LessEqual] \(-325\), \(-6\)\ x1 + 3\ x2 - 6\ x3 - 4\ x4 - 10\ x5 - 6\ x6 \[LessEqual] \(-325\), \(-6\)\ x1 + 3\ x2 - 6\ x3 - 6\ x4 - 10\ x5 - 4\ x6 \[LessEqual] \(-325\), \(-6\)\ x1 - 4\ x2 + 3\ x3 - 10\ x4 - 6\ x5 - 6\ x6 \[LessEqual] \(-325\), \(-6\)\ x1 - 4\ x2 - 10\ x3 + 3\ x4 - 6\ x5 - 6\ x6 \[LessEqual] \(-325\), \(-6\)\ x1 - 6\ x2 + 3\ x3 - 10\ x4 - 4\ x5 - 6\ x6 \[LessEqual] \(-325\), \(-6\)\ x1 - 6\ x2 + 3\ x3 - 10\ x4 - 6\ x5 - 4\ x6 \[LessEqual] \(-325\), \(-6\)\ x1 - 6\ x2 - 10\ x3 + 3\ x4 - 4\ x5 - 6\ x6 \[LessEqual] \(-325\), \(-6\)\ x1 - 6\ x2 - 10\ x3 + 3\ x4 - 6\ x5 - 4\ x6 \[LessEqual] \(-325\), \(-6\)\ x1 - 10\ x2 - 4\ x3 - 6\ x4 + 3\ x5 - 6\ x6 \[LessEqual] \(-325\), \(-6\)\ x1 - 10\ x2 - 6\ x3 - 4\ x4 + 3\ x5 - 6\ x6 \[LessEqual] \(-325\), \(-6\)\ x1 - 10\ x2 - 6\ x3 - 6\ x4 + 3\ x5 - 4\ x6 \[LessEqual] \(-325\), \(-10\)\ x1 - 4\ x2 - 6\ x3 - 6\ x4 - 6\ x5 + 3\ x6 \[LessEqual] \(-325\), \(-10\)\ x1 - 6\ x2 - 4\ x3 - 6\ x4 - 6\ x5 + 3\ x6 \[LessEqual] \(-325\), \(-10\)\ x1 - 6\ x2 - 6\ x3 - 4\ x4 - 6\ x5 + 3\ x6 \[LessEqual] \(-325\), \(-10\)\ x1 - 6\ x2 - 6\ x3 - 6\ x4 - 4\ x5 + 3\ x6 \[LessEqual] \(-325\), 5\ x1 - 2\ x2 - 4\ x3 - 4\ x4 - 4\ x5 - 8\ x6 \[LessEqual] \(-139\), 5\ x1 - 4\ x2 - 2\ x3 - 4\ x4 - 4\ x5 - 8\ x6 \[LessEqual] \(-139\), 5\ x1 - 4\ x2 - 4\ x3 - 2\ x4 - 4\ x5 - 8\ x6 \[LessEqual] \(-139\), 5\ x1 - 4\ x2 - 4\ x3 - 4\ x4 - 2\ x5 - 8\ x6 \[LessEqual] \(-139\), \(-2\)\ x1 + 5\ x2 - 4\ x3 - 4\ x4 - 8\ x5 - 4\ x6 \[LessEqual] \(-139\), \(-2\)\ x1 - 4\ x2 + 5\ x3 - 8\ x4 - 4\ x5 - 4\ x6 \[LessEqual] \(-139\), \(-2\)\ x1 - 4\ x2 - 8\ x3 + 5\ x4 - 4\ x5 - 4\ x6 \[LessEqual] \(-139\), \(-2\)\ x1 - 8\ x2 - 4\ x3 - 4\ x4 + 5\ x5 - 4\ x6 \[LessEqual] \(-139\), \(-4\)\ x1 + 5\ x2 - 2\ x3 - 4\ x4 - 8\ x5 - 4\ x6 \[LessEqual] \(-139\), \(-4\)\ x1 + 5\ x2 - 4\ x3 - 2\ x4 - 8\ x5 - 4\ x6 \[LessEqual] \(-139\), \(-4\)\ x1 + 5\ x2 - 4\ x3 - 4\ x4 - 8\ x5 - 2\ x6 \[LessEqual] \(-139\), \(-4\)\ x1 - 2\ x2 + 5\ x3 - 8\ x4 - 4\ x5 - 4\ x6 \[LessEqual] \(-139\), \(-4\)\ x1 - 2\ x2 - 8\ x3 + 5\ x4 - 4\ x5 - 4\ x6 \[LessEqual] \(-139\), \(-4\)\ x1 - 4\ x2 + 5\ x3 - 8\ x4 - 2\ x5 - 4\ x6 \[LessEqual] \(-139\), \(-4\)\ x1 - 4\ x2 + 5\ x3 - 8\ x4 - 4\ x5 - 2\ x6 \[LessEqual] \(-139\), \(-4\)\ x1 - 4\ x2 - 8\ x3 + 5\ x4 - 2\ x5 - 4\ x6 \[LessEqual] \(-139\), \(-4\)\ x1 - 4\ x2 - 8\ x3 + 5\ x4 - 4\ x5 - 2\ x6 \[LessEqual] \(-139\), \(-4\)\ x1 - 8\ x2 - 2\ x3 - 4\ x4 + 5\ x5 - 4\ x6 \[LessEqual] \(-139\), \(-4\)\ x1 - 8\ x2 - 4\ x3 - 2\ x4 + 5\ x5 - 4\ x6 \[LessEqual] \(-139\), \(-4\)\ x1 - 8\ x2 - 4\ x3 - 4\ x4 + 5\ x5 - 2\ x6 \[LessEqual] \(-139\), \(-8\)\ x1 - 2\ x2 - 4\ x3 - 4\ x4 - 4\ x5 + 5\ x6 \[LessEqual] \(-139\), \(-8\)\ x1 - 4\ x2 - 2\ x3 - 4\ x4 - 4\ x5 + 5\ x6 \[LessEqual] \(-139\), \(-8\)\ x1 - 4\ x2 - 4\ x3 - 2\ x4 - 4\ x5 + 5\ x6 \[LessEqual] \(-139\), \(-8\)\ x1 - 4\ x2 - 4\ x3 - 4\ x4 - 2\ x5 + 5\ x6 \[LessEqual] \(-139\), 13\ x1 + 6\ x2 + 4\ x3 + 4\ x4 + 4\ x5 \[LessEqual] 653, 13\ x1 + 4\ x2 + 6\ x3 + 4\ x4 + 4\ x5 \[LessEqual] 653, 13\ x1 + 4\ x2 + 4\ x3 + 6\ x4 + 4\ x5 \[LessEqual] 653, 13\ x1 + 4\ x2 + 4\ x3 + 4\ x4 + 6\ x5 \[LessEqual] 653, 6\ x1 + 13\ x2 + 4\ x3 + 4\ x4 + 4\ x6 \[LessEqual] 653, 6\ x1 + 4\ x2 + 13\ x3 + 4\ x5 + 4\ x6 \[LessEqual] 653, 6\ x1 + 4\ x2 + 13\ x4 + 4\ x5 + 4\ x6 \[LessEqual] 653, 6\ x1 + 4\ x3 + 4\ x4 + 13\ x5 + 4\ x6 \[LessEqual] 653, 4\ x1 + 13\ x2 + 6\ x3 + 4\ x4 + 4\ x6 \[LessEqual] 653, 4\ x1 + 13\ x2 + 4\ x3 + 6\ x4 + 4\ x6 \[LessEqual] 653, 4\ x1 + 13\ x2 + 4\ x3 + 4\ x4 + 6\ x6 \[LessEqual] 653, 4\ x1 + 6\ x2 + 13\ x3 + 4\ x5 + 4\ x6 \[LessEqual] 653, 4\ x1 + 6\ x2 + 13\ x4 + 4\ x5 + 4\ x6 \[LessEqual] 653, 4\ x1 + 4\ x2 + 13\ x3 + 6\ x5 + 4\ x6 \[LessEqual] 653, 4\ x1 + 4\ x2 + 13\ x3 + 4\ x5 + 6\ x6 \[LessEqual] 653, 4\ x1 + 4\ x2 + 13\ x4 + 6\ x5 + 4\ x6 \[LessEqual] 653, 4\ x1 + 4\ x2 + 13\ x4 + 4\ x5 + 6\ x6 \[LessEqual] 653, 4\ x1 + 6\ x3 + 4\ x4 + 13\ x5 + 4\ x6 \[LessEqual] 653, 4\ x1 + 4\ x3 + 6\ x4 + 13\ x5 + 4\ x6 \[LessEqual] 653, 4\ x1 + 4\ x3 + 4\ x4 + 13\ x5 + 6\ x6 \[LessEqual] 653, 6\ x2 + 4\ x3 + 4\ x4 + 4\ x5 + 13\ x6 \[LessEqual] 653, 4\ x2 + 6\ x3 + 4\ x4 + 4\ x5 + 13\ x6 \[LessEqual] 653, 4\ x2 + 4\ x3 + 6\ x4 + 4\ x5 + 13\ x6 \[LessEqual] 653, 4\ x2 + 4\ x3 + 4\ x4 + 6\ x5 + 13\ x6 \[LessEqual] 653, \(-x3\) - x4 - 2\ x6 \[LessEqual] \(-28\), \(-x3\) - x4 - 2\ x5 \[LessEqual] \(-28\), \(-x2\) - x5 - 2\ x6 \[LessEqual] \(-28\), \(-x2\) - 2\ x4 - x5 \[LessEqual] \(-28\), \(-x2\) - 2\ x3 - x5 \[LessEqual] \(-28\), \(-2\)\ x2 - x3 - x4 \[LessEqual] \(-28\), \(-x1\) - 2\ x5 - x6 \[LessEqual] \(-28\), \(-x1\) - 2\ x4 - x6 \[LessEqual] \(-28\), \(-x1\) - 2\ x3 - x6 \[LessEqual] \(-28\), \(-x1\) - 2\ x2 - x6 \[LessEqual] \(-28\), \(-2\)\ x1 - x3 - x4 \[LessEqual] \(-28\), \(-2\)\ x1 - x2 - x5 \[LessEqual] \(-28\), \(-x3\) - 2\ x4 - 2\ x5 - 3\ x6 \[LessEqual] \(-88\), \(-x3\) - 2\ x4 - 3\ x5 - 2\ x6 \[LessEqual] \(-88\), \(-x2\) - 2\ x4 - 2\ x5 - 3\ x6 \[LessEqual] \(-88\), \(-x2\) - 3\ x4 - 2\ x5 - 2\ x6 \[LessEqual] \(-88\), \(-2\)\ x2 - 2\ x3 - x5 - 3\ x6 \[LessEqual] \(-88\), \(-2\)\ x2 - 2\ x3 - x4 - 3\ x6 \[LessEqual] \(-88\), \(-2\)\ x2 - 3\ x3 - x5 - 2\ x6 \[LessEqual] \(-88\), \(-3\)\ x2 - 2\ x3 - x4 - 2\ x6 \[LessEqual] \(-88\), \(-x1\) - 2\ x4 - 3\ x5 - 2\ x6 \[LessEqual] \(-88\), \(-x1\) - 3\ x4 - 2\ x5 - 2\ x6 \[LessEqual] \(-88\), \(-x1\) - 2\ x2 - 3\ x3 - 2\ x6 \[LessEqual] \(-88\), \(-x1\) - 3\ x2 - 2\ x3 - 2\ x6 \[LessEqual] \(-88\), \(-2\)\ x1 - 2\ x3 - 3\ x5 - x6 \[LessEqual] \(-88\), \(-2\)\ x1 - 2\ x3 - x4 - 3\ x5 \[LessEqual] \(-88\), \(-2\)\ x1 - 3\ x3 - 2\ x5 - x6 \[LessEqual] \(-88\), \(-2\)\ x1 - x2 - 3\ x3 - 2\ x5 \[LessEqual] \(-88\), \(-2\)\ x1 - 2\ x2 - 3\ x4 - x6 \[LessEqual] \(-88\), \(-2\)\ x1 - 2\ x2 - 3\ x4 - x5 \[LessEqual] \(-88\), \(-2\)\ x1 - 3\ x2 - 2\ x4 - x6 \[LessEqual] \(-88\), \(-2\)\ x1 - 3\ x2 - x3 - 2\ x4 \[LessEqual] \(-88\), \(-3\)\ x1 - 2\ x3 - x4 - 2\ x5 \[LessEqual] \(-88\), \(-3\)\ x1 - x2 - 2\ x3 - 2\ x5 \[LessEqual] \(-88\), \(-3\)\ x1 - 2\ x2 - 2\ x4 - x5 \[LessEqual] \(-88\), \(-3\)\ x1 - 2\ x2 - x3 - 2\ x4 \[LessEqual] \(-88\), \(-x2\) - 2\ x3 - 2\ x4 - 2\ x5 - 4\ x6 \[LessEqual] \(-127\), \(-2\)\ x2 - x3 - 2\ x4 - 2\ x5 - 4\ x6 \[LessEqual] \(-127\), \(-2\)\ x2 - 2\ x3 - x4 - 2\ x5 - 4\ x6 \[LessEqual] \(-127\), \(-2\)\ x2 - 2\ x3 - 2\ x4 - x5 - 4\ x6 \[LessEqual] \(-127\), \(-x1\) - 2\ x3 - 2\ x4 - 4\ x5 - 2\ x6 \[LessEqual] \(-127\), \(-x1\) - 2\ x2 - 4\ x4 - 2\ x5 - 2\ x6 \[LessEqual] \(-127\), \(-x1\) - 2\ x2 - 4\ x3 - 2\ x5 - 2\ x6 \[LessEqual] \(-127\), \(-x1\) - 4\ x2 - 2\ x3 - 2\ x4 - 2\ x6 \[LessEqual] \(-127\), \(-2\)\ x1 - x3 - 2\ x4 - 4\ x5 - 2\ x6 \[LessEqual] \(-127\), \(-2\)\ x1 - 2\ x3 - x4 - 4\ x5 - 2\ x6 \[LessEqual] \(-127\), \(-2\)\ x1 - 2\ x3 - 2\ x4 - 4\ x5 - x6 \[LessEqual] \(-127\), \(-2\)\ x1 - x2 - 4\ x4 - 2\ x5 - 2\ x6 \[LessEqual] \(-127\), \(-2\)\ x1 - x2 - 4\ x3 - 2\ x5 - 2\ x6 \[LessEqual] \(-127\), \(-2\)\ x1 - 2\ x2 - 4\ x4 - x5 - 2\ x6 \[LessEqual] \(-127\), \(-2\)\ x1 - 2\ x2 - 4\ x4 - 2\ x5 - x6 \[LessEqual] \(-127\), \(-2\)\ x1 - 2\ x2 - 4\ x3 - x5 - 2\ x6 \[LessEqual] \(-127\), \(-2\)\ x1 - 2\ x2 - 4\ x3 - 2\ x5 - x6 \[LessEqual] \(-127\), \(-2\)\ x1 - 4\ x2 - x3 - 2\ x4 - 2\ x6 \[LessEqual] \(-127\), \(-2\)\ x1 - 4\ x2 - 2\ x3 - x4 - 2\ x6 \[LessEqual] \(-127\), \(-2\)\ x1 - 4\ x2 - 2\ x3 - 2\ x4 - x6 \[LessEqual] \(-127\), \(-4\)\ x1 - x2 - 2\ x3 - 2\ x4 - 2\ x5 \[LessEqual] \(-127\), \(-4\)\ x1 - 2\ x2 - x3 - 2\ x4 - 2\ x5 \[LessEqual] \(-127\), \(-4\)\ x1 - 2\ x2 - 2\ x3 - x4 - 2\ x5 \[LessEqual] \(-127\), \(-4\)\ x1 - 2\ x2 - 2\ x3 - 2\ x4 - x5 \[LessEqual] \(-127\), x1 - x2 - 2\ x3 - 2\ x4 - 2\ x5 - 4\ x6 \[LessEqual] \(-106\), x1 - 2\ x2 - x3 - 2\ x4 - 2\ x5 - 4\ x6 \[LessEqual] \(-106\), x1 - 2\ x2 - 2\ x3 - x4 - 2\ x5 - 4\ x6 \[LessEqual] \(-106\), x1 - 2\ x2 - 2\ x3 - 2\ x4 - x5 - 4\ x6 \[LessEqual] \(-106\), \(-x1\) + x2 - 2\ x3 - 2\ x4 - 4\ x5 - 2\ x6 \[LessEqual] \(-106\), \(-x1\) - 2\ x2 + x3 - 4\ x4 - 2\ x5 - 2\ x6 \[LessEqual] \(-106\), \(-x1\) - 2\ x2 - 4\ x3 + x4 - 2\ x5 - 2\ x6 \[LessEqual] \(-106\), \(-x1\) - 4\ x2 - 2\ x3 - 2\ x4 + x5 - 2\ x6 \[LessEqual] \(-106\), \(-2\)\ x1 + x2 - x3 - 2\ x4 - 4\ x5 - 2\ x6 \[LessEqual] \(-106\), \(-2\)\ x1 + x2 - 2\ x3 - x4 - 4\ x5 - 2\ x6 \[LessEqual] \(-106\), \(-2\)\ x1 + x2 - 2\ x3 - 2\ x4 - 4\ x5 - x6 \[LessEqual] \(-106\), \(-2\)\ x1 - x2 + x3 - 4\ x4 - 2\ x5 - 2\ x6 \[LessEqual] \(-106\), \(-2\)\ x1 - x2 - 4\ x3 + x4 - 2\ x5 - 2\ x6 \[LessEqual] \(-106\), \(-2\)\ x1 - 2\ x2 + x3 - 4\ x4 - x5 - 2\ x6 \[LessEqual] \(-106\), \(-2\)\ x1 - 2\ x2 + x3 - 4\ x4 - 2\ x5 - x6 \[LessEqual] \(-106\), \(-2\)\ x1 - 2\ x2 - 4\ x3 + x4 - x5 - 2\ x6 \[LessEqual] \(-106\), \(-2\)\ x1 - 2\ x2 - 4\ x3 + x4 - 2\ x5 - x6 \[LessEqual] \(-106\), \(-2\)\ x1 - 4\ x2 - x3 - 2\ x4 + x5 - 2\ x6 \[LessEqual] \(-106\), \(-2\)\ x1 - 4\ x2 - 2\ x3 - x4 + x5 - 2\ x6 \[LessEqual] \(-106\), \(-2\)\ x1 - 4\ x2 - 2\ x3 - 2\ x4 + x5 - x6 \[LessEqual] \(-106\), \(-4\)\ x1 - x2 - 2\ x3 - 2\ x4 - 2\ x5 + x6 \[LessEqual] \(-106\), \(-4\)\ x1 - 2\ x2 - x3 - 2\ x4 - 2\ x5 + x6 \[LessEqual] \(-106\), \(-4\)\ x1 - 2\ x2 - 2\ x3 - x4 - 2\ x5 + x6 \[LessEqual] \(-106\), \(-4\)\ x1 - 2\ x2 - 2\ x3 - 2\ x4 - x5 + x6 \[LessEqual] \(-106\), x1 - 2\ x2 - 2\ x3 - 2\ x4 - 4\ x5 - 4\ x6 \[LessEqual] \(-139\), x1 - 2\ x2 - 2\ x3 - 4\ x4 - 2\ x5 - 4\ x6 \[LessEqual] \(-139\), x1 - 2\ x2 - 4\ x3 - 2\ x4 - 2\ x5 - 4\ x6 \[LessEqual] \(-139\), x1 - 4\ x2 - 2\ x3 - 2\ x4 - 2\ x5 - 4\ x6 \[LessEqual] \(-139\), \(-2\)\ x1 + x2 - 2\ x3 - 2\ x4 - 4\ x5 - 4\ x6 \[LessEqual] \(-139\), \(-2\)\ x1 + x2 - 2\ x3 - 4\ x4 - 4\ x5 - 2\ x6 \[LessEqual] \(-139\), \(-2\)\ x1 + x2 - 4\ x3 - 2\ x4 - 4\ x5 - 2\ x6 \[LessEqual] \(-139\), \(-2\)\ x1 - 2\ x2 + x3 - 4\ x4 - 2\ x5 - 4\ x6 \[LessEqual] \(-139\), \(-2\)\ x1 - 2\ x2 + x3 - 4\ x4 - 4\ x5 - 2\ x6 \[LessEqual] \(-139\), \(-2\)\ x1 - 2\ x2 - 4\ x3 + x4 - 2\ x5 - 4\ x6 \[LessEqual] \(-139\), \(-2\)\ x1 - 2\ x2 - 4\ x3 + x4 - 4\ x5 - 2\ x6 \[LessEqual] \(-139\), \(-2\)\ x1 - 4\ x2 + x3 - 4\ x4 - 2\ x5 - 2\ x6 \[LessEqual] \(-139\), \(-2\)\ x1 - 4\ x2 - 2\ x3 - 2\ x4 + x5 - 4\ x6 \[LessEqual] \(-139\), \(-2\)\ x1 - 4\ x2 - 2\ x3 - 4\ x4 + x5 - 2\ x6 \[LessEqual] \(-139\), \(-2\)\ x1 - 4\ x2 - 4\ x3 + x4 - 2\ x5 - 2\ x6 \[LessEqual] \(-139\), \(-2\)\ x1 - 4\ x2 - 4\ x3 - 2\ x4 + x5 - 2\ x6 \[LessEqual] \(-139\), \(-4\)\ x1 + x2 - 2\ x3 - 2\ x4 - 4\ x5 - 2\ x6 \[LessEqual] \(-139\), \(-4\)\ x1 - 2\ x2 + x3 - 4\ x4 - 2\ x5 - 2\ x6 \[LessEqual] \(-139\), \(-4\)\ x1 - 2\ x2 - 2\ x3 - 2\ x4 - 4\ x5 + x6 \[LessEqual] \(-139\), \(-4\)\ x1 - 2\ x2 - 2\ x3 - 4\ x4 - 2\ x5 + x6 \[LessEqual] \(-139\), \(-4\)\ x1 - 2\ x2 - 4\ x3 + x4 - 2\ x5 - 2\ x6 \[LessEqual] \(-139\), \(-4\)\ x1 - 2\ x2 - 4\ x3 - 2\ x4 - 2\ x5 + x6 \[LessEqual] \(-139\), \(-4\)\ x1 - 4\ x2 - 2\ x3 - 2\ x4 + x5 - 2\ x6 \[LessEqual] \(-139\), \(-4\)\ x1 - 4\ x2 - 2\ x3 - 2\ x4 - 2\ x5 + x6 \[LessEqual] \(-139\), 3\ x1 - 6\ x3 - 8\ x4 \[LessEqual] \(-3\), 3\ x1 - 8\ x3 - 6\ x4 \[LessEqual] \(-3\), 3\ x1 - 6\ x2 - 8\ x5 \[LessEqual] \(-3\), 3\ x1 - 8\ x2 - 6\ x5 \[LessEqual] \(-3\), 3\ x2 - 6\ x3 - 8\ x4 \[LessEqual] \(-3\), 3\ x2 - 8\ x3 - 6\ x4 \[LessEqual] \(-3\), \(-6\)\ x3 - 8\ x4 + 3\ x5 \[LessEqual] \(-3\), \(-6\)\ x3 - 8\ x4 + 3\ x6 \[LessEqual] \(-3\), \(-8\)\ x3 - 6\ x4 + 3\ x5 \[LessEqual] \(-3\), \(-8\)\ x3 - 6\ x4 + 3\ x6 \[LessEqual] \(-3\), \(-6\)\ x2 + 3\ x3 - 8\ x5 \[LessEqual] \(-3\), \(-6\)\ x2 + 3\ x4 - 8\ x5 \[LessEqual] \(-3\), \(-6\)\ x2 - 8\ x5 + 3\ x6 \[LessEqual] \(-3\), \(-8\)\ x2 + 3\ x3 - 6\ x5 \[LessEqual] \(-3\), \(-8\)\ x2 + 3\ x4 - 6\ x5 \[LessEqual] \(-3\), \(-8\)\ x2 - 6\ x5 + 3\ x6 \[LessEqual] \(-3\), \(-6\)\ x1 + 3\ x2 - 8\ x6 \[LessEqual] \(-3\), \(-6\)\ x1 + 3\ x3 - 8\ x6 \[LessEqual] \(-3\), \(-6\)\ x1 + 3\ x4 - 8\ x6 \[LessEqual] \(-3\), \(-6\)\ x1 + 3\ x5 - 8\ x6 \[LessEqual] \(-3\), \(-8\)\ x1 + 3\ x2 - 6\ x6 \[LessEqual] \(-3\), \(-8\)\ x1 + 3\ x3 - 6\ x6 \[LessEqual] \(-3\), \(-8\)\ x1 + 3\ x4 - 6\ x6 \[LessEqual] \(-3\), \(-8\)\ x1 + 3\ x5 - 6\ x6 \[LessEqual] \(-3\), 9\ x1 + 6\ x2 - 6\ x3 + 4\ x5 + 6\ x6 \[LessEqual] 523, 9\ x1 + 4\ x2 - 6\ x4 + 6\ x5 + 6\ x6 \[LessEqual] 523, 9\ x1 + 4\ x3 + 6\ x4 - 6\ x5 + 6\ x6 \[LessEqual] 523, 9\ x1 - 6\ x2 + 6\ x3 + 4\ x4 + 6\ x6 \[LessEqual] 523, 6\ x1 + 9\ x2 - 6\ x3 + 6\ x5 + 4\ x6 \[LessEqual] 523, 6\ x1 + 6\ x2 - 6\ x4 + 9\ x5 + 4\ x6 \[LessEqual] 523, 6\ x1 + 6\ x2 - 6\ x4 + 4\ x5 + 9\ x6 \[LessEqual] 523, 6\ x1 + 4\ x2 - 6\ x3 + 6\ x5 + 9\ x6 \[LessEqual] 523, 6\ x1 + 6\ x3 + 9\ x4 - 6\ x5 + 4\ x6 \[LessEqual] 523, 6\ x1 + 6\ x3 + 4\ x4 - 6\ x5 + 9\ x6 \[LessEqual] 523, 6\ x1 - 6\ x2 + 9\ x3 + 6\ x4 + 4\ x6 \[LessEqual] 523, 6\ x1 - 6\ x2 + 4\ x3 + 6\ x4 + 9\ x6 \[LessEqual] 523, 4\ x1 + 9\ x2 - 6\ x4 + 6\ x5 + 6\ x6 \[LessEqual] 523, 4\ x1 + 6\ x2 - 6\ x3 + 9\ x5 + 6\ x6 \[LessEqual] 523, 4\ x1 + 9\ x3 + 6\ x4 - 6\ x5 + 6\ x6 \[LessEqual] 523, 4\ x1 - 6\ x2 + 6\ x3 + 9\ x4 + 6\ x6 \[LessEqual] 523, 9\ x2 + 4\ x3 + 6\ x4 + 6\ x5 - 6\ x6 \[LessEqual] 523, 6\ x2 + 6\ x3 + 9\ x4 + 4\ x5 - 6\ x6 \[LessEqual] 523, 6\ x2 + 6\ x3 + 4\ x4 + 9\ x5 - 6\ x6 \[LessEqual] 523, 4\ x2 + 9\ x3 + 6\ x4 + 6\ x5 - 6\ x6 \[LessEqual] 523, \(-6\)\ x1 + 9\ x2 + 6\ x3 + 4\ x4 + 6\ x5 \[LessEqual] 523, \(-6\)\ x1 + 6\ x2 + 9\ x3 + 6\ x4 + 4\ x5 \[LessEqual] 523, \(-6\)\ x1 + 6\ x2 + 4\ x3 + 6\ x4 + 9\ x5 \[LessEqual] 523, \(-6\)\ x1 + 4\ x2 + 6\ x3 + 9\ x4 + 6\ x5 \[LessEqual] 523, 81\ x1 + 54\ x2 - 18\ x3 + 48\ x5 + 32\ x6 \[LessEqual] 4529, 81\ x1 + 48\ x2 - 18\ x4 + 54\ x5 + 32\ x6 \[LessEqual] 4529, 81\ x1 + 48\ x3 + 54\ x4 - 18\ x5 + 32\ x6 \[LessEqual] 4529, 81\ x1 - 18\ x2 + 54\ x3 + 48\ x4 + 32\ x6 \[LessEqual] 4529, 54\ x1 + 81\ x2 - 18\ x3 + 32\ x5 + 48\ x6 \[LessEqual] 4529, 54\ x1 + 32\ x2 - 18\ x4 + 81\ x5 + 48\ x6 \[LessEqual] 4529, 54\ x1 + 32\ x3 + 81\ x4 - 18\ x5 + 48\ x6 \[LessEqual] 4529, 54\ x1 - 18\ x2 + 81\ x3 + 32\ x4 + 48\ x6 \[LessEqual] 4529, 48\ x1 + 81\ x2 - 18\ x4 + 32\ x5 + 54\ x6 \[LessEqual] 4529, 48\ x1 + 32\ x2 - 18\ x3 + 81\ x5 + 54\ x6 \[LessEqual] 4529, 48\ x1 + 81\ x3 + 32\ x4 - 18\ x5 + 54\ x6 \[LessEqual] 4529, 48\ x1 - 18\ x2 + 32\ x3 + 81\ x4 + 54\ x6 \[LessEqual] 4529, 32\ x1 + 54\ x2 - 18\ x4 + 48\ x5 + 81\ x6 \[LessEqual] 4529, 32\ x1 + 48\ x2 - 18\ x3 + 54\ x5 + 81\ x6 \[LessEqual] 4529, 32\ x1 + 54\ x3 + 48\ x4 - 18\ x5 + 81\ x6 \[LessEqual] 4529, 32\ x1 - 18\ x2 + 48\ x3 + 54\ x4 + 81\ x6 \[LessEqual] 4529, 81\ x2 + 48\ x3 + 54\ x4 + 32\ x5 - 18\ x6 \[LessEqual] 4529, 54\ x2 + 32\ x3 + 81\ x4 + 48\ x5 - 18\ x6 \[LessEqual] 4529, 48\ x2 + 81\ x3 + 32\ x4 + 54\ x5 - 18\ x6 \[LessEqual] 4529, 32\ x2 + 54\ x3 + 48\ x4 + 81\ x5 - 18\ x6 \[LessEqual] 4529, \(-18\)\ x1 + 81\ x2 + 54\ x3 + 48\ x4 + 32\ x5 \[LessEqual] 4529, \(-18\)\ x1 + 54\ x2 + 81\ x3 + 32\ x4 + 48\ x5 \[LessEqual] 4529, \(-18\)\ x1 + 48\ x2 + 32\ x3 + 81\ x4 + 54\ x5 \[LessEqual] 4529, \(-18\)\ x1 + 32\ x2 + 48\ x3 + 54\ x4 + 81\ x5 \[LessEqual] 4529, 14\ x1 + 11\ x2 + 2\ x3 + 2\ x4 + 8\ x5 + 8\ x6 \[LessEqual] 915, 14\ x1 + 8\ x2 + 2\ x3 + 2\ x4 + 11\ x5 + 8\ x6 \[LessEqual] 915, 14\ x1 + 2\ x2 + 11\ x3 + 8\ x4 + 2\ x5 + 8\ x6 \[LessEqual] 915, 14\ x1 + 2\ x2 + 8\ x3 + 11\ x4 + 2\ x5 + 8\ x6 \[LessEqual] 915, 11\ x1 + 14\ x2 + 2\ x3 + 2\ x4 + 8\ x5 + 8\ x6 \[LessEqual] 915, 11\ x1 + 8\ x2 + 2\ x3 + 2\ x4 + 14\ x5 + 8\ x6 \[LessEqual] 915, 11\ x1 + 2\ x2 + 14\ x3 + 8\ x4 + 2\ x5 + 8\ x6 \[LessEqual] 915, 11\ x1 + 2\ x2 + 8\ x3 + 14\ x4 + 2\ x5 + 8\ x6 \[LessEqual] 915, 8\ x1 + 14\ x2 + 2\ x3 + 2\ x4 + 8\ x5 + 11\ x6 \[LessEqual] 915, 8\ x1 + 11\ x2 + 2\ x3 + 2\ x4 + 8\ x5 + 14\ x6 \[LessEqual] 915, 8\ x1 + 8\ x2 + 2\ x3 + 2\ x4 + 14\ x5 + 11\ x6 \[LessEqual] 915, 8\ x1 + 8\ x2 + 2\ x3 + 2\ x4 + 11\ x5 + 14\ x6 \[LessEqual] 915, 8\ x1 + 2\ x2 + 14\ x3 + 8\ x4 + 2\ x5 + 11\ x6 \[LessEqual] 915, 8\ x1 + 2\ x2 + 11\ x3 + 8\ x4 + 2\ x5 + 14\ x6 \[LessEqual] 915, 8\ x1 + 2\ x2 + 8\ x3 + 14\ x4 + 2\ x5 + 11\ x6 \[LessEqual] 915, 8\ x1 + 2\ x2 + 8\ x3 + 11\ x4 + 2\ x5 + 14\ x6 \[LessEqual] 915, 2\ x1 + 14\ x2 + 11\ x3 + 8\ x4 + 8\ x5 + 2\ x6 \[LessEqual] 915, 2\ x1 + 14\ x2 + 8\ x3 + 11\ x4 + 8\ x5 + 2\ x6 \[LessEqual] 915, 2\ x1 + 11\ x2 + 14\ x3 + 8\ x4 + 8\ x5 + 2\ x6 \[LessEqual] 915, 2\ x1 + 11\ x2 + 8\ x3 + 14\ x4 + 8\ x5 + 2\ x6 \[LessEqual] 915, 2\ x1 + 8\ x2 + 14\ x3 + 8\ x4 + 11\ x5 + 2\ x6 \[LessEqual] 915, 2\ x1 + 8\ x2 + 11\ x3 + 8\ x4 + 14\ x5 + 2\ x6 \[LessEqual] 915, 2\ x1 + 8\ x2 + 8\ x3 + 14\ x4 + 11\ x5 + 2\ x6 \[LessEqual] 915, 2\ x1 + 8\ x2 + 8\ x3 + 11\ x4 + 14\ x5 + 2\ x6 \[LessEqual] 915, x1 - 2\ x5 \[LessEqual] 25, x1 - 2\ x4 \[LessEqual] 25, x1 - 2\ x3 \[LessEqual] 25, x1 - 2\ x2 \[LessEqual] 25, x2 - 2\ x6 \[LessEqual] 25, x2 - 2\ x4 \[LessEqual] 25, x2 - 2\ x3 \[LessEqual] 25, x3 - 2\ x6 \[LessEqual] 25, x3 - 2\ x5 \[LessEqual] 25, x4 - 2\ x6 \[LessEqual] 25, x4 - 2\ x5 \[LessEqual] 25, x5 - 2\ x6 \[LessEqual] 25, \(-2\)\ x5 + x6 \[LessEqual] 25, \(-2\)\ x4 + x5 \[LessEqual] 25, \(-2\)\ x4 + x6 \[LessEqual] 25, \(-2\)\ x3 + x5 \[LessEqual] 25, \(-2\)\ x3 + x6 \[LessEqual] 25, \(-2\)\ x2 + x3 \[LessEqual] 25, \(-2\)\ x2 + x4 \[LessEqual] 25, \(-2\)\ x2 + x6 \[LessEqual] 25, \(-2\)\ x1 + x2 \[LessEqual] 25, \(-2\)\ x1 + x3 \[LessEqual] 25, \(-2\)\ x1 + x4 \[LessEqual] 25, \(-2\)\ x1 + x5 \[LessEqual] 25, 9\ x1 - 24\ x3 - 18\ x4 - 2\ x5 \[LessEqual] \(-41\), 9\ x1 - 2\ x2 - 18\ x3 - 24\ x4 \[LessEqual] \(-41\), 9\ x1 - 18\ x2 - 2\ x3 - 24\ x5 \[LessEqual] \(-41\), 9\ x1 - 24\ x2 - 2\ x4 - 18\ x5 \[LessEqual] \(-41\), 9\ x2 - 24\ x3 - 18\ x4 - 2\ x6 \[LessEqual] \(-41\), \(-18\)\ x3 - 24\ x4 + 9\ x5 - 2\ x6 \[LessEqual] \(-41\), \(-18\)\ x3 - 24\ x4 - 2\ x5 + 9\ x6 \[LessEqual] \(-41\), \(-2\)\ x2 - 24\ x3 - 18\ x4 + 9\ x6 \[LessEqual] \(-41\), \(-18\)\ x2 + 9\ x4 - 24\ x5 - 2\ x6 \[LessEqual] \(-41\), \(-18\)\ x2 - 2\ x4 - 24\ x5 + 9\ x6 \[LessEqual] \(-41\), \(-24\)\ x2 + 9\ x3 - 18\ x5 - 2\ x6 \[LessEqual] \(-41\), \(-24\)\ x2 - 2\ x3 - 18\ x5 + 9\ x6 \[LessEqual] \(-41\), \(-2\)\ x1 + 9\ x2 - 18\ x3 - 24\ x4 \[LessEqual] \(-41\), \(-2\)\ x1 - 24\ x3 - 18\ x4 + 9\ x5 \[LessEqual] \(-41\), \(-2\)\ x1 - 18\ x2 + 9\ x3 - 24\ x5 \[LessEqual] \(-41\), \(-2\)\ x1 - 24\ x2 + 9\ x4 - 18\ x5 \[LessEqual] \(-41\), \(-18\)\ x1 + 9\ x2 - 2\ x3 - 24\ x6 \[LessEqual] \(-41\), \(-18\)\ x1 + 9\ x4 - 2\ x5 - 24\ x6 \[LessEqual] \(-41\), \(-18\)\ x1 - 2\ x4 + 9\ x5 - 24\ x6 \[LessEqual] \(-41\), \(-18\)\ x1 - 2\ x2 + 9\ x3 - 24\ x6 \[LessEqual] \(-41\), \(-24\)\ x1 + 9\ x2 - 2\ x4 - 18\ x6 \[LessEqual] \(-41\), \(-24\)\ x1 + 9\ x3 - 2\ x5 - 18\ x6 \[LessEqual] \(-41\), \(-24\)\ x1 - 2\ x3 + 9\ x5 - 18\ x6 \[LessEqual] \(-41\), \(-24\)\ x1 - 2\ x2 + 9\ x4 - 18\ x6 \[LessEqual] \(-41\), 3\ x1 - 4\ x3 - 6\ x4 \[LessEqual] 23, 3\ x1 - 6\ x3 - 4\ x4 \[LessEqual] 23, 3\ x1 - 4\ x2 - 6\ x5 \[LessEqual] 23, 3\ x1 - 6\ x2 - 4\ x5 \[LessEqual] 23, 3\ x2 - 4\ x3 - 6\ x4 \[LessEqual] 23, 3\ x2 - 6\ x3 - 4\ x4 \[LessEqual] 23, \(-4\)\ x3 - 6\ x4 + 3\ x5 \[LessEqual] 23, \(-4\)\ x3 - 6\ x4 + 3\ x6 \[LessEqual] 23, \(-6\)\ x3 - 4\ x4 + 3\ x5 \[LessEqual] 23, \(-6\)\ x3 - 4\ x4 + 3\ x6 \[LessEqual] 23, \(-4\)\ x2 + 3\ x3 - 6\ x5 \[LessEqual] 23, \(-4\)\ x2 + 3\ x4 - 6\ x5 \[LessEqual] 23, \(-4\)\ x2 - 6\ x5 + 3\ x6 \[LessEqual] 23, \(-6\)\ x2 + 3\ x3 - 4\ x5 \[LessEqual] 23, \(-6\)\ x2 + 3\ x4 - 4\ x5 \[LessEqual] 23, \(-6\)\ x2 - 4\ x5 + 3\ x6 \[LessEqual] 23, \(-4\)\ x1 + 3\ x2 - 6\ x6 \[LessEqual] 23, \(-4\)\ x1 + 3\ x3 - 6\ x6 \[LessEqual] 23, \(-4\)\ x1 + 3\ x4 - 6\ x6 \[LessEqual] 23, \(-4\)\ x1 + 3\ x5 - 6\ x6 \[LessEqual] 23, \(-6\)\ x1 + 3\ x2 - 4\ x6 \[LessEqual] 23, \(-6\)\ x1 + 3\ x3 - 4\ x6 \[LessEqual] 23, \(-6\)\ x1 + 3\ x4 - 4\ x6 \[LessEqual] 23, \(-6\)\ x1 + 3\ x5 - 4\ x6 \[LessEqual] 23, 15\ x1 + 6\ x2 + 4\ x3 + 4\ x4 + 6\ x5 \[LessEqual] 743, 15\ x1 + 4\ x2 + 6\ x3 + 6\ x4 + 4\ x5 \[LessEqual] 743, 6\ x1 + 15\ x2 + 4\ x3 + 4\ x4 + 6\ x6 \[LessEqual] 743, 6\ x1 + 4\ x2 + 15\ x3 + 4\ x5 + 6\ x6 \[LessEqual] 743, 6\ x1 + 4\ x2 + 15\ x4 + 4\ x5 + 6\ x6 \[LessEqual] 743, 6\ x1 + 4\ x3 + 4\ x4 + 15\ x5 + 6\ x6 \[LessEqual] 743, 4\ x1 + 15\ x2 + 6\ x3 + 6\ x4 + 4\ x6 \[LessEqual] 743, 4\ x1 + 6\ x2 + 15\ x3 + 6\ x5 + 4\ x6 \[LessEqual] 743, 4\ x1 + 6\ x2 + 15\ x4 + 6\ x5 + 4\ x6 \[LessEqual] 743, 4\ x1 + 6\ x3 + 6\ x4 + 15\ x5 + 4\ x6 \[LessEqual] 743, 6\ x2 + 4\ x3 + 4\ x4 + 6\ x5 + 15\ x6 \[LessEqual] 743, 4\ x2 + 6\ x3 + 6\ x4 + 4\ x5 + 15\ x6 \[LessEqual] 743, 9\ x1 + 6\ x2 - 2\ x3 + 4\ x5 + 6\ x6 \[LessEqual] 527, 9\ x1 + 4\ x2 - 2\ x4 + 6\ x5 + 6\ x6 \[LessEqual] 527, 9\ x1 + 4\ x3 + 6\ x4 - 2\ x5 + 6\ x6 \[LessEqual] 527, 9\ x1 - 2\ x2 + 6\ x3 + 4\ x4 + 6\ x6 \[LessEqual] 527, 6\ x1 + 9\ x2 - 2\ x3 + 6\ x5 + 4\ x6 \[LessEqual] 527, 6\ x1 + 6\ x2 - 2\ x4 + 9\ x5 + 4\ x6 \[LessEqual] 527, 6\ x1 + 6\ x2 - 2\ x4 + 4\ x5 + 9\ x6 \[LessEqual] 527, 6\ x1 + 4\ x2 - 2\ x3 + 6\ x5 + 9\ x6 \[LessEqual] 527, 6\ x1 + 6\ x3 + 9\ x4 - 2\ x5 + 4\ x6 \[LessEqual] 527, 6\ x1 + 6\ x3 + 4\ x4 - 2\ x5 + 9\ x6 \[LessEqual] 527, 6\ x1 - 2\ x2 + 9\ x3 + 6\ x4 + 4\ x6 \[LessEqual] 527, 6\ x1 - 2\ x2 + 4\ x3 + 6\ x4 + 9\ x6 \[LessEqual] 527, 4\ x1 + 9\ x2 - 2\ x4 + 6\ x5 + 6\ x6 \[LessEqual] 527, 4\ x1 + 6\ x2 - 2\ x3 + 9\ x5 + 6\ x6 \[LessEqual] 527, 4\ x1 + 9\ x3 + 6\ x4 - 2\ x5 + 6\ x6 \[LessEqual] 527, 4\ x1 - 2\ x2 + 6\ x3 + 9\ x4 + 6\ x6 \[LessEqual] 527, 9\ x2 + 4\ x3 + 6\ x4 + 6\ x5 - 2\ x6 \[LessEqual] 527, 6\ x2 + 6\ x3 + 9\ x4 + 4\ x5 - 2\ x6 \[LessEqual] 527, 6\ x2 + 6\ x3 + 4\ x4 + 9\ x5 - 2\ x6 \[LessEqual] 527, 4\ x2 + 9\ x3 + 6\ x4 + 6\ x5 - 2\ x6 \[LessEqual] 527, \(-2\)\ x1 + 9\ x2 + 6\ x3 + 4\ x4 + 6\ x5 \[LessEqual] 527, \(-2\)\ x1 + 6\ x2 + 9\ x3 + 6\ x4 + 4\ x5 \[LessEqual] 527, \(-2\)\ x1 + 6\ x2 + 4\ x3 + 6\ x4 + 9\ x5 \[LessEqual] 527, \(-2\)\ x1 + 4\ x2 + 6\ x3 + 9\ x4 + 6\ x5 \[LessEqual] 527, 11\ x1 + 8\ x2 + 2\ x3 + 2\ x4 + 2\ x5 + 5\ x6 \[LessEqual] 636, 11\ x1 + 2\ x2 + 8\ x3 + 2\ x4 + 2\ x5 + 5\ x6 \[LessEqual] 636, 11\ x1 + 2\ x2 + 2\ x3 + 8\ x4 + 2\ x5 + 5\ x6 \[LessEqual] 636, 11\ x1 + 2\ x2 + 2\ x3 + 2\ x4 + 8\ x5 + 5\ x6 \[LessEqual] 636, 8\ x1 + 11\ x2 + 2\ x3 + 2\ x4 + 5\ x5 + 2\ x6 \[LessEqual] 636, 8\ x1 + 5\ x2 + 2\ x3 + 2\ x4 + 11\ x5 + 2\ x6 \[LessEqual] 636, 8\ x1 + 2\ x2 + 11\ x3 + 5\ x4 + 2\ x5 + 2\ x6 \[LessEqual] 636, 8\ x1 + 2\ x2 + 5\ x3 + 11\ x4 + 2\ x5 + 2\ x6 \[LessEqual] 636, 5\ x1 + 8\ x2 + 2\ x3 + 2\ x4 + 2\ x5 + 11\ x6 \[LessEqual] 636, 5\ x1 + 2\ x2 + 8\ x3 + 2\ x4 + 2\ x5 + 11\ x6 \[LessEqual] 636, 5\ x1 + 2\ x2 + 2\ x3 + 8\ x4 + 2\ x5 + 11\ x6 \[LessEqual] 636, 5\ x1 + 2\ x2 + 2\ x3 + 2\ x4 + 8\ x5 + 11\ x6 \[LessEqual] 636, 2\ x1 + 11\ x2 + 8\ x3 + 2\ x4 + 5\ x5 + 2\ x6 \[LessEqual] 636, 2\ x1 + 11\ x2 + 2\ x3 + 8\ x4 + 5\ x5 + 2\ x6 \[LessEqual] 636, 2\ x1 + 11\ x2 + 2\ x3 + 2\ x4 + 5\ x5 + 8\ x6 \[LessEqual] 636, 2\ x1 + 8\ x2 + 11\ x3 + 5\ x4 + 2\ x5 + 2\ x6 \[LessEqual] 636, 2\ x1 + 8\ x2 + 5\ x3 + 11\ x4 + 2\ x5 + 2\ x6 \[LessEqual] 636, 2\ x1 + 5\ x2 + 8\ x3 + 2\ x4 + 11\ x5 + 2\ x6 \[LessEqual] 636, 2\ x1 + 5\ x2 + 2\ x3 + 8\ x4 + 11\ x5 + 2\ x6 \[LessEqual] 636, 2\ x1 + 5\ x2 + 2\ x3 + 2\ x4 + 11\ x5 + 8\ x6 \[LessEqual] 636, 2\ x1 + 2\ x2 + 11\ x3 + 5\ x4 + 8\ x5 + 2\ x6 \[LessEqual] 636, 2\ x1 + 2\ x2 + 11\ x3 + 5\ x4 + 2\ x5 + 8\ x6 \[LessEqual] 636, 2\ x1 + 2\ x2 + 5\ x3 + 11\ x4 + 8\ x5 + 2\ x6 \[LessEqual] 636, 2\ x1 + 2\ x2 + 5\ x3 + 11\ x4 + 2\ x5 + 8\ x6 \[LessEqual] 636, 3\ x1 - 2\ x5 \[LessEqual] 79, 3\ x1 - 2\ x4 \[LessEqual] 79, 3\ x1 - 2\ x3 \[LessEqual] 79, 3\ x1 - 2\ x2 \[LessEqual] 79, 3\ x2 - 2\ x6 \[LessEqual] 79, 3\ x2 - 2\ x4 \[LessEqual] 79, 3\ x2 - 2\ x3 \[LessEqual] 79, 3\ x3 - 2\ x6 \[LessEqual] 79, 3\ x3 - 2\ x5 \[LessEqual] 79, 3\ x4 - 2\ x6 \[LessEqual] 79, 3\ x4 - 2\ x5 \[LessEqual] 79, 3\ x5 - 2\ x6 \[LessEqual] 79, \(-2\)\ x5 + 3\ x6 \[LessEqual] 79, \(-2\)\ x4 + 3\ x5 \[LessEqual] 79, \(-2\)\ x4 + 3\ x6 \[LessEqual] 79, \(-2\)\ x3 + 3\ x5 \[LessEqual] 79, \(-2\)\ x3 + 3\ x6 \[LessEqual] 79, \(-2\)\ x2 + 3\ x3 \[LessEqual] 79, \(-2\)\ x2 + 3\ x4 \[LessEqual] 79, \(-2\)\ x2 + 3\ x6 \[LessEqual] 79, \(-2\)\ x1 + 3\ x2 \[LessEqual] 79, \(-2\)\ x1 + 3\ x3 \[LessEqual] 79, \(-2\)\ x1 + 3\ x4 \[LessEqual] 79, \(-2\)\ x1 + 3\ x5 \[LessEqual] 79, 6\ x1 + 3\ x2 + 2\ x3 + 2\ x4 + 3\ x5 \[LessEqual] 334, 6\ x1 + 2\ x2 + 3\ x3 + 3\ x4 + 2\ x5 \[LessEqual] 334, 3\ x1 + 6\ x2 + 2\ x3 + 2\ x4 + 3\ x6 \[LessEqual] 334, 3\ x1 + 2\ x2 + 6\ x3 + 2\ x5 + 3\ x6 \[LessEqual] 334, 3\ x1 + 2\ x2 + 6\ x4 + 2\ x5 + 3\ x6 \[LessEqual] 334, 3\ x1 + 2\ x3 + 2\ x4 + 6\ x5 + 3\ x6 \[LessEqual] 334, 2\ x1 + 6\ x2 + 3\ x3 + 3\ x4 + 2\ x6 \[LessEqual] 334, 2\ x1 + 3\ x2 + 6\ x3 + 3\ x5 + 2\ x6 \[LessEqual] 334, 2\ x1 + 3\ x2 + 6\ x4 + 3\ x5 + 2\ x6 \[LessEqual] 334, 2\ x1 + 3\ x3 + 3\ x4 + 6\ x5 + 2\ x6 \[LessEqual] 334, 3\ x2 + 2\ x3 + 2\ x4 + 3\ x5 + 6\ x6 \[LessEqual] 334, 2\ x2 + 3\ x3 + 3\ x4 + 2\ x5 + 6\ x6 \[LessEqual] 334, x1 - 2\ x5 + x6 \[LessEqual] 48, x1 - 2\ x4 + x6 \[LessEqual] 48, x1 - 2\ x3 + x6 \[LessEqual] 48, x1 - 2\ x2 + x6 \[LessEqual] 48, x2 + x5 - 2\ x6 \[LessEqual] 48, x2 - 2\ x4 + x5 \[LessEqual] 48, x2 - 2\ x3 + x5 \[LessEqual] 48, x3 + x4 - 2\ x6 \[LessEqual] 48, x3 + x4 - 2\ x5 \[LessEqual] 48, \(-2\)\ x2 + x3 + x4 \[LessEqual] 48, \(-2\)\ x1 + x2 + x5 \[LessEqual] 48, \(-2\)\ x1 + x3 + x4 \[LessEqual] 48, 3\ x1 - 2\ x3 - 12\ x5 - 2\ x6 \[LessEqual] 5, 3\ x1 - 12\ x3 - 2\ x5 - 2\ x6 \[LessEqual] 5, 3\ x1 - 2\ x2 - 12\ x4 - 2\ x6 \[LessEqual] 5, 3\ x1 - 12\ x2 - 2\ x4 - 2\ x6 \[LessEqual] 5, 3\ x2 - 2\ x3 - 2\ x5 - 12\ x6 \[LessEqual] 5, 3\ x2 - 12\ x3 - 2\ x5 - 2\ x6 \[LessEqual] 5, \(-2\)\ x3 + 3\ x4 - 2\ x5 - 12\ x6 \[LessEqual] 5, \(-2\)\ x3 + 3\ x4 - 12\ x5 - 2\ x6 \[LessEqual] 5, \(-2\)\ x2 + 3\ x3 - 2\ x4 - 12\ x6 \[LessEqual] 5, \(-2\)\ x2 - 2\ x4 + 3\ x5 - 12\ x6 \[LessEqual] 5, \(-2\)\ x2 - 12\ x4 + 3\ x5 - 2\ x6 \[LessEqual] 5, \(-12\)\ x2 + 3\ x3 - 2\ x4 - 2\ x6 \[LessEqual] 5, \(-2\)\ x1 + 3\ x2 - 12\ x4 - 2\ x5 \[LessEqual] 5, \(-2\)\ x1 + 3\ x3 - 2\ x4 - 12\ x5 \[LessEqual] 5, \(-2\)\ x1 - 2\ x4 - 12\ x5 + 3\ x6 \[LessEqual] 5, \(-2\)\ x1 - 12\ x4 - 2\ x5 + 3\ x6 \[LessEqual] 5, \(-2\)\ x1 - 2\ x2 - 12\ x3 + 3\ x5 \[LessEqual] 5, \(-2\)\ x1 - 2\ x2 - 12\ x3 + 3\ x6 \[LessEqual] 5, \(-2\)\ x1 - 12\ x2 - 2\ x3 + 3\ x4 \[LessEqual] 5, \(-2\)\ x1 - 12\ x2 - 2\ x3 + 3\ x6 \[LessEqual] 5, \(-12\)\ x1 + 3\ x2 - 2\ x4 - 2\ x5 \[LessEqual] 5, \(-12\)\ x1 + 3\ x3 - 2\ x4 - 2\ x5 \[LessEqual] 5, \(-12\)\ x1 - 2\ x2 - 2\ x3 + 3\ x4 \[LessEqual] 5, \(-12\)\ x1 - 2\ x2 - 2\ x3 + 3\ x5 \[LessEqual] 5, x1 - 8\ x3 - 2\ x4 - 2\ x5 - 2\ x6 \[LessEqual] \(-71\), x1 - 2\ x2 - 2\ x3 - 8\ x5 - 2\ x6 \[LessEqual] \(-71\), x1 - 2\ x2 - 2\ x3 - 8\ x4 - 2\ x6 \[LessEqual] \(-71\), x1 - 8\ x2 - 2\ x4 - 2\ x5 - 2\ x6 \[LessEqual] \(-71\), x2 - 8\ x3 - 2\ x4 - 2\ x5 - 2\ x6 \[LessEqual] \(-71\), \(-2\)\ x2 - 2\ x3 + x4 - 8\ x5 - 2\ x6 \[LessEqual] \(-71\), \(-2\)\ x2 - 2\ x3 - 8\ x4 + x5 - 2\ x6 \[LessEqual] \(-71\), \(-8\)\ x2 + x3 - 2\ x4 - 2\ x5 - 2\ x6 \[LessEqual] \(-71\), \(-2\)\ x1 + x2 - 2\ x3 - 2\ x5 - 8\ x6 \[LessEqual] \(-71\), \(-2\)\ x1 + x2 - 2\ x3 - 8\ x4 - 2\ x5 \[LessEqual] \(-71\), \(-2\)\ x1 - 2\ x3 + x4 - 2\ x5 - 8\ x6 \[LessEqual] \(-71\), \(-2\)\ x1 - 2\ x3 - 8\ x4 - 2\ x5 + x6 \[LessEqual] \(-71\), \(-2\)\ x1 - 2\ x2 + x3 - 2\ x4 - 8\ x6 \[LessEqual] \(-71\), \(-2\)\ x1 - 2\ x2 + x3 - 2\ x4 - 8\ x5 \[LessEqual] \(-71\), \(-2\)\ x1 - 2\ x2 - 2\ x4 + x5 - 8\ x6 \[LessEqual] \(-71\), \(-2\)\ x1 - 2\ x2 - 2\ x4 - 8\ x5 + x6 \[LessEqual] \(-71\), \(-2\)\ x1 - 2\ x2 - 8\ x3 - 2\ x4 + x5 \[LessEqual] \(-71\), \(-2\)\ x1 - 2\ x2 - 8\ x3 - 2\ x4 + x6 \[LessEqual] \(-71\), \(-2\)\ x1 - 8\ x2 - 2\ x3 + x4 - 2\ x5 \[LessEqual] \(-71\), \(-2\)\ x1 - 8\ x2 - 2\ x3 - 2\ x5 + x6 \[LessEqual] \(-71\), \(-8\)\ x1 + x2 - 2\ x4 - 2\ x5 - 2\ x6 \[LessEqual] \(-71\), \(-8\)\ x1 + x3 - 2\ x4 - 2\ x5 - 2\ x6 \[LessEqual] \(-71\), \(-8\)\ x1 - 2\ x2 - 2\ x3 + x4 - 2\ x6 \[LessEqual] \(-71\), \(-8\)\ x1 - 2\ x2 - 2\ x3 + x5 - 2\ x6 \[LessEqual] \(-71\), 10\ x1 + 7\ x2 - 2\ x3 + 6\ x5 + 4\ x6 \[LessEqual] 569, 10\ x1 + 6\ x2 - 2\ x4 + 7\ x5 + 4\ x6 \[LessEqual] 569, 10\ x1 + 6\ x3 + 7\ x4 - 2\ x5 + 4\ x6 \[LessEqual] 569, 10\ x1 - 2\ x2 + 7\ x3 + 6\ x4 + 4\ x6 \[LessEqual] 569, 7\ x1 + 10\ x2 - 2\ x3 + 4\ x5 + 6\ x6 \[LessEqual] 569, 7\ x1 + 4\ x2 - 2\ x4 + 10\ x5 + 6\ x6 \[LessEqual] 569, 7\ x1 + 4\ x3 + 10\ x4 - 2\ x5 + 6\ x6 \[LessEqual] 569, 7\ x1 - 2\ x2 + 10\ x3 + 4\ x4 + 6\ x6 \[LessEqual] 569, 6\ x1 + 10\ x2 - 2\ x4 + 4\ x5 + 7\ x6 \[LessEqual] 569, 6\ x1 + 4\ x2 - 2\ x3 + 10\ x5 + 7\ x6 \[LessEqual] 569, 6\ x1 + 10\ x3 + 4\ x4 - 2\ x5 + 7\ x6 \[LessEqual] 569, 6\ x1 - 2\ x2 + 4\ x3 + 10\ x4 + 7\ x6 \[LessEqual] 569, 4\ x1 + 7\ x2 - 2\ x4 + 6\ x5 + 10\ x6 \[LessEqual] 569, 4\ x1 + 6\ x2 - 2\ x3 + 7\ x5 + 10\ x6 \[LessEqual] 569, 4\ x1 + 7\ x3 + 6\ x4 - 2\ x5 + 10\ x6 \[LessEqual] 569, 4\ x1 - 2\ x2 + 6\ x3 + 7\ x4 + 10\ x6 \[LessEqual] 569, 10\ x2 + 6\ x3 + 7\ x4 + 4\ x5 - 2\ x6 \[LessEqual] 569, 7\ x2 + 4\ x3 + 10\ x4 + 6\ x5 - 2\ x6 \[LessEqual] 569, 6\ x2 + 10\ x3 + 4\ x4 + 7\ x5 - 2\ x6 \[LessEqual] 569, 4\ x2 + 7\ x3 + 6\ x4 + 10\ x5 - 2\ x6 \[LessEqual] 569, \(-2\)\ x1 + 10\ x2 + 7\ x3 + 6\ x4 + 4\ x5 \[LessEqual] 569, \(-2\)\ x1 + 7\ x2 + 10\ x3 + 4\ x4 + 6\ x5 \[LessEqual] 569, \(-2\)\ x1 + 6\ x2 + 4\ x3 + 10\ x4 + 7\ x5 \[LessEqual] 569, \(-2\)\ x1 + 4\ x2 + 6\ x3 + 7\ x4 + 10\ x5 \[LessEqual] 569, 3\ x1 - 8\ x3 - 6\ x4 - 6\ x5 - 6\ x6 \[LessEqual] \(-197\), 3\ x1 - 6\ x2 - 6\ x3 - 8\ x5 - 6\ x6 \[LessEqual] \(-197\), 3\ x1 - 6\ x2 - 6\ x3 - 8\ x4 - 6\ x6 \[LessEqual] \(-197\), 3\ x1 - 8\ x2 - 6\ x4 - 6\ x5 - 6\ x6 \[LessEqual] \(-197\), 3\ x2 - 8\ x3 - 6\ x4 - 6\ x5 - 6\ x6 \[LessEqual] \(-197\), \(-6\)\ x2 - 6\ x3 + 3\ x4 - 8\ x5 - 6\ x6 \[LessEqual] \(-197\), \(-6\)\ x2 - 6\ x3 - 8\ x4 + 3\ x5 - 6\ x6 \[LessEqual] \(-197\), \(-8\)\ x2 + 3\ x3 - 6\ x4 - 6\ x5 - 6\ x6 \[LessEqual] \(-197\), \(-6\)\ x1 + 3\ x2 - 6\ x3 - 6\ x5 - 8\ x6 \[LessEqual] \(-197\), \(-6\)\ x1 + 3\ x2 - 6\ x3 - 8\ x4 - 6\ x5 \[LessEqual] \(-197\), \(-6\)\ x1 - 6\ x3 + 3\ x4 - 6\ x5 - 8\ x6 \[LessEqual] \(-197\), \(-6\)\ x1 - 6\ x3 - 8\ x4 - 6\ x5 + 3\ x6 \[LessEqual] \(-197\), \(-6\)\ x1 - 6\ x2 + 3\ x3 - 6\ x4 - 8\ x6 \[LessEqual] \(-197\), \(-6\)\ x1 - 6\ x2 + 3\ x3 - 6\ x4 - 8\ x5 \[LessEqual] \(-197\), \(-6\)\ x1 - 6\ x2 - 6\ x4 + 3\ x5 - 8\ x6 \[LessEqual] \(-197\), \(-6\)\ x1 - 6\ x2 - 6\ x4 - 8\ x5 + 3\ x6 \[LessEqual] \(-197\), \(-6\)\ x1 - 6\ x2 - 8\ x3 - 6\ x4 + 3\ x5 \[LessEqual] \(-197\), \(-6\)\ x1 - 6\ x2 - 8\ x3 - 6\ x4 + 3\ x6 \[LessEqual] \(-197\), \(-6\)\ x1 - 8\ x2 - 6\ x3 + 3\ x4 - 6\ x5 \[LessEqual] \(-197\), \(-6\)\ x1 - 8\ x2 - 6\ x3 - 6\ x5 + 3\ x6 \[LessEqual] \(-197\), \(-8\)\ x1 + 3\ x2 - 6\ x4 - 6\ x5 - 6\ x6 \[LessEqual] \(-197\), \(-8\)\ x1 + 3\ x3 - 6\ x4 - 6\ x5 - 6\ x6 \[LessEqual] \(-197\), \(-8\)\ x1 - 6\ x2 - 6\ x3 + 3\ x4 - 6\ x6 \[LessEqual] \(-197\), \(-8\)\ x1 - 6\ x2 - 6\ x3 + 3\ x5 - 6\ x6 \[LessEqual] \(-197\), 15\ x1 + 6\ x2 + 6\ x3 + 6\ x4 + 4\ x5 \[LessEqual] 775, 15\ x1 + 6\ x2 + 6\ x3 + 4\ x4 + 6\ x5 \[LessEqual] 775, 15\ x1 + 6\ x2 + 4\ x3 + 6\ x4 + 6\ x5 \[LessEqual] 775, 15\ x1 + 4\ x2 + 6\ x3 + 6\ x4 + 6\ x5 \[LessEqual] 775, 6\ x1 + 15\ x2 + 6\ x3 + 6\ x4 + 4\ x6 \[LessEqual] 775, 6\ x1 + 15\ x2 + 6\ x3 + 4\ x4 + 6\ x6 \[LessEqual] 775, 6\ x1 + 15\ x2 + 4\ x3 + 6\ x4 + 6\ x6 \[LessEqual] 775, 6\ x1 + 6\ x2 + 15\ x3 + 6\ x5 + 4\ x6 \[LessEqual] 775, 6\ x1 + 6\ x2 + 15\ x3 + 4\ x5 + 6\ x6 \[LessEqual] 775, 6\ x1 + 6\ x2 + 15\ x4 + 6\ x5 + 4\ x6 \[LessEqual] 775, 6\ x1 + 6\ x2 + 15\ x4 + 4\ x5 + 6\ x6 \[LessEqual] 775, 6\ x1 + 4\ x2 + 15\ x3 + 6\ x5 + 6\ x6 \[LessEqual] 775, 6\ x1 + 4\ x2 + 15\ x4 + 6\ x5 + 6\ x6 \[LessEqual] 775, 6\ x1 + 6\ x3 + 6\ x4 + 15\ x5 + 4\ x6 \[LessEqual] 775, 6\ x1 + 6\ x3 + 4\ x4 + 15\ x5 + 6\ x6 \[LessEqual] 775, 6\ x1 + 4\ x3 + 6\ x4 + 15\ x5 + 6\ x6 \[LessEqual] 775, 4\ x1 + 15\ x2 + 6\ x3 + 6\ x4 + 6\ x6 \[LessEqual] 775, 4\ x1 + 6\ x2 + 15\ x3 + 6\ x5 + 6\ x6 \[LessEqual] 775, 4\ x1 + 6\ x2 + 15\ x4 + 6\ x5 + 6\ x6 \[LessEqual] 775, 4\ x1 + 6\ x3 + 6\ x4 + 15\ x5 + 6\ x6 \[LessEqual] 775, 6\ x2 + 6\ x3 + 6\ x4 + 4\ x5 + 15\ x6 \[LessEqual] 775, 6\ x2 + 6\ x3 + 4\ x4 + 6\ x5 + 15\ x6 \[LessEqual] 775, 6\ x2 + 4\ x3 + 6\ x4 + 6\ x5 + 15\ x6 \[LessEqual] 775, 4\ x2 + 6\ x3 + 6\ x4 + 6\ x5 + 15\ x6 \[LessEqual] 775, 2\ x1 - x2 - 2\ x3 - 2\ x4 - x5 - 4\ x6 \[LessEqual] \(-62\), 2\ x1 - 2\ x2 - x3 - x4 - 2\ x5 - 4\ x6 \[LessEqual] \(-62\), \(-x1\) + 2\ x2 - 2\ x3 - 2\ x4 - 4\ x5 - x6 \[LessEqual] \(-62\), \(-x1\) - 2\ x2 + 2\ x3 - 4\ x4 - 2\ x5 - x6 \[LessEqual] \(-62\), \(-x1\) - 2\ x2 - 4\ x3 + 2\ x4 - 2\ x5 - x6 \[LessEqual] \(-62\), \(-x1\) - 4\ x2 - 2\ x3 - 2\ x4 + 2\ x5 - x6 \[LessEqual] \(-62\), \(-2\)\ x1 + 2\ x2 - x3 - x4 - 4\ x5 - 2\ x6 \[LessEqual] \(-62\), \(-2\)\ x1 - x2 + 2\ x3 - 4\ x4 - x5 - 2\ x6 \[LessEqual] \(-62\), \(-2\)\ x1 - x2 - 4\ x3 + 2\ x4 - x5 - 2\ x6 \[LessEqual] \(-62\), \(-2\)\ x1 - 4\ x2 - x3 - x4 + 2\ x5 - 2\ x6 \[LessEqual] \(-62\), \(-4\)\ x1 - x2 - 2\ x3 - 2\ x4 - x5 + 2\ x6 \[LessEqual] \(-62\), \(-4\)\ x1 - 2\ x2 - x3 - x4 - 2\ x5 + 2\ x6 \[LessEqual] \(-62\), 6\ x1 + 3\ x2 + 2\ x3 + 3\ x4 + 2\ x5 \[LessEqual] 334, 6\ x1 + 2\ x2 + 3\ x3 + 2\ x4 + 3\ x5 \[LessEqual] 334, 3\ x1 + 6\ x2 + 2\ x3 + 3\ x4 + 2\ x6 \[LessEqual] 334, 3\ x1 + 3\ x2 + 6\ x4 + 2\ x5 + 2\ x6 \[LessEqual] 334, 3\ x1 + 2\ x2 + 6\ x3 + 3\ x5 + 2\ x6 \[LessEqual] 334, 3\ x1 + 3\ x3 + 2\ x4 + 6\ x5 + 2\ x6 \[LessEqual] 334, 2\ x1 + 6\ x2 + 3\ x3 + 2\ x4 + 3\ x6 \[LessEqual] 334, 2\ x1 + 3\ x2 + 6\ x3 + 2\ x5 + 3\ x6 \[LessEqual] 334, 2\ x1 + 2\ x2 + 6\ x4 + 3\ x5 + 3\ x6 \[LessEqual] 334, 2\ x1 + 2\ x3 + 3\ x4 + 6\ x5 + 3\ x6 \[LessEqual] 334, 3\ x2 + 3\ x3 + 2\ x4 + 2\ x5 + 6\ x6 \[LessEqual] 334, 2\ x2 + 2\ x3 + 3\ x4 + 3\ x5 + 6\ x6 \[LessEqual] 334, 3\ x1 - 6\ x2 - 6\ x3 - 6\ x4 - 8\ x5 - 12\ x6 \[LessEqual] \(-401\), 3\ x1 - 6\ x2 - 6\ x3 - 8\ x4 - 6\ x5 - 12\ x6 \[LessEqual] \(-401\), 3\ x1 - 6\ x2 - 8\ x3 - 6\ x4 - 6\ x5 - 12\ x6 \[LessEqual] \(-401\), 3\ x1 - 8\ x2 - 6\ x3 - 6\ x4 - 6\ x5 - 12\ x6 \[LessEqual] \(-401\), \(-6\)\ x1 + 3\ x2 - 6\ x3 - 6\ x4 - 12\ x5 - 8\ x6 \[LessEqual] \(-401\), \(-6\)\ x1 + 3\ x2 - 6\ x3 - 8\ x4 - 12\ x5 - 6\ x6 \[LessEqual] \(-401\), \(-6\)\ x1 + 3\ x2 - 8\ x3 - 6\ x4 - 12\ x5 - 6\ x6 \[LessEqual] \(-401\), \(-6\)\ x1 - 6\ x2 + 3\ x3 - 12\ x4 - 6\ x5 - 8\ x6 \[LessEqual] \(-401\), \(-6\)\ x1 - 6\ x2 + 3\ x3 - 12\ x4 - 8\ x5 - 6\ x6 \[LessEqual] \(-401\), \(-6\)\ x1 - 6\ x2 - 12\ x3 + 3\ x4 - 6\ x5 - 8\ x6 \[LessEqual] \(-401\), \(-6\)\ x1 - 6\ x2 - 12\ x3 + 3\ x4 - 8\ x5 - 6\ x6 \[LessEqual] \(-401\), \(-6\)\ x1 - 8\ x2 + 3\ x3 - 12\ x4 - 6\ x5 - 6\ x6 \[LessEqual] \(-401\), \(-6\)\ x1 - 8\ x2 - 12\ x3 + 3\ x4 - 6\ x5 - 6\ x6 \[LessEqual] \(-401\), \(-6\)\ x1 - 12\ x2 - 6\ x3 - 6\ x4 + 3\ x5 - 8\ x6 \[LessEqual] \(-401\), \(-6\)\ x1 - 12\ x2 - 6\ x3 - 8\ x4 + 3\ x5 - 6\ x6 \[LessEqual] \(-401\), \(-6\)\ x1 - 12\ x2 - 8\ x3 - 6\ x4 + 3\ x5 - 6\ x6 \[LessEqual] \(-401\), \(-8\)\ x1 + 3\ x2 - 6\ x3 - 6\ x4 - 12\ x5 - 6\ x6 \[LessEqual] \(-401\), \(-8\)\ x1 - 6\ x2 + 3\ x3 - 12\ x4 - 6\ x5 - 6\ x6 \[LessEqual] \(-401\), \(-8\)\ x1 - 6\ x2 - 12\ x3 + 3\ x4 - 6\ x5 - 6\ x6 \[LessEqual] \(-401\), \(-8\)\ x1 - 12\ x2 - 6\ x3 - 6\ x4 + 3\ x5 - 6\ x6 \[LessEqual] \(-401\), \(-12\)\ x1 - 6\ x2 - 6\ x3 - 6\ x4 - 8\ x5 + 3\ x6 \[LessEqual] \(-401\), \(-12\)\ x1 - 6\ x2 - 6\ x3 - 8\ x4 - 6\ x5 + 3\ x6 \[LessEqual] \(-401\), \(-12\)\ x1 - 6\ x2 - 8\ x3 - 6\ x4 - 6\ x5 + 3\ x6 \[LessEqual] \(-401\), \(-12\)\ x1 - 8\ x2 - 6\ x3 - 6\ x4 - 6\ x5 + 3\ x6 \[LessEqual] \(-401\), 5\ x1 - 4\ x2 - 4\ x3 - 4\ x4 - 6\ x5 - 10\ x6 \[LessEqual] \(-215\), 5\ x1 - 4\ x2 - 4\ x3 - 6\ x4 - 4\ x5 - 10\ x6 \[LessEqual] \(-215\), 5\ x1 - 4\ x2 - 6\ x3 - 4\ x4 - 4\ x5 - 10\ x6 \[LessEqual] \(-215\), 5\ x1 - 6\ x2 - 4\ x3 - 4\ x4 - 4\ x5 - 10\ x6 \[LessEqual] \(-215\), \(-4\)\ x1 + 5\ x2 - 4\ x3 - 4\ x4 - 10\ x5 - 6\ x6 \[LessEqual] \(-215\), \(-4\)\ x1 + 5\ x2 - 4\ x3 - 6\ x4 - 10\ x5 - 4\ x6 \[LessEqual] \(-215\), \(-4\)\ x1 + 5\ x2 - 6\ x3 - 4\ x4 - 10\ x5 - 4\ x6 \[LessEqual] \(-215\), \(-4\)\ x1 - 4\ x2 + 5\ x3 - 10\ x4 - 4\ x5 - 6\ x6 \[LessEqual] \(-215\), \(-4\)\ x1 - 4\ x2 + 5\ x3 - 10\ x4 - 6\ x5 - 4\ x6 \[LessEqual] \(-215\), \(-4\)\ x1 - 4\ x2 - 10\ x3 + 5\ x4 - 4\ x5 - 6\ x6 \[LessEqual] \(-215\), \(-4\)\ x1 - 4\ x2 - 10\ x3 + 5\ x4 - 6\ x5 - 4\ x6 \[LessEqual] \(-215\), \(-4\)\ x1 - 6\ x2 + 5\ x3 - 10\ x4 - 4\ x5 - 4\ x6 \[LessEqual] \(-215\), \(-4\)\ x1 - 6\ x2 - 10\ x3 + 5\ x4 - 4\ x5 - 4\ x6 \[LessEqual] \(-215\), \(-4\)\ x1 - 10\ x2 - 4\ x3 - 4\ x4 + 5\ x5 - 6\ x6 \[LessEqual] \(-215\), \(-4\)\ x1 - 10\ x2 - 4\ x3 - 6\ x4 + 5\ x5 - 4\ x6 \[LessEqual] \(-215\), \(-4\)\ x1 - 10\ x2 - 6\ x3 - 4\ x4 + 5\ x5 - 4\ x6 \[LessEqual] \(-215\), \(-6\)\ x1 + 5\ x2 - 4\ x3 - 4\ x4 - 10\ x5 - 4\ x6 \[LessEqual] \(-215\), \(-6\)\ x1 - 4\ x2 + 5\ x3 - 10\ x4 - 4\ x5 - 4\ x6 \[LessEqual] \(-215\), \(-6\)\ x1 - 4\ x2 - 10\ x3 + 5\ x4 - 4\ x5 - 4\ x6 \[LessEqual] \(-215\), \(-6\)\ x1 - 10\ x2 - 4\ x3 - 4\ x4 + 5\ x5 - 4\ x6 \[LessEqual] \(-215\), \(-10\)\ x1 - 4\ x2 - 4\ x3 - 4\ x4 - 6\ x5 + 5\ x6 \[LessEqual] \(-215\), \(-10\)\ x1 - 4\ x2 - 4\ x3 - 6\ x4 - 4\ x5 + 5\ x6 \[LessEqual] \(-215\), \(-10\)\ x1 - 4\ x2 - 6\ x3 - 4\ x4 - 4\ x5 + 5\ x6 \[LessEqual] \(-215\), \(-10\)\ x1 - 6\ x2 - 4\ x3 - 4\ x4 - 4\ x5 + 5\ x6 \[LessEqual] \(-215\), 9\ x1 - 2\ x5 - 6\ x6 \[LessEqual] 169, 9\ x1 - 2\ x4 - 6\ x6 \[LessEqual] 169, 9\ x1 - 2\ x3 - 6\ x6 \[LessEqual] 169, 9\ x1 - 2\ x2 - 6\ x6 \[LessEqual] 169, 9\ x2 - 6\ x5 - 2\ x6 \[LessEqual] 169, 9\ x2 - 2\ x4 - 6\ x5 \[LessEqual] 169, 9\ x2 - 2\ x3 - 6\ x5 \[LessEqual] 169, 9\ x3 - 6\ x4 - 2\ x6 \[LessEqual] 169, 9\ x3 - 6\ x4 - 2\ x5 \[LessEqual] 169, \(-6\)\ x3 + 9\ x4 - 2\ x6 \[LessEqual] 169, \(-6\)\ x3 + 9\ x4 - 2\ x5 \[LessEqual] 169, \(-2\)\ x2 + 9\ x3 - 6\ x4 \[LessEqual] 169, \(-2\)\ x2 - 6\ x3 + 9\ x4 \[LessEqual] 169, \(-6\)\ x2 + 9\ x5 - 2\ x6 \[LessEqual] 169, \(-6\)\ x2 - 2\ x4 + 9\ x5 \[LessEqual] 169, \(-6\)\ x2 - 2\ x3 + 9\ x5 \[LessEqual] 169, \(-2\)\ x1 + 9\ x2 - 6\ x5 \[LessEqual] 169, \(-2\)\ x1 + 9\ x3 - 6\ x4 \[LessEqual] 169, \(-2\)\ x1 - 6\ x3 + 9\ x4 \[LessEqual] 169, \(-2\)\ x1 - 6\ x2 + 9\ x5 \[LessEqual] 169, \(-6\)\ x1 - 2\ x5 + 9\ x6 \[LessEqual] 169, \(-6\)\ x1 - 2\ x4 + 9\ x6 \[LessEqual] 169, \(-6\)\ x1 - 2\ x3 + 9\ x6 \[LessEqual] 169, \(-6\)\ x1 - 2\ x2 + 9\ x6 \[LessEqual] 169, 11\ x1 + 2\ x2 + 2\ x3 + 2\ x4 - 4\ x6 \[LessEqual] 367, 11\ x1 + 2\ x2 + 2\ x3 + 2\ x5 - 4\ x6 \[LessEqual] 367, 11\ x1 + 2\ x2 + 2\ x4 + 2\ x5 - 4\ x6 \[LessEqual] 367, 11\ x1 + 2\ x3 + 2\ x4 + 2\ x5 - 4\ x6 \[LessEqual] 367, 2\ x1 + 11\ x2 + 2\ x3 + 2\ x4 - 4\ x5 \[LessEqual] 367, 2\ x1 + 11\ x2 + 2\ x3 - 4\ x5 + 2\ x6 \[LessEqual] 367, 2\ x1 + 11\ x2 + 2\ x4 - 4\ x5 + 2\ x6 \[LessEqual] 367, 2\ x1 + 2\ x2 + 11\ x3 - 4\ x4 + 2\ x5 \[LessEqual] 367, 2\ x1 + 2\ x2 + 11\ x3 - 4\ x4 + 2\ x6 \[LessEqual] 367, 2\ x1 + 2\ x2 - 4\ x3 + 11\ x4 + 2\ x5 \[LessEqual] 367, 2\ x1 + 2\ x2 - 4\ x3 + 11\ x4 + 2\ x6 \[LessEqual] 367, 2\ x1 + 11\ x3 - 4\ x4 + 2\ x5 + 2\ x6 \[LessEqual] 367, 2\ x1 - 4\ x3 + 11\ x4 + 2\ x5 + 2\ x6 \[LessEqual] 367, 2\ x1 - 4\ x2 + 2\ x3 + 2\ x4 + 11\ x5 \[LessEqual] 367, 2\ x1 - 4\ x2 + 2\ x3 + 11\ x5 + 2\ x6 \[LessEqual] 367, 2\ x1 - 4\ x2 + 2\ x4 + 11\ x5 + 2\ x6 \[LessEqual] 367, 11\ x2 + 2\ x3 + 2\ x4 - 4\ x5 + 2\ x6 \[LessEqual] 367, 2\ x2 + 11\ x3 - 4\ x4 + 2\ x5 + 2\ x6 \[LessEqual] 367, 2\ x2 - 4\ x3 + 11\ x4 + 2\ x5 + 2\ x6 \[LessEqual] 367, \(-4\)\ x2 + 2\ x3 + 2\ x4 + 11\ x5 + 2\ x6 \[LessEqual] 367, \(-4\)\ x1 + 2\ x2 + 2\ x3 + 2\ x4 + 11\ x6 \[LessEqual] 367, \(-4\)\ x1 + 2\ x2 + 2\ x3 + 2\ x5 + 11\ x6 \[LessEqual] 367, \(-4\)\ x1 + 2\ x2 + 2\ x4 + 2\ x5 + 11\ x6 \[LessEqual] 367, \(-4\)\ x1 + 2\ x3 + 2\ x4 + 2\ x5 + 11\ x6 \[LessEqual] 367, 8\ x1 + 5\ x2 + 2\ x3 + 2\ x4 + 2\ x5 + 2\ x6 \[LessEqual] 435, 8\ x1 + 2\ x2 + 5\ x3 + 2\ x4 + 2\ x5 + 2\ x6 \[LessEqual] 435, 8\ x1 + 2\ x2 + 2\ x3 + 5\ x4 + 2\ x5 + 2\ x6 \[LessEqual] 435, 8\ x1 + 2\ x2 + 2\ x3 + 2\ x4 + 5\ x5 + 2\ x6 \[LessEqual] 435, 5\ x1 + 8\ x2 + 2\ x3 + 2\ x4 + 2\ x5 + 2\ x6 \[LessEqual] 435, 5\ x1 + 2\ x2 + 8\ x3 + 2\ x4 + 2\ x5 + 2\ x6 \[LessEqual] 435, 5\ x1 + 2\ x2 + 2\ x3 + 8\ x4 + 2\ x5 + 2\ x6 \[LessEqual] 435, 5\ x1 + 2\ x2 + 2\ x3 + 2\ x4 + 8\ x5 + 2\ x6 \[LessEqual] 435, 2\ x1 + 8\ x2 + 5\ x3 + 2\ x4 + 2\ x5 + 2\ x6 \[LessEqual] 435, 2\ x1 + 8\ x2 + 2\ x3 + 5\ x4 + 2\ x5 + 2\ x6 \[LessEqual] 435, 2\ x1 + 8\ x2 + 2\ x3 + 2\ x4 + 2\ x5 + 5\ x6 \[LessEqual] 435, 2\ x1 + 5\ x2 + 8\ x3 + 2\ x4 + 2\ x5 + 2\ x6 \[LessEqual] 435, 2\ x1 + 5\ x2 + 2\ x3 + 8\ x4 + 2\ x5 + 2\ x6 \[LessEqual] 435, 2\ x1 + 5\ x2 + 2\ x3 + 2\ x4 + 2\ x5 + 8\ x6 \[LessEqual] 435, 2\ x1 + 2\ x2 + 8\ x3 + 2\ x4 + 5\ x5 + 2\ x6 \[LessEqual] 435, 2\ x1 + 2\ x2 + 8\ x3 + 2\ x4 + 2\ x5 + 5\ x6 \[LessEqual] 435, 2\ x1 + 2\ x2 + 5\ x3 + 2\ x4 + 8\ x5 + 2\ x6 \[LessEqual] 435, 2\ x1 + 2\ x2 + 5\ x3 + 2\ x4 + 2\ x5 + 8\ x6 \[LessEqual] 435, 2\ x1 + 2\ x2 + 2\ x3 + 8\ x4 + 5\ x5 + 2\ x6 \[LessEqual] 435, 2\ x1 + 2\ x2 + 2\ x3 + 8\ x4 + 2\ x5 + 5\ x6 \[LessEqual] 435, 2\ x1 + 2\ x2 + 2\ x3 + 5\ x4 + 8\ x5 + 2\ x6 \[LessEqual] 435, 2\ x1 + 2\ x2 + 2\ x3 + 5\ x4 + 2\ x5 + 8\ x6 \[LessEqual] 435, 2\ x1 + 2\ x2 + 2\ x3 + 2\ x4 + 8\ x5 + 5\ x6 \[LessEqual] 435, 2\ x1 + 2\ x2 + 2\ x3 + 2\ x4 + 5\ x5 + 8\ x6 \[LessEqual] 435, 19\ x1 + 10\ x2 + 4\ x3 + 4\ x4 + 4\ x5 + 4\ x6 \[LessEqual] 951, 19\ x1 + 4\ x2 + 10\ x3 + 4\ x4 + 4\ x5 + 4\ x6 \[LessEqual] 951, 19\ x1 + 4\ x2 + 4\ x3 + 10\ x4 + 4\ x5 + 4\ x6 \[LessEqual] 951, 19\ x1 + 4\ x2 + 4\ x3 + 4\ x4 + 10\ x5 + 4\ x6 \[LessEqual] 951, 10\ x1 + 19\ x2 + 4\ x3 + 4\ x4 + 4\ x5 + 4\ x6 \[LessEqual] 951, 10\ x1 + 4\ x2 + 19\ x3 + 4\ x4 + 4\ x5 + 4\ x6 \[LessEqual] 951, 10\ x1 + 4\ x2 + 4\ x3 + 19\ x4 + 4\ x5 + 4\ x6 \[LessEqual] 951, 10\ x1 + 4\ x2 + 4\ x3 + 4\ x4 + 19\ x5 + 4\ x6 \[LessEqual] 951, 4\ x1 + 19\ x2 + 10\ x3 + 4\ x4 + 4\ x5 + 4\ x6 \[LessEqual] 951, 4\ x1 + 19\ x2 + 4\ x3 + 10\ x4 + 4\ x5 + 4\ x6 \[LessEqual] 951, 4\ x1 + 19\ x2 + 4\ x3 + 4\ x4 + 4\ x5 + 10\ x6 \[LessEqual] 951, 4\ x1 + 10\ x2 + 19\ x3 + 4\ x4 + 4\ x5 + 4\ x6 \[LessEqual] 951, 4\ x1 + 10\ x2 + 4\ x3 + 19\ x4 + 4\ x5 + 4\ x6 \[LessEqual] 951, 4\ x1 + 10\ x2 + 4\ x3 + 4\ x4 + 4\ x5 + 19\ x6 \[LessEqual] 951, 4\ x1 + 4\ x2 + 19\ x3 + 4\ x4 + 10\ x5 + 4\ x6 \[LessEqual] 951, 4\ x1 + 4\ x2 + 19\ x3 + 4\ x4 + 4\ x5 + 10\ x6 \[LessEqual] 951, 4\ x1 + 4\ x2 + 10\ x3 + 4\ x4 + 19\ x5 + 4\ x6 \[LessEqual] 951, 4\ x1 + 4\ x2 + 10\ x3 + 4\ x4 + 4\ x5 + 19\ x6 \[LessEqual] 951, 4\ x1 + 4\ x2 + 4\ x3 + 19\ x4 + 10\ x5 + 4\ x6 \[LessEqual] 951, 4\ x1 + 4\ x2 + 4\ x3 + 19\ x4 + 4\ x5 + 10\ x6 \[LessEqual] 951, 4\ x1 + 4\ x2 + 4\ x3 + 10\ x4 + 19\ x5 + 4\ x6 \[LessEqual] 951, 4\ x1 + 4\ x2 + 4\ x3 + 10\ x4 + 4\ x5 + 19\ x6 \[LessEqual] 951, 4\ x1 + 4\ x2 + 4\ x3 + 4\ x4 + 19\ x5 + 10\ x6 \[LessEqual] 951, 4\ x1 + 4\ x2 + 4\ x3 + 4\ x4 + 10\ x5 + 19\ x6 \[LessEqual] 951, \(-x2\) - 4\ x3 - 4\ x4 - x5 - 2\ x6 \[LessEqual] \(-120\), \(-4\)\ x2 - x3 - x4 - 4\ x5 - 2\ x6 \[LessEqual] \(-120\), \(-x1\) - 4\ x3 - 4\ x4 - 2\ x5 - x6 \[LessEqual] \(-120\), \(-x1\) - 2\ x2 - 4\ x3 - 4\ x4 - x6 \[LessEqual] \(-120\), \(-x1\) - 4\ x2 - 2\ x4 - 4\ x5 - x6 \[LessEqual] \(-120\), \(-x1\) - 4\ x2 - 2\ x3 - 4\ x5 - x6 \[LessEqual] \(-120\), \(-2\)\ x1 - x2 - 4\ x3 - 4\ x4 - x5 \[LessEqual] \(-120\), \(-2\)\ x1 - 4\ x2 - x3 - x4 - 4\ x5 \[LessEqual] \(-120\), \(-4\)\ x1 - x3 - x4 - 2\ x5 - 4\ x6 \[LessEqual] \(-120\), \(-4\)\ x1 - x2 - 2\ x4 - x5 - 4\ x6 \[LessEqual] \(-120\), \(-4\)\ x1 - x2 - 2\ x3 - x5 - 4\ x6 \[LessEqual] \(-120\), \(-4\)\ x1 - 2\ x2 - x3 - x4 - 4\ x6 \[LessEqual] \(-120\), x1 - 2\ x3 - 2\ x4 - 2\ x5 - 2\ x6 \[LessEqual] \(-63\), x1 - 2\ x2 - 2\ x4 - 2\ x5 - 2\ x6 \[LessEqual] \(-63\), x1 - 2\ x2 - 2\ x3 - 2\ x5 - 2\ x6 \[LessEqual] \(-63\), x1 - 2\ x2 - 2\ x3 - 2\ x4 - 2\ x6 \[LessEqual] \(-63\), x2 - 2\ x3 - 2\ x4 - 2\ x5 - 2\ x6 \[LessEqual] \(-63\), \(-2\)\ x2 + x3 - 2\ x4 - 2\ x5 - 2\ x6 \[LessEqual] \(-63\), \(-2\)\ x2 - 2\ x3 + x4 - 2\ x5 - 2\ x6 \[LessEqual] \(-63\), \(-2\)\ x2 - 2\ x3 - 2\ x4 + x5 - 2\ x6 \[LessEqual] \(-63\), \(-2\)\ x1 + x2 - 2\ x4 - 2\ x5 - 2\ x6 \[LessEqual] \(-63\), \(-2\)\ x1 + x2 - 2\ x3 - 2\ x5 - 2\ x6 \[LessEqual] \(-63\), \(-2\)\ x1 + x2 - 2\ x3 - 2\ x4 - 2\ x5 \[LessEqual] \(-63\), \(-2\)\ x1 + x3 - 2\ x4 - 2\ x5 - 2\ x6 \[LessEqual] \(-63\), \(-2\)\ x1 - 2\ x3 + x4 - 2\ x5 - 2\ x6 \[LessEqual] \(-63\), \(-2\)\ x1 - 2\ x3 - 2\ x4 - 2\ x5 + x6 \[LessEqual] \(-63\), \(-2\)\ x1 - 2\ x2 + x3 - 2\ x4 - 2\ x6 \[LessEqual] \(-63\), \(-2\)\ x1 - 2\ x2 + x3 - 2\ x4 - 2\ x5 \[LessEqual] \(-63\), \(-2\)\ x1 - 2\ x2 - 2\ x4 + x5 - 2\ x6 \[LessEqual] \(-63\), \(-2\)\ x1 - 2\ x2 - 2\ x4 - 2\ x5 + x6 \[LessEqual] \(-63\), \(-2\)\ x1 - 2\ x2 - 2\ x3 + x4 - 2\ x6 \[LessEqual] \(-63\), \(-2\)\ x1 - 2\ x2 - 2\ x3 + x4 - 2\ x5 \[LessEqual] \(-63\), \(-2\)\ x1 - 2\ x2 - 2\ x3 + x5 - 2\ x6 \[LessEqual] \(-63\), \(-2\)\ x1 - 2\ x2 - 2\ x3 - 2\ x5 + x6 \[LessEqual] \(-63\), \(-2\)\ x1 - 2\ x2 - 2\ x3 - 2\ x4 + x5 \[LessEqual] \(-63\), \(-2\)\ x1 - 2\ x2 - 2\ x3 - 2\ x4 + x6 \[LessEqual] \(-63\), 3\ x1 - 6\ x2 - 8\ x3 - 8\ x4 - 6\ x5 - 12\ x6 \[LessEqual] \(-421\), 3\ x1 - 8\ x2 - 6\ x3 - 6\ x4 - 8\ x5 - 12\ x6 \[LessEqual] \(-421\), \(-6\)\ x1 + 3\ x2 - 8\ x3 - 8\ x4 - 12\ x5 - 6\ x6 \[LessEqual] \(-421\), \(-6\)\ x1 - 8\ x2 + 3\ x3 - 12\ x4 - 8\ x5 - 6\ x6 \[LessEqual] \(-421\), \(-6\)\ x1 - 8\ x2 - 12\ x3 + 3\ x4 - 8\ x5 - 6\ x6 \[LessEqual] \(-421\), \(-6\)\ x1 - 12\ x2 - 8\ x3 - 8\ x4 + 3\ x5 - 6\ x6 \[LessEqual] \(-421\), \(-8\)\ x1 + 3\ x2 - 6\ x3 - 6\ x4 - 12\ x5 - 8\ x6 \[LessEqual] \(-421\), \(-8\)\ x1 - 6\ x2 + 3\ x3 - 12\ x4 - 6\ x5 - 8\ x6 \[LessEqual] \(-421\), \(-8\)\ x1 - 6\ x2 - 12\ x3 + 3\ x4 - 6\ x5 - 8\ x6 \[LessEqual] \(-421\), \(-8\)\ x1 - 12\ x2 - 6\ x3 - 6\ x4 + 3\ x5 - 8\ x6 \[LessEqual] \(-421\), \(-12\)\ x1 - 6\ x2 - 8\ x3 - 8\ x4 - 6\ x5 + 3\ x6 \[LessEqual] \(-421\), \(-12\)\ x1 - 8\ x2 - 6\ x3 - 6\ x4 - 8\ x5 + 3\ x6 \[LessEqual] \(-421\), 7\ x1 - 2\ x2 - 4\ x3 - 4\ x4 - 2\ x5 - 8\ x6 \[LessEqual] \(-49\), 7\ x1 - 4\ x2 - 2\ x3 - 2\ x4 - 4\ x5 - 8\ x6 \[LessEqual] \(-49\), \(-2\)\ x1 + 7\ x2 - 4\ x3 - 4\ x4 - 8\ x5 - 2\ x6 \[LessEqual] \(-49\), \(-2\)\ x1 - 4\ x2 + 7\ x3 - 8\ x4 - 4\ x5 - 2\ x6 \[LessEqual] \(-49\), \(-2\)\ x1 - 4\ x2 - 8\ x3 + 7\ x4 - 4\ x5 - 2\ x6 \[LessEqual] \(-49\), \(-2\)\ x1 - 8\ x2 - 4\ x3 - 4\ x4 + 7\ x5 - 2\ x6 \[LessEqual] \(-49\), \(-4\)\ x1 + 7\ x2 - 2\ x3 - 2\ x4 - 8\ x5 - 4\ x6 \[LessEqual] \(-49\), \(-4\)\ x1 - 2\ x2 + 7\ x3 - 8\ x4 - 2\ x5 - 4\ x6 \[LessEqual] \(-49\), \(-4\)\ x1 - 2\ x2 - 8\ x3 + 7\ x4 - 2\ x5 - 4\ x6 \[LessEqual] \(-49\), \(-4\)\ x1 - 8\ x2 - 2\ x3 - 2\ x4 + 7\ x5 - 4\ x6 \[LessEqual] \(-49\), \(-8\)\ x1 - 2\ x2 - 4\ x3 - 4\ x4 - 2\ x5 + 7\ x6 \[LessEqual] \(-49\), \(-8\)\ x1 - 4\ x2 - 2\ x3 - 2\ x4 - 4\ x5 + 7\ x6 \[LessEqual] \(-49\), 15\ x1 + 6\ x2 + 4\ x3 + 6\ x4 + 4\ x5 \[LessEqual] 743, 15\ x1 + 4\ x2 + 6\ x3 + 4\ x4 + 6\ x5 \[LessEqual] 743, 6\ x1 + 15\ x2 + 4\ x3 + 6\ x4 + 4\ x6 \[LessEqual] 743, 6\ x1 + 6\ x2 + 15\ x4 + 4\ x5 + 4\ x6 \[LessEqual] 743, 6\ x1 + 4\ x2 + 15\ x3 + 6\ x5 + 4\ x6 \[LessEqual] 743, 6\ x1 + 6\ x3 + 4\ x4 + 15\ x5 + 4\ x6 \[LessEqual] 743, 4\ x1 + 15\ x2 + 6\ x3 + 4\ x4 + 6\ x6 \[LessEqual] 743, 4\ x1 + 6\ x2 + 15\ x3 + 4\ x5 + 6\ x6 \[LessEqual] 743, 4\ x1 + 4\ x2 + 15\ x4 + 6\ x5 + 6\ x6 \[LessEqual] 743, 4\ x1 + 4\ x3 + 6\ x4 + 15\ x5 + 6\ x6 \[LessEqual] 743, 6\ x2 + 6\ x3 + 4\ x4 + 4\ x5 + 15\ x6 \[LessEqual] 743, 4\ x2 + 4\ x3 + 6\ x4 + 6\ x5 + 15\ x6 \[LessEqual] 743, x1 + x2 + x5 - 2\ x6 \[LessEqual] 67, x1 + x2 - 2\ x5 + x6 \[LessEqual] 67, x1 + x3 + x4 - 2\ x6 \[LessEqual] 67, x1 + x3 - 2\ x4 + x6 \[LessEqual] 67, x1 - 2\ x3 + x4 + x6 \[LessEqual] 67, x1 - 2\ x2 + x5 + x6 \[LessEqual] 67, x2 + x3 + x4 - 2\ x5 \[LessEqual] 67, x2 + x3 - 2\ x4 + x5 \[LessEqual] 67, x2 - 2\ x3 + x4 + x5 \[LessEqual] 67, \(-2\)\ x2 + x3 + x4 + x5 \[LessEqual] 67, \(-2\)\ x1 + x2 + x5 + x6 \[LessEqual] 67, \(-2\)\ x1 + x3 + x4 + x6 \[LessEqual] 67, 19\ x1 + 10\ x2 + 4\ x3 + 4\ x4 + 4\ x6 \[LessEqual] 911, 19\ x1 + 4\ x2 + 10\ x3 + 4\ x5 + 4\ x6 \[LessEqual] 911, 19\ x1 + 4\ x2 + 10\ x4 + 4\ x5 + 4\ x6 \[LessEqual] 911, 19\ x1 + 4\ x3 + 4\ x4 + 10\ x5 + 4\ x6 \[LessEqual] 911, 10\ x1 + 19\ x2 + 4\ x3 + 4\ x4 + 4\ x5 \[LessEqual] 911, 10\ x1 + 4\ x2 + 19\ x3 + 4\ x4 + 4\ x5 \[LessEqual] 911, 10\ x1 + 4\ x2 + 4\ x3 + 19\ x4 + 4\ x5 \[LessEqual] 911, 10\ x1 + 4\ x2 + 4\ x3 + 4\ x4 + 19\ x5 \[LessEqual] 911, 4\ x1 + 19\ x2 + 10\ x3 + 4\ x5 + 4\ x6 \[LessEqual] 911, 4\ x1 + 19\ x2 + 10\ x4 + 4\ x5 + 4\ x6 \[LessEqual] 911, 4\ x1 + 10\ x2 + 19\ x3 + 4\ x4 + 4\ x6 \[LessEqual] 911, 4\ x1 + 10\ x2 + 4\ x3 + 19\ x4 + 4\ x6 \[LessEqual] 911, 4\ x1 + 10\ x2 + 4\ x3 + 4\ x4 + 19\ x6 \[LessEqual] 911, 4\ x1 + 4\ x2 + 10\ x3 + 19\ x5 + 4\ x6 \[LessEqual] 911, 4\ x1 + 4\ x2 + 10\ x3 + 4\ x5 + 19\ x6 \[LessEqual] 911, 4\ x1 + 4\ x2 + 10\ x4 + 19\ x5 + 4\ x6 \[LessEqual] 911, 4\ x1 + 4\ x2 + 10\ x4 + 4\ x5 + 19\ x6 \[LessEqual] 911, 4\ x1 + 19\ x3 + 4\ x4 + 10\ x5 + 4\ x6 \[LessEqual] 911, 4\ x1 + 4\ x3 + 19\ x4 + 10\ x5 + 4\ x6 \[LessEqual] 911, 4\ x1 + 4\ x3 + 4\ x4 + 10\ x5 + 19\ x6 \[LessEqual] 911, 19\ x2 + 4\ x3 + 4\ x4 + 4\ x5 + 10\ x6 \[LessEqual] 911, 4\ x2 + 19\ x3 + 4\ x4 + 4\ x5 + 10\ x6 \[LessEqual] 911, 4\ x2 + 4\ x3 + 19\ x4 + 4\ x5 + 10\ x6 \[LessEqual] 911, 4\ x2 + 4\ x3 + 4\ x4 + 19\ x5 + 10\ x6 \[LessEqual] 911, \(-x3\) - x5 - 3\ x6 \[LessEqual] \(-32\), \(-x3\) - 3\ x5 - x6 \[LessEqual] \(-32\), \(-3\)\ x3 - x5 - x6 \[LessEqual] \(-32\), \(-x2\) - x4 - 3\ x6 \[LessEqual] \(-32\), \(-x2\) - 3\ x4 - x6 \[LessEqual] \(-32\), \(-3\)\ x2 - x4 - x6 \[LessEqual] \(-32\), \(-x1\) - x4 - 3\ x5 \[LessEqual] \(-32\), \(-x1\) - 3\ x4 - x5 \[LessEqual] \(-32\), \(-x1\) - x2 - 3\ x3 \[LessEqual] \(-32\), \(-x1\) - 3\ x2 - x3 \[LessEqual] \(-32\), \(-3\)\ x1 - x4 - x5 \[LessEqual] \(-32\), \(-3\)\ x1 - x2 - x3 \[LessEqual] \(-32\), \(-2\)\ x2 - 3\ x3 - 3\ x4 - 3\ x5 - 5\ x6 \[LessEqual] \(-199\), \(-3\)\ x2 - 2\ x3 - 3\ x4 - 3\ x5 - 5\ x6 \[LessEqual] \(-199\), \(-3\)\ x2 - 3\ x3 - 2\ x4 - 3\ x5 - 5\ x6 \[LessEqual] \(-199\), \(-3\)\ x2 - 3\ x3 - 3\ x4 - 2\ x5 - 5\ x6 \[LessEqual] \(-199\), \(-2\)\ x1 - 3\ x3 - 3\ x4 - 5\ x5 - 3\ x6 \[LessEqual] \(-199\), \(-2\)\ x1 - 3\ x2 - 5\ x4 - 3\ x5 - 3\ x6 \[LessEqual] \(-199\), \(-2\)\ x1 - 3\ x2 - 5\ x3 - 3\ x5 - 3\ x6 \[LessEqual] \(-199\), \(-2\)\ x1 - 5\ x2 - 3\ x3 - 3\ x4 - 3\ x6 \[LessEqual] \(-199\), \(-3\)\ x1 - 2\ x3 - 3\ x4 - 5\ x5 - 3\ x6 \[LessEqual] \(-199\), \(-3\)\ x1 - 3\ x3 - 2\ x4 - 5\ x5 - 3\ x6 \[LessEqual] \(-199\), \(-3\)\ x1 - 3\ x3 - 3\ x4 - 5\ x5 - 2\ x6 \[LessEqual] \(-199\), \(-3\)\ x1 - 2\ x2 - 5\ x4 - 3\ x5 - 3\ x6 \[LessEqual] \(-199\), \(-3\)\ x1 - 2\ x2 - 5\ x3 - 3\ x5 - 3\ x6 \[LessEqual] \(-199\), \(-3\)\ x1 - 3\ x2 - 5\ x4 - 2\ x5 - 3\ x6 \[LessEqual] \(-199\), \(-3\)\ x1 - 3\ x2 - 5\ x4 - 3\ x5 - 2\ x6 \[LessEqual] \(-199\), \(-3\)\ x1 - 3\ x2 - 5\ x3 - 2\ x5 - 3\ x6 \[LessEqual] \(-199\), \(-3\)\ x1 - 3\ x2 - 5\ x3 - 3\ x5 - 2\ x6 \[LessEqual] \(-199\), \(-3\)\ x1 - 5\ x2 - 2\ x3 - 3\ x4 - 3\ x6 \[LessEqual] \(-199\), \(-3\)\ x1 - 5\ x2 - 3\ x3 - 2\ x4 - 3\ x6 \[LessEqual] \(-199\), \(-3\)\ x1 - 5\ x2 - 3\ x3 - 3\ x4 - 2\ x6 \[LessEqual] \(-199\), \(-5\)\ x1 - 2\ x2 - 3\ x3 - 3\ x4 - 3\ x5 \[LessEqual] \(-199\), \(-5\)\ x1 - 3\ x2 - 2\ x3 - 3\ x4 - 3\ x5 \[LessEqual] \(-199\), \(-5\)\ x1 - 3\ x2 - 3\ x3 - 2\ x4 - 3\ x5 \[LessEqual] \(-199\), \(-5\)\ x1 - 3\ x2 - 3\ x3 - 3\ x4 - 2\ x5 \[LessEqual] \(-199\), 3\ x1 - 2\ x3 - 12\ x5 \[LessEqual] 43, 3\ x1 - 12\ x3 - 2\ x5 \[LessEqual] 43, 3\ x1 - 2\ x2 - 12\ x4 \[LessEqual] 43, 3\ x1 - 12\ x2 - 2\ x4 \[LessEqual] 43, 3\ x2 - 2\ x3 - 12\ x6 \[LessEqual] 43, 3\ x2 - 12\ x3 - 2\ x6 \[LessEqual] 43, 3\ x4 - 2\ x5 - 12\ x6 \[LessEqual] 43, 3\ x4 - 12\ x5 - 2\ x6 \[LessEqual] 43, \(-2\)\ x4 + 3\ x5 - 12\ x6 \[LessEqual] 43, \(-2\)\ x4 - 12\ x5 + 3\ x6 \[LessEqual] 43, \(-12\)\ x4 + 3\ x5 - 2\ x6 \[LessEqual] 43, \(-12\)\ x4 - 2\ x5 + 3\ x6 \[LessEqual] 43, \(-2\)\ x2 + 3\ x3 - 12\ x6 \[LessEqual] 43, \(-2\)\ x2 - 12\ x3 + 3\ x6 \[LessEqual] 43, \(-12\)\ x2 + 3\ x3 - 2\ x6 \[LessEqual] 43, \(-12\)\ x2 - 2\ x3 + 3\ x6 \[LessEqual] 43, \(-2\)\ x1 + 3\ x2 - 12\ x4 \[LessEqual] 43, \(-2\)\ x1 + 3\ x3 - 12\ x5 \[LessEqual] 43, \(-2\)\ x1 - 12\ x3 + 3\ x5 \[LessEqual] 43, \(-2\)\ x1 - 12\ x2 + 3\ x4 \[LessEqual] 43, \(-12\)\ x1 + 3\ x2 - 2\ x4 \[LessEqual] 43, \(-12\)\ x1 + 3\ x3 - 2\ x5 \[LessEqual] 43, \(-12\)\ x1 - 2\ x3 + 3\ x5 \[LessEqual] 43, \(-12\)\ x1 - 2\ x2 + 3\ x4 \[LessEqual] 43, 5\ x1 - 4\ x2 - 6\ x3 - 10\ x4 - 12\ x5 - 16\ x6 \[LessEqual] \(-469\), 5\ x1 - 6\ x2 - 4\ x3 - 12\ x4 - 10\ x5 - 16\ x6 \[LessEqual] \(-469\), 5\ x1 - 10\ x2 - 12\ x3 - 4\ x4 - 6\ x5 - 16\ x6 \[LessEqual] \(-469\), 5\ x1 - 12\ x2 - 10\ x3 - 6\ x4 - 4\ x5 - 16\ x6 \[LessEqual] \(-469\), \(-4\)\ x1 + 5\ x2 - 6\ x3 - 10\ x4 - 16\ x5 - 12\ x6 \[LessEqual] \(-469\), \(-4\)\ x1 - 6\ x2 + 5\ x3 - 16\ x4 - 10\ x5 - 12\ x6 \[LessEqual] \(-469\), \(-4\)\ x1 - 10\ x2 - 16\ x3 + 5\ x4 - 6\ x5 - 12\ x6 \[LessEqual] \(-469\), \(-4\)\ x1 - 16\ x2 - 10\ x3 - 6\ x4 + 5\ x5 - 12\ x6 \[LessEqual] \(-469\), \(-6\)\ x1 + 5\ x2 - 4\ x3 - 12\ x4 - 16\ x5 - 10\ x6 \[LessEqual] \(-469\), \(-6\)\ x1 - 4\ x2 + 5\ x3 - 16\ x4 - 12\ x5 - 10\ x6 \[LessEqual] \(-469\), \(-6\)\ x1 - 12\ x2 - 16\ x3 + 5\ x4 - 4\ x5 - 10\ x6 \[LessEqual] \(-469\), \(-6\)\ x1 - 16\ x2 - 12\ x3 - 4\ x4 + 5\ x5 - 10\ x6 \[LessEqual] \(-469\), \(-10\)\ x1 + 5\ x2 - 12\ x3 - 4\ x4 - 16\ x5 - 6\ x6 \[LessEqual] \(-469\), \(-10\)\ x1 - 4\ x2 - 16\ x3 + 5\ x4 - 12\ x5 - 6\ x6 \[LessEqual] \(-469\), \(-10\)\ x1 - 12\ x2 + 5\ x3 - 16\ x4 - 4\ x5 - 6\ x6 \[LessEqual] \(-469\), \(-10\)\ x1 - 16\ x2 - 4\ x3 - 12\ x4 + 5\ x5 - 6\ x6 \[LessEqual] \(-469\), \(-12\)\ x1 + 5\ x2 - 10\ x3 - 6\ x4 - 16\ x5 - 4\ x6 \[LessEqual] \(-469\), \(-12\)\ x1 - 6\ x2 - 16\ x3 + 5\ x4 - 10\ x5 - 4\ x6 \[LessEqual] \(-469\), \(-12\)\ x1 - 10\ x2 + 5\ x3 - 16\ x4 - 6\ x5 - 4\ x6 \[LessEqual] \(-469\), \(-12\)\ x1 - 16\ x2 - 6\ x3 - 10\ x4 + 5\ x5 - 4\ x6 \[LessEqual] \(-469\), \(-16\)\ x1 - 4\ x2 - 10\ x3 - 6\ x4 - 12\ x5 + 5\ x6 \[LessEqual] \(-469\), \(-16\)\ x1 - 6\ x2 - 12\ x3 - 4\ x4 - 10\ x5 + 5\ x6 \[LessEqual] \(-469\), \(-16\)\ x1 - 10\ x2 - 4\ x3 - 12\ x4 - 6\ x5 + 5\ x6 \[LessEqual] \(-469\), \(-16\)\ x1 - 12\ x2 - 6\ x3 - 10\ x4 - 4\ x5 + 5\ x6 \[LessEqual] \(-469\), 23\ x1 + 14\ x2 + 2\ x3 - 4\ x4 + 14\ x5 + 14\ x6 \[LessEqual] 1383, 23\ x1 + 14\ x2 - 4\ x3 + 2\ x4 + 14\ x5 + 14\ x6 \[LessEqual] 1383, 23\ x1 + 2\ x2 + 14\ x3 + 14\ x4 - 4\ x5 + 14\ x6 \[LessEqual] 1383, 23\ x1 - 4\ x2 + 14\ x3 + 14\ x4 + 2\ x5 + 14\ x6 \[LessEqual] 1383, 14\ x1 + 23\ x2 + 2\ x3 - 4\ x4 + 14\ x5 + 14\ x6 \[LessEqual] 1383, 14\ x1 + 23\ x2 - 4\ x3 + 2\ x4 + 14\ x5 + 14\ x6 \[LessEqual] 1383, 14\ x1 + 14\ x2 + 2\ x3 - 4\ x4 + 23\ x5 + 14\ x6 \[LessEqual] 1383, 14\ x1 + 14\ x2 + 2\ x3 - 4\ x4 + 14\ x5 + 23\ x6 \[LessEqual] 1383, 14\ x1 + 14\ x2 - 4\ x3 + 2\ x4 + 23\ x5 + 14\ x6 \[LessEqual] 1383, 14\ x1 + 14\ x2 - 4\ x3 + 2\ x4 + 14\ x5 + 23\ x6 \[LessEqual] 1383, 14\ x1 + 2\ x2 + 23\ x3 + 14\ x4 - 4\ x5 + 14\ x6 \[LessEqual] 1383, 14\ x1 + 2\ x2 + 14\ x3 + 23\ x4 - 4\ x5 + 14\ x6 \[LessEqual] 1383, 14\ x1 + 2\ x2 + 14\ x3 + 14\ x4 - 4\ x5 + 23\ x6 \[LessEqual] 1383, 14\ x1 - 4\ x2 + 23\ x3 + 14\ x4 + 2\ x5 + 14\ x6 \[LessEqual] 1383, 14\ x1 - 4\ x2 + 14\ x3 + 23\ x4 + 2\ x5 + 14\ x6 \[LessEqual] 1383, 14\ x1 - 4\ x2 + 14\ x3 + 14\ x4 + 2\ x5 + 23\ x6 \[LessEqual] 1383, 2\ x1 + 23\ x2 + 14\ x3 + 14\ x4 + 14\ x5 - 4\ x6 \[LessEqual] 1383, 2\ x1 + 14\ x2 + 23\ x3 + 14\ x4 + 14\ x5 - 4\ x6 \[LessEqual] 1383, 2\ x1 + 14\ x2 + 14\ x3 + 23\ x4 + 14\ x5 - 4\ x6 \[LessEqual] 1383, 2\ x1 + 14\ x2 + 14\ x3 + 14\ x4 + 23\ x5 - 4\ x6 \[LessEqual] 1383, \(-4\)\ x1 + 23\ x2 + 14\ x3 + 14\ x4 + 14\ x5 + 2\ x6 \[LessEqual] 1383, \(-4\)\ x1 + 14\ x2 + 23\ x3 + 14\ x4 + 14\ x5 + 2\ x6 \[LessEqual] 1383, \(-4\)\ x1 + 14\ x2 + 14\ x3 + 23\ x4 + 14\ x5 + 2\ x6 \[LessEqual] 1383, \(-4\)\ x1 + 14\ x2 + 14\ x3 + 14\ x4 + 23\ x5 + 2\ x6 \[LessEqual] 1383, 27\ x1 + 18\ x2 - 6\ x3 + 16\ x5 + 18\ x6 \[LessEqual] 1633, 27\ x1 + 16\ x2 - 6\ x4 + 18\ x5 + 18\ x6 \[LessEqual] 1633, 27\ x1 + 16\ x3 + 18\ x4 - 6\ x5 + 18\ x6 \[LessEqual] 1633, 27\ x1 - 6\ x2 + 18\ x3 + 16\ x4 + 18\ x6 \[LessEqual] 1633, 18\ x1 + 27\ x2 - 6\ x3 + 18\ x5 + 16\ x6 \[LessEqual] 1633, 18\ x1 + 18\ x2 - 6\ x4 + 27\ x5 + 16\ x6 \[LessEqual] 1633, 18\ x1 + 18\ x2 - 6\ x4 + 16\ x5 + 27\ x6 \[LessEqual] 1633, 18\ x1 + 16\ x2 - 6\ x3 + 18\ x5 + 27\ x6 \[LessEqual] 1633, 18\ x1 + 18\ x3 + 27\ x4 - 6\ x5 + 16\ x6 \[LessEqual] 1633, 18\ x1 + 18\ x3 + 16\ x4 - 6\ x5 + 27\ x6 \[LessEqual] 1633, 18\ x1 - 6\ x2 + 27\ x3 + 18\ x4 + 16\ x6 \[LessEqual] 1633, 18\ x1 - 6\ x2 + 16\ x3 + 18\ x4 + 27\ x6 \[LessEqual] 1633, 16\ x1 + 27\ x2 - 6\ x4 + 18\ x5 + 18\ x6 \[LessEqual] 1633, 16\ x1 + 18\ x2 - 6\ x3 + 27\ x5 + 18\ x6 \[LessEqual] 1633, 16\ x1 + 27\ x3 + 18\ x4 - 6\ x5 + 18\ x6 \[LessEqual] 1633, 16\ x1 - 6\ x2 + 18\ x3 + 27\ x4 + 18\ x6 \[LessEqual] 1633, 27\ x2 + 16\ x3 + 18\ x4 + 18\ x5 - 6\ x6 \[LessEqual] 1633, 18\ x2 + 18\ x3 + 27\ x4 + 16\ x5 - 6\ x6 \[LessEqual] 1633, 18\ x2 + 18\ x3 + 16\ x4 + 27\ x5 - 6\ x6 \[LessEqual] 1633, 16\ x2 + 27\ x3 + 18\ x4 + 18\ x5 - 6\ x6 \[LessEqual] 1633, \(-6\)\ x1 + 27\ x2 + 18\ x3 + 16\ x4 + 18\ x5 \[LessEqual] 1633, \(-6\)\ x1 + 18\ x2 + 27\ x3 + 18\ x4 + 16\ x5 \[LessEqual] 1633, \(-6\)\ x1 + 18\ x2 + 16\ x3 + 18\ x4 + 27\ x5 \[LessEqual] 1633, \(-6\)\ x1 + 16\ x2 + 18\ x3 + 27\ x4 + 18\ x5 \[LessEqual] 1633, 25\ x1 + 16\ x2 + 10\ x3 + 4\ x4 + 10\ x5 + 4\ x6 \[LessEqual] 1419, 25\ x1 + 10\ x2 + 16\ x3 + 10\ x4 + 4\ x5 + 4\ x6 \[LessEqual] 1419, 25\ x1 + 10\ x2 + 4\ x3 + 10\ x4 + 16\ x5 + 4\ x6 \[LessEqual] 1419, 25\ x1 + 4\ x2 + 10\ x3 + 16\ x4 + 10\ x5 + 4\ x6 \[LessEqual] 1419, 16\ x1 + 25\ x2 + 10\ x3 + 4\ x4 + 4\ x5 + 10\ x6 \[LessEqual] 1419, 16\ x1 + 10\ x2 + 25\ x3 + 4\ x4 + 4\ x5 + 10\ x6 \[LessEqual] 1419, 16\ x1 + 4\ x2 + 4\ x3 + 25\ x4 + 10\ x5 + 10\ x6 \[LessEqual] 1419, 16\ x1 + 4\ x2 + 4\ x3 + 10\ x4 + 25\ x5 + 10\ x6 \[LessEqual] 1419, 10\ x1 + 25\ x2 + 16\ x3 + 10\ x4 + 4\ x5 + 4\ x6 \[LessEqual] 1419, 10\ x1 + 25\ x2 + 4\ x3 + 10\ x4 + 4\ x5 + 16\ x6 \[LessEqual] 1419, 10\ x1 + 16\ x2 + 25\ x3 + 4\ x4 + 10\ x5 + 4\ x6 \[LessEqual] 1419, 10\ x1 + 10\ x2 + 4\ x3 + 25\ x4 + 16\ x5 + 4\ x6 \[LessEqual] 1419, 10\ x1 + 10\ x2 + 4\ x3 + 25\ x4 + 4\ x5 + 16\ x6 \[LessEqual] 1419, 10\ x1 + 4\ x2 + 25\ x3 + 4\ x4 + 10\ x5 + 16\ x6 \[LessEqual] 1419, 10\ x1 + 4\ x2 + 10\ x3 + 16\ x4 + 25\ x5 + 4\ x6 \[LessEqual] 1419, 10\ x1 + 4\ x2 + 10\ x3 + 4\ x4 + 25\ x5 + 16\ x6 \[LessEqual] 1419, 4\ x1 + 25\ x2 + 10\ x3 + 16\ x4 + 4\ x5 + 10\ x6 \[LessEqual] 1419, 4\ x1 + 16\ x2 + 4\ x3 + 25\ x4 + 10\ x5 + 10\ x6 \[LessEqual] 1419, 4\ x1 + 16\ x2 + 4\ x3 + 10\ x4 + 10\ x5 + 25\ x6 \[LessEqual] 1419, 4\ x1 + 10\ x2 + 25\ x3 + 4\ x4 + 16\ x5 + 10\ x6 \[LessEqual] 1419, 4\ x1 + 10\ x2 + 10\ x3 + 16\ x4 + 4\ x5 + 25\ x6 \[LessEqual] 1419, 4\ x1 + 10\ x2 + 10\ x3 + 4\ x4 + 16\ x5 + 25\ x6 \[LessEqual] 1419, 4\ x1 + 4\ x2 + 16\ x3 + 10\ x4 + 25\ x5 + 10\ x6 \[LessEqual] 1419, 4\ x1 + 4\ x2 + 16\ x3 + 10\ x4 + 10\ x5 + 25\ x6 \[LessEqual] 1419, 25\ x1 + 14\ x2 + 10\ x3 + 4\ x4 + 10\ x5 + 4\ x6 \[LessEqual] 1381, 25\ x1 + 10\ x2 + 14\ x3 + 10\ x4 + 4\ x5 + 4\ x6 \[LessEqual] 1381, 25\ x1 + 10\ x2 + 4\ x3 + 10\ x4 + 14\ x5 + 4\ x6 \[LessEqual] 1381, 25\ x1 + 4\ x2 + 10\ x3 + 14\ x4 + 10\ x5 + 4\ x6 \[LessEqual] 1381, 14\ x1 + 25\ x2 + 10\ x3 + 4\ x4 + 4\ x5 + 10\ x6 \[LessEqual] 1381, 14\ x1 + 10\ x2 + 25\ x3 + 4\ x4 + 4\ x5 + 10\ x6 \[LessEqual] 1381, 14\ x1 + 4\ x2 + 4\ x3 + 25\ x4 + 10\ x5 + 10\ x6 \[LessEqual] 1381, 14\ x1 + 4\ x2 + 4\ x3 + 10\ x4 + 25\ x5 + 10\ x6 \[LessEqual] 1381, 10\ x1 + 25\ x2 + 14\ x3 + 10\ x4 + 4\ x5 + 4\ x6 \[LessEqual] 1381, 10\ x1 + 25\ x2 + 4\ x3 + 10\ x4 + 4\ x5 + 14\ x6 \[LessEqual] 1381, 10\ x1 + 14\ x2 + 25\ x3 + 4\ x4 + 10\ x5 + 4\ x6 \[LessEqual] 1381, 10\ x1 + 10\ x2 + 4\ x3 + 25\ x4 + 14\ x5 + 4\ x6 \[LessEqual] 1381, 10\ x1 + 10\ x2 + 4\ x3 + 25\ x4 + 4\ x5 + 14\ x6 \[LessEqual] 1381, 10\ x1 + 4\ x2 + 25\ x3 + 4\ x4 + 10\ x5 + 14\ x6 \[LessEqual] 1381, 10\ x1 + 4\ x2 + 10\ x3 + 14\ x4 + 25\ x5 + 4\ x6 \[LessEqual] 1381, 10\ x1 + 4\ x2 + 10\ x3 + 4\ x4 + 25\ x5 + 14\ x6 \[LessEqual] 1381, 4\ x1 + 25\ x2 + 10\ x3 + 14\ x4 + 4\ x5 + 10\ x6 \[LessEqual] 1381, 4\ x1 + 14\ x2 + 4\ x3 + 25\ x4 + 10\ x5 + 10\ x6 \[LessEqual] 1381, 4\ x1 + 14\ x2 + 4\ x3 + 10\ x4 + 10\ x5 + 25\ x6 \[LessEqual] 1381, 4\ x1 + 10\ x2 + 25\ x3 + 4\ x4 + 14\ x5 + 10\ x6 \[LessEqual] 1381, 4\ x1 + 10\ x2 + 10\ x3 + 14\ x4 + 4\ x5 + 25\ x6 \[LessEqual] 1381, 4\ x1 + 10\ x2 + 10\ x3 + 4\ x4 + 14\ x5 + 25\ x6 \[LessEqual] 1381, 4\ x1 + 4\ x2 + 14\ x3 + 10\ x4 + 25\ x5 + 10\ x6 \[LessEqual] 1381, 4\ x1 + 4\ x2 + 14\ x3 + 10\ x4 + 10\ x5 + 25\ x6 \[LessEqual] 1381, 27\ x1 + 18\ x2 - 6\ x3 + 16\ x5 + 16\ x6 \[LessEqual] 1595, 27\ x1 + 16\ x2 - 6\ x4 + 18\ x5 + 16\ x6 \[LessEqual] 1595, 27\ x1 + 16\ x3 + 18\ x4 - 6\ x5 + 16\ x6 \[LessEqual] 1595, 27\ x1 - 6\ x2 + 18\ x3 + 16\ x4 + 16\ x6 \[LessEqual] 1595, 18\ x1 + 27\ x2 - 6\ x3 + 16\ x5 + 16\ x6 \[LessEqual] 1595, 18\ x1 + 16\ x2 - 6\ x4 + 27\ x5 + 16\ x6 \[LessEqual] 1595, 18\ x1 + 16\ x3 + 27\ x4 - 6\ x5 + 16\ x6 \[LessEqual] 1595, 18\ x1 - 6\ x2 + 27\ x3 + 16\ x4 + 16\ x6 \[LessEqual] 1595, 16\ x1 + 27\ x2 - 6\ x4 + 16\ x5 + 18\ x6 \[LessEqual] 1595, 16\ x1 + 18\ x2 - 6\ x4 + 16\ x5 + 27\ x6 \[LessEqual] 1595, 16\ x1 + 16\ x2 - 6\ x3 + 27\ x5 + 18\ x6 \[LessEqual] 1595, 16\ x1 + 16\ x2 - 6\ x3 + 18\ x5 + 27\ x6 \[LessEqual] 1595, 16\ x1 + 27\ x3 + 16\ x4 - 6\ x5 + 18\ x6 \[LessEqual] 1595, 16\ x1 + 18\ x3 + 16\ x4 - 6\ x5 + 27\ x6 \[LessEqual] 1595, 16\ x1 - 6\ x2 + 16\ x3 + 27\ x4 + 18\ x6 \[LessEqual] 1595, 16\ x1 - 6\ x2 + 16\ x3 + 18\ x4 + 27\ x6 \[LessEqual] 1595, 27\ x2 + 16\ x3 + 18\ x4 + 16\ x5 - 6\ x6 \[LessEqual] 1595, 18\ x2 + 16\ x3 + 27\ x4 + 16\ x5 - 6\ x6 \[LessEqual] 1595, 16\ x2 + 27\ x3 + 16\ x4 + 18\ x5 - 6\ x6 \[LessEqual] 1595, 16\ x2 + 18\ x3 + 16\ x4 + 27\ x5 - 6\ x6 \[LessEqual] 1595, \(-6\)\ x1 + 27\ x2 + 18\ x3 + 16\ x4 + 16\ x5 \[LessEqual] 1595, \(-6\)\ x1 + 18\ x2 + 27\ x3 + 16\ x4 + 16\ x5 \[LessEqual] 1595, \(-6\)\ x1 + 16\ x2 + 16\ x3 + 27\ x4 + 18\ x5 \[LessEqual] 1595, \(-6\)\ x1 + 16\ x2 + 16\ x3 + 18\ x4 + 27\ x5 \[LessEqual] 1595, 8\ x1 + 5\ x2 + 2\ x3 + 2\ x4 + 4\ x5 + 2\ x6 \[LessEqual] 467, 8\ x1 + 4\ x2 + 2\ x3 + 2\ x4 + 5\ x5 + 2\ x6 \[LessEqual] 467, 8\ x1 + 2\ x2 + 5\ x3 + 4\ x4 + 2\ x5 + 2\ x6 \[LessEqual] 467, 8\ x1 + 2\ x2 + 4\ x3 + 5\ x4 + 2\ x5 + 2\ x6 \[LessEqual] 467, 5\ x1 + 8\ x2 + 2\ x3 + 2\ x4 + 2\ x5 + 4\ x6 \[LessEqual] 467, 5\ x1 + 2\ x2 + 8\ x3 + 2\ x4 + 2\ x5 + 4\ x6 \[LessEqual] 467, 5\ x1 + 2\ x2 + 2\ x3 + 8\ x4 + 2\ x5 + 4\ x6 \[LessEqual] 467, 5\ x1 + 2\ x2 + 2\ x3 + 2\ x4 + 8\ x5 + 4\ x6 \[LessEqual] 467, 4\ x1 + 8\ x2 + 2\ x3 + 2\ x4 + 2\ x5 + 5\ x6 \[LessEqual] 467, 4\ x1 + 2\ x2 + 8\ x3 + 2\ x4 + 2\ x5 + 5\ x6 \[LessEqual] 467, 4\ x1 + 2\ x2 + 2\ x3 + 8\ x4 + 2\ x5 + 5\ x6 \[LessEqual] 467, 4\ x1 + 2\ x2 + 2\ x3 + 2\ x4 + 8\ x5 + 5\ x6 \[LessEqual] 467, 2\ x1 + 8\ x2 + 5\ x3 + 4\ x4 + 2\ x5 + 2\ x6 \[LessEqual] 467, 2\ x1 + 8\ x2 + 4\ x3 + 5\ x4 + 2\ x5 + 2\ x6 \[LessEqual] 467, 2\ x1 + 5\ x2 + 8\ x3 + 2\ x4 + 4\ x5 + 2\ x6 \[LessEqual] 467, 2\ x1 + 5\ x2 + 2\ x3 + 8\ x4 + 4\ x5 + 2\ x6 \[LessEqual] 467, 2\ x1 + 5\ x2 + 2\ x3 + 2\ x4 + 4\ x5 + 8\ x6 \[LessEqual] 467, 2\ x1 + 4\ x2 + 8\ x3 + 2\ x4 + 5\ x5 + 2\ x6 \[LessEqual] 467, 2\ x1 + 4\ x2 + 2\ x3 + 8\ x4 + 5\ x5 + 2\ x6 \[LessEqual] 467, 2\ x1 + 4\ x2 + 2\ x3 + 2\ x4 + 5\ x5 + 8\ x6 \[LessEqual] 467, 2\ x1 + 2\ x2 + 5\ x3 + 4\ x4 + 8\ x5 + 2\ x6 \[LessEqual] 467, 2\ x1 + 2\ x2 + 5\ x3 + 4\ x4 + 2\ x5 + 8\ x6 \[LessEqual] 467, 2\ x1 + 2\ x2 + 4\ x3 + 5\ x4 + 8\ x5 + 2\ x6 \[LessEqual] 467, 2\ x1 + 2\ x2 + 4\ x3 + 5\ x4 + 2\ x5 + 8\ x6 \[LessEqual] 467, x1 - 2\ x2 - 3\ x3 - 3\ x4 - 3\ x5 - 5\ x6 \[LessEqual] \(-176\), x1 - 3\ x2 - 2\ x3 - 3\ x4 - 3\ x5 - 5\ x6 \[LessEqual] \(-176\), x1 - 3\ x2 - 3\ x3 - 2\ x4 - 3\ x5 - 5\ x6 \[LessEqual] \(-176\), x1 - 3\ x2 - 3\ x3 - 3\ x4 - 2\ x5 - 5\ x6 \[LessEqual] \(-176\), \(-2\)\ x1 + x2 - 3\ x3 - 3\ x4 - 5\ x5 - 3\ x6 \[LessEqual] \(-176\), \(-2\)\ x1 - 3\ x2 + x3 - 5\ x4 - 3\ x5 - 3\ x6 \[LessEqual] \(-176\), \(-2\)\ x1 - 3\ x2 - 5\ x3 + x4 - 3\ x5 - 3\ x6 \[LessEqual] \(-176\), \(-2\)\ x1 - 5\ x2 - 3\ x3 - 3\ x4 + x5 - 3\ x6 \[LessEqual] \(-176\), \(-3\)\ x1 + x2 - 2\ x3 - 3\ x4 - 5\ x5 - 3\ x6 \[LessEqual] \(-176\), \(-3\)\ x1 + x2 - 3\ x3 - 2\ x4 - 5\ x5 - 3\ x6 \[LessEqual] \(-176\), \(-3\)\ x1 + x2 - 3\ x3 - 3\ x4 - 5\ x5 - 2\ x6 \[LessEqual] \(-176\), \(-3\)\ x1 - 2\ x2 + x3 - 5\ x4 - 3\ x5 - 3\ x6 \[LessEqual] \(-176\), \(-3\)\ x1 - 2\ x2 - 5\ x3 + x4 - 3\ x5 - 3\ x6 \[LessEqual] \(-176\), \(-3\)\ x1 - 3\ x2 + x3 - 5\ x4 - 2\ x5 - 3\ x6 \[LessEqual] \(-176\), \(-3\)\ x1 - 3\ x2 + x3 - 5\ x4 - 3\ x5 - 2\ x6 \[LessEqual] \(-176\), \(-3\)\ x1 - 3\ x2 - 5\ x3 + x4 - 2\ x5 - 3\ x6 \[LessEqual] \(-176\), \(-3\)\ x1 - 3\ x2 - 5\ x3 + x4 - 3\ x5 - 2\ x6 \[LessEqual] \(-176\), \(-3\)\ x1 - 5\ x2 - 2\ x3 - 3\ x4 + x5 - 3\ x6 \[LessEqual] \(-176\), \(-3\)\ x1 - 5\ x2 - 3\ x3 - 2\ x4 + x5 - 3\ x6 \[LessEqual] \(-176\), \(-3\)\ x1 - 5\ x2 - 3\ x3 - 3\ x4 + x5 - 2\ x6 \[LessEqual] \(-176\), \(-5\)\ x1 - 2\ x2 - 3\ x3 - 3\ x4 - 3\ x5 + x6 \[LessEqual] \(-176\), \(-5\)\ x1 - 3\ x2 - 2\ x3 - 3\ x4 - 3\ x5 + x6 \[LessEqual] \(-176\), \(-5\)\ x1 - 3\ x2 - 3\ x3 - 2\ x4 - 3\ x5 + x6 \[LessEqual] \(-176\), \(-5\)\ x1 - 3\ x2 - 3\ x3 - 3\ x4 - 2\ x5 + x6 \[LessEqual] \(-176\), 2\ x1 - x2 - 2\ x3 - 2\ x4 - 2\ x5 - 4\ x6 \[LessEqual] \(-83\), 2\ x1 - 2\ x2 - x3 - 2\ x4 - 2\ x5 - 4\ x6 \[LessEqual] \(-83\), 2\ x1 - 2\ x2 - 2\ x3 - x4 - 2\ x5 - 4\ x6 \[LessEqual] \(-83\), 2\ x1 - 2\ x2 - 2\ x3 - 2\ x4 - x5 - 4\ x6 \[LessEqual] \(-83\), \(-x1\) + 2\ x2 - 2\ x3 - 2\ x4 - 4\ x5 - 2\ x6 \[LessEqual] \(-83\), \(-x1\) - 2\ x2 + 2\ x3 - 4\ x4 - 2\ x5 - 2\ x6 \[LessEqual] \(-83\), \(-x1\) - 2\ x2 - 4\ x3 + 2\ x4 - 2\ x5 - 2\ x6 \[LessEqual] \(-83\), \(-x1\) - 4\ x2 - 2\ x3 - 2\ x4 + 2\ x5 - 2\ x6 \[LessEqual] \(-83\), \(-2\)\ x1 + 2\ x2 - x3 - 2\ x4 - 4\ x5 - 2\ x6 \[LessEqual] \(-83\), \(-2\)\ x1 + 2\ x2 - 2\ x3 - x4 - 4\ x5 - 2\ x6 \[LessEqual] \(-83\), \(-2\)\ x1 + 2\ x2 - 2\ x3 - 2\ x4 - 4\ x5 - x6 \[LessEqual] \(-83\), \(-2\)\ x1 - x2 + 2\ x3 - 4\ x4 - 2\ x5 - 2\ x6 \[LessEqual] \(-83\), \(-2\)\ x1 - x2 - 4\ x3 + 2\ x4 - 2\ x5 - 2\ x6 \[LessEqual] \(-83\), \(-2\)\ x1 - 2\ x2 + 2\ x3 - 4\ x4 - x5 - 2\ x6 \[LessEqual] \(-83\), \(-2\)\ x1 - 2\ x2 + 2\ x3 - 4\ x4 - 2\ x5 - x6 \[LessEqual] \(-83\), \(-2\)\ x1 - 2\ x2 - 4\ x3 + 2\ x4 - x5 - 2\ x6 \[LessEqual] \(-83\), \(-2\)\ x1 - 2\ x2 - 4\ x3 + 2\ x4 - 2\ x5 - x6 \[LessEqual] \(-83\), \(-2\)\ x1 - 4\ x2 - x3 - 2\ x4 + 2\ x5 - 2\ x6 \[LessEqual] \(-83\), \(-2\)\ x1 - 4\ x2 - 2\ x3 - x4 + 2\ x5 - 2\ x6 \[LessEqual] \(-83\), \(-2\)\ x1 - 4\ x2 - 2\ x3 - 2\ x4 + 2\ x5 - x6 \[LessEqual] \(-83\), \(-4\)\ x1 - x2 - 2\ x3 - 2\ x4 - 2\ x5 + 2\ x6 \[LessEqual] \(-83\), \(-4\)\ x1 - 2\ x2 - x3 - 2\ x4 - 2\ x5 + 2\ x6 \[LessEqual] \(-83\), \(-4\)\ x1 - 2\ x2 - 2\ x3 - x4 - 2\ x5 + 2\ x6 \[LessEqual] \(-83\), \(-4\)\ x1 - 2\ x2 - 2\ x3 - 2\ x4 - x5 + 2\ x6 \[LessEqual] \(-83\), 7\ x1 + 4\ x2 - 2\ x4 + 4\ x5 + 4\ x6 \[LessEqual] 395, 7\ x1 + 4\ x2 - 2\ x3 + 4\ x5 + 4\ x6 \[LessEqual] 395, 7\ x1 + 4\ x3 + 4\ x4 - 2\ x5 + 4\ x6 \[LessEqual] 395, 7\ x1 - 2\ x2 + 4\ x3 + 4\ x4 + 4\ x6 \[LessEqual] 395, 4\ x1 + 7\ x2 - 2\ x4 + 4\ x5 + 4\ x6 \[LessEqual] 395, 4\ x1 + 7\ x2 - 2\ x3 + 4\ x5 + 4\ x6 \[LessEqual] 395, 4\ x1 + 4\ x2 - 2\ x4 + 7\ x5 + 4\ x6 \[LessEqual] 395, 4\ x1 + 4\ x2 - 2\ x4 + 4\ x5 + 7\ x6 \[LessEqual] 395, 4\ x1 + 4\ x2 - 2\ x3 + 7\ x5 + 4\ x6 \[LessEqual] 395, 4\ x1 + 4\ x2 - 2\ x3 + 4\ x5 + 7\ x6 \[LessEqual] 395, 4\ x1 + 7\ x3 + 4\ x4 - 2\ x5 + 4\ x6 \[LessEqual] 395, 4\ x1 + 4\ x3 + 7\ x4 - 2\ x5 + 4\ x6 \[LessEqual] 395, 4\ x1 + 4\ x3 + 4\ x4 - 2\ x5 + 7\ x6 \[LessEqual] 395, 4\ x1 - 2\ x2 + 7\ x3 + 4\ x4 + 4\ x6 \[LessEqual] 395, 4\ x1 - 2\ x2 + 4\ x3 + 7\ x4 + 4\ x6 \[LessEqual] 395, 4\ x1 - 2\ x2 + 4\ x3 + 4\ x4 + 7\ x6 \[LessEqual] 395, 7\ x2 + 4\ x3 + 4\ x4 + 4\ x5 - 2\ x6 \[LessEqual] 395, 4\ x2 + 7\ x3 + 4\ x4 + 4\ x5 - 2\ x6 \[LessEqual] 395, 4\ x2 + 4\ x3 + 7\ x4 + 4\ x5 - 2\ x6 \[LessEqual] 395, 4\ x2 + 4\ x3 + 4\ x4 + 7\ x5 - 2\ x6 \[LessEqual] 395, \(-2\)\ x1 + 7\ x2 + 4\ x3 + 4\ x4 + 4\ x5 \[LessEqual] 395, \(-2\)\ x1 + 4\ x2 + 7\ x3 + 4\ x4 + 4\ x5 \[LessEqual] 395, \(-2\)\ x1 + 4\ x2 + 4\ x3 + 7\ x4 + 4\ x5 \[LessEqual] 395, \(-2\)\ x1 + 4\ x2 + 4\ x3 + 4\ x4 + 7\ x5 \[LessEqual] 395, 5\ x1 + 3\ x2 + 2\ x3 + 2\ x4 + 2\ x5 \[LessEqual] 290, 5\ x1 + 2\ x2 + 3\ x3 + 2\ x4 + 2\ x5 \[LessEqual] 290, 5\ x1 + 2\ x2 + 2\ x3 + 3\ x4 + 2\ x5 \[LessEqual] 290, 5\ x1 + 2\ x2 + 2\ x3 + 2\ x4 + 3\ x5 \[LessEqual] 290, 3\ x1 + 5\ x2 + 2\ x3 + 2\ x4 + 2\ x6 \[LessEqual] 290, 3\ x1 + 2\ x2 + 5\ x3 + 2\ x5 + 2\ x6 \[LessEqual] 290, 3\ x1 + 2\ x2 + 5\ x4 + 2\ x5 + 2\ x6 \[LessEqual] 290, 3\ x1 + 2\ x3 + 2\ x4 + 5\ x5 + 2\ x6 \[LessEqual] 290, 2\ x1 + 5\ x2 + 3\ x3 + 2\ x4 + 2\ x6 \[LessEqual] 290, 2\ x1 + 5\ x2 + 2\ x3 + 3\ x4 + 2\ x6 \[LessEqual] 290, 2\ x1 + 5\ x2 + 2\ x3 + 2\ x4 + 3\ x6 \[LessEqual] 290, 2\ x1 + 3\ x2 + 5\ x3 + 2\ x5 + 2\ x6 \[LessEqual] 290, 2\ x1 + 3\ x2 + 5\ x4 + 2\ x5 + 2\ x6 \[LessEqual] 290, 2\ x1 + 2\ x2 + 5\ x3 + 3\ x5 + 2\ x6 \[LessEqual] 290, 2\ x1 + 2\ x2 + 5\ x3 + 2\ x5 + 3\ x6 \[LessEqual] 290, 2\ x1 + 2\ x2 + 5\ x4 + 3\ x5 + 2\ x6 \[LessEqual] 290, 2\ x1 + 2\ x2 + 5\ x4 + 2\ x5 + 3\ x6 \[LessEqual] 290, 2\ x1 + 3\ x3 + 2\ x4 + 5\ x5 + 2\ x6 \[LessEqual] 290, 2\ x1 + 2\ x3 + 3\ x4 + 5\ x5 + 2\ x6 \[LessEqual] 290, 2\ x1 + 2\ x3 + 2\ x4 + 5\ x5 + 3\ x6 \[LessEqual] 290, 3\ x2 + 2\ x3 + 2\ x4 + 2\ x5 + 5\ x6 \[LessEqual] 290, 2\ x2 + 3\ x3 + 2\ x4 + 2\ x5 + 5\ x6 \[LessEqual] 290, 2\ x2 + 2\ x3 + 3\ x4 + 2\ x5 + 5\ x6 \[LessEqual] 290, 2\ x2 + 2\ x3 + 2\ x4 + 3\ x5 + 5\ x6 \[LessEqual] 290, 9\ x1 + 6\ x2 + 2\ x3 + 6\ x5 + 6\ x6 \[LessEqual] 597, 9\ x1 + 6\ x2 + 2\ x4 + 6\ x5 + 6\ x6 \[LessEqual] 597, 9\ x1 + 2\ x2 + 6\ x3 + 6\ x4 + 6\ x6 \[LessEqual] 597, 9\ x1 + 6\ x3 + 6\ x4 + 2\ x5 + 6\ x6 \[LessEqual] 597, 6\ x1 + 9\ x2 + 2\ x3 + 6\ x5 + 6\ x6 \[LessEqual] 597, 6\ x1 + 9\ x2 + 2\ x4 + 6\ x5 + 6\ x6 \[LessEqual] 597, 6\ x1 + 6\ x2 + 2\ x3 + 9\ x5 + 6\ x6 \[LessEqual] 597, 6\ x1 + 6\ x2 + 2\ x3 + 6\ x5 + 9\ x6 \[LessEqual] 597, 6\ x1 + 6\ x2 + 2\ x4 + 9\ x5 + 6\ x6 \[LessEqual] 597, 6\ x1 + 6\ x2 + 2\ x4 + 6\ x5 + 9\ x6 \[LessEqual] 597, 6\ x1 + 2\ x2 + 9\ x3 + 6\ x4 + 6\ x6 \[LessEqual] 597, 6\ x1 + 2\ x2 + 6\ x3 + 9\ x4 + 6\ x6 \[LessEqual] 597, 6\ x1 + 2\ x2 + 6\ x3 + 6\ x4 + 9\ x6 \[LessEqual] 597, 6\ x1 + 9\ x3 + 6\ x4 + 2\ x5 + 6\ x6 \[LessEqual] 597, 6\ x1 + 6\ x3 + 9\ x4 + 2\ x5 + 6\ x6 \[LessEqual] 597, 6\ x1 + 6\ x3 + 6\ x4 + 2\ x5 + 9\ x6 \[LessEqual] 597, 2\ x1 + 9\ x2 + 6\ x3 + 6\ x4 + 6\ x5 \[LessEqual] 597, 2\ x1 + 6\ x2 + 9\ x3 + 6\ x4 + 6\ x5 \[LessEqual] 597, 2\ x1 + 6\ x2 + 6\ x3 + 9\ x4 + 6\ x5 \[LessEqual] 597, 2\ x1 + 6\ x2 + 6\ x3 + 6\ x4 + 9\ x5 \[LessEqual] 597, 9\ x2 + 6\ x3 + 6\ x4 + 6\ x5 + 2\ x6 \[LessEqual] 597, 6\ x2 + 9\ x3 + 6\ x4 + 6\ x5 + 2\ x6 \[LessEqual] 597, 6\ x2 + 6\ x3 + 9\ x4 + 6\ x5 + 2\ x6 \[LessEqual] 597, 6\ x2 + 6\ x3 + 6\ x4 + 9\ x5 + 2\ x6 \[LessEqual] 597, 5\ x1 + 2\ x2 + 2\ x3 + 2\ x4 + 2\ x6 \[LessEqual] 277, 5\ x1 + 2\ x2 + 2\ x3 + 2\ x5 + 2\ x6 \[LessEqual] 277, 5\ x1 + 2\ x2 + 2\ x4 + 2\ x5 + 2\ x6 \[LessEqual] 277, 5\ x1 + 2\ x3 + 2\ x4 + 2\ x5 + 2\ x6 \[LessEqual] 277, 2\ x1 + 5\ x2 + 2\ x3 + 2\ x4 + 2\ x5 \[LessEqual] 277, 2\ x1 + 5\ x2 + 2\ x3 + 2\ x5 + 2\ x6 \[LessEqual] 277, 2\ x1 + 5\ x2 + 2\ x4 + 2\ x5 + 2\ x6 \[LessEqual] 277, 2\ x1 + 2\ x2 + 5\ x3 + 2\ x4 + 2\ x5 \[LessEqual] 277, 2\ x1 + 2\ x2 + 5\ x3 + 2\ x4 + 2\ x6 \[LessEqual] 277, 2\ x1 + 2\ x2 + 2\ x3 + 5\ x4 + 2\ x5 \[LessEqual] 277, 2\ x1 + 2\ x2 + 2\ x3 + 5\ x4 + 2\ x6 \[LessEqual] 277, 2\ x1 + 2\ x2 + 2\ x3 + 2\ x4 + 5\ x5 \[LessEqual] 277, 2\ x1 + 2\ x2 + 2\ x3 + 2\ x4 + 5\ x6 \[LessEqual] 277, 2\ x1 + 2\ x2 + 2\ x3 + 5\ x5 + 2\ x6 \[LessEqual] 277, 2\ x1 + 2\ x2 + 2\ x3 + 2\ x5 + 5\ x6 \[LessEqual] 277, 2\ x1 + 2\ x2 + 2\ x4 + 5\ x5 + 2\ x6 \[LessEqual] 277, 2\ x1 + 2\ x2 + 2\ x4 + 2\ x5 + 5\ x6 \[LessEqual] 277, 2\ x1 + 5\ x3 + 2\ x4 + 2\ x5 + 2\ x6 \[LessEqual] 277, 2\ x1 + 2\ x3 + 5\ x4 + 2\ x5 + 2\ x6 \[LessEqual] 277, 2\ x1 + 2\ x3 + 2\ x4 + 2\ x5 + 5\ x6 \[LessEqual] 277, 5\ x2 + 2\ x3 + 2\ x4 + 2\ x5 + 2\ x6 \[LessEqual] 277, 2\ x2 + 5\ x3 + 2\ x4 + 2\ x5 + 2\ x6 \[LessEqual] 277, 2\ x2 + 2\ x3 + 5\ x4 + 2\ x5 + 2\ x6 \[LessEqual] 277, 2\ x2 + 2\ x3 + 2\ x4 + 5\ x5 + 2\ x6 \[LessEqual] 277, 8\ x1 + 5\ x2 + 2\ x3 + 2\ x4 + 2\ x6 \[LessEqual] 415, 8\ x1 + 2\ x2 + 5\ x3 + 2\ x5 + 2\ x6 \[LessEqual] 415, 8\ x1 + 2\ x2 + 5\ x4 + 2\ x5 + 2\ x6 \[LessEqual] 415, 8\ x1 + 2\ x3 + 2\ x4 + 5\ x5 + 2\ x6 \[LessEqual] 415, 5\ x1 + 8\ x2 + 2\ x3 + 2\ x4 + 2\ x5 \[LessEqual] 415, 5\ x1 + 2\ x2 + 8\ x3 + 2\ x4 + 2\ x5 \[LessEqual] 415, 5\ x1 + 2\ x2 + 2\ x3 + 8\ x4 + 2\ x5 \[LessEqual] 415, 5\ x1 + 2\ x2 + 2\ x3 + 2\ x4 + 8\ x5 \[LessEqual] 415, 2\ x1 + 8\ x2 + 5\ x3 + 2\ x5 + 2\ x6 \[LessEqual] 415, 2\ x1 + 8\ x2 + 5\ x4 + 2\ x5 + 2\ x6 \[LessEqual] 415, 2\ x1 + 5\ x2 + 8\ x3 + 2\ x4 + 2\ x6 \[LessEqual] 415, 2\ x1 + 5\ x2 + 2\ x3 + 8\ x4 + 2\ x6 \[LessEqual] 415, 2\ x1 + 5\ x2 + 2\ x3 + 2\ x4 + 8\ x6 \[LessEqual] 415, 2\ x1 + 2\ x2 + 5\ x3 + 8\ x5 + 2\ x6 \[LessEqual] 415, 2\ x1 + 2\ x2 + 5\ x3 + 2\ x5 + 8\ x6 \[LessEqual] 415, 2\ x1 + 2\ x2 + 5\ x4 + 8\ x5 + 2\ x6 \[LessEqual] 415, 2\ x1 + 2\ x2 + 5\ x4 + 2\ x5 + 8\ x6 \[LessEqual] 415, 2\ x1 + 8\ x3 + 2\ x4 + 5\ x5 + 2\ x6 \[LessEqual] 415, 2\ x1 + 2\ x3 + 8\ x4 + 5\ x5 + 2\ x6 \[LessEqual] 415, 2\ x1 + 2\ x3 + 2\ x4 + 5\ x5 + 8\ x6 \[LessEqual] 415, 8\ x2 + 2\ x3 + 2\ x4 + 2\ x5 + 5\ x6 \[LessEqual] 415, 2\ x2 + 8\ x3 + 2\ x4 + 2\ x5 + 5\ x6 \[LessEqual] 415, 2\ x2 + 2\ x3 + 8\ x4 + 2\ x5 + 5\ x6 \[LessEqual] 415, 2\ x2 + 2\ x3 + 2\ x4 + 8\ x5 + 5\ x6 \[LessEqual] 415, 3\ x1 + 2\ x2 - 6\ x3 \[LessEqual] 115, 3\ x1 + 2\ x4 - 6\ x5 \[LessEqual] 115, 3\ x1 - 6\ x4 + 2\ x5 \[LessEqual] 115, 3\ x1 - 6\ x2 + 2\ x3 \[LessEqual] 115, 2\ x1 + 3\ x2 - 6\ x3 \[LessEqual] 115, 2\ x1 + 3\ x4 - 6\ x5 \[LessEqual] 115, 2\ x1 - 6\ x4 + 3\ x5 \[LessEqual] 115, 2\ x1 - 6\ x2 + 3\ x3 \[LessEqual] 115, 3\ x2 + 2\ x4 - 6\ x6 \[LessEqual] 115, 3\ x2 - 6\ x4 + 2\ x6 \[LessEqual] 115, 2\ x2 + 3\ x4 - 6\ x6 \[LessEqual] 115, 2\ x2 - 6\ x4 + 3\ x6 \[LessEqual] 115, 3\ x3 + 2\ x5 - 6\ x6 \[LessEqual] 115, 3\ x3 - 6\ x5 + 2\ x6 \[LessEqual] 115, 2\ x3 + 3\ x5 - 6\ x6 \[LessEqual] 115, 2\ x3 - 6\ x5 + 3\ x6 \[LessEqual] 115, \(-6\)\ x3 + 3\ x5 + 2\ x6 \[LessEqual] 115, \(-6\)\ x3 + 2\ x5 + 3\ x6 \[LessEqual] 115, \(-6\)\ x2 + 3\ x4 + 2\ x6 \[LessEqual] 115, \(-6\)\ x2 + 2\ x4 + 3\ x6 \[LessEqual] 115, \(-6\)\ x1 + 3\ x2 + 2\ x3 \[LessEqual] 115, \(-6\)\ x1 + 2\ x2 + 3\ x3 \[LessEqual] 115, \(-6\)\ x1 + 3\ x4 + 2\ x5 \[LessEqual] 115, \(-6\)\ x1 + 2\ x4 + 3\ x5 \[LessEqual] 115, 9\ x1 + 6\ x2 - 2\ x3 \[LessEqual] 361, 9\ x1 + 6\ x4 - 2\ x5 \[LessEqual] 361, 9\ x1 - 2\ x4 + 6\ x5 \[LessEqual] 361, 9\ x1 - 2\ x2 + 6\ x3 \[LessEqual] 361, 6\ x1 + 9\ x2 - 2\ x3 \[LessEqual] 361, 6\ x1 + 9\ x4 - 2\ x5 \[LessEqual] 361, 6\ x1 - 2\ x4 + 9\ x5 \[LessEqual] 361, 6\ x1 - 2\ x2 + 9\ x3 \[LessEqual] 361, 9\ x2 + 6\ x4 - 2\ x6 \[LessEqual] 361, 9\ x2 - 2\ x4 + 6\ x6 \[LessEqual] 361, 6\ x2 + 9\ x4 - 2\ x6 \[LessEqual] 361, 6\ x2 - 2\ x4 + 9\ x6 \[LessEqual] 361, 9\ x3 + 6\ x5 - 2\ x6 \[LessEqual] 361, 9\ x3 - 2\ x5 + 6\ x6 \[LessEqual] 361, 6\ x3 + 9\ x5 - 2\ x6 \[LessEqual] 361, 6\ x3 - 2\ x5 + 9\ x6 \[LessEqual] 361, \(-2\)\ x3 + 9\ x5 + 6\ x6 \[LessEqual] 361, \(-2\)\ x3 + 6\ x5 + 9\ x6 \[LessEqual] 361, \(-2\)\ x2 + 9\ x4 + 6\ x6 \[LessEqual] 361, \(-2\)\ x2 + 6\ x4 + 9\ x6 \[LessEqual] 361, \(-2\)\ x1 + 9\ x2 + 6\ x3 \[LessEqual] 361, \(-2\)\ x1 + 6\ x2 + 9\ x3 \[LessEqual] 361, \(-2\)\ x1 + 9\ x4 + 6\ x5 \[LessEqual] 361, \(-2\)\ x1 + 6\ x4 + 9\ x5 \[LessEqual] 361, \(-x3\) - x4 - x6 \[LessEqual] \(-24\), \(-x3\) - x4 - x5 \[LessEqual] \(-24\), \(-x2\) - x5 - x6 \[LessEqual] \(-24\), \(-x2\) - x4 - x5 \[LessEqual] \(-24\), \(-x2\) - x3 - x5 \[LessEqual] \(-24\), \(-x2\) - x3 - x4 \[LessEqual] \(-24\), \(-x1\) - x5 - x6 \[LessEqual] \(-24\), \(-x1\) - x4 - x6 \[LessEqual] \(-24\), \(-x1\) - x3 - x6 \[LessEqual] \(-24\), \(-x1\) - x3 - x4 \[LessEqual] \(-24\), \(-x1\) - x2 - x6 \[LessEqual] \(-24\), \(-x1\) - x2 - x5 \[LessEqual] \(-24\), \(-2\)\ x2 - 3\ x3 - 2\ x4 - 3\ x5 - 5\ x6 \[LessEqual] \(-182\), \(-3\)\ x2 - 2\ x3 - 3\ x4 - 2\ x5 - 5\ x6 \[LessEqual] \(-182\), \(-2\)\ x1 - 3\ x3 - 2\ x4 - 5\ x5 - 3\ x6 \[LessEqual] \(-182\), \(-2\)\ x1 - 2\ x2 - 5\ x3 - 3\ x5 - 3\ x6 \[LessEqual] \(-182\), \(-2\)\ x1 - 3\ x2 - 5\ x4 - 2\ x5 - 3\ x6 \[LessEqual] \(-182\), \(-2\)\ x1 - 5\ x2 - 2\ x3 - 3\ x4 - 3\ x6 \[LessEqual] \(-182\), \(-3\)\ x1 - 2\ x3 - 3\ x4 - 5\ x5 - 2\ x6 \[LessEqual] \(-182\), \(-3\)\ x1 - 2\ x2 - 5\ x4 - 3\ x5 - 2\ x6 \[LessEqual] \(-182\), \(-3\)\ x1 - 3\ x2 - 5\ x3 - 2\ x5 - 2\ x6 \[LessEqual] \(-182\), \(-3\)\ x1 - 5\ x2 - 3\ x3 - 2\ x4 - 2\ x6 \[LessEqual] \(-182\), \(-5\)\ x1 - 2\ x2 - 2\ x3 - 3\ x4 - 3\ x5 \[LessEqual] \(-182\), \(-5\)\ x1 - 3\ x2 - 3\ x3 - 2\ x4 - 2\ x5 \[LessEqual] \(-182\), \(-3\)\ x2 - 4\ x3 - 4\ x4 - 3\ x5 - 6\ x6 \[LessEqual] \(-248\), \(-4\)\ x2 - 3\ x3 - 3\ x4 - 4\ x5 - 6\ x6 \[LessEqual] \(-248\), \(-3\)\ x1 - 4\ x3 - 4\ x4 - 6\ x5 - 3\ x6 \[LessEqual] \(-248\), \(-3\)\ x1 - 4\ x2 - 6\ x4 - 4\ x5 - 3\ x6 \[LessEqual] \(-248\), \(-3\)\ x1 - 4\ x2 - 6\ x3 - 4\ x5 - 3\ x6 \[LessEqual] \(-248\), \(-3\)\ x1 - 6\ x2 - 4\ x3 - 4\ x4 - 3\ x6 \[LessEqual] \(-248\), \(-4\)\ x1 - 3\ x3 - 3\ x4 - 6\ x5 - 4\ x6 \[LessEqual] \(-248\), \(-4\)\ x1 - 3\ x2 - 6\ x4 - 3\ x5 - 4\ x6 \[LessEqual] \(-248\), \(-4\)\ x1 - 3\ x2 - 6\ x3 - 3\ x5 - 4\ x6 \[LessEqual] \(-248\), \(-4\)\ x1 - 6\ x2 - 3\ x3 - 3\ x4 - 4\ x6 \[LessEqual] \(-248\), \(-6\)\ x1 - 3\ x2 - 4\ x3 - 4\ x4 - 3\ x5 \[LessEqual] \(-248\), \(-6\)\ x1 - 4\ x2 - 3\ x3 - 3\ x4 - 4\ x5 \[LessEqual] \(-248\), 4\ x1 + x2 + x4 - 2\ x6 \[LessEqual] 130, 4\ x1 + x3 + x5 - 2\ x6 \[LessEqual] 130, x1 + 4\ x2 + x4 - 2\ x5 \[LessEqual] 130, x1 + x2 - 2\ x3 + 4\ x4 \[LessEqual] 130, x1 + 4\ x3 - 2\ x4 + x5 \[LessEqual] 130, x1 - 2\ x2 + x3 + 4\ x5 \[LessEqual] 130, 4\ x2 + x3 - 2\ x5 + x6 \[LessEqual] 130, x2 + 4\ x3 - 2\ x4 + x6 \[LessEqual] 130, \(-2\)\ x3 + 4\ x4 + x5 + x6 \[LessEqual] 130, \(-2\)\ x2 + x4 + 4\ x5 + x6 \[LessEqual] 130, \(-2\)\ x1 + x2 + x3 + 4\ x6 \[LessEqual] 130, \(-2\)\ x1 + x4 + x5 + 4\ x6 \[LessEqual] 130, \(-3\)\ x3 - 3\ x4 - x5 - x6 \[LessEqual] \(-71\), \(-x2\) - 3\ x3 - 3\ x4 - x6 \[LessEqual] \(-71\), \(-3\)\ x2 - x4 - 3\ x5 - x6 \[LessEqual] \(-71\), \(-3\)\ x2 - x3 - 3\ x5 - x6 \[LessEqual] \(-71\), \(-x1\) - 3\ x3 - 3\ x4 - x5 \[LessEqual] \(-71\), \(-x1\) - x2 - 3\ x3 - 3\ x4 \[LessEqual] \(-71\), \(-x1\) - 3\ x2 - x4 - 3\ x5 \[LessEqual] \(-71\), \(-x1\) - 3\ x2 - x3 - 3\ x5 \[LessEqual] \(-71\), \(-3\)\ x1 - x4 - x5 - 3\ x6 \[LessEqual] \(-71\), \(-3\)\ x1 - x3 - x5 - 3\ x6 \[LessEqual] \(-71\), \(-3\)\ x1 - x2 - x4 - 3\ x6 \[LessEqual] \(-71\), \(-3\)\ x1 - x2 - x3 - 3\ x6 \[LessEqual] \(-71\), \(-3\)\ x3 - x4 - x5 - x6 \[LessEqual] \(-47\), \(-x2\) - x3 - 3\ x5 - x6 \[LessEqual] \(-47\), \(-x2\) - x3 - 3\ x4 - x6 \[LessEqual] \(-47\), \(-3\)\ x2 - x4 - x5 - x6 \[LessEqual] \(-47\), \(-x1\) - x3 - x5 - 3\ x6 \[LessEqual] \(-47\), \(-x1\) - x3 - 3\ x4 - x5 \[LessEqual] \(-47\), \(-x1\) - x2 - x4 - 3\ x6 \[LessEqual] \(-47\), \(-x1\) - x2 - x4 - 3\ x5 \[LessEqual] \(-47\), \(-x1\) - x2 - 3\ x3 - x4 \[LessEqual] \(-47\), \(-x1\) - 3\ x2 - x3 - x5 \[LessEqual] \(-47\), \(-3\)\ x1 - x4 - x5 - x6 \[LessEqual] \(-47\), \(-3\)\ x1 - x2 - x3 - x6 \[LessEqual] \(-47\), x1 - 2\ x2 - 8\ x3 - 8\ x4 - 2\ x5 - 4\ x6 \[LessEqual] \(-215\), x1 - 8\ x2 - 2\ x3 - 2\ x4 - 8\ x5 - 4\ x6 \[LessEqual] \(-215\), \(-2\)\ x1 + x2 - 8\ x3 - 8\ x4 - 4\ x5 - 2\ x6 \[LessEqual] \(-215\), \(-2\)\ x1 - 4\ x2 - 8\ x3 - 8\ x4 + x5 - 2\ x6 \[LessEqual] \(-215\), \(-2\)\ x1 - 8\ x2 + x3 - 4\ x4 - 8\ x5 - 2\ x6 \[LessEqual] \(-215\), \(-2\)\ x1 - 8\ x2 - 4\ x3 + x4 - 8\ x5 - 2\ x6 \[LessEqual] \(-215\), \(-4\)\ x1 - 2\ x2 - 8\ x3 - 8\ x4 - 2\ x5 + x6 \[LessEqual] \(-215\), \(-4\)\ x1 - 8\ x2 - 2\ x3 - 2\ x4 - 8\ x5 + x6 \[LessEqual] \(-215\), \(-8\)\ x1 + x2 - 2\ x3 - 2\ x4 - 4\ x5 - 8\ x6 \[LessEqual] \(-215\), \(-8\)\ x1 - 2\ x2 + x3 - 4\ x4 - 2\ x5 - 8\ x6 \[LessEqual] \(-215\), \(-8\)\ x1 - 2\ x2 - 4\ x3 + x4 - 2\ x5 - 8\ x6 \[LessEqual] \(-215\), \(-8\)\ x1 - 4\ x2 - 2\ x3 - 2\ x4 + x5 - 8\ x6 \[LessEqual] \(-215\), 9\ x1 + 6\ x2 + 4\ x5 + 6\ x6 \[LessEqual] 535, 9\ x1 + 4\ x2 + 6\ x5 + 6\ x6 \[LessEqual] 535, 9\ x1 + 6\ x3 + 4\ x4 + 6\ x6 \[LessEqual] 535, 9\ x1 + 4\ x3 + 6\ x4 + 6\ x6 \[LessEqual] 535, 6\ x1 + 9\ x2 + 6\ x5 + 4\ x6 \[LessEqual] 535, 6\ x1 + 6\ x2 + 9\ x5 + 4\ x6 \[LessEqual] 535, 6\ x1 + 6\ x2 + 4\ x5 + 9\ x6 \[LessEqual] 535, 6\ x1 + 4\ x2 + 6\ x5 + 9\ x6 \[LessEqual] 535, 6\ x1 + 9\ x3 + 6\ x4 + 4\ x6 \[LessEqual] 535, 6\ x1 + 6\ x3 + 9\ x4 + 4\ x6 \[LessEqual] 535, 6\ x1 + 6\ x3 + 4\ x4 + 9\ x6 \[LessEqual] 535, 6\ x1 + 4\ x3 + 6\ x4 + 9\ x6 \[LessEqual] 535, 4\ x1 + 9\ x2 + 6\ x5 + 6\ x6 \[LessEqual] 535, 4\ x1 + 6\ x2 + 9\ x5 + 6\ x6 \[LessEqual] 535, 4\ x1 + 9\ x3 + 6\ x4 + 6\ x6 \[LessEqual] 535, 4\ x1 + 6\ x3 + 9\ x4 + 6\ x6 \[LessEqual] 535, 9\ x2 + 6\ x3 + 4\ x4 + 6\ x5 \[LessEqual] 535, 9\ x2 + 4\ x3 + 6\ x4 + 6\ x5 \[LessEqual] 535, 6\ x2 + 9\ x3 + 6\ x4 + 4\ x5 \[LessEqual] 535, 6\ x2 + 6\ x3 + 9\ x4 + 4\ x5 \[LessEqual] 535, 6\ x2 + 6\ x3 + 4\ x4 + 9\ x5 \[LessEqual] 535, 6\ x2 + 4\ x3 + 6\ x4 + 9\ x5 \[LessEqual] 535, 4\ x2 + 9\ x3 + 6\ x4 + 6\ x5 \[LessEqual] 535, 4\ x2 + 6\ x3 + 9\ x4 + 6\ x5 \[LessEqual] 535, x1 + x2 - 2\ x6 \[LessEqual] 44, x1 + x2 - 2\ x5 \[LessEqual] 44, x1 + x3 - 2\ x6 \[LessEqual] 44, x1 + x3 - 2\ x4 \[LessEqual] 44, x1 + x4 - 2\ x6 \[LessEqual] 44, x1 + x5 - 2\ x6 \[LessEqual] 44, x1 - 2\ x3 + x4 \[LessEqual] 44, x1 - 2\ x2 + x5 \[LessEqual] 44, x2 + x3 - 2\ x5 \[LessEqual] 44, x2 + x3 - 2\ x4 \[LessEqual] 44, x2 + x4 - 2\ x5 \[LessEqual] 44, x2 - 2\ x5 + x6 \[LessEqual] 44, x2 - 2\ x3 + x4 \[LessEqual] 44, x3 - 2\ x4 + x5 \[LessEqual] 44, x3 - 2\ x4 + x6 \[LessEqual] 44, \(-2\)\ x3 + x4 + x5 \[LessEqual] 44, \(-2\)\ x3 + x4 + x6 \[LessEqual] 44, \(-2\)\ x2 + x3 + x5 \[LessEqual] 44, \(-2\)\ x2 + x4 + x5 \[LessEqual] 44, \(-2\)\ x2 + x5 + x6 \[LessEqual] 44, \(-2\)\ x1 + x2 + x6 \[LessEqual] 44, \(-2\)\ x1 + x3 + x6 \[LessEqual] 44, \(-2\)\ x1 + x4 + x6 \[LessEqual] 44, \(-2\)\ x1 + x5 + x6 \[LessEqual] 44, 3\ x1 + 3\ x2 - 2\ x6 \[LessEqual] 136, 3\ x1 + 3\ x2 - 2\ x5 \[LessEqual] 136, 3\ x1 + 3\ x3 - 2\ x6 \[LessEqual] 136, 3\ x1 + 3\ x3 - 2\ x4 \[LessEqual] 136, 3\ x1 + 3\ x4 - 2\ x6 \[LessEqual] 136, 3\ x1 + 3\ x5 - 2\ x6 \[LessEqual] 136, 3\ x1 - 2\ x3 + 3\ x4 \[LessEqual] 136, 3\ x1 - 2\ x2 + 3\ x5 \[LessEqual] 136, 3\ x2 + 3\ x3 - 2\ x5 \[LessEqual] 136, 3\ x2 + 3\ x3 - 2\ x4 \[LessEqual] 136, 3\ x2 + 3\ x4 - 2\ x5 \[LessEqual] 136, 3\ x2 - 2\ x5 + 3\ x6 \[LessEqual] 136, 3\ x2 - 2\ x3 + 3\ x4 \[LessEqual] 136, 3\ x3 - 2\ x4 + 3\ x5 \[LessEqual] 136, 3\ x3 - 2\ x4 + 3\ x6 \[LessEqual] 136, \(-2\)\ x3 + 3\ x4 + 3\ x5 \[LessEqual] 136, \(-2\)\ x3 + 3\ x4 + 3\ x6 \[LessEqual] 136, \(-2\)\ x2 + 3\ x3 + 3\ x5 \[LessEqual] 136, \(-2\)\ x2 + 3\ x4 + 3\ x5 \[LessEqual] 136, \(-2\)\ x2 + 3\ x5 + 3\ x6 \[LessEqual] 136, \(-2\)\ x1 + 3\ x2 + 3\ x6 \[LessEqual] 136, \(-2\)\ x1 + 3\ x3 + 3\ x6 \[LessEqual] 136, \(-2\)\ x1 + 3\ x4 + 3\ x6 \[LessEqual] 136, \(-2\)\ x1 + 3\ x5 + 3\ x6 \[LessEqual] 136, 3\ x1 - 2\ x5 - 2\ x6 \[LessEqual] 47, 3\ x1 - 2\ x4 - 2\ x6 \[LessEqual] 47, 3\ x1 - 2\ x3 - 2\ x6 \[LessEqual] 47, 3\ x1 - 2\ x2 - 2\ x6 \[LessEqual] 47, 3\ x2 - 2\ x5 - 2\ x6 \[LessEqual] 47, 3\ x2 - 2\ x4 - 2\ x5 \[LessEqual] 47, 3\ x2 - 2\ x3 - 2\ x5 \[LessEqual] 47, 3\ x3 - 2\ x4 - 2\ x6 \[LessEqual] 47, 3\ x3 - 2\ x4 - 2\ x5 \[LessEqual] 47, \(-2\)\ x3 + 3\ x4 - 2\ x6 \[LessEqual] 47, \(-2\)\ x3 + 3\ x4 - 2\ x5 \[LessEqual] 47, \(-2\)\ x2 + 3\ x3 - 2\ x4 \[LessEqual] 47, \(-2\)\ x2 + 3\ x5 - 2\ x6 \[LessEqual] 47, \(-2\)\ x2 - 2\ x4 + 3\ x5 \[LessEqual] 47, \(-2\)\ x2 - 2\ x3 + 3\ x4 \[LessEqual] 47, \(-2\)\ x2 - 2\ x3 + 3\ x5 \[LessEqual] 47, \(-2\)\ x1 + 3\ x2 - 2\ x5 \[LessEqual] 47, \(-2\)\ x1 + 3\ x3 - 2\ x4 \[LessEqual] 47, \(-2\)\ x1 - 2\ x5 + 3\ x6 \[LessEqual] 47, \(-2\)\ x1 - 2\ x4 + 3\ x6 \[LessEqual] 47, \(-2\)\ x1 - 2\ x3 + 3\ x4 \[LessEqual] 47, \(-2\)\ x1 - 2\ x3 + 3\ x6 \[LessEqual] 47, \(-2\)\ x1 - 2\ x2 + 3\ x5 \[LessEqual] 47, \(-2\)\ x1 - 2\ x2 + 3\ x6 \[LessEqual] 47, 11\ x1 + 2\ x2 + 2\ x4 - 4\ x6 \[LessEqual] 335, 11\ x1 + 2\ x3 + 2\ x5 - 4\ x6 \[LessEqual] 335, 2\ x1 + 11\ x2 + 2\ x4 - 4\ x5 \[LessEqual] 335, 2\ x1 + 2\ x2 - 4\ x3 + 11\ x4 \[LessEqual] 335, 2\ x1 + 11\ x3 - 4\ x4 + 2\ x5 \[LessEqual] 335, 2\ x1 - 4\ x2 + 2\ x3 + 11\ x5 \[LessEqual] 335, 11\ x2 + 2\ x3 - 4\ x5 + 2\ x6 \[LessEqual] 335, 2\ x2 + 11\ x3 - 4\ x4 + 2\ x6 \[LessEqual] 335, \(-4\)\ x3 + 11\ x4 + 2\ x5 + 2\ x6 \[LessEqual] 335, \(-4\)\ x2 + 2\ x4 + 11\ x5 + 2\ x6 \[LessEqual] 335, \(-4\)\ x1 + 2\ x2 + 2\ x3 + 11\ x6 \[LessEqual] 335, \(-4\)\ x1 + 2\ x4 + 2\ x5 + 11\ x6 \[LessEqual] 335, 3\ x1 - 2\ x3 - 6\ x4 - 6\ x5 - 6\ x6 \[LessEqual] \(-161\), 3\ x1 - 2\ x2 - 6\ x4 - 6\ x5 - 6\ x6 \[LessEqual] \(-161\), 3\ x1 - 6\ x2 - 6\ x3 - 2\ x5 - 6\ x6 \[LessEqual] \(-161\), 3\ x1 - 6\ x2 - 6\ x3 - 2\ x4 - 6\ x6 \[LessEqual] \(-161\), 3\ x2 - 2\ x3 - 6\ x4 - 6\ x5 - 6\ x6 \[LessEqual] \(-161\), \(-2\)\ x2 + 3\ x3 - 6\ x4 - 6\ x5 - 6\ x6 \[LessEqual] \(-161\), \(-6\)\ x2 - 6\ x3 + 3\ x4 - 2\ x5 - 6\ x6 \[LessEqual] \(-161\), \(-6\)\ x2 - 6\ x3 - 2\ x4 + 3\ x5 - 6\ x6 \[LessEqual] \(-161\), \(-2\)\ x1 + 3\ x2 - 6\ x4 - 6\ x5 - 6\ x6 \[LessEqual] \(-161\), \(-2\)\ x1 + 3\ x3 - 6\ x4 - 6\ x5 - 6\ x6 \[LessEqual] \(-161\), \(-2\)\ x1 - 6\ x2 - 6\ x3 + 3\ x4 - 6\ x6 \[LessEqual] \(-161\), \(-2\)\ x1 - 6\ x2 - 6\ x3 + 3\ x5 - 6\ x6 \[LessEqual] \(-161\), \(-6\)\ x1 + 3\ x2 - 6\ x3 - 6\ x5 - 2\ x6 \[LessEqual] \(-161\), \(-6\)\ x1 + 3\ x2 - 6\ x3 - 2\ x4 - 6\ x5 \[LessEqual] \(-161\), \(-6\)\ x1 - 6\ x3 + 3\ x4 - 6\ x5 - 2\ x6 \[LessEqual] \(-161\), \(-6\)\ x1 - 6\ x3 - 2\ x4 - 6\ x5 + 3\ x6 \[LessEqual] \(-161\), \(-6\)\ x1 - 2\ x2 - 6\ x3 + 3\ x4 - 6\ x5 \[LessEqual] \(-161\), \(-6\)\ x1 - 2\ x2 - 6\ x3 - 6\ x5 + 3\ x6 \[LessEqual] \(-161\), \(-6\)\ x1 - 6\ x2 + 3\ x3 - 6\ x4 - 2\ x6 \[LessEqual] \(-161\), \(-6\)\ x1 - 6\ x2 + 3\ x3 - 6\ x4 - 2\ x5 \[LessEqual] \(-161\), \(-6\)\ x1 - 6\ x2 - 6\ x4 + 3\ x5 - 2\ x6 \[LessEqual] \(-161\), \(-6\)\ x1 - 6\ x2 - 6\ x4 - 2\ x5 + 3\ x6 \[LessEqual] \(-161\), \(-6\)\ x1 - 6\ x2 - 2\ x3 - 6\ x4 + 3\ x5 \[LessEqual] \(-161\), \(-6\)\ x1 - 6\ x2 - 2\ x3 - 6\ x4 + 3\ x6 \[LessEqual] \(-161\), 9\ x1 + 6\ x2 - 2\ x4 + 6\ x5 + 6\ x6 \[LessEqual] 555, 9\ x1 + 6\ x2 - 2\ x3 + 6\ x5 + 6\ x6 \[LessEqual] 555, 9\ x1 + 6\ x3 + 6\ x4 - 2\ x5 + 6\ x6 \[LessEqual] 555, 9\ x1 - 2\ x2 + 6\ x3 + 6\ x4 + 6\ x6 \[LessEqual] 555, 6\ x1 + 9\ x2 - 2\ x4 + 6\ x5 + 6\ x6 \[LessEqual] 555, 6\ x1 + 9\ x2 - 2\ x3 + 6\ x5 + 6\ x6 \[LessEqual] 555, 6\ x1 + 6\ x2 - 2\ x4 + 9\ x5 + 6\ x6 \[LessEqual] 555, 6\ x1 + 6\ x2 - 2\ x4 + 6\ x5 + 9\ x6 \[LessEqual] 555, 6\ x1 + 6\ x2 - 2\ x3 + 9\ x5 + 6\ x6 \[LessEqual] 555, 6\ x1 + 6\ x2 - 2\ x3 + 6\ x5 + 9\ x6 \[LessEqual] 555, 6\ x1 + 9\ x3 + 6\ x4 - 2\ x5 + 6\ x6 \[LessEqual] 555, 6\ x1 + 6\ x3 + 9\ x4 - 2\ x5 + 6\ x6 \[LessEqual] 555, 6\ x1 + 6\ x3 + 6\ x4 - 2\ x5 + 9\ x6 \[LessEqual] 555, 6\ x1 - 2\ x2 + 9\ x3 + 6\ x4 + 6\ x6 \[LessEqual] 555, 6\ x1 - 2\ x2 + 6\ x3 + 9\ x4 + 6\ x6 \[LessEqual] 555, 6\ x1 - 2\ x2 + 6\ x3 + 6\ x4 + 9\ x6 \[LessEqual] 555, 9\ x2 + 6\ x3 + 6\ x4 + 6\ x5 - 2\ x6 \[LessEqual] 555, 6\ x2 + 9\ x3 + 6\ x4 + 6\ x5 - 2\ x6 \[LessEqual] 555, 6\ x2 + 6\ x3 + 9\ x4 + 6\ x5 - 2\ x6 \[LessEqual] 555, 6\ x2 + 6\ x3 + 6\ x4 + 9\ x5 - 2\ x6 \[LessEqual] 555, \(-2\)\ x1 + 9\ x2 + 6\ x3 + 6\ x4 + 6\ x5 \[LessEqual] 555, \(-2\)\ x1 + 6\ x2 + 9\ x3 + 6\ x4 + 6\ x5 \[LessEqual] 555, \(-2\)\ x1 + 6\ x2 + 6\ x3 + 9\ x4 + 6\ x5 \[LessEqual] 555, \(-2\)\ x1 + 6\ x2 + 6\ x3 + 6\ x4 + 9\ x5 \[LessEqual] 555, 15\ x1 + 10\ x2 + 6\ x3 + 6\ x5 + 6\ x6 \[LessEqual] 895, 15\ x1 + 6\ x2 + 10\ x3 + 6\ x4 + 6\ x6 \[LessEqual] 895, 15\ x1 + 6\ x2 + 6\ x4 + 10\ x5 + 6\ x6 \[LessEqual] 895, 15\ x1 + 6\ x3 + 10\ x4 + 6\ x5 + 6\ x6 \[LessEqual] 895, 10\ x1 + 15\ x2 + 6\ x3 + 6\ x5 + 6\ x6 \[LessEqual] 895, 10\ x1 + 6\ x2 + 15\ x3 + 6\ x4 + 6\ x6 \[LessEqual] 895, 10\ x1 + 6\ x2 + 6\ x4 + 15\ x5 + 6\ x6 \[LessEqual] 895, 10\ x1 + 6\ x3 + 15\ x4 + 6\ x5 + 6\ x6 \[LessEqual] 895, 6\ x1 + 15\ x2 + 10\ x3 + 6\ x4 + 6\ x5 \[LessEqual] 895, 6\ x1 + 15\ x2 + 6\ x4 + 6\ x5 + 10\ x6 \[LessEqual] 895, 6\ x1 + 10\ x2 + 15\ x3 + 6\ x4 + 6\ x5 \[LessEqual] 895, 6\ x1 + 10\ x2 + 6\ x4 + 6\ x5 + 15\ x6 \[LessEqual] 895, 6\ x1 + 6\ x2 + 6\ x3 + 15\ x4 + 10\ x5 \[LessEqual] 895, 6\ x1 + 6\ x2 + 6\ x3 + 15\ x4 + 10\ x6 \[LessEqual] 895, 6\ x1 + 6\ x2 + 6\ x3 + 10\ x4 + 15\ x5 \[LessEqual] 895, 6\ x1 + 6\ x2 + 6\ x3 + 10\ x4 + 15\ x6 \[LessEqual] 895, 6\ x1 + 6\ x2 + 6\ x3 + 15\ x5 + 10\ x6 \[LessEqual] 895, 6\ x1 + 6\ x2 + 6\ x3 + 10\ x5 + 15\ x6 \[LessEqual] 895, 6\ x1 + 15\ x3 + 6\ x4 + 6\ x5 + 10\ x6 \[LessEqual] 895, 6\ x1 + 10\ x3 + 6\ x4 + 6\ x5 + 15\ x6 \[LessEqual] 895, 15\ x2 + 6\ x3 + 10\ x4 + 6\ x5 + 6\ x6 \[LessEqual] 895, 10\ x2 + 6\ x3 + 15\ x4 + 6\ x5 + 6\ x6 \[LessEqual] 895, 6\ x2 + 15\ x3 + 6\ x4 + 10\ x5 + 6\ x6 \[LessEqual] 895, 6\ x2 + 10\ x3 + 6\ x4 + 15\ x5 + 6\ x6 \[LessEqual] 895, x1 + x2 - 2\ x3 \[LessEqual] 46, x1 + x4 - 2\ x5 \[LessEqual] 46, x1 - 2\ x4 + x5 \[LessEqual] 46, x1 - 2\ x2 + x3 \[LessEqual] 46, x2 + x4 - 2\ x6 \[LessEqual] 46, x2 - 2\ x4 + x6 \[LessEqual] 46, x3 + x5 - 2\ x6 \[LessEqual] 46, x3 - 2\ x5 + x6 \[LessEqual] 46, \(-2\)\ x3 + x5 + x6 \[LessEqual] 46, \(-2\)\ x2 + x4 + x6 \[LessEqual] 46, \(-2\)\ x1 + x2 + x3 \[LessEqual] 46, \(-2\)\ x1 + x4 + x5 \[LessEqual] 46, 6\ x1 + 3\ x2 + 2\ x3 + 2\ x4 + 2\ x5 \[LessEqual] 313, 6\ x1 + 2\ x2 + 3\ x3 + 2\ x4 + 2\ x5 \[LessEqual] 313, 6\ x1 + 2\ x2 + 2\ x3 + 3\ x4 + 2\ x5 \[LessEqual] 313, 6\ x1 + 2\ x2 + 2\ x3 + 2\ x4 + 3\ x5 \[LessEqual] 313, 3\ x1 + 6\ x2 + 2\ x3 + 2\ x4 + 2\ x6 \[LessEqual] 313, 3\ x1 + 2\ x2 + 6\ x3 + 2\ x5 + 2\ x6 \[LessEqual] 313, 3\ x1 + 2\ x2 + 6\ x4 + 2\ x5 + 2\ x6 \[LessEqual] 313, 3\ x1 + 2\ x3 + 2\ x4 + 6\ x5 + 2\ x6 \[LessEqual] 313, 2\ x1 + 6\ x2 + 3\ x3 + 2\ x4 + 2\ x6 \[LessEqual] 313, 2\ x1 + 6\ x2 + 2\ x3 + 3\ x4 + 2\ x6 \[LessEqual] 313, 2\ x1 + 6\ x2 + 2\ x3 + 2\ x4 + 3\ x6 \[LessEqual] 313, 2\ x1 + 3\ x2 + 6\ x3 + 2\ x5 + 2\ x6 \[LessEqual] 313, 2\ x1 + 3\ x2 + 6\ x4 + 2\ x5 + 2\ x6 \[LessEqual] 313, 2\ x1 + 2\ x2 + 6\ x3 + 3\ x5 + 2\ x6 \[LessEqual] 313, 2\ x1 + 2\ x2 + 6\ x3 + 2\ x5 + 3\ x6 \[LessEqual] 313, 2\ x1 + 2\ x2 + 6\ x4 + 3\ x5 + 2\ x6 \[LessEqual] 313, 2\ x1 + 2\ x2 + 6\ x4 + 2\ x5 + 3\ x6 \[LessEqual] 313, 2\ x1 + 3\ x3 + 2\ x4 + 6\ x5 + 2\ x6 \[LessEqual] 313, 2\ x1 + 2\ x3 + 3\ x4 + 6\ x5 + 2\ x6 \[LessEqual] 313, 2\ x1 + 2\ x3 + 2\ x4 + 6\ x5 + 3\ x6 \[LessEqual] 313, 3\ x2 + 2\ x3 + 2\ x4 + 2\ x5 + 6\ x6 \[LessEqual] 313, 2\ x2 + 3\ x3 + 2\ x4 + 2\ x5 + 6\ x6 \[LessEqual] 313, 2\ x2 + 2\ x3 + 3\ x4 + 2\ x5 + 6\ x6 \[LessEqual] 313, 2\ x2 + 2\ x3 + 2\ x4 + 3\ x5 + 6\ x6 \[LessEqual] 313, 25\ x1 + 10\ x2 + 4\ x3 + 10\ x4 + 4\ x5 + 4\ x6 \[LessEqual] 1221, 25\ x1 + 4\ x2 + 10\ x3 + 4\ x4 + 10\ x5 + 4\ x6 \[LessEqual] 1221, 10\ x1 + 25\ x2 + 4\ x3 + 10\ x4 + 4\ x5 + 4\ x6 \[LessEqual] 1221, 10\ x1 + 10\ x2 + 4\ x3 + 25\ x4 + 4\ x5 + 4\ x6 \[LessEqual] 1221, 10\ x1 + 4\ x2 + 25\ x3 + 4\ x4 + 10\ x5 + 4\ x6 \[LessEqual] 1221, 10\ x1 + 4\ x2 + 10\ x3 + 4\ x4 + 25\ x5 + 4\ x6 \[LessEqual] 1221, 4\ x1 + 25\ x2 + 10\ x3 + 4\ x4 + 4\ x5 + 10\ x6 \[LessEqual] 1221, 4\ x1 + 10\ x2 + 25\ x3 + 4\ x4 + 4\ x5 + 10\ x6 \[LessEqual] 1221, 4\ x1 + 10\ x2 + 10\ x3 + 4\ x4 + 4\ x5 + 25\ x6 \[LessEqual] 1221, 4\ x1 + 4\ x2 + 4\ x3 + 25\ x4 + 10\ x5 + 10\ x6 \[LessEqual] 1221, 4\ x1 + 4\ x2 + 4\ x3 + 10\ x4 + 25\ x5 + 10\ x6 \[LessEqual] 1221, 4\ x1 + 4\ x2 + 4\ x3 + 10\ x4 + 10\ x5 + 25\ x6 \[LessEqual] 1221, 5\ x1 + 2\ x2 + 2\ x3 + 2\ x4 \[LessEqual] 245, 5\ x1 + 2\ x2 + 2\ x3 + 2\ x5 \[LessEqual] 245, 5\ x1 + 2\ x2 + 2\ x4 + 2\ x5 \[LessEqual] 245, 5\ x1 + 2\ x3 + 2\ x4 + 2\ x5 \[LessEqual] 245, 2\ x1 + 5\ x2 + 2\ x3 + 2\ x4 \[LessEqual] 245, 2\ x1 + 5\ x2 + 2\ x3 + 2\ x6 \[LessEqual] 245, 2\ x1 + 5\ x2 + 2\ x4 + 2\ x6 \[LessEqual] 245, 2\ x1 + 2\ x2 + 5\ x3 + 2\ x5 \[LessEqual] 245, 2\ x1 + 2\ x2 + 5\ x3 + 2\ x6 \[LessEqual] 245, 2\ x1 + 2\ x2 + 5\ x4 + 2\ x5 \[LessEqual] 245, 2\ x1 + 2\ x2 + 5\ x4 + 2\ x6 \[LessEqual] 245, 2\ x1 + 5\ x3 + 2\ x5 + 2\ x6 \[LessEqual] 245, 2\ x1 + 2\ x3 + 2\ x4 + 5\ x5 \[LessEqual] 245, 2\ x1 + 2\ x3 + 5\ x5 + 2\ x6 \[LessEqual] 245, 2\ x1 + 5\ x4 + 2\ x5 + 2\ x6 \[LessEqual] 245, 2\ x1 + 2\ x4 + 5\ x5 + 2\ x6 \[LessEqual] 245, 5\ x2 + 2\ x3 + 2\ x4 + 2\ x6 \[LessEqual] 245, 2\ x2 + 5\ x3 + 2\ x5 + 2\ x6 \[LessEqual] 245, 2\ x2 + 2\ x3 + 2\ x4 + 5\ x6 \[LessEqual] 245, 2\ x2 + 2\ x3 + 2\ x5 + 5\ x6 \[LessEqual] 245, 2\ x2 + 5\ x4 + 2\ x5 + 2\ x6 \[LessEqual] 245, 2\ x2 + 2\ x4 + 2\ x5 + 5\ x6 \[LessEqual] 245, 2\ x3 + 2\ x4 + 5\ x5 + 2\ x6 \[LessEqual] 245, 2\ x3 + 2\ x4 + 2\ x5 + 5\ x6 \[LessEqual] 245, \(-x2\) - x3 - x4 - x5 - 2\ x6 \[LessEqual] \(-75\), \(-x1\) - x3 - x4 - 2\ x5 - x6 \[LessEqual] \(-75\), \(-x1\) - x2 - 2\ x4 - x5 - x6 \[LessEqual] \(-75\), \(-x1\) - x2 - 2\ x3 - x5 - x6 \[LessEqual] \(-75\), \(-x1\) - 2\ x2 - x3 - x4 - x6 \[LessEqual] \(-75\), \(-2\)\ x1 - x2 - x3 - x4 - x5 \[LessEqual] \(-75\), 3\ x1 - x3 - x5 - 3\ x6 \[LessEqual] 31, 3\ x1 - x2 - x4 - 3\ x6 \[LessEqual] 31, 3\ x2 - x3 - 3\ x5 - x6 \[LessEqual] 31, \(-3\)\ x3 + 3\ x4 - x5 - x6 \[LessEqual] 31, \(-x2\) + 3\ x3 - 3\ x4 - x6 \[LessEqual] 31, \(-3\)\ x2 - x4 + 3\ x5 - x6 \[LessEqual] 31, \(-x1\) + 3\ x2 - x4 - 3\ x5 \[LessEqual] 31, \(-x1\) + 3\ x3 - 3\ x4 - x5 \[LessEqual] 31, \(-x1\) - x2 - 3\ x3 + 3\ x4 \[LessEqual] 31, \(-x1\) - 3\ x2 - x3 + 3\ x5 \[LessEqual] 31, \(-3\)\ x1 - x4 - x5 + 3\ x6 \[LessEqual] 31, \(-3\)\ x1 - x2 - x3 + 3\ x6 \[LessEqual] 31, 3\ x1 - 2\ x3 - 6\ x4 - 8\ x5 - 8\ x6 \[LessEqual] \(-207\), 3\ x1 - 2\ x2 - 8\ x4 - 6\ x5 - 8\ x6 \[LessEqual] \(-207\), 3\ x1 - 6\ x2 - 8\ x3 - 2\ x5 - 8\ x6 \[LessEqual] \(-207\), 3\ x1 - 8\ x2 - 6\ x3 - 2\ x4 - 8\ x6 \[LessEqual] \(-207\), 3\ x2 - 2\ x3 - 6\ x4 - 8\ x5 - 8\ x6 \[LessEqual] \(-207\), \(-2\)\ x2 + 3\ x3 - 8\ x4 - 6\ x5 - 8\ x6 \[LessEqual] \(-207\), \(-6\)\ x2 - 8\ x3 + 3\ x4 - 2\ x5 - 8\ x6 \[LessEqual] \(-207\), \(-8\)\ x2 - 6\ x3 - 2\ x4 + 3\ x5 - 8\ x6 \[LessEqual] \(-207\), \(-2\)\ x1 + 3\ x2 - 8\ x4 - 8\ x5 - 6\ x6 \[LessEqual] \(-207\), \(-2\)\ x1 + 3\ x3 - 8\ x4 - 8\ x5 - 6\ x6 \[LessEqual] \(-207\), \(-2\)\ x1 - 8\ x2 - 8\ x3 + 3\ x4 - 6\ x6 \[LessEqual] \(-207\), \(-2\)\ x1 - 8\ x2 - 8\ x3 + 3\ x5 - 6\ x6 \[LessEqual] \(-207\), \(-6\)\ x1 + 3\ x2 - 8\ x3 - 8\ x5 - 2\ x6 \[LessEqual] \(-207\), \(-6\)\ x1 - 8\ x3 + 3\ x4 - 8\ x5 - 2\ x6 \[LessEqual] \(-207\), \(-6\)\ x1 - 8\ x2 + 3\ x3 - 8\ x4 - 2\ x6 \[LessEqual] \(-207\), \(-6\)\ x1 - 8\ x2 - 8\ x4 + 3\ x5 - 2\ x6 \[LessEqual] \(-207\), \(-8\)\ x1 + 3\ x2 - 6\ x3 - 2\ x4 - 8\ x5 \[LessEqual] \(-207\), \(-8\)\ x1 - 6\ x3 - 2\ x4 - 8\ x5 + 3\ x6 \[LessEqual] \(-207\), \(-8\)\ x1 - 2\ x2 - 8\ x3 + 3\ x4 - 6\ x5 \[LessEqual] \(-207\), \(-8\)\ x1 - 2\ x2 - 8\ x3 - 6\ x5 + 3\ x6 \[LessEqual] \(-207\), \(-8\)\ x1 - 6\ x2 + 3\ x3 - 8\ x4 - 2\ x5 \[LessEqual] \(-207\), \(-8\)\ x1 - 6\ x2 - 8\ x4 - 2\ x5 + 3\ x6 \[LessEqual] \(-207\), \(-8\)\ x1 - 8\ x2 - 2\ x3 - 6\ x4 + 3\ x5 \[LessEqual] \(-207\), \(-8\)\ x1 - 8\ x2 - 2\ x3 - 6\ x4 + 3\ x6 \[LessEqual] \(-207\), 9\ x1 + 2\ x2 - 4\ x6 \[LessEqual] 245, 9\ x1 + 2\ x3 - 4\ x6 \[LessEqual] 245, 9\ x1 + 2\ x4 - 4\ x6 \[LessEqual] 245, 9\ x1 + 2\ x5 - 4\ x6 \[LessEqual] 245, 2\ x1 + 9\ x2 - 4\ x5 \[LessEqual] 245, 2\ x1 + 9\ x3 - 4\ x4 \[LessEqual] 245, 2\ x1 - 4\ x3 + 9\ x4 \[LessEqual] 245, 2\ x1 - 4\ x2 + 9\ x5 \[LessEqual] 245, 9\ x2 + 2\ x3 - 4\ x5 \[LessEqual] 245, 9\ x2 + 2\ x4 - 4\ x5 \[LessEqual] 245, 9\ x2 - 4\ x5 + 2\ x6 \[LessEqual] 245, 2\ x2 + 9\ x3 - 4\ x4 \[LessEqual] 245, 2\ x2 - 4\ x3 + 9\ x4 \[LessEqual] 245, 9\ x3 - 4\ x4 + 2\ x5 \[LessEqual] 245, 9\ x3 - 4\ x4 + 2\ x6 \[LessEqual] 245, \(-4\)\ x3 + 9\ x4 + 2\ x5 \[LessEqual] 245, \(-4\)\ x3 + 9\ x4 + 2\ x6 \[LessEqual] 245, \(-4\)\ x2 + 2\ x3 + 9\ x5 \[LessEqual] 245, \(-4\)\ x2 + 2\ x4 + 9\ x5 \[LessEqual] 245, \(-4\)\ x2 + 9\ x5 + 2\ x6 \[LessEqual] 245, \(-4\)\ x1 + 2\ x2 + 9\ x6 \[LessEqual] 245, \(-4\)\ x1 + 2\ x3 + 9\ x6 \[LessEqual] 245, \(-4\)\ x1 + 2\ x4 + 9\ x6 \[LessEqual] 245, \(-4\)\ x1 + 2\ x5 + 9\ x6 \[LessEqual] 245, x1 - 2\ x3 - 2\ x4 \[LessEqual] 1, x1 - 2\ x2 - 2\ x5 \[LessEqual] 1, x2 - 2\ x3 - 2\ x4 \[LessEqual] 1, \(-2\)\ x3 - 2\ x4 + x5 \[LessEqual] 1, \(-2\)\ x3 - 2\ x4 + x6 \[LessEqual] 1, \(-2\)\ x2 + x3 - 2\ x5 \[LessEqual] 1, \(-2\)\ x2 + x4 - 2\ x5 \[LessEqual] 1, \(-2\)\ x2 - 2\ x5 + x6 \[LessEqual] 1, \(-2\)\ x1 + x2 - 2\ x6 \[LessEqual] 1, \(-2\)\ x1 + x3 - 2\ x6 \[LessEqual] 1, \(-2\)\ x1 + x4 - 2\ x6 \[LessEqual] 1, \(-2\)\ x1 + x5 - 2\ x6 \[LessEqual] 1, 9\ x1 - 2\ x3 - 2\ x5 - 6\ x6 \[LessEqual] 137, 9\ x1 - 2\ x2 - 2\ x4 - 6\ x6 \[LessEqual] 137, 9\ x2 - 2\ x3 - 6\ x5 - 2\ x6 \[LessEqual] 137, \(-6\)\ x3 + 9\ x4 - 2\ x5 - 2\ x6 \[LessEqual] 137, \(-2\)\ x2 + 9\ x3 - 6\ x4 - 2\ x6 \[LessEqual] 137, \(-6\)\ x2 - 2\ x4 + 9\ x5 - 2\ x6 \[LessEqual] 137, \(-2\)\ x1 + 9\ x2 - 2\ x4 - 6\ x5 \[LessEqual] 137, \(-2\)\ x1 + 9\ x3 - 6\ x4 - 2\ x5 \[LessEqual] 137, \(-2\)\ x1 - 2\ x2 - 6\ x3 + 9\ x4 \[LessEqual] 137, \(-2\)\ x1 - 6\ x2 - 2\ x3 + 9\ x5 \[LessEqual] 137, \(-6\)\ x1 - 2\ x4 - 2\ x5 + 9\ x6 \[LessEqual] 137, \(-6\)\ x1 - 2\ x2 - 2\ x3 + 9\ x6 \[LessEqual] 137, 4\ x1 + x2 + x5 - 2\ x6 \[LessEqual] 130, 4\ x1 + x3 + x4 - 2\ x6 \[LessEqual] 130, x1 + 4\ x2 - 2\ x5 + x6 \[LessEqual] 130, x1 + 4\ x3 - 2\ x4 + x6 \[LessEqual] 130, x1 - 2\ x3 + 4\ x4 + x6 \[LessEqual] 130, x1 - 2\ x2 + 4\ x5 + x6 \[LessEqual] 130, 4\ x2 + x3 + x4 - 2\ x5 \[LessEqual] 130, x2 + 4\ x3 - 2\ x4 + x5 \[LessEqual] 130, x2 - 2\ x3 + 4\ x4 + x5 \[LessEqual] 130, \(-2\)\ x2 + x3 + x4 + 4\ x5 \[LessEqual] 130, \(-2\)\ x1 + x2 + x5 + 4\ x6 \[LessEqual] 130, \(-2\)\ x1 + x3 + x4 + 4\ x6 \[LessEqual] 130, 3\ x1 + x2 - 2\ x6 \[LessEqual] 86, 3\ x1 + x3 - 2\ x6 \[LessEqual] 86, 3\ x1 + x4 - 2\ x6 \[LessEqual] 86, 3\ x1 + x5 - 2\ x6 \[LessEqual] 86, x1 + 3\ x2 - 2\ x5 \[LessEqual] 86, x1 + 3\ x3 - 2\ x4 \[LessEqual] 86, x1 - 2\ x3 + 3\ x4 \[LessEqual] 86, x1 - 2\ x2 + 3\ x5 \[LessEqual] 86, 3\ x2 + x3 - 2\ x5 \[LessEqual] 86, 3\ x2 + x4 - 2\ x5 \[LessEqual] 86, 3\ x2 - 2\ x5 + x6 \[LessEqual] 86, x2 + 3\ x3 - 2\ x4 \[LessEqual] 86, x2 - 2\ x3 + 3\ x4 \[LessEqual] 86, 3\ x3 - 2\ x4 + x5 \[LessEqual] 86, 3\ x3 - 2\ x4 + x6 \[LessEqual] 86, \(-2\)\ x3 + 3\ x4 + x5 \[LessEqual] 86, \(-2\)\ x3 + 3\ x4 + x6 \[LessEqual] 86, \(-2\)\ x2 + x3 + 3\ x5 \[LessEqual] 86, \(-2\)\ x2 + x4 + 3\ x5 \[LessEqual] 86, \(-2\)\ x2 + 3\ x5 + x6 \[LessEqual] 86, \(-2\)\ x1 + x2 + 3\ x6 \[LessEqual] 86, \(-2\)\ x1 + x3 + 3\ x6 \[LessEqual] 86, \(-2\)\ x1 + x4 + 3\ x6 \[LessEqual] 86, \(-2\)\ x1 + x5 + 3\ x6 \[LessEqual] 86, 5\ x1 + 2\ x2 + 2\ x6 \[LessEqual] 219, 5\ x1 + 2\ x3 + 2\ x6 \[LessEqual] 219, 5\ x1 + 2\ x4 + 2\ x6 \[LessEqual] 219, 5\ x1 + 2\ x5 + 2\ x6 \[LessEqual] 219, 2\ x1 + 5\ x2 + 2\ x5 \[LessEqual] 219, 2\ x1 + 2\ x2 + 5\ x5 \[LessEqual] 219, 2\ x1 + 2\ x2 + 5\ x6 \[LessEqual] 219, 2\ x1 + 5\ x3 + 2\ x4 \[LessEqual] 219, 2\ x1 + 2\ x3 + 5\ x4 \[LessEqual] 219, 2\ x1 + 2\ x3 + 5\ x6 \[LessEqual] 219, 2\ x1 + 2\ x4 + 5\ x6 \[LessEqual] 219, 2\ x1 + 2\ x5 + 5\ x6 \[LessEqual] 219, 5\ x2 + 2\ x3 + 2\ x5 \[LessEqual] 219, 5\ x2 + 2\ x4 + 2\ x5 \[LessEqual] 219, 5\ x2 + 2\ x5 + 2\ x6 \[LessEqual] 219, 2\ x2 + 5\ x3 + 2\ x4 \[LessEqual] 219, 2\ x2 + 2\ x3 + 5\ x4 \[LessEqual] 219, 2\ x2 + 2\ x3 + 5\ x5 \[LessEqual] 219, 2\ x2 + 2\ x4 + 5\ x5 \[LessEqual] 219, 2\ x2 + 5\ x5 + 2\ x6 \[LessEqual] 219, 5\ x3 + 2\ x4 + 2\ x5 \[LessEqual] 219, 5\ x3 + 2\ x4 + 2\ x6 \[LessEqual] 219, 2\ x3 + 5\ x4 + 2\ x5 \[LessEqual] 219, 2\ x3 + 5\ x4 + 2\ x6 \[LessEqual] 219, 11\ x1 + 2\ x2 + 2\ x5 - 4\ x6 \[LessEqual] 335, 11\ x1 + 2\ x3 + 2\ x4 - 4\ x6 \[LessEqual] 335, 2\ x1 + 11\ x2 - 4\ x5 + 2\ x6 \[LessEqual] 335, 2\ x1 + 11\ x3 - 4\ x4 + 2\ x6 \[LessEqual] 335, 2\ x1 - 4\ x3 + 11\ x4 + 2\ x6 \[LessEqual] 335, 2\ x1 - 4\ x2 + 11\ x5 + 2\ x6 \[LessEqual] 335, 11\ x2 + 2\ x3 + 2\ x4 - 4\ x5 \[LessEqual] 335, 2\ x2 + 11\ x3 - 4\ x4 + 2\ x5 \[LessEqual] 335, 2\ x2 - 4\ x3 + 11\ x4 + 2\ x5 \[LessEqual] 335, \(-4\)\ x2 + 2\ x3 + 2\ x4 + 11\ x5 \[LessEqual] 335, \(-4\)\ x1 + 2\ x2 + 2\ x5 + 11\ x6 \[LessEqual] 335, \(-4\)\ x1 + 2\ x3 + 2\ x4 + 11\ x6 \[LessEqual] 335, \(-9\)\ x3 - 11\ x4 - 3\ x5 - 3\ x6 \[LessEqual] \(-225\), \(-3\)\ x2 - 11\ x3 - 9\ x4 - 3\ x6 \[LessEqual] \(-225\), \(-9\)\ x2 - 3\ x4 - 11\ x5 - 3\ x6 \[LessEqual] \(-225\), \(-11\)\ x2 - 3\ x3 - 9\ x5 - 3\ x6 \[LessEqual] \(-225\), \(-3\)\ x1 - 11\ x3 - 9\ x4 - 3\ x5 \[LessEqual] \(-225\), \(-3\)\ x1 - 3\ x2 - 9\ x3 - 11\ x4 \[LessEqual] \(-225\), \(-3\)\ x1 - 9\ x2 - 3\ x3 - 11\ x5 \[LessEqual] \(-225\), \(-3\)\ x1 - 11\ x2 - 3\ x4 - 9\ x5 \[LessEqual] \(-225\), \(-9\)\ x1 - 3\ x4 - 3\ x5 - 11\ x6 \[LessEqual] \(-225\), \(-9\)\ x1 - 3\ x2 - 3\ x3 - 11\ x6 \[LessEqual] \(-225\), \(-11\)\ x1 - 3\ x3 - 3\ x5 - 9\ x6 \[LessEqual] \(-225\), \(-11\)\ x1 - 3\ x2 - 3\ x4 - 9\ x6 \[LessEqual] \(-225\), \(-3\)\ x3 - 3\ x4 - x6 \[LessEqual] \(-52\), \(-3\)\ x3 - 3\ x4 - x5 \[LessEqual] \(-52\), \(-x2\) - 3\ x3 - 3\ x4 \[LessEqual] \(-52\), \(-3\)\ x2 - 3\ x5 - x6 \[LessEqual] \(-52\), \(-3\)\ x2 - x4 - 3\ x5 \[LessEqual] \(-52\), \(-3\)\ x2 - x3 - 3\ x5 \[LessEqual] \(-52\), \(-x1\) - 3\ x3 - 3\ x4 \[LessEqual] \(-52\), \(-x1\) - 3\ x2 - 3\ x5 \[LessEqual] \(-52\), \(-3\)\ x1 - x5 - 3\ x6 \[LessEqual] \(-52\), \(-3\)\ x1 - x4 - 3\ x6 \[LessEqual] \(-52\), \(-3\)\ x1 - x3 - 3\ x6 \[LessEqual] \(-52\), \(-3\)\ x1 - x2 - 3\ x6 \[LessEqual] \(-52\), 19\ x1 + 10\ x2 + 4\ x3 + 4\ x4 + 10\ x5 + 4\ x6 \[LessEqual] 1047, 19\ x1 + 4\ x2 + 10\ x3 + 10\ x4 + 4\ x5 + 4\ x6 \[LessEqual] 1047, 10\ x1 + 19\ x2 + 4\ x3 + 4\ x4 + 4\ x5 + 10\ x6 \[LessEqual] 1047, 10\ x1 + 4\ x2 + 19\ x3 + 4\ x4 + 4\ x5 + 10\ x6 \[LessEqual] 1047, 10\ x1 + 4\ x2 + 4\ x3 + 19\ x4 + 4\ x5 + 10\ x6 \[LessEqual] 1047, 10\ x1 + 4\ x2 + 4\ x3 + 4\ x4 + 19\ x5 + 10\ x6 \[LessEqual] 1047, 4\ x1 + 19\ x2 + 10\ x3 + 10\ x4 + 4\ x5 + 4\ x6 \[LessEqual] 1047, 4\ x1 + 10\ x2 + 19\ x3 + 4\ x4 + 10\ x5 + 4\ x6 \[LessEqual] 1047, 4\ x1 + 10\ x2 + 4\ x3 + 19\ x4 + 10\ x5 + 4\ x6 \[LessEqual] 1047, 4\ x1 + 10\ x2 + 4\ x3 + 4\ x4 + 10\ x5 + 19\ x6 \[LessEqual] 1047, 4\ x1 + 4\ x2 + 10\ x3 + 10\ x4 + 19\ x5 + 4\ x6 \[LessEqual] 1047, 4\ x1 + 4\ x2 + 10\ x3 + 10\ x4 + 4\ x5 + 19\ x6 \[LessEqual] 1047, x1 - 2\ x2 - 3\ x3 - 2\ x4 - 3\ x5 - 5\ x6 \[LessEqual] \(-161\), x1 - 3\ x2 - 2\ x3 - 3\ x4 - 2\ x5 - 5\ x6 \[LessEqual] \(-161\), \(-2\)\ x1 + x2 - 3\ x3 - 2\ x4 - 5\ x5 - 3\ x6 \[LessEqual] \(-161\), \(-2\)\ x1 - 2\ x2 - 5\ x3 + x4 - 3\ x5 - 3\ x6 \[LessEqual] \(-161\), \(-2\)\ x1 - 3\ x2 + x3 - 5\ x4 - 2\ x5 - 3\ x6 \[LessEqual] \(-161\), \(-2\)\ x1 - 5\ x2 - 2\ x3 - 3\ x4 + x5 - 3\ x6 \[LessEqual] \(-161\), \(-3\)\ x1 + x2 - 2\ x3 - 3\ x4 - 5\ x5 - 2\ x6 \[LessEqual] \(-161\), \(-3\)\ x1 - 2\ x2 + x3 - 5\ x4 - 3\ x5 - 2\ x6 \[LessEqual] \(-161\), \(-3\)\ x1 - 3\ x2 - 5\ x3 + x4 - 2\ x5 - 2\ x6 \[LessEqual] \(-161\), \(-3\)\ x1 - 5\ x2 - 3\ x3 - 2\ x4 + x5 - 2\ x6 \[LessEqual] \(-161\), \(-5\)\ x1 - 2\ x2 - 2\ x3 - 3\ x4 - 3\ x5 + x6 \[LessEqual] \(-161\), \(-5\)\ x1 - 3\ x2 - 3\ x3 - 2\ x4 - 2\ x5 + x6 \[LessEqual] \(-161\), 5\ x1 + 5\ x2 + 2\ x3 + 2\ x4 + 2\ x5 + 2\ x6 \[LessEqual] 360, 5\ x1 + 2\ x2 + 5\ x3 + 2\ x4 + 2\ x5 + 2\ x6 \[LessEqual] 360, 5\ x1 + 2\ x2 + 2\ x3 + 5\ x4 + 2\ x5 + 2\ x6 \[LessEqual] 360, 5\ x1 + 2\ x2 + 2\ x3 + 2\ x4 + 5\ x5 + 2\ x6 \[LessEqual] 360, 2\ x1 + 5\ x2 + 5\ x3 + 2\ x4 + 2\ x5 + 2\ x6 \[LessEqual] 360, 2\ x1 + 5\ x2 + 2\ x3 + 5\ x4 + 2\ x5 + 2\ x6 \[LessEqual] 360, 2\ x1 + 5\ x2 + 2\ x3 + 2\ x4 + 2\ x5 + 5\ x6 \[LessEqual] 360, 2\ x1 + 2\ x2 + 5\ x3 + 2\ x4 + 5\ x5 + 2\ x6 \[LessEqual] 360, 2\ x1 + 2\ x2 + 5\ x3 + 2\ x4 + 2\ x5 + 5\ x6 \[LessEqual] 360, 2\ x1 + 2\ x2 + 2\ x3 + 5\ x4 + 5\ x5 + 2\ x6 \[LessEqual] 360, 2\ x1 + 2\ x2 + 2\ x3 + 5\ x4 + 2\ x5 + 5\ x6 \[LessEqual] 360, 2\ x1 + 2\ x2 + 2\ x3 + 2\ x4 + 5\ x5 + 5\ x6 \[LessEqual] 360, x1 - 2\ x3 - 2\ x4 + x6 \[LessEqual] 22, x1 - 2\ x2 - 2\ x5 + x6 \[LessEqual] 22, x2 - 2\ x3 - 2\ x4 + x5 \[LessEqual] 22, \(-2\)\ x2 + x3 + x4 - 2\ x5 \[LessEqual] 22, \(-2\)\ x1 + x2 + x5 - 2\ x6 \[LessEqual] 22, \(-2\)\ x1 + x3 + x4 - 2\ x6 \[LessEqual] 22, 5\ x1 + 2\ x2 + 2\ x4 + 2\ x6 \[LessEqual] 251, 5\ x1 + 2\ x3 + 2\ x5 + 2\ x6 \[LessEqual] 251, 2\ x1 + 5\ x2 + 2\ x4 + 2\ x5 \[LessEqual] 251, 2\ x1 + 2\ x2 + 2\ x3 + 5\ x4 \[LessEqual] 251, 2\ x1 + 2\ x2 + 2\ x3 + 5\ x5 \[LessEqual] 251, 2\ x1 + 2\ x2 + 2\ x3 + 5\ x6 \[LessEqual] 251, 2\ x1 + 5\ x3 + 2\ x4 + 2\ x5 \[LessEqual] 251, 2\ x1 + 2\ x4 + 2\ x5 + 5\ x6 \[LessEqual] 251, 5\ x2 + 2\ x3 + 2\ x5 + 2\ x6 \[LessEqual] 251, 2\ x2 + 5\ x3 + 2\ x4 + 2\ x6 \[LessEqual] 251, 2\ x2 + 2\ x4 + 5\ x5 + 2\ x6 \[LessEqual] 251, 2\ x3 + 5\ x4 + 2\ x5 + 2\ x6 \[LessEqual] 251, 5\ x1 + 2\ x2 + 2\ x5 \[LessEqual] 213, 5\ x1 + 2\ x3 + 2\ x4 \[LessEqual] 213, 2\ x1 + 5\ x2 + 2\ x6 \[LessEqual] 213, 2\ x1 + 5\ x3 + 2\ x6 \[LessEqual] 213, 2\ x1 + 5\ x4 + 2\ x6 \[LessEqual] 213, 2\ x1 + 5\ x5 + 2\ x6 \[LessEqual] 213, 5\ x2 + 2\ x3 + 2\ x4 \[LessEqual] 213, 2\ x2 + 5\ x3 + 2\ x5 \[LessEqual] 213, 2\ x2 + 5\ x4 + 2\ x5 \[LessEqual] 213, 2\ x2 + 2\ x5 + 5\ x6 \[LessEqual] 213, 2\ x3 + 2\ x4 + 5\ x5 \[LessEqual] 213, 2\ x3 + 2\ x4 + 5\ x6 \[LessEqual] 213, 5\ x1 - 4\ x2 - 6\ x3 - 4\ x4 - 6\ x5 - 10\ x6 \[LessEqual] \(-247\), 5\ x1 - 6\ x2 - 4\ x3 - 6\ x4 - 4\ x5 - 10\ x6 \[LessEqual] \(-247\), \(-4\)\ x1 + 5\ x2 - 6\ x3 - 4\ x4 - 10\ x5 - 6\ x6 \[LessEqual] \(-247\), \(-4\)\ x1 - 4\ x2 - 10\ x3 + 5\ x4 - 6\ x5 - 6\ x6 \[LessEqual] \(-247\), \(-4\)\ x1 - 6\ x2 + 5\ x3 - 10\ x4 - 4\ x5 - 6\ x6 \[LessEqual] \(-247\), \(-4\)\ x1 - 10\ x2 - 4\ x3 - 6\ x4 + 5\ x5 - 6\ x6 \[LessEqual] \(-247\), \(-6\)\ x1 + 5\ x2 - 4\ x3 - 6\ x4 - 10\ x5 - 4\ x6 \[LessEqual] \(-247\), \(-6\)\ x1 - 4\ x2 + 5\ x3 - 10\ x4 - 6\ x5 - 4\ x6 \[LessEqual] \(-247\), \(-6\)\ x1 - 6\ x2 - 10\ x3 + 5\ x4 - 4\ x5 - 4\ x6 \[LessEqual] \(-247\), \(-6\)\ x1 - 10\ x2 - 6\ x3 - 4\ x4 + 5\ x5 - 4\ x6 \[LessEqual] \(-247\), \(-10\)\ x1 - 4\ x2 - 4\ x3 - 6\ x4 - 6\ x5 + 5\ x6 \[LessEqual] \(-247\), \(-10\)\ x1 - 6\ x2 - 6\ x3 - 4\ x4 - 4\ x5 + 5\ x6 \[LessEqual] \(-247\), 9\ x1 + 9\ x2 - 2\ x4 + 6\ x5 + 6\ x6 \[LessEqual] 612, 9\ x1 + 6\ x2 - 2\ x3 + 9\ x5 + 6\ x6 \[LessEqual] 612, 9\ x1 + 9\ x3 + 6\ x4 - 2\ x5 + 6\ x6 \[LessEqual] 612, 9\ x1 - 2\ x2 + 6\ x3 + 9\ x4 + 6\ x6 \[LessEqual] 612, 6\ x1 + 9\ x2 - 2\ x3 + 6\ x5 + 9\ x6 \[LessEqual] 612, 6\ x1 + 6\ x2 - 2\ x4 + 9\ x5 + 9\ x6 \[LessEqual] 612, 6\ x1 + 6\ x3 + 9\ x4 - 2\ x5 + 9\ x6 \[LessEqual] 612, 6\ x1 - 2\ x2 + 9\ x3 + 6\ x4 + 9\ x6 \[LessEqual] 612, 9\ x2 + 9\ x3 + 6\ x4 + 6\ x5 - 2\ x6 \[LessEqual] 612, 6\ x2 + 6\ x3 + 9\ x4 + 9\ x5 - 2\ x6 \[LessEqual] 612, \(-2\)\ x1 + 9\ x2 + 6\ x3 + 9\ x4 + 6\ x5 \[LessEqual] 612, \(-2\)\ x1 + 6\ x2 + 9\ x3 + 6\ x4 + 9\ x5 \[LessEqual] 612, 4\ x1 + x2 - 2\ x6 \[LessEqual] 109, 4\ x1 + x3 - 2\ x6 \[LessEqual] 109, 4\ x1 + x4 - 2\ x6 \[LessEqual] 109, 4\ x1 + x5 - 2\ x6 \[LessEqual] 109, x1 + 4\ x2 - 2\ x5 \[LessEqual] 109, x1 + 4\ x3 - 2\ x4 \[LessEqual] 109, x1 - 2\ x3 + 4\ x4 \[LessEqual] 109, x1 - 2\ x2 + 4\ x5 \[LessEqual] 109, 4\ x2 + x3 - 2\ x5 \[LessEqual] 109, 4\ x2 + x4 - 2\ x5 \[LessEqual] 109, 4\ x2 - 2\ x5 + x6 \[LessEqual] 109, x2 + 4\ x3 - 2\ x4 \[LessEqual] 109, x2 - 2\ x3 + 4\ x4 \[LessEqual] 109, 4\ x3 - 2\ x4 + x5 \[LessEqual] 109, 4\ x3 - 2\ x4 + x6 \[LessEqual] 109, \(-2\)\ x3 + 4\ x4 + x5 \[LessEqual] 109, \(-2\)\ x3 + 4\ x4 + x6 \[LessEqual] 109, \(-2\)\ x2 + x3 + 4\ x5 \[LessEqual] 109, \(-2\)\ x2 + x4 + 4\ x5 \[LessEqual] 109, \(-2\)\ x2 + 4\ x5 + x6 \[LessEqual] 109, \(-2\)\ x1 + x2 + 4\ x6 \[LessEqual] 109, \(-2\)\ x1 + x3 + 4\ x6 \[LessEqual] 109, \(-2\)\ x1 + x4 + 4\ x6 \[LessEqual] 109, \(-2\)\ x1 + x5 + 4\ x6 \[LessEqual] 109, 5\ x1 + 5\ x2 + 2\ x3 + 5\ x4 + 2\ x5 + 2\ x6 \[LessEqual] 423, 5\ x1 + 2\ x2 + 5\ x3 + 2\ x4 + 5\ x5 + 2\ x6 \[LessEqual] 423, 2\ x1 + 5\ x2 + 5\ x3 + 2\ x4 + 2\ x5 + 5\ x6 \[LessEqual] 423, 2\ x1 + 2\ x2 + 2\ x3 + 5\ x4 + 5\ x5 + 5\ x6 \[LessEqual] 423, 5\ x1 + 5\ x2 + 2\ x3 + 2\ x5 + 2\ x6 \[LessEqual] 330, 5\ x1 + 2\ x2 + 5\ x3 + 2\ x4 + 2\ x6 \[LessEqual] 330, 5\ x1 + 2\ x2 + 2\ x4 + 5\ x5 + 2\ x6 \[LessEqual] 330, 5\ x1 + 2\ x3 + 5\ x4 + 2\ x5 + 2\ x6 \[LessEqual] 330, 2\ x1 + 5\ x2 + 5\ x3 + 2\ x4 + 2\ x5 \[LessEqual] 330, 2\ x1 + 5\ x2 + 2\ x4 + 2\ x5 + 5\ x6 \[LessEqual] 330, 2\ x1 + 2\ x2 + 2\ x3 + 5\ x4 + 5\ x5 \[LessEqual] 330, 2\ x1 + 2\ x2 + 2\ x3 + 5\ x4 + 5\ x6 \[LessEqual] 330, 2\ x1 + 2\ x2 + 2\ x3 + 5\ x5 + 5\ x6 \[LessEqual] 330, 2\ x1 + 5\ x3 + 2\ x4 + 2\ x5 + 5\ x6 \[LessEqual] 330, 5\ x2 + 2\ x3 + 5\ x4 + 2\ x5 + 2\ x6 \[LessEqual] 330, 2\ x2 + 5\ x3 + 2\ x4 + 5\ x5 + 2\ x6 \[LessEqual] 330, 8\ x1 + 5\ x2 + 2\ x3 + 2\ x4 + 5\ x5 + 2\ x6 \[LessEqual] 486, 8\ x1 + 2\ x2 + 5\ x3 + 5\ x4 + 2\ x5 + 2\ x6 \[LessEqual] 486, 5\ x1 + 8\ x2 + 2\ x3 + 2\ x4 + 2\ x5 + 5\ x6 \[LessEqual] 486, 5\ x1 + 2\ x2 + 8\ x3 + 2\ x4 + 2\ x5 + 5\ x6 \[LessEqual] 486, 5\ x1 + 2\ x2 + 2\ x3 + 8\ x4 + 2\ x5 + 5\ x6 \[LessEqual] 486, 5\ x1 + 2\ x2 + 2\ x3 + 2\ x4 + 8\ x5 + 5\ x6 \[LessEqual] 486, 2\ x1 + 8\ x2 + 5\ x3 + 5\ x4 + 2\ x5 + 2\ x6 \[LessEqual] 486, 2\ x1 + 5\ x2 + 8\ x3 + 2\ x4 + 5\ x5 + 2\ x6 \[LessEqual] 486, 2\ x1 + 5\ x2 + 2\ x3 + 8\ x4 + 5\ x5 + 2\ x6 \[LessEqual] 486, 2\ x1 + 5\ x2 + 2\ x3 + 2\ x4 + 5\ x5 + 8\ x6 \[LessEqual] 486, 2\ x1 + 2\ x2 + 5\ x3 + 5\ x4 + 8\ x5 + 2\ x6 \[LessEqual] 486, 2\ x1 + 2\ x2 + 5\ x3 + 5\ x4 + 2\ x5 + 8\ x6 \[LessEqual] 486, 9\ x1 + 6\ x2 + 6\ x5 + 4\ x6 \[LessEqual] 529, 9\ x1 + 6\ x3 + 6\ x4 + 4\ x6 \[LessEqual] 529, 6\ x1 + 9\ x2 + 4\ x5 + 6\ x6 \[LessEqual] 529, 6\ x1 + 4\ x2 + 9\ x5 + 6\ x6 \[LessEqual] 529, 6\ x1 + 9\ x3 + 4\ x4 + 6\ x6 \[LessEqual] 529, 6\ x1 + 4\ x3 + 9\ x4 + 6\ x6 \[LessEqual] 529, 4\ x1 + 6\ x2 + 6\ x5 + 9\ x6 \[LessEqual] 529, 4\ x1 + 6\ x3 + 6\ x4 + 9\ x6 \[LessEqual] 529, 9\ x2 + 6\ x3 + 6\ x4 + 4\ x5 \[LessEqual] 529, 6\ x2 + 9\ x3 + 4\ x4 + 6\ x5 \[LessEqual] 529, 6\ x2 + 4\ x3 + 9\ x4 + 6\ x5 \[LessEqual] 529, 4\ x2 + 6\ x3 + 6\ x4 + 9\ x5 \[LessEqual] 529, \(-x3\) - x4 \[LessEqual] \(-12\), \(-x2\) - x5 \[LessEqual] \(-12\), \(-x1\) - x6 \[LessEqual] \(-12\), \(-x3\) - x4 - x5 - x6 \[LessEqual] \(-45\), \(-x2\) - x4 - x5 - x6 \[LessEqual] \(-45\), \(-x2\) - x3 - x5 - x6 \[LessEqual] \(-45\), \(-x2\) - x3 - x4 - x6 \[LessEqual] \(-45\), \(-x1\) - x4 - x5 - x6 \[LessEqual] \(-45\), \(-x1\) - x3 - x5 - x6 \[LessEqual] \(-45\), \(-x1\) - x3 - x4 - x5 \[LessEqual] \(-45\), \(-x1\) - x2 - x4 - x6 \[LessEqual] \(-45\), \(-x1\) - x2 - x4 - x5 \[LessEqual] \(-45\), \(-x1\) - x2 - x3 - x6 \[LessEqual] \(-45\), \(-x1\) - x2 - x3 - x5 \[LessEqual] \(-45\), \(-x1\) - x2 - x3 - x4 \[LessEqual] \(-45\), 3\ x1 + 3\ x2 + 2\ x5 + 2\ x6 \[LessEqual] 208, 3\ x1 + 2\ x2 + 3\ x5 + 2\ x6 \[LessEqual] 208, 3\ x1 + 3\ x3 + 2\ x4 + 2\ x6 \[LessEqual] 208, 3\ x1 + 2\ x3 + 3\ x4 + 2\ x6 \[LessEqual] 208, 2\ x1 + 3\ x2 + 2\ x5 + 3\ x6 \[LessEqual] 208, 2\ x1 + 2\ x2 + 3\ x5 + 3\ x6 \[LessEqual] 208, 2\ x1 + 3\ x3 + 2\ x4 + 3\ x6 \[LessEqual] 208, 2\ x1 + 2\ x3 + 3\ x4 + 3\ x6 \[LessEqual] 208, 3\ x2 + 3\ x3 + 2\ x4 + 2\ x5 \[LessEqual] 208, 3\ x2 + 2\ x3 + 3\ x4 + 2\ x5 \[LessEqual] 208, 2\ x2 + 3\ x3 + 2\ x4 + 3\ x5 \[LessEqual] 208, 2\ x2 + 2\ x3 + 3\ x4 + 3\ x5 \[LessEqual] 208, 5\ x1 + 2\ x2 - 4\ x4 - 4\ x5 - 4\ x6 \[LessEqual] 25, 5\ x1 + 2\ x3 - 4\ x4 - 4\ x5 - 4\ x6 \[LessEqual] 25, 5\ x1 - 4\ x2 - 4\ x3 + 2\ x4 - 4\ x6 \[LessEqual] 25, 5\ x1 - 4\ x2 - 4\ x3 + 2\ x5 - 4\ x6 \[LessEqual] 25, 2\ x1 + 5\ x2 - 4\ x4 - 4\ x5 - 4\ x6 \[LessEqual] 25, 2\ x1 + 5\ x3 - 4\ x4 - 4\ x5 - 4\ x6 \[LessEqual] 25, 2\ x1 - 4\ x2 - 4\ x3 + 5\ x4 - 4\ x6 \[LessEqual] 25, 2\ x1 - 4\ x2 - 4\ x3 + 5\ x5 - 4\ x6 \[LessEqual] 25, 5\ x2 + 2\ x3 - 4\ x4 - 4\ x5 - 4\ x6 \[LessEqual] 25, 2\ x2 + 5\ x3 - 4\ x4 - 4\ x5 - 4\ x6 \[LessEqual] 25, \(-4\)\ x2 - 4\ x3 + 5\ x4 + 2\ x5 - 4\ x6 \[LessEqual] 25, \(-4\)\ x2 - 4\ x3 + 2\ x4 + 5\ x5 - 4\ x6 \[LessEqual] 25, \(-4\)\ x1 + 5\ x2 - 4\ x3 + 2\ x4 - 4\ x5 \[LessEqual] 25, \(-4\)\ x1 + 5\ x2 - 4\ x3 - 4\ x5 + 2\ x6 \[LessEqual] 25, \(-4\)\ x1 + 2\ x2 - 4\ x3 + 5\ x4 - 4\ x5 \[LessEqual] 25, \(-4\)\ x1 + 2\ x2 - 4\ x3 - 4\ x5 + 5\ x6 \[LessEqual] 25, \(-4\)\ x1 - 4\ x3 + 5\ x4 - 4\ x5 + 2\ x6 \[LessEqual] 25, \(-4\)\ x1 - 4\ x3 + 2\ x4 - 4\ x5 + 5\ x6 \[LessEqual] 25, \(-4\)\ x1 - 4\ x2 + 5\ x3 - 4\ x4 + 2\ x5 \[LessEqual] 25, \(-4\)\ x1 - 4\ x2 + 5\ x3 - 4\ x4 + 2\ x6 \[LessEqual] 25, \(-4\)\ x1 - 4\ x2 + 2\ x3 - 4\ x4 + 5\ x5 \[LessEqual] 25, \(-4\)\ x1 - 4\ x2 + 2\ x3 - 4\ x4 + 5\ x6 \[LessEqual] 25, \(-4\)\ x1 - 4\ x2 - 4\ x4 + 5\ x5 + 2\ x6 \[LessEqual] 25, \(-4\)\ x1 - 4\ x2 - 4\ x4 + 2\ x5 + 5\ x6 \[LessEqual] 25, 9\ x1 + 6\ x2 + 4\ x3 \[LessEqual] 421, 9\ x1 + 4\ x2 + 6\ x3 \[LessEqual] 421, 9\ x1 + 6\ x4 + 4\ x5 \[LessEqual] 421, 9\ x1 + 4\ x4 + 6\ x5 \[LessEqual] 421, 6\ x1 + 9\ x2 + 4\ x3 \[LessEqual] 421, 6\ x1 + 4\ x2 + 9\ x3 \[LessEqual] 421, 6\ x1 + 9\ x4 + 4\ x5 \[LessEqual] 421, 6\ x1 + 4\ x4 + 9\ x5 \[LessEqual] 421, 4\ x1 + 9\ x2 + 6\ x3 \[LessEqual] 421, 4\ x1 + 6\ x2 + 9\ x3 \[LessEqual] 421, 4\ x1 + 9\ x4 + 6\ x5 \[LessEqual] 421, 4\ x1 + 6\ x4 + 9\ x5 \[LessEqual] 421, 9\ x2 + 6\ x4 + 4\ x6 \[LessEqual] 421, 9\ x2 + 4\ x4 + 6\ x6 \[LessEqual] 421, 6\ x2 + 9\ x4 + 4\ x6 \[LessEqual] 421, 6\ x2 + 4\ x4 + 9\ x6 \[LessEqual] 421, 4\ x2 + 9\ x4 + 6\ x6 \[LessEqual] 421, 4\ x2 + 6\ x4 + 9\ x6 \[LessEqual] 421, 9\ x3 + 6\ x5 + 4\ x6 \[LessEqual] 421, 9\ x3 + 4\ x5 + 6\ x6 \[LessEqual] 421, 6\ x3 + 9\ x5 + 4\ x6 \[LessEqual] 421, 6\ x3 + 4\ x5 + 9\ x6 \[LessEqual] 421, 4\ x3 + 9\ x5 + 6\ x6 \[LessEqual] 421, 4\ x3 + 6\ x5 + 9\ x6 \[LessEqual] 421, 5\ x1 + 2\ x2 + 2\ x3 + 2\ x4 + 2\ x5 + 2\ x6 \[LessEqual] 297, 2\ x1 + 5\ x2 + 2\ x3 + 2\ x4 + 2\ x5 + 2\ x6 \[LessEqual] 297, 2\ x1 + 2\ x2 + 5\ x3 + 2\ x4 + 2\ x5 + 2\ x6 \[LessEqual] 297, 2\ x1 + 2\ x2 + 2\ x3 + 5\ x4 + 2\ x5 + 2\ x6 \[LessEqual] 297, 2\ x1 + 2\ x2 + 2\ x3 + 2\ x4 + 5\ x5 + 2\ x6 \[LessEqual] 297, 2\ x1 + 2\ x2 + 2\ x3 + 2\ x4 + 2\ x5 + 5\ x6 \[LessEqual] 297, 3\ x1 - 2\ x3 - 2\ x5 \[LessEqual] 53, 3\ x1 - 2\ x2 - 2\ x4 \[LessEqual] 53, 3\ x2 - 2\ x3 - 2\ x6 \[LessEqual] 53, 3\ x4 - 2\ x5 - 2\ x6 \[LessEqual] 53, \(-2\)\ x4 + 3\ x5 - 2\ x6 \[LessEqual] 53, \(-2\)\ x4 - 2\ x5 + 3\ x6 \[LessEqual] 53, \(-2\)\ x2 + 3\ x3 - 2\ x6 \[LessEqual] 53, \(-2\)\ x2 - 2\ x3 + 3\ x6 \[LessEqual] 53, \(-2\)\ x1 + 3\ x2 - 2\ x4 \[LessEqual] 53, \(-2\)\ x1 + 3\ x3 - 2\ x5 \[LessEqual] 53, \(-2\)\ x1 - 2\ x3 + 3\ x5 \[LessEqual] 53, \(-2\)\ x1 - 2\ x2 + 3\ x4 \[LessEqual] 53, x1 + x2 + x5 \[LessEqual] 69, x1 + x2 + x6 \[LessEqual] 69, x1 + x3 + x4 \[LessEqual] 69, x1 + x3 + x6 \[LessEqual] 69, x1 + x4 + x6 \[LessEqual] 69, x1 + x5 + x6 \[LessEqual] 69, x2 + x3 + x4 \[LessEqual] 69, x2 + x3 + x5 \[LessEqual] 69, x2 + x4 + x5 \[LessEqual] 69, x2 + x5 + x6 \[LessEqual] 69, x3 + x4 + x5 \[LessEqual] 69, x3 + x4 + x6 \[LessEqual] 69, 3\ x1 + 2\ x2 \[LessEqual] 123, 3\ x1 + 2\ x3 \[LessEqual] 123, 3\ x1 + 2\ x4 \[LessEqual] 123, 3\ x1 + 2\ x5 \[LessEqual] 123, 2\ x1 + 3\ x2 \[LessEqual] 123, 2\ x1 + 3\ x3 \[LessEqual] 123, 2\ x1 + 3\ x4 \[LessEqual] 123, 2\ x1 + 3\ x5 \[LessEqual] 123, 3\ x2 + 2\ x3 \[LessEqual] 123, 3\ x2 + 2\ x4 \[LessEqual] 123, 3\ x2 + 2\ x6 \[LessEqual] 123, 2\ x2 + 3\ x3 \[LessEqual] 123, 2\ x2 + 3\ x4 \[LessEqual] 123, 2\ x2 + 3\ x6 \[LessEqual] 123, 3\ x3 + 2\ x5 \[LessEqual] 123, 3\ x3 + 2\ x6 \[LessEqual] 123, 2\ x3 + 3\ x5 \[LessEqual] 123, 2\ x3 + 3\ x6 \[LessEqual] 123, 3\ x4 + 2\ x5 \[LessEqual] 123, 3\ x4 + 2\ x6 \[LessEqual] 123, 2\ x4 + 3\ x5 \[LessEqual] 123, 2\ x4 + 3\ x6 \[LessEqual] 123, 3\ x5 + 2\ x6 \[LessEqual] 123, 2\ x5 + 3\ x6 \[LessEqual] 123, 5\ x1 + 2\ x2 + 2\ x4 \[LessEqual] 213, 5\ x1 + 2\ x3 + 2\ x5 \[LessEqual] 213, 2\ x1 + 5\ x2 + 2\ x4 \[LessEqual] 213, 2\ x1 + 2\ x2 + 5\ x4 \[LessEqual] 213, 2\ x1 + 5\ x3 + 2\ x5 \[LessEqual] 213, 2\ x1 + 2\ x3 + 5\ x5 \[LessEqual] 213, 5\ x2 + 2\ x3 + 2\ x6 \[LessEqual] 213, 2\ x2 + 5\ x3 + 2\ x6 \[LessEqual] 213, 2\ x2 + 2\ x3 + 5\ x6 \[LessEqual] 213, 5\ x4 + 2\ x5 + 2\ x6 \[LessEqual] 213, 2\ x4 + 5\ x5 + 2\ x6 \[LessEqual] 213, 2\ x4 + 2\ x5 + 5\ x6 \[LessEqual] 213, 5\ x1 + 2\ x2 + 2\ x3 + 2\ x4 + 2\ x5 \[LessEqual] 267, 2\ x1 + 5\ x2 + 2\ x3 + 2\ x4 + 2\ x6 \[LessEqual] 267, 2\ x1 + 2\ x2 + 5\ x3 + 2\ x5 + 2\ x6 \[LessEqual] 267, 2\ x1 + 2\ x2 + 5\ x4 + 2\ x5 + 2\ x6 \[LessEqual] 267, 2\ x1 + 2\ x3 + 2\ x4 + 5\ x5 + 2\ x6 \[LessEqual] 267, 2\ x2 + 2\ x3 + 2\ x4 + 2\ x5 + 5\ x6 \[LessEqual] 267, \(-x6\) \[LessEqual] 0, \(-x5\) \[LessEqual] 0, \(-x4\) \[LessEqual] 0, \(-x3\) \[LessEqual] 0, \(-x2\) \[LessEqual] 0, \(-x1\) \[LessEqual] 0, x1 - 2\ x2 - 2\ x3 - 2\ x4 - 2\ x5 - 4\ x6 \[LessEqual] \(-129\), \(-2\)\ x1 + x2 - 2\ x3 - 2\ x4 - 4\ x5 - 2\ x6 \[LessEqual] \(-129\), \(-2\)\ x1 - 2\ x2 + x3 - 4\ x4 - 2\ x5 - 2\ x6 \[LessEqual] \(-129\), \(-2\)\ x1 - 2\ x2 - 4\ x3 + x4 - 2\ x5 - 2\ x6 \[LessEqual] \(-129\), \(-2\)\ x1 - 4\ x2 - 2\ x3 - 2\ x4 + x5 - 2\ x6 \[LessEqual] \(-129\), \(-4\)\ x1 - 2\ x2 - 2\ x3 - 2\ x4 - 2\ x5 + x6 \[LessEqual] \(-129\), x1 + x2 + x4 \[LessEqual] 69, x1 + x3 + x5 \[LessEqual] 69, x2 + x3 + x6 \[LessEqual] 69, x4 + x5 + x6 \[LessEqual] 69, 3\ x1 + 3\ x2 + 3\ x5 + 2\ x6 \[LessEqual] 227, 3\ x1 + 3\ x2 + 2\ x5 + 3\ x6 \[LessEqual] 227, 3\ x1 + 2\ x2 + 3\ x5 + 3\ x6 \[LessEqual] 227, 3\ x1 + 3\ x3 + 3\ x4 + 2\ x6 \[LessEqual] 227, 3\ x1 + 3\ x3 + 2\ x4 + 3\ x6 \[LessEqual] 227, 3\ x1 + 2\ x3 + 3\ x4 + 3\ x6 \[LessEqual] 227, 2\ x1 + 3\ x2 + 3\ x5 + 3\ x6 \[LessEqual] 227, 2\ x1 + 3\ x3 + 3\ x4 + 3\ x6 \[LessEqual] 227, 3\ x2 + 3\ x3 + 3\ x4 + 2\ x5 \[LessEqual] 227, 3\ x2 + 3\ x3 + 2\ x4 + 3\ x5 \[LessEqual] 227, 3\ x2 + 2\ x3 + 3\ x4 + 3\ x5 \[LessEqual] 227, 2\ x2 + 3\ x3 + 3\ x4 + 3\ x5 \[LessEqual] 227, 3\ x1 + 2\ x2 + 2\ x5 + 2\ x6 \[LessEqual] 187, 3\ x1 + 2\ x3 + 2\ x4 + 2\ x6 \[LessEqual] 187, 2\ x1 + 3\ x2 + 2\ x5 + 2\ x6 \[LessEqual] 187, 2\ x1 + 2\ x2 + 3\ x5 + 2\ x6 \[LessEqual] 187, 2\ x1 + 2\ x2 + 2\ x5 + 3\ x6 \[LessEqual] 187, 2\ x1 + 3\ x3 + 2\ x4 + 2\ x6 \[LessEqual] 187, 2\ x1 + 2\ x3 + 3\ x4 + 2\ x6 \[LessEqual] 187, 2\ x1 + 2\ x3 + 2\ x4 + 3\ x6 \[LessEqual] 187, 3\ x2 + 2\ x3 + 2\ x4 + 2\ x5 \[LessEqual] 187, 2\ x2 + 3\ x3 + 2\ x4 + 2\ x5 \[LessEqual] 187, 2\ x2 + 2\ x3 + 3\ x4 + 2\ x5 \[LessEqual] 187, 2\ x2 + 2\ x3 + 2\ x4 + 3\ x5 \[LessEqual] 187, \(-x3\) - 3\ x4 - 3\ x5 - 3\ x6 \[LessEqual] \(-121\), \(-x2\) - 3\ x4 - 3\ x5 - 3\ x6 \[LessEqual] \(-121\), \(-3\)\ x2 - 3\ x3 - x5 - 3\ x6 \[LessEqual] \(-121\), \(-3\)\ x2 - 3\ x3 - x4 - 3\ x6 \[LessEqual] \(-121\), \(-x1\) - 3\ x4 - 3\ x5 - 3\ x6 \[LessEqual] \(-121\), \(-x1\) - 3\ x2 - 3\ x3 - 3\ x6 \[LessEqual] \(-121\), \(-3\)\ x1 - 3\ x3 - 3\ x5 - x6 \[LessEqual] \(-121\), \(-3\)\ x1 - 3\ x3 - x4 - 3\ x5 \[LessEqual] \(-121\), \(-3\)\ x1 - x2 - 3\ x3 - 3\ x5 \[LessEqual] \(-121\), \(-3\)\ x1 - 3\ x2 - 3\ x4 - x6 \[LessEqual] \(-121\), \(-3\)\ x1 - 3\ x2 - 3\ x4 - x5 \[LessEqual] \(-121\), \(-3\)\ x1 - 3\ x2 - x3 - 3\ x4 \[LessEqual] \(-121\), 3\ x1 + 2\ x2 + 2\ x3 \[LessEqual] 151, 3\ x1 + 2\ x4 + 2\ x5 \[LessEqual] 151, 2\ x1 + 3\ x2 + 2\ x3 \[LessEqual] 151, 2\ x1 + 2\ x2 + 3\ x3 \[LessEqual] 151, 2\ x1 + 3\ x4 + 2\ x5 \[LessEqual] 151, 2\ x1 + 2\ x4 + 3\ x5 \[LessEqual] 151, 3\ x2 + 2\ x4 + 2\ x6 \[LessEqual] 151, 2\ x2 + 3\ x4 + 2\ x6 \[LessEqual] 151, 2\ x2 + 2\ x4 + 3\ x6 \[LessEqual] 151, 3\ x3 + 2\ x5 + 2\ x6 \[LessEqual] 151, 2\ x3 + 3\ x5 + 2\ x6 \[LessEqual] 151, 2\ x3 + 2\ x5 + 3\ x6 \[LessEqual] 151, 3\ x1 - 2\ x3 - 2\ x5 - 2\ x6 \[LessEqual] 15, 3\ x1 - 2\ x2 - 2\ x4 - 2\ x6 \[LessEqual] 15, 3\ x2 - 2\ x3 - 2\ x5 - 2\ x6 \[LessEqual] 15, \(-2\)\ x3 + 3\ x4 - 2\ x5 - 2\ x6 \[LessEqual] 15, \(-2\)\ x2 + 3\ x3 - 2\ x4 - 2\ x6 \[LessEqual] 15, \(-2\)\ x2 - 2\ x4 + 3\ x5 - 2\ x6 \[LessEqual] 15, \(-2\)\ x1 + 3\ x2 - 2\ x4 - 2\ x5 \[LessEqual] 15, \(-2\)\ x1 + 3\ x3 - 2\ x4 - 2\ x5 \[LessEqual] 15, \(-2\)\ x1 - 2\ x4 - 2\ x5 + 3\ x6 \[LessEqual] 15, \(-2\)\ x1 - 2\ x2 - 2\ x3 + 3\ x4 \[LessEqual] 15, \(-2\)\ x1 - 2\ x2 - 2\ x3 + 3\ x5 \[LessEqual] 15, \(-2\)\ x1 - 2\ x2 - 2\ x3 + 3\ x6 \[LessEqual] 15, 3\ x1 - 2\ x6 \[LessEqual] 63, 3\ x2 - 2\ x5 \[LessEqual] 63, 3\ x3 - 2\ x4 \[LessEqual] 63, \(-2\)\ x3 + 3\ x4 \[LessEqual] 63, \(-2\)\ x2 + 3\ x5 \[LessEqual] 63, \(-2\)\ x1 + 3\ x6 \[LessEqual] 63, 3\ x1 + 2\ x2 + 2\ x5 + 3\ x6 \[LessEqual] 208, 3\ x1 + 2\ x3 + 2\ x4 + 3\ x6 \[LessEqual] 208, 2\ x1 + 3\ x2 + 3\ x5 + 2\ x6 \[LessEqual] 208, 2\ x1 + 3\ x3 + 3\ x4 + 2\ x6 \[LessEqual] 208, 3\ x2 + 2\ x3 + 2\ x4 + 3\ x5 \[LessEqual] 208, 2\ x2 + 3\ x3 + 3\ x4 + 2\ x5 \[LessEqual] 208, 5\ x1 + 2\ x2 + 2\ x3 + 2\ x4 + 2\ x5 + 5\ x6 \[LessEqual] 360, 2\ x1 + 5\ x2 + 2\ x3 + 2\ x4 + 5\ x5 + 2\ x6 \[LessEqual] 360, 2\ x1 + 2\ x2 + 5\ x3 + 5\ x4 + 2\ x5 + 2\ x6 \[LessEqual] 360, x1 - 2\ x4 - 2\ x5 - 2\ x6 \[LessEqual] \(-47\), x1 - 2\ x2 - 2\ x3 - 2\ x6 \[LessEqual] \(-47\), x2 - 2\ x4 - 2\ x5 - 2\ x6 \[LessEqual] \(-47\), x3 - 2\ x4 - 2\ x5 - 2\ x6 \[LessEqual] \(-47\), \(-2\)\ x2 - 2\ x3 + x4 - 2\ x6 \[LessEqual] \(-47\), \(-2\)\ x2 - 2\ x3 + x5 - 2\ x6 \[LessEqual] \(-47\), \(-2\)\ x1 + x2 - 2\ x3 - 2\ x5 \[LessEqual] \(-47\), \(-2\)\ x1 - 2\ x3 + x4 - 2\ x5 \[LessEqual] \(-47\), \(-2\)\ x1 - 2\ x3 - 2\ x5 + x6 \[LessEqual] \(-47\), \(-2\)\ x1 - 2\ x2 + x3 - 2\ x4 \[LessEqual] \(-47\), \(-2\)\ x1 - 2\ x2 - 2\ x4 + x5 \[LessEqual] \(-47\), \(-2\)\ x1 - 2\ x2 - 2\ x4 + x6 \[LessEqual] \(-47\), x1 \[LessEqual] 29, x2 \[LessEqual] 29, x3 \[LessEqual] 29, x4 \[LessEqual] 29, x5 \[LessEqual] 29, x6 \[LessEqual] 29, \(-x3\) - x5 - x6 \[LessEqual] \(-30\), \(-x2\) - x4 - x6 \[LessEqual] \(-30\), \(-x1\) - x4 - x5 \[LessEqual] \(-30\), \(-x1\) - x2 - x3 \[LessEqual] \(-30\), x1 + x6 \[LessEqual] 50, x2 + x5 \[LessEqual] 50, x3 + x4 \[LessEqual] 50, x1 + x2 - 2\ x4 - 2\ x5 - 2\ x6 \[LessEqual] \(-28\), x1 + x3 - 2\ x4 - 2\ x5 - 2\ x6 \[LessEqual] \(-28\), x1 - 2\ x2 - 2\ x3 + x4 - 2\ x6 \[LessEqual] \(-28\), x1 - 2\ x2 - 2\ x3 + x5 - 2\ x6 \[LessEqual] \(-28\), x2 + x3 - 2\ x4 - 2\ x5 - 2\ x6 \[LessEqual] \(-28\), \(-2\)\ x2 - 2\ x3 + x4 + x5 - 2\ x6 \[LessEqual] \(-28\), \(-2\)\ x1 + x2 - 2\ x3 + x4 - 2\ x5 \[LessEqual] \(-28\), \(-2\)\ x1 + x2 - 2\ x3 - 2\ x5 + x6 \[LessEqual] \(-28\), \(-2\)\ x1 - 2\ x3 + x4 - 2\ x5 + x6 \[LessEqual] \(-28\), \(-2\)\ x1 - 2\ x2 + x3 - 2\ x4 + x5 \[LessEqual] \(-28\), \(-2\)\ x1 - 2\ x2 + x3 - 2\ x4 + x6 \[LessEqual] \(-28\), \(-2\)\ x1 - 2\ x2 - 2\ x4 + x5 + x6 \[LessEqual] \(-28\), x1 + x2 + x5 + x6 \[LessEqual] 81, x1 + x3 + x4 + x6 \[LessEqual] 81, x2 + x3 + x4 + x5 \[LessEqual] 81, x1 + x2 \[LessEqual] 48, x1 + x3 \[LessEqual] 48, x1 + x4 \[LessEqual] 48, x1 + x5 \[LessEqual] 48, x2 + x3 \[LessEqual] 48, x2 + x4 \[LessEqual] 48, x2 + x6 \[LessEqual] 48, x3 + x5 \[LessEqual] 48, x3 + x6 \[LessEqual] 48, x4 + x5 \[LessEqual] 48, x4 + x6 \[LessEqual] 48, x5 + x6 \[LessEqual] 48, 3\ x1 + 3\ x2 + 2\ x3 \[LessEqual] 170, 3\ x1 + 2\ x2 + 3\ x3 \[LessEqual] 170, 3\ x1 + 3\ x4 + 2\ x5 \[LessEqual] 170, 3\ x1 + 2\ x4 + 3\ x5 \[LessEqual] 170, 2\ x1 + 3\ x2 + 3\ x3 \[LessEqual] 170, 2\ x1 + 3\ x4 + 3\ x5 \[LessEqual] 170, 3\ x2 + 3\ x4 + 2\ x6 \[LessEqual] 170, 3\ x2 + 2\ x4 + 3\ x6 \[LessEqual] 170, 2\ x2 + 3\ x4 + 3\ x6 \[LessEqual] 170, 3\ x3 + 3\ x5 + 2\ x6 \[LessEqual] 170, 3\ x3 + 2\ x5 + 3\ x6 \[LessEqual] 170, 2\ x3 + 3\ x5 + 3\ x6 \[LessEqual] 170, x1 + x2 + x3 \[LessEqual] 63, x1 + x4 + x5 \[LessEqual] 63, x2 + x4 + x6 \[LessEqual] 63, x3 + x5 + x6 \[LessEqual] 63, \(-x4\) - x5 - x6 \[LessEqual] \(-36\), \(-x2\) - x3 - x6 \[LessEqual] \(-36\), \(-x1\) - x3 - x5 \[LessEqual] \(-36\), \(-x1\) - x2 - x4 \[LessEqual] \(-36\), \(-x1\) - x2 - x3 - x4 - x5 - x6 \[LessEqual] \(-90\)};\)\)}], "Input", CellOpen->False], Cell[CellGroupData[{ Cell[BoxData[{ \(Length[acdzconv]\), "\[IndentingNewLine]", \(Length[acdzineq]\)}], "Input"], Cell[BoxData[ \(12828\)], "Output"], Cell[BoxData[ \(2980\)], "Output"] }, Open ]] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell["Reduced Systems", "Section"], Cell["\<\ In this section we compute the reduced systems corresponding to the Minkowski sum polytope P of the nine Albouy-Chenciner-Dziobek equations. After eliminating the trivial ones, we analyze the rest using Groenber bases. \ \>", "Text"], Cell[CellGroupData[{ Cell["Nontrivial facets", "Subsection"], Cell["\<\ The inequalities produced by Porta involve variables x1, ..., x6. First we define some utility functions for substituting six values for these variables and for reading off the left and right sides of the inequality. The left side will be a linear form in the xi and the right side is a constant. The inequalities are all of the form lhs <= rhs \ \>", "Text"], Cell[BoxData[{ \(\(Subst[v_]\ := \ {x1 \[Rule] v[\([1]\)], \ x2 \[Rule] v[\([2]\)], \ x3 \[Rule] v[\([3]\)], x4 \[Rule] v[\([4]\)], x5 \[Rule] v[\([5]\)], x6 \[Rule] v[\([6]\)]};\)\), "\[IndentingNewLine]", \(lhs[LessEqual[a_, b_]]\ := \ a\), "\[IndentingNewLine]", \(rhs[LessEqual[a_, b_]]\ := \ b\), "\[IndentingNewLine]", \(\)}], "Input"], Cell[TextData[{ "A very important step is to test each of the facet inequalities to see if \ the corresponding reduced system is trivial. The reduced system \ corresponding to a certain vector ", StyleBox["\[Alpha]", FontFamily->"Symbol", FontWeight->"Bold"], StyleBox[" ", FontFamily->"Symbol"], "is obtained as follows. For each polynomial of the system we want to \ select all the terms whose exponent vectors ", StyleBox["k ", FontWeight->"Bold"], " which minimize the linear form ", StyleBox["\[Alpha]", FontFamily->"Symbol"], "1 k1 + ... + ", StyleBox["\[Alpha]", FontFamily->"Symbol"], "6 k6 . The corresponding vectors ", StyleBox["k", FontWeight->"Bold"], " lie on a face of the Newton polytope defined by the supporting hyperplane \ ", StyleBox["\[Alpha]", FontFamily->"Symbol"], "1 k1 + ... + ", StyleBox["\[Alpha]", FontFamily->"Symbol"], "6 k6 >= min where min is the minimum value of the form. It is clear that \ finding these terms is a task which can be done using the exponent lists \ rather than the equations themselves.", "\n\nNote that the Porta inequalities defining the facets are expressed as \ lhs <= const so must look for the maximum values of the left hand sides on \ each list of exponents and then select those exponents which attain this \ maximum value. The first two functions below carry out these steps. Then \ the corresponding reduced polynomial will consist of a single term if there \ is just one exponent vector which achieve the maximum value. The third \ function below checks this and returns a 1 if the given reduced polynomial is \ nontrivial. Finally, the fourth function tests a list of polynomials and \ returns True if and only if all of the resulting reduced polynomials do not \ reduce to a single term." }], "Text"], Cell[BoxData[ \(\(\(\[IndentingNewLine]\)\(FindMax[linform_, vertlist_]\ := \ Max[\ Map[linform /. Subst[#] &, vertlist]]\[IndentingNewLine]\[IndentingNewLine] GetMaximalExponents[ineq_, vertlist_] := \[IndentingNewLine]With[{linform = lhs[ineq], maxval\ = \ FindMax[lhs[ineq], vertlist]}, \ Select[vertlist, \((\((linform /. Subst[#])\)\ \[Equal] maxval)\) &]]\[IndentingNewLine]\[IndentingNewLine]\ \[IndentingNewLine]\ (*returns\ 1\ if\ the\ inequality\ determines\ a\ \ reduced\ polynomial\ with\ more\ than\ one\ term\ *) \[IndentingNewLine] Nontrivial[ineq_, vertlist_] := \ If[Length[GetMaximalExponents[ineq, vertlist]] > 1, 1, 0]\[IndentingNewLine]\[IndentingNewLine] (*\ returns\ 1\ if\ ineq\ is\ nontrivial\ all\ of\ the\ reduced\ \ polynomials\ whose\ exponents\ are\ in\ vllist\ \((list\ of\ exponent\ lists)\ \)\ *) \[IndentingNewLine] AllNontrivial[ineq_, vllist_]\ := \[IndentingNewLine]If[ Min[Map[Nontrivial[ineq, #] &, vllist]] > 0, True, False]\)\)\)], "Input"], Cell["\<\ We use this function to test each of the 2980 facets for nontriviality. Fortunately, only 53 of them survive the test. \ \>", "Text"], Cell[CellGroupData[{ Cell[BoxData[{ \(\(nontrivialfacets\ = \ Select[acdzineq, AllNontrivial[#, explist9] &];\)\), "\[IndentingNewLine]", \(Length[%]\)}], "Input"], Cell[BoxData[ \(53\)], "Output"] }, Open ]], Cell[TextData[{ "Before displaying the answer we read off the normal vectors ", StyleBox["\[Alpha]", FontFamily->"Symbol", FontWeight->"Bold"], " (putting in a minus sign to reverse the inequalities) and use these \ vectors to sort them into a convenient order. Finally we display the answer \ as a table. The inequalities are still in Porta form however. The \ inequalities displayed in Table 1 in the paper have all been reversed and the \ variables xi replaced by ki." }], "Text"], Cell[CellGroupData[{ Cell[BoxData[{ \(\(\(GetAlpha[ LessEqual[a_, b_]] := \ \(-Coefficient[ a, {x1, x2, x3, x4, x5, x6}]\)\)\(\[IndentingNewLine]\) \)\), "\[IndentingNewLine]", \(\(\(nontrivialfacets\ = \ Sort[nontrivialfacets, \(({1, 1, 1, 1, 1, 1} . GetAlpha[#1] > {1, 1, 1, 1, 1, 1} . GetAlpha[#2])\) &];\)\(\[IndentingNewLine]\) \)\), "\[IndentingNewLine]", \({\({Table[i, {i, 1, 27}], Take[nontrivialfacets, 27]} // Transpose\) // MatrixForm, \[IndentingNewLine]\({Table[i, {i, 28, 53}], Drop[nontrivialfacets, 27]} // Transpose\) // MatrixForm}\)}], "Input"], Cell[BoxData[ RowBox[{"{", RowBox[{ TagBox[ RowBox[{"(", "\[NoBreak]", GridBox[{ { "1", \(\(-x1\) - x2 - x3 - x4 - x5 - x6 \[LessEqual] \(-90\)\)}, { "2", \(\(-2\)\ x1 - 2\ x2 - 2\ x4 + x5 + x6 \[LessEqual] \(-28\)\)}, { "3", \(\(-2\)\ x1 - 2\ x2 + x3 - 2\ x4 + x6 \[LessEqual] \(-28\)\)}, { "4", \(\(-2\)\ x1 - 2\ x2 + x3 - 2\ x4 + x5 \[LessEqual] \(-28\)\)}, { "5", \(\(-2\)\ x1 - 2\ x3 + x4 - 2\ x5 + x6 \[LessEqual] \(-28\)\)}, { "6", \(\(-2\)\ x1 + x2 - 2\ x3 - 2\ x5 + x6 \[LessEqual] \(-28\)\)}, { "7", \(\(-2\)\ x1 + x2 - 2\ x3 + x4 - 2\ x5 \[LessEqual] \(-28\)\)}, { "8", \(\(-2\)\ x2 - 2\ x3 + x4 + x5 - 2\ x6 \[LessEqual] \(-28\)\)}, { "9", \(x2 + x3 - 2\ x4 - 2\ x5 - 2\ x6 \[LessEqual] \(-28\)\)}, { "10", \(x1 - 2\ x2 - 2\ x3 + x5 - 2\ x6 \[LessEqual] \(-28\)\)}, { "11", \(x1 - 2\ x2 - 2\ x3 + x4 - 2\ x6 \[LessEqual] \(-28\)\)}, { "12", \(x1 + x3 - 2\ x4 - 2\ x5 - 2\ x6 \[LessEqual] \(-28\)\)}, { "13", \(x1 + x2 - 2\ x4 - 2\ x5 - 2\ x6 \[LessEqual] \(-28\)\)}, {"14", \(\(-x1\) - x2 - x4 \[LessEqual] \(-36\)\)}, {"15", \(\(-x1\) - x3 - x5 \[LessEqual] \(-36\)\)}, {"16", \(\(-x2\) - x3 - x6 \[LessEqual] \(-36\)\)}, {"17", \(\(-x4\) - x5 - x6 \[LessEqual] \(-36\)\)}, {"18", \(\(-x1\) - x2 - x3 \[LessEqual] \(-30\)\)}, {"19", \(\(-x1\) - x4 - x5 \[LessEqual] \(-30\)\)}, {"20", \(\(-x2\) - x4 - x6 \[LessEqual] \(-30\)\)}, {"21", \(\(-x3\) - x5 - x6 \[LessEqual] \(-30\)\)}, {"22", \(x3 + x4 \[LessEqual] 50\)}, {"23", \(x2 + x5 \[LessEqual] 50\)}, {"24", \(x1 + x6 \[LessEqual] 50\)}, {"25", \(x3 + x5 + x6 \[LessEqual] 63\)}, {"26", \(x2 + x4 + x6 \[LessEqual] 63\)}, {"27", \(x1 + x4 + x5 \[LessEqual] 63\)} }], "\[NoBreak]", ")"}], Function[ BoxForm`e$, MatrixForm[ BoxForm`e$]]], ",", TagBox[ RowBox[{"(", "\[NoBreak]", GridBox[{ {"28", \(x1 + x2 + x3 \[LessEqual] 63\)}, {"29", \(x4 + x5 + x6 \[LessEqual] 69\)}, {"30", \(x2 + x3 + x6 \[LessEqual] 69\)}, {"31", \(x1 + x3 + x5 \[LessEqual] 69\)}, {"32", \(x1 + x2 + x4 \[LessEqual] 69\)}, {"33", \(x2 + x3 + x4 + x5 \[LessEqual] 81\)}, {"34", \(x1 + x3 + x4 + x6 \[LessEqual] 81\)}, {"35", \(x1 + x2 + x5 + x6 \[LessEqual] 81\)}, {"36", \(2\ x3 + 3\ x5 + 3\ x6 \[LessEqual] 170\)}, {"37", \(3\ x3 + 2\ x5 + 3\ x6 \[LessEqual] 170\)}, {"38", \(3\ x3 + 3\ x5 + 2\ x6 \[LessEqual] 170\)}, {"39", \(2\ x2 + 3\ x4 + 3\ x6 \[LessEqual] 170\)}, {"40", \(3\ x2 + 2\ x4 + 3\ x6 \[LessEqual] 170\)}, {"41", \(3\ x2 + 3\ x4 + 2\ x6 \[LessEqual] 170\)}, {"42", \(2\ x1 + 3\ x4 + 3\ x5 \[LessEqual] 170\)}, {"43", \(2\ x1 + 3\ x2 + 3\ x3 \[LessEqual] 170\)}, {"44", \(3\ x1 + 2\ x4 + 3\ x5 \[LessEqual] 170\)}, {"45", \(3\ x1 + 3\ x4 + 2\ x5 \[LessEqual] 170\)}, {"46", \(3\ x1 + 2\ x2 + 3\ x3 \[LessEqual] 170\)}, {"47", \(3\ x1 + 3\ x2 + 2\ x3 \[LessEqual] 170\)}, {"48", \(2\ x2 + 3\ x3 + 3\ x4 + 2\ x5 \[LessEqual] 208\)}, {"49", \(3\ x2 + 2\ x3 + 2\ x4 + 3\ x5 \[LessEqual] 208\)}, {"50", \(2\ x1 + 3\ x3 + 3\ x4 + 2\ x6 \[LessEqual] 208\)}, {"51", \(2\ x1 + 3\ x2 + 3\ x5 + 2\ x6 \[LessEqual] 208\)}, {"52", \(3\ x1 + 2\ x3 + 2\ x4 + 3\ x6 \[LessEqual] 208\)}, {"53", \(3\ x1 + 2\ x2 + 2\ x5 + 3\ x6 \[LessEqual] 208\)} }], "\[NoBreak]", ")"}], Function[ BoxForm`e$, MatrixForm[ BoxForm`e$]]]}], "}"}]], "Output"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["Nontrivial lower-dimensional faces and permutation symmetry", \ "Subsection"], Cell["\<\ We also need to find all the lower-dimensional faces of P which lead to nontrivial reduced systems. Every face of P is determined by some supporting hyperplane which, in turn, is represented by some linear inequality. If two or more facets of P are incident, then their intersection \ is a face and one can find an inequality for that face by simply adding the corresponding inequalities for the facets. Finally, we can test this face for nontriviality using the functions defined in the last subsection. \ \>", "Text"], Cell["\<\ To begin we define functions for determining whether or not a collection of facets are incident. We just find a list of the vertices of the polytope in each facet and see if the lists have a nonempty intersection. \ The first function below takes an inequality and a vertex list and finds all \ the vertices on the list which satisfy the corresponding equality. \ \>", "Text"], Cell[BoxData[ \(FindFacet[ineq_, vlist_] := Select[vlist, \((\((lhs[ineq] /. Subst[#])\) === rhs[ineq])\) &]\)], "Input"], Cell["\<\ We specify a potential face by a set of facets. We have a list of 53 nontrivial facets and we can specify any one of them by its position on this list (its index). Then a set of facets is given by a list of such indices (always in order). For example, the index list {1, 22, 36} would represent the face determined by intersecting the facets corresponding to inequalities 1, 22, and 36 in our list. The next function takes such an index list, an inequality list and a list of vertices defining a polytope and determines if the facets from the list are really incident in the polytope. \ \>", "Text"], Cell[BoxData[ \(FacetsIncident[indlist_, ineqlist_, vlist_]\ := \ With[{f = Map[FindFacet[#, vlist] &, Part[ineqlist, indlist]]}, \[IndentingNewLine]If[ Length[Intersection @@ f] > 0, True, False]]\)], "Input"], Cell["\<\ Once we have some incident facets, we can test to see if the resulting face is nontrivial. We just create an inequality defining that face by adding the inequalities from the facets and use this inequality in the function AllNontrivial defined in the last subsection. \ \>", "Text"], Cell[BoxData[{ \(\(\(AddLEInequalities[indlist_, ineqlist_] := Module[{ins, rights, \ lefts}, \[IndentingNewLine]ins\ = \ Part[ineqlist, indlist]; \[IndentingNewLine]rights\ = \ Map[rhs, ins]; \[IndentingNewLine]lefts\ = \ Map[lhs, ins]; \[IndentingNewLine]LessEqual[Plus @@ lefts, Plus @@ rights]]\)\(\[IndentingNewLine]\) \)\), "\[IndentingNewLine]", \(NontrivialFace[indlist_, ineqlist_, explist_]\ := \ With[{in = AddLEInequalities[indlist, ineqlist]}, \[IndentingNewLine]AllNontrivial[in, explist]]\)}], "Input"], Cell["\<\ Before applying this to our list of 53 nontrival facets we introduce some functions to describe the action of the permutation group S4. This group, called sigma4 below, is just represented by a list of all 24 possible permutations of {1 ,2, 3, 4}. The group acts on the subscripts of the mi and the rij variables and therefore induces an action on the Minkowski sum polytope P. If two faces of \ P are symmetric in this way, then it suffices to check the reduced system of one of them. First we will describe the action of S4 on our list of inequalities. To do this we replace the variables x1, ..., x6 by new variables k[i,j] which reflect their roles as exponents of the variables rij. \ \>", "Text"], Cell[CellGroupData[{ Cell[BoxData[{ \(\(\(sigma4\ = \ Permutations[{1, 2, 3, 4}]\)\(\[IndentingNewLine]\) \)\), "\[IndentingNewLine]", \(k[i_, i_] := 0\), "\n", \(\(\(k[i_, j_] := k[j, i] /; j < i\)\(\n\) \)\), "\n", \(\(\(kvars\ = \ {k[1, 2], k[1, 3], k[1, 4], k[2, 3], k[2, 4], k[3, 4]};\)\(\[IndentingNewLine]\) \)\), "\[IndentingNewLine]", \(\(kineqs\ = \ nontrivialfacets /. {x1 \[Rule] k[1, 2], x2 \[Rule] k[1, 3], x3 \[Rule] k[1, 4], x4 \[Rule] k[2, 3], x5 \[Rule] k[2, 4], x6 \[Rule] k[3, 4]};\)\)}], "Input"], Cell[BoxData[ \({{1, 2, 3, 4}, {1, 2, 4, 3}, {1, 3, 2, 4}, {1, 3, 4, 2}, {1, 4, 2, 3}, {1, 4, 3, 2}, {2, 1, 3, 4}, {2, 1, 4, 3}, {2, 3, 1, 4}, {2, 3, 4, 1}, {2, 4, 1, 3}, {2, 4, 3, 1}, {3, 1, 2, 4}, {3, 1, 4, 2}, {3, 2, 1, 4}, {3, 2, 4, 1}, {3, 4, 1, 2}, {3, 4, 2, 1}, {4, 1, 2, 3}, {4, 1, 3, 2}, {4, 2, 1, 3}, {4, 2, 3, 1}, {4, 3, 1, 2}, {4, 3, 2, 1}}\)], "Output"] }, Open ]], Cell["\<\ Next we define the action of a permuation on a variable, k[i,j]. The corresponding action on a inequality is obtained by simply acting on all the variables in the inequality. The first two functions below implement this. Once we have permuted the variables in an inequality, it will be equal \ to one of the other inequalities on our list. The third function below looks \ up the index of the permuted inequality in the list. So we know have an action of S4 on the numbers 1 -- 53. Finally, the fourth function below extends this action to index lists, consisting of several number from 1 -- 53. This implements the action of the symmetry on the faces of P. \ \>", "Text"], Cell[CellGroupData[{ Cell[BoxData[{ \(\(\(Permute[perm_, k[i_, j_]] := \ k[perm[\([i]\)], perm[\([j]\)]]\)\(\n\) \)\), "\n", \(\(\(Permute[perm_, LessEqual[a_, b_]] := \ With[{coeffs = \ Coefficient[a, kvars]}, \[IndentingNewLine]LessEqual[ coeffs . Map[Permute[perm, #] &, kvars], b]]\)\(\n\) \)\), "\[IndentingNewLine]", \(\(\(PermutedIndex[perm_, ineqlist_, ind_]\ := \ With[{pineq\ = \ Permute[perm, ineqlist[\([ind]\)]]}, \[IndentingNewLine]\(Position[ineqlist, pineq]\)[\([1, 1]\)]\[IndentingNewLine]]\)\(\[IndentingNewLine]\) \)\), "\n", \(PermutedIndexList[perm_, ineqlist_, indlist_]\ := \ Sort[Map[PermutedIndex[perm, ineqlist, #] &, indlist]]\), "\[IndentingNewLine]", \(\)}], "Input"], Cell[BoxData[ RowBox[{\(General::"spell1"\), \(\(:\)\(\ \)\), "\<\"Possible spelling \ error: new symbol name \\\"\\!\\(pineq\\)\\\" is similar to existing symbol \ \\\"\\!\\(ineq\\)\\\". \\!\\(\\*ButtonBox[\\\"More\[Ellipsis]\\\", \ ButtonStyle->\\\"RefGuideLinkText\\\", ButtonFrame->None, \ ButtonData:>\\\"General::spell1\\\"]\\)\"\>"}]], "Message"] }, Open ]], Cell["\<\ The first function below finds the orbit of a face (represented by an index list) under the group action, i.e, all the symmetrical faces; the Union command puts the orbit in lexicographic order. Then the second function below reads off the minimal representative for the orbit with respect to lexicographic order. \ \>", "Text"], Cell[BoxData[{ \(\(\(IndexListOrbit[pgroup_, ineqlist_, indlist_] := \ Union[Map[PermutedIndexList[#, ineqlist, indlist] &, pgroup]]\)\(\[IndentingNewLine]\) \)\), "\[IndentingNewLine]", \(MinimalOrbitRep[pgroup_, ineqlist_, indlist_] := \ First[IndexListOrbit[pgroup, ineqlist, indlist]]\)}], "Input"], Cell["\<\ To facilitate a recursive approach to finding the nontrivial faces we begin by defining a function which finds subfaces of a given face. If the \ given face is represented by a list of k indices (i.e., it is an intersection \ of k nontrivial facets) we want to construct a list of subfaces, each defined \ by a list of k+1 indices. We will always represent faces by ordered index lists, so that when we extend a list, we only need to consider values for the \ k+1 st index which are greater than the k-th given index. \ \>", "Text"], Cell[BoxData[{ \(ExtendIndexList[ineqlist_, {}]\ := \ Table[{i}, {i, 1, Length[ineqlist]}]\), "\[IndentingNewLine]", \(ExtendIndexList[ineqlist_, indlist_]\ := \ Table[indlist~Join~{i}, {i, Last[indlist] + 1, Length[ineqlist]}]\), "\[IndentingNewLine]", \(\)}], "Input"], Cell["\<\ The next two functions put all of this group theory to work. Given a face, represented by an index list of size k, we want to make a list of all possible extensions to lists of size k+1, in such a way that the list of possible extensions contains just the minimal representative from each symmetry group orbit. In other words, its a list of all possible extensions up to symmetry. Then we do the same for a list of faces and combine the results. The first functions below works as follows. As explained in section 4.2 of the paper, we only need to extend each k-tuple {i1, ..., ik} by appending (k+1)-st indices i(k+1) > ik. Then we compute minimal repesentative of the orbit and append it to a running list of representatives. Taking the Union at the end eliminates duplications and puts the list in lexicographical order. The second function below just applies this procedure to each element of a list of faces and Union's the results. So we are in a positions to inductively construct all the nontrivial faces. \ \>", "Text"], Cell[BoxData[{ \(\(\(ExtendedMinimalOrbitReps[pgroup_, ineqlist_, indlist_]\ := \ Module[{i, ext, minrep, oreps = {}}, \[IndentingNewLine]ext\ = \ ExtendIndexList[ineqlist, indlist]; \[IndentingNewLine]For[i = 1, i \[LessEqual] Length[ext], \(i++\), \[IndentingNewLine]minrep = MinimalOrbitRep[pgroup, ineqlist, ext[\([i]\)]]; \[IndentingNewLine]AppendTo[oreps, minrep];\[IndentingNewLine]]; \[IndentingNewLine]oreps // Union]\)\(\[IndentingNewLine]\) \)\), "\[IndentingNewLine]", \(ExtendedMinimalOrbitRepsList[pgroup_, ineqlist_, indlistlist_]\ := \ \[IndentingNewLine]\(Map[ ExtendedMinimalOrbitReps[pgroup, ineqlist, #] &, indlistlist] // Flatten[#, 1] &\) // Union\)}], "Input"], Cell["\<\ We begin with the empty list of faces and we construct all the nontrivial facets up to symmetry. First we construct a list of minimal orbit representatives for the facets \ \>", "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(faces1\ \ = \ ExtendedMinimalOrbitRepsList[sigma4, kineqs, {{}}]\)], "Input"], Cell[BoxData[ RowBox[{\(General::"spell1"\), \(\(:\)\(\ \)\), "\<\"Possible spelling \ error: new symbol name \\\"\\!\\(faces1\\)\\\" is similar to existing symbol \ \\\"\\!\\(facets1\\)\\\". \\!\\(\\*ButtonBox[\\\"More\[Ellipsis]\\\", \ ButtonStyle->\\\"RefGuideLinkText\\\", ButtonFrame->None, \ ButtonData:>\\\"General::spell1\\\"]\\)\"\>"}]], "Message"], Cell[BoxData[ \({{1}, {2}, {14}, {18}, {22}, {25}, {29}, {33}, {36}, {48}}\)], "Output"] }, Open ]], Cell["\<\ At the next step we first find minimal orbit reps for the extensions of the minimal reps for the facets. This will be a list of pairs of indices. We then eliminate all the pairs for which the two facets are not incident and those for which the resulting reduced systems is trivial. \ \>", "Text"], Cell[CellGroupData[{ Cell[BoxData[{ \(faces2\ \ = \ ExtendedMinimalOrbitRepsList[sigma4, kineqs, faces1]\), "\[IndentingNewLine]", \(faces2\ = \ Select[faces2, \((NontrivialFace[#, nontrivialfacets, explist9]\ && FacetsIncident[#, nontrivialfacets, acdzconv])\) &]\)}], "Input"], Cell[BoxData[ \({{1, 2}, {1, 14}, {1, 18}, {1, 22}, {1, 25}, {1, 29}, {1, 33}, {1, 36}, {1, 48}, {2, 3}, {2, 5}, {2, 6}, {2, 7}, {2, 13}, {2, 14}, {2, 15}, {2, 17}, {2, 18}, {2, 19}, {2, 21}, {2, 22}, {2, 23}, {2, 25}, {2, 26}, {2, 28}, {2, 29}, {2, 30}, {2, 32}, {2, 33}, {2, 35}, {2, 36}, {2, 37}, {2, 39}, {2, 40}, {2, 41}, {2, 43}, {2, 47}, {2, 48}, {2, 49}, {2, 51}, {14, 15}, {14, 18}, {14, 21}, {14, 22}, {14, 25}, {14, 26}, {14, 29}, {14, 32}, {14, 33}, {14, 36}, {14, 39}, {14, 41}, {14, 48}, {18, 19}, {18, 22}, {18, 25}, {18, 28}, {18, 29}, {18, 30}, {18, 33}, {18, 36}, {18, 37}, {18, 43}, {18, 48}, {22, 23}, {22, 25}, {22, 29}, {22, 33}, {22, 35}, {22, 36}, {22, 37}, {22, 48}, {22, 49}, {22, 51}, {25, 26}, {25, 29}, {25, 32}, {25, 33}, {25, 36}, {25, 39}, {25, 41}, {25, 48}, {29, 30}, {29, 33}, {29, 36}, {29, 37}, {29, 43}, {29, 48}, {33, 34}, {33, 36}, {33, 38}, {33, 48}, {33, 50}, {33, 52}, {36, 37}, {36, 39}, {36, 40}, {36, 41}, {36, 47}, {36, 48}, {36, 49}, {36, 51}, {48, 49}, {48, 50}, {48, 51}, {48, 53}}\)], "Output"], Cell[BoxData[ \({{1, 14}, {1, 18}, {2, 14}, {2, 25}, {2, 36}, {14, 25}, {14, 36}, {18, 29}, {22, 48}, {25, 36}, {33, 48}}\)], "Output"] }, Open ]], Cell["\<\ Now we use the same method to inductively construct minimal representatives for all of the nontriival faces. \ \>", "Text"], Cell[CellGroupData[{ Cell[BoxData[{ \(\(faces3\ \ = \ ExtendedMinimalOrbitRepsList[sigma4, kineqs, faces2];\)\), "\[IndentingNewLine]", \(\(\(faces3\ = \ Select[faces3, \((NontrivialFace[#, nontrivialfacets, explist9]\ && FacetsIncident[#, nontrivialfacets, acdzconv])\) &]\)\(\[IndentingNewLine]\) \)\), "\[IndentingNewLine]", \(\(faces4\ \ = \ ExtendedMinimalOrbitRepsList[sigma4, kineqs, faces3];\)\), "\[IndentingNewLine]", \(\(\(faces4\ = \ Select[faces4, \((NontrivialFace[#, nontrivialfacets, explist9]\ && FacetsIncident[#, nontrivialfacets, acdzconv])\) &]\)\(\[IndentingNewLine]\) \)\), "\[IndentingNewLine]", \(\(faces5\ = \ ExtendedMinimalOrbitRepsList[sigma4, kineqs, faces4];\)\), "\[IndentingNewLine]", \(faces5\ = \ Select[faces5, \((NontrivialFace[#, nontrivialfacets, explist9]\ && FacetsIncident[#, nontrivialfacets, acdzconv])\) &]\)}], "Input"], Cell[BoxData[ \({{2, 14, 25}, {2, 14, 36}, {2, 25, 36}, {14, 25, 36}}\)], "Output"], Cell[BoxData[ \({{2, 14, 25, 36}}\)], "Output"], Cell[BoxData[ \({}\)], "Output"] }, Open ]], Cell["\<\ Finally we eliminate any faces which have only normals with indices 1 -- 21 because we are only considering faces with (inward) normal vectors in \ the half-space (-1,-1,-1,-1,-1,-1,-1).(a1, ... , a6 ) >= 0. The normals in the list of inequalities above have to be reversed, so the inequalities 1 -- 21 are in the wrong half-space. We are left with the following list of faces \ to check. \ \>", "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(nontrivialfacereps\ = {{22}, {25}, {29}, {33}, {36}, {48}, {2, 25}, {2, 36}, {14, 25}, {14, 36}, {18, 29}, {22, 48}, {25, 36}, {33, 48}, {2, 14, 25}, {2, 14, 36}, {2, 25, 36}, {14, 25, 36}, {2, 14, 25, 36}}\)], "Input"], Cell[BoxData[ \({{22}, {25}, {29}, {33}, {36}, {48}, {2, 25}, {2, 36}, {14, 25}, {14, 36}, {18, 29}, {22, 48}, {25, 36}, {33, 48}, {2, 14, 25}, {2, 14, 36}, {2, 25, 36}, {14, 25, 36}, {2, 14, 25, 36}}\)], "Output"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["Analyzing the reduced systems", "Subsection"], Cell["\<\ Here is the list of faces to be analyzed from the last subsection. \ \>", "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(nontrivialfacereps\)], "Input"], Cell[BoxData[ \({{22}, {25}, {29}, {33}, {36}, {48}, {2, 25}, {2, 36}, {14, 25}, {14, 36}, {18, 29}, {22, 48}, {25, 36}, {33, 48}, {2, 14, 25}, {2, 14, 36}, {2, 25, 36}, {14, 25, 36}, {2, 14, 25, 36}}\)], "Output"] }, Open ]], Cell["\<\ By definition, the reduced polynomial corresponding to a certain inequality of the form lhs >= rhs consists of those terms for which the exponent vector minimizes the linear form lhs. Since all of our inequalities \ are reversed, we take the maximal terms instead. To get the reduced system we just reduce each polynomial. To find the reduced system corresponding to a face defined by a list of indices of inequalites we add the inequalities to obtain a single defining inequality for the face. \ \>", "Text"], Cell[BoxData[{ \(\(\(ReducePoly[p_, ineq_]\ := Module[{q, linform, maxval, explist, vars}, \[IndentingNewLine]vars\ = \ {r12, r13, r14, r23, r24, r34}; \[IndentingNewLine]q = Expand[p]; \[IndentingNewLine]linform\ = \ lhs[ineq]; \[IndentingNewLine]explist\ = \ GetAllExponents[q, vars]; \[IndentingNewLine]maxval\ = \ FindMax[linform, explist]; \[IndentingNewLine]Select[ q, \((\((linform /. Subst[GetExponents[#, vars]])\) \[Equal] maxval)\) &]\[IndentingNewLine]]\)\(\[IndentingNewLine]\) \)\), "\n", \(\(\(ReducedSystem[LessEqual[lhs_, rhs_], eqlist_]\ := \ Map[ReducePoly[#, LessEqual[lhs, rhs]] &, eqlist]\)\(\n\) \)\), "\[IndentingNewLine]", \(ReducedSystem[indlist_, ineqlist_, eqlist_]\ := \ ReducedSystem[AddLEInequalities[indlist, ineqlist], eqlist]\)}], "Input"], Cell["\<\ Here are some utility functions to eliminate factors of variables (in our case, the rij) from the equations of the reduced systems \ \>", "Text"], Cell[BoxData[{ \(\(\(RemoveFactor[poly_, var_]\ := Module[{i, pow, p}, \[IndentingNewLine]p\ = \ Expand[poly]; \[IndentingNewLine]pow = \ Min[Table[ Exponent[p[\([i]\)], var], {i, 1, Length[p]}]]; \[IndentingNewLine]If[ pow > 0 && pow < Infinity, \((poly/var^pow)\) // Factor, poly]]\)\(\n\) \)\), "\[IndentingNewLine]", \(CleanUp[poly_, vars_]\ := \ \[IndentingNewLine]Fold[RemoveFactor, poly, vars\ ]\)}], "Input"], Cell["\<\ Now we begin to analyze all the reduced systems on our list of nontrivial faces. To eliminate the quasi-homogeneity of the reduced systems we add in a normalization condition. \ \>", "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(nzeq\ = \ r12*r13*r14*r23*r24*r34 - 1\)], "Input"], Cell[BoxData[ \(\(-1\) + r12\ r13\ r14\ r23\ r24\ r34\)], "Output"] }, Open ]], Cell["\<\ We will start from the end of the list of nontrivial faces, the face determined by intersections facets 2, 14, 25, 36. The method is to find \ and clean up the reduced system, append the normalization conditions and then \ use the GroebnerBasis command to eliminate the variables rij and find polynomial constraints on the masses. \ \>", "Text"], Cell[CellGroupData[{ Cell[BoxData[{ \(red\ = \ ReducedSystem[{2, 14, 25, 36}, nontrivialfacets, acdzeqs] // Factor\), "\[IndentingNewLine]", \(red\ = Map[CleanUp[#, vars4bp] &, red]\), "\[IndentingNewLine]", \(GroebnerBasis[red~Join~{nzeq}, {m1, m2, m3, m4}, vars4bp] // Factor\)}], "Input"], Cell[BoxData[ \({\(-r14\^3\)\ \((m3\ r12\^3\ r13\^3 - m3\ r12\ r13\^5 + m3\ r12\ r13\^3\ r23\^2 + m3\ r12\^3\ r23\^3 + m3\ r12\ r13\^2\ r23\^3 + 2\ m1\ r13\^3\ r23\^3 + 2\ m2\ r13\^3\ r23\^3 - m3\ r12\ r23\^5)\)\ r24\^3, r14\^3\ \((m2\ r12\^5\ r13 - m2\ r12\^3\ r13\^3 - m2\ r12\^3\ r13\ r23\^2 - 2\ m1\ r12\^3\ r23\^3 - 2\ m3\ r12\^3\ r23\^3 - m2\ r12\^2\ r13\ r23\^3 - m2\ r13\^3\ r23\^3 + m2\ r13\ r23\^5)\)\ r34\^3, \(-\((2\ m2\ r12\^3\ r13\^3 + 2\ m3\ r12\^3\ r13\^3 - m1\ r12\^5\ r23 + m1\ r12\^3\ r13\^2\ r23 + m1\ r12\^2\ r13\^3\ r23 - m1\ r13\^5\ r23 + m1\ r12\^3\ r23\^3 + m1\ r13\^3\ r23\^3)\)\)\ r24\^3\ r34\^3, r14\ r24\^3\ r34\^3\ \((m2\ r13\^3\ r24\^2 + m3\ r12\^3\ r34\^2)\), \(-r14\^3\)\ r24\ r34\^3\ \((m3\ r12\^3\ \ r24\^2 + m1\ r23\^3\ r24\^2 - m3\ r12\^3\ r34\^2)\), r14\^3\ r24\^3\ r34\ \((m2\ r13\^3\ r24\^2 - m2\ r13\^3\ r34\^2 - m1\ r23\^3\ r34\^2)\), r14\^3\ \((r12 - r23)\)\ \((r12\^2 + r12\ r23 + r23\^2)\)\ r34\^3, \((r12 - r13)\)\ \((r12\^2 + r12\ r13 + r13\^2)\)\ r24\^3\ r34\^3, r14\^3\ \((r13 - r23)\)\ \((r13\^2 + r13\ r23 + r23\^2)\)\ r24\^3}\)], "Output"], Cell[BoxData[ \({\(-m3\)\ r12\^3\ r13\^3 + m3\ r12\ r13\^5 - m3\ r12\ r13\^3\ r23\^2 - m3\ r12\^3\ r23\^3 - m3\ r12\ r13\^2\ r23\^3 - 2\ m1\ r13\^3\ r23\^3 - 2\ m2\ r13\^3\ r23\^3 + m3\ r12\ r23\^5, m2\ r12\^5\ r13 - m2\ r12\^3\ r13\^3 - m2\ r12\^3\ r13\ r23\^2 - 2\ m1\ r12\^3\ r23\^3 - 2\ m3\ r12\^3\ r23\^3 - m2\ r12\^2\ r13\ r23\^3 - m2\ r13\^3\ r23\^3 + m2\ r13\ r23\^5, \(-2\)\ m2\ r12\^3\ r13\^3 - 2\ m3\ r12\^3\ r13\^3 + m1\ r12\^5\ r23 - m1\ r12\^3\ r13\^2\ r23 - m1\ r12\^2\ r13\^3\ r23 + m1\ r13\^5\ r23 - m1\ r12\^3\ r23\^3 - m1\ r13\^3\ r23\^3, m2\ r13\^3\ r24\^2 + m3\ r12\^3\ r34\^2, \(-m3\)\ r12\^3\ r24\^2 - m1\ r23\^3\ r24\^2 + m3\ r12\^3\ r34\^2, m2\ r13\^3\ r24\^2 - m2\ r13\^3\ r34\^2 - m1\ r23\^3\ r34\^2, \((r12 - r23)\)\ \((r12\^2 + r12\ r23 + r23\^2)\), \((r12 - r13)\)\ \((r12\^2 + r12\ r13 + r13\^2)\), \((r13 - r23)\)\ \((r13\^2 + r13\ r23 + r23\^2)\)}\)], "Output"], Cell[BoxData[ \({m1 + m2 + m3}\)], "Output"] }, Open ]], Cell["\<\ The result shows that the reduced system corresponding to this face can have solutions in the algebraic torus only if m1+m2+m3 = 0. Many of the other reduced systems produce similar results. Here are the computations for the various triples of indices in the list of nontrivial faces. \ \>", "Text"], Cell[CellGroupData[{ Cell[BoxData[{ \(\(red\ = \ ReducedSystem[{2, 14, 25}, nontrivialfacets, acdzeqs] // Factor;\)\), "\[IndentingNewLine]", \(red\ = Map[CleanUp[#, vars4bp] &, red]\), "\[IndentingNewLine]", \(\(\(GroebnerBasis[red~Join~{nzeq}, {m1, m2, m3, m4}, vars4bp] // Factor\)\(\[IndentingNewLine]\) \)\), "\[IndentingNewLine]", \(\(red\ = \ ReducedSystem[{2, 14, 36}, nontrivialfacets, acdzeqs] // Factor;\)\), "\n", \(red\ = Map[CleanUp[#, vars4bp] &, red]\), "\n", \(\(\(GroebnerBasis[red~Join~{nzeq}, {m1, m2, m3, m4}, vars4bp] // Factor\)\(\[IndentingNewLine]\) \)\), "\[IndentingNewLine]", \(\(red\ = \ ReducedSystem[{2, 25, 36}, nontrivialfacets, acdzeqs] // Factor;\)\), "\n", \(red\ = Map[CleanUp[#, vars4bp] &, red]\), "\n", \(\(\(GroebnerBasis[red~Join~{nzeq}, {m1, m2, m3, m4}, vars4bp] // Factor\)\(\[IndentingNewLine]\) \)\), "\[IndentingNewLine]", \(\(red\ = \ ReducedSystem[{14, 25, 36}, nontrivialfacets, acdzeqs] // Factor;\)\), "\n", \(red\ = Map[CleanUp[#, vars4bp] &, red]\), "\n", \(GroebnerBasis[red~Join~{nzeq}, {m1, m2, m3, m4}, vars4bp] // Factor\)}], "Input"], Cell[BoxData[ \({\(-m3\)\ r12\^3\ r13\^3 + m3\ r12\ r13\^5 - m3\ r12\ r13\^3\ r23\^2 - m3\ r12\^3\ r23\^3 - m3\ r12\ r13\^2\ r23\^3 - 2\ m1\ r13\^3\ r23\^3 - 2\ m2\ r13\^3\ r23\^3 + m3\ r12\ r23\^5, m2\ r12\^5\ r13 - m2\ r12\^3\ r13\^3 - m2\ r12\^3\ r13\ r23\^2 - 2\ m1\ r12\^3\ r23\^3 - 2\ m3\ r12\^3\ r23\^3 - m2\ r12\^2\ r13\ r23\^3 - m2\ r13\^3\ r23\^3 + m2\ r13\ r23\^5, \(-2\)\ m2\ r12\^3\ r13\^3 - 2\ m3\ r12\^3\ r13\^3 + m1\ r12\^5\ r23 - m1\ r12\^3\ r13\^2\ r23 - m1\ r12\^2\ r13\^3\ r23 + m1\ r13\^5\ r23 - m1\ r12\^3\ r23\^3 - m1\ r13\^3\ r23\^3, m2\ r13\^3\ r24\^2 + m3\ r12\^3\ r34\^2, \(-m3\)\ r12\^3\ r24\^2 - m1\ r23\^3\ r24\^2 + m3\ r12\^3\ r34\^2, m2\ r13\^3\ r24\^2 - m2\ r13\^3\ r34\^2 - m1\ r23\^3\ r34\^2, \((r12 - r23)\)\ \((r12\^2 + r12\ r23 + r23\^2)\), \((r12 - r13)\)\ \((r12\^2 + r12\ r13 + r13\^2)\), \((r13 - r23)\)\ \((r13\^2 + r13\ r23 + r23\^2)\)}\)], "Output"], Cell[BoxData[ \({m1 + m2 + m3}\)], "Output"], Cell[BoxData[ \({\(-m3\)\ r12\^3\ r13\^3 + m3\ r12\ r13\^5 - m3\ r12\ r13\^3\ r23\^2 - m3\ r12\^3\ r23\^3 - m3\ r12\ r13\^2\ r23\^3 - 2\ m1\ r13\^3\ r23\^3 - 2\ m2\ r13\^3\ r23\^3 + m3\ r12\ r23\^5, m2\ r12\^5\ r13 - m2\ r12\^3\ r13\^3 - m2\ r12\^3\ r13\ r23\^2 - 2\ m1\ r12\^3\ r23\^3 - 2\ m3\ r12\^3\ r23\^3 - m2\ r12\^2\ r13\ r23\^3 - m2\ r13\^3\ r23\^3 + m2\ r13\ r23\^5, \(-2\)\ m2\ r12\^3\ r13\^3 - 2\ m3\ r12\^3\ r13\^3 + m1\ r12\^5\ r23 - m1\ r12\^3\ r13\^2\ r23 - m1\ r12\^2\ r13\^3\ r23 + m1\ r13\^5\ r23 - m1\ r12\^3\ r23\^3 - m1\ r13\^3\ r23\^3, m2\ r13\^3\ r24\^2 + m3\ r12\^3\ r34\^2, \(-m3\)\ r12\^3\ r24\^2 - m1\ r23\^3\ r24\^2 + m3\ r12\^3\ r34\^2, m2\ r13\^3\ r24\^2 - m2\ r13\^3\ r34\^2 - m1\ r23\^3\ r34\^2, \((r12 - r23)\)\ \((r12\^2 + r12\ r23 + r23\^2)\), \((r12 - r13)\)\ \((r12\^2 + r12\ r13 + r13\^2)\), \((r13 - r23)\)\ \((r13\^2 + r13\ r23 + r23\^2)\)}\)], "Output"], Cell[BoxData[ \({m1 + m2 + m3}\)], "Output"], Cell[BoxData[ \({\(-m3\)\ r12\^3\ r13\^3 + m3\ r12\ r13\^5 - m3\ r12\ r13\^3\ r23\^2 - m3\ r12\^3\ r23\^3 - m3\ r12\ r13\^2\ r23\^3 - 2\ m1\ r13\^3\ r23\^3 - 2\ m2\ r13\^3\ r23\^3 + m3\ r12\ r23\^5, m2\ r12\^5\ r13 - m2\ r12\^3\ r13\^3 - m2\ r12\^3\ r13\ r23\^2 - 2\ m1\ r12\^3\ r23\^3 - 2\ m3\ r12\^3\ r23\^3 - m2\ r12\^2\ r13\ r23\^3 - m2\ r13\^3\ r23\^3 + m2\ r13\ r23\^5, \(-2\)\ m2\ r12\^3\ r13\^3 - 2\ m3\ r12\^3\ r13\^3 + m1\ r12\^5\ r23 - m1\ r12\^3\ r13\^2\ r23 - m1\ r12\^2\ r13\^3\ r23 + m1\ r13\^5\ r23 - m1\ r12\^3\ r23\^3 - m1\ r13\^3\ r23\^3, m2\ r13\^3\ r24\^2 + m3\ r12\^3\ r34\^2, \(-m3\)\ r12\^3\ r24\^2 - m1\ r23\^3\ r24\^2 + m3\ r12\^3\ r34\^2, m2\ r13\^3\ r24\^2 - m2\ r13\^3\ r34\^2 - m1\ r23\^3\ r34\^2, \((r12 - r23)\)\ \((r12\^2 + r12\ r23 + r23\^2)\), \((r12 - r13)\)\ \((r12\^2 + r12\ r13 + r13\^2)\), \((r13 - r23)\)\ \((r13\^2 + r13\ r23 + r23\^2)\)}\)], "Output"], Cell[BoxData[ \({m1 + m2 + m3}\)], "Output"], Cell[BoxData[ \({\(-m3\)\ r12\^3\ r13\^3 + m3\ r12\ r13\^5 - m3\ r12\ r13\^3\ r23\^2 - m3\ r12\^3\ r23\^3 - m3\ r12\ r13\^2\ r23\^3 - 2\ m1\ r13\^3\ r23\^3 - 2\ m2\ r13\^3\ r23\^3 + m3\ r12\ r23\^5, m2\ r12\^5\ r13 - m2\ r12\^3\ r13\^3 - m2\ r12\^3\ r13\ r23\^2 - 2\ m1\ r12\^3\ r23\^3 - 2\ m3\ r12\^3\ r23\^3 - m2\ r12\^2\ r13\ r23\^3 - m2\ r13\^3\ r23\^3 + m2\ r13\ r23\^5, \(-2\)\ m2\ r12\^3\ r13\^3 - 2\ m3\ r12\^3\ r13\^3 + m1\ r12\^5\ r23 - m1\ r12\^3\ r13\^2\ r23 - m1\ r12\^2\ r13\^3\ r23 + m1\ r13\^5\ r23 - m1\ r12\^3\ r23\^3 - m1\ r13\^3\ r23\^3, m2\ r13\^3\ r24\^2 + m3\ r12\^3\ r34\^2, \(-m3\)\ r12\^3\ r24\^2 - m1\ r23\^3\ r24\^2 + m3\ r12\^3\ r34\^2, m2\ r13\^3\ r24\^2 - m2\ r13\^3\ r34\^2 - m1\ r23\^3\ r34\^2, \((r12 - r23)\)\ \((r12\^2 + r12\ r23 + r23\^2)\), \((r12 - r13)\)\ \((r12\^2 + r12\ r13 + r13\^2)\), \((r13 - r23)\)\ \((r13\^2 + r13\ r23 + r23\^2)\)}\)], "Output"], Cell[BoxData[ \({m1 + m2 + m3}\)], "Output"] }, Open ]], Cell["\<\ Here are the computations for the pairs of indices in nontrivial face list. In each case we obtain some mass polynomials of the form mi, mi \ + mj, mi + mj + mk, or m1+m2+m3+m4. \ \>", "Text"], Cell[CellGroupData[{ Cell[BoxData[{ \(\(red\ = \ ReducedSystem[{2, 25}, nontrivialfacets, acdzeqs] // Factor;\)\), "\[IndentingNewLine]", \(red\ = Map[CleanUp[#, vars4bp] &, red]\), "\[IndentingNewLine]", \(\(\(GroebnerBasis[red~Join~{nzeq}, {m1, m2, m3, m4}, vars4bp] // Factor\)\(\[IndentingNewLine]\) \)\), "\[IndentingNewLine]", \(\(red\ = \ ReducedSystem[{2, 36}, nontrivialfacets, acdzeqs] // Factor;\)\), "\n", \(red\ = Map[CleanUp[#, vars4bp] &, red]\), "\n", \(\(\(GroebnerBasis[red~Join~{nzeq}, {m1, m2, m3, m4}, vars4bp] // Factor\)\(\[IndentingNewLine]\) \)\), "\[IndentingNewLine]", \(\(red\ = \ ReducedSystem[{14, 25}, nontrivialfacets, acdzeqs] // Factor;\)\), "\n", \(red\ = Map[CleanUp[#, vars4bp] &, red]\), "\n", \(\(\(GroebnerBasis[red~Join~{nzeq}, {m1, m2, m3, m4}, vars4bp] // Factor\)\(\[IndentingNewLine]\) \)\), "\[IndentingNewLine]", \(\(red\ = \ ReducedSystem[{14, 36}, nontrivialfacets, acdzeqs] // Factor;\)\), "\n", \(red\ = Map[CleanUp[#, vars4bp] &, red]\), "\n", \(\(\(GroebnerBasis[red~Join~{nzeq}, {m1, m2, m3, m4}, vars4bp] // Factor\)\(\[IndentingNewLine]\) \)\), "\[IndentingNewLine]", \(\(red\ = \ ReducedSystem[{18, 29}, nontrivialfacets, acdzeqs] // Factor;\)\), "\[IndentingNewLine]", \(red\ = Map[CleanUp[#, vars4bp] &, red]\), "\[IndentingNewLine]", \(\(\(GroebnerBasis[red~Join~{nzeq}, {m1, m2, m3, m4}, vars4bp] // Factor\)\(\[IndentingNewLine]\) \)\), "\[IndentingNewLine]", \(\(red\ = \ ReducedSystem[{22, 48}, nontrivialfacets, acdzeqs] // Factor;\)\), "\n", \(red\ = Map[CleanUp[#, vars4bp] &, red]\), "\n", \(\(\(GroebnerBasis[red~Join~{nzeq}, {m1, m2, m3, m4}, vars4bp] // Factor\)\(\[IndentingNewLine]\) \)\), "\[IndentingNewLine]", \(\(red\ = \ ReducedSystem[{25, 36}, nontrivialfacets, acdzeqs] // Factor;\)\), "\n", \(red\ = Map[CleanUp[#, vars4bp] &, red]\), "\n", \(\(\(GroebnerBasis[red~Join~{nzeq}, {m1, m2, m3, m4}, vars4bp] // Factor\)\(\[IndentingNewLine]\) \)\), "\[IndentingNewLine]", \(\(red\ = \ ReducedSystem[{33, 48}, nontrivialfacets, acdzeqs] // Factor;\)\), "\n", \(red\ = Map[CleanUp[#, vars4bp] &, red]\), "\n", \(GroebnerBasis[red~Join~{nzeq}, {m1, m2, m3, m4}, vars4bp] // Factor\)}], "Input"], Cell[BoxData[ \({\(-m3\)\ r12\^3\ r13\^3 + m3\ r12\ r13\^5 - m3\ r12\ r13\^3\ r23\^2 - m3\ r12\^3\ r23\^3 - m3\ r12\ r13\^2\ r23\^3 - 2\ m1\ r13\^3\ r23\^3 - 2\ m2\ r13\^3\ r23\^3 + m3\ r12\ r23\^5, m2\ r12\^5\ r13 - m2\ r12\^3\ r13\^3 - m2\ r12\^3\ r13\ r23\^2 - 2\ m1\ r12\^3\ r23\^3 - 2\ m3\ r12\^3\ r23\^3 - m2\ r12\^2\ r13\ r23\^3 - m2\ r13\^3\ r23\^3 + m2\ r13\ r23\^5, \(-2\)\ m2\ r12\^3\ r13\^3 - 2\ m3\ r12\^3\ r13\^3 + m1\ r12\^5\ r23 - m1\ r12\^3\ r13\^2\ r23 - m1\ r12\^2\ r13\^3\ r23 + m1\ r13\^5\ r23 - m1\ r12\^3\ r23\^3 - m1\ r13\^3\ r23\^3, m2\ r13\^3\ r24\^2 + m3\ r12\^3\ r34\^2, \(-m3\)\ r12\^3\ r24\^2 - m1\ r23\^3\ r24\^2 + m3\ r12\^3\ r34\^2, m2\ r13\^3\ r24\^2 - m2\ r13\^3\ r34\^2 - m1\ r23\^3\ r34\^2, \((r12 - r23)\)\ \((r12\^2 + r12\ r23 + r23\^2)\), \((r12 - r13)\)\ \((r12\^2 + r12\ r13 + r13\^2)\), \((r13 - r23)\)\ \((r13\^2 + r13\ r23 + r23\^2)\)}\)], "Output"], Cell[BoxData[ \({m1 + m2 + m3}\)], "Output"], Cell[BoxData[ \({\(-m3\)\ r12\^3\ r13\^3\ r14\^3 + m3\ r12\ r13\^5\ r14\^3 - m3\ r12\ r13\^3\ r14\^3\ r23\^2 - m3\ r12\^3\ r14\^3\ r23\^3 - m3\ r12\ r13\^2\ r14\^3\ r23\^3 - 2\ m1\ r13\^3\ r14\^3\ r23\^3 - 2\ m2\ r13\^3\ r14\^3\ r23\^3 + m3\ r12\ r14\^3\ r23\^5 + m4\ r12\ r13\^3\ r23\^3\ r24\^2, m2\ r12\^5\ r13\ r14\^3 - m2\ r12\^3\ r13\^3\ r14\^3 - m2\ r12\^3\ r13\ r14\^3\ r23\^2 - 2\ m1\ r12\^3\ r14\^3\ r23\^3 - 2\ m3\ r12\^3\ r14\^3\ r23\^3 - m2\ r12\^2\ r13\ r14\^3\ r23\^3 - m2\ r13\^3\ r14\^3\ r23\^3 + m2\ r13\ r14\^3\ r23\^5 + m4\ r12\^3\ r13\ r23\^3\ r34\^2, \(-2\)\ m2\ r12\^3\ r13\^3 - 2\ m3\ r12\^3\ r13\^3 + m1\ r12\^5\ r23 - m1\ r12\^3\ r13\^2\ r23 - m1\ r12\^2\ r13\^3\ r23 + m1\ r13\^5\ r23 - m1\ r12\^3\ r23\^3 - m1\ r13\^3\ r23\^3, m2\ r13\^3\ r24\^2 + m3\ r12\^3\ r34\^2, \(-m3\)\ r12\^3\ r24\^2 - m1\ r23\^3\ r24\^2 + m3\ r12\^3\ r34\^2, m2\ r13\^3\ r24\^2 - m2\ r13\^3\ r34\^2 - m1\ r23\^3\ r34\^2, \((r12 - r23)\)\ \((r12\^2 + r12\ r23 + r23\^2)\), \((r12 - r13)\)\ \((r12\^2 + r12\ r13 + r13\^2)\), \((r13 - r23)\)\ \((r13\^2 + r13\ r23 + r23\^2)\)}\)], "Output"], Cell[BoxData[ \({m4, m1 + m2 + m3}\)], "Output"], Cell[BoxData[ \({\(-m3\)\ r12\^3\ r13\^3 + m3\ r12\ r13\^5 - m3\ r12\ r13\^3\ r23\^2 - m3\ r12\^3\ r23\^3 - m3\ r12\ r13\^2\ r23\^3 - 2\ m1\ r13\^3\ r23\^3 - 2\ m2\ r13\^3\ r23\^3 + m3\ r12\ r23\^5, m2\ r12\^5\ r13 - m2\ r12\^3\ r13\^3 - m2\ r12\^3\ r13\ r23\^2 - 2\ m1\ r12\^3\ r23\^3 - 2\ m3\ r12\^3\ r23\^3 - m2\ r12\^2\ r13\ r23\^3 - m2\ r13\^3\ r23\^3 + m2\ r13\ r23\^5, \(-2\)\ m2\ r12\^3\ r13\^3 - 2\ m3\ r12\^3\ r13\^3 + m1\ r12\^5\ r23 - m1\ r12\^3\ r13\^2\ r23 - m1\ r12\^2\ r13\^3\ r23 + m1\ r13\^5\ r23 - m1\ r12\^3\ r23\^3 - m1\ r13\^3\ r23\^3, \(-m3\)\ r12\^3\ r14\^2 - m2\ r13\^3\ r14\^2 + m2\ r13\^3\ r24\^2 + m3\ r12\^3\ r34\^2, m1\ r14\^2\ r23\^3 - m3\ r12\^3\ r24\^2 - m1\ r23\^3\ r24\^2 + m3\ r12\^3\ r34\^2, m1\ r14\^2\ r23\^3 + m2\ r13\^3\ r24\^2 - m2\ r13\^3\ r34\^2 - m1\ r23\^3\ r34\^2, \((r12 - r23)\)\ \((r12\^2 + r12\ r23 + r23\^2)\), \((r12 - r13)\)\ \((r12\^2 + r12\ r13 + r13\^2)\), \((r13 - r23)\)\ \((r13\^2 + r13\ r23 + r23\^2)\)}\)], "Output"], Cell[BoxData[ \({\(-m1\) - m2 - m3}\)], "Output"], Cell[BoxData[ \({\(-m3\)\ r12\^3\ r13\^3 + m3\ r12\ r13\^5 - m3\ r12\ r13\^3\ r23\^2 - m3\ r12\^3\ r23\^3 - m3\ r12\ r13\^2\ r23\^3 - 2\ m1\ r13\^3\ r23\^3 - 2\ m2\ r13\^3\ r23\^3 + m3\ r12\ r23\^5, m2\ r12\^5\ r13 - m2\ r12\^3\ r13\^3 - m2\ r12\^3\ r13\ r23\^2 - 2\ m1\ r12\^3\ r23\^3 - 2\ m3\ r12\^3\ r23\^3 - m2\ r12\^2\ r13\ r23\^3 - m2\ r13\^3\ r23\^3 + m2\ r13\ r23\^5, \(-2\)\ m2\ r12\^3\ r13\^3 - 2\ m3\ r12\^3\ r13\^3 + m1\ r12\^5\ r23 - m1\ r12\^3\ r13\^2\ r23 - m1\ r12\^2\ r13\^3\ r23 + m1\ r13\^5\ r23 - m1\ r12\^3\ r23\^3 - m1\ r13\^3\ r23\^3, m2\ r13\^3\ r24\^2 + m3\ r12\^3\ r34\^2, \(-m3\)\ r12\^3\ r24\^2 - m1\ r23\^3\ r24\^2 + m3\ r12\^3\ r34\^2, m2\ r13\^3\ r24\^2 - m2\ r13\^3\ r34\^2 - m1\ r23\^3\ r34\^2, \((r12 - r23)\)\ \((r12\^2 + r12\ r23 + r23\^2)\), \((r12 - r13)\)\ \((r12\^2 + r12\ r13 + r13\^2)\), \((r13 - r23)\)\ \((r13\^2 + r13\ r23 + r23\^2)\)}\)], "Output"], Cell[BoxData[ \({m1 + m2 + m3}\)], "Output"], Cell[BoxData[ \({m3\ r14\^3\ r23\^2 + m4\ r13\^3\ r24\^2, m2\ r14\^3\ r23\^2 + m4\ r12\^3\ r34\^2, \(-m1\)\ \((r12 + r13)\)\ \((r12\^2 - r12\ r13 + r13\^2)\), m2\ r13\^3\ r24\^2 + m3\ r12\^3\ r34\^2, \(-m1\)\ \((r12 + r14)\)\ \((r12\^2 - r12\ r14 + r14\^2)\), \(-m1\)\ \((r13 + r14)\)\ \((r13\^2 - r13\ r14 + r14\^2)\), \((r12 - r14)\)\ \((r12\^2 + r12\ r14 + r14\^2)\), \((r12 - r13)\)\ \((r12\^2 + r12\ r13 + r13\^2)\), \((r13 - r14)\)\ \((r13\^2 + r13\ r14 + r14\^2)\)}\)], "Output"], Cell[BoxData[ \({m4, m3, m2, m1}\)], "Output"], Cell[BoxData[ \({m4\ r13\^3\ r14\^2 + m3\ r23\^2\ r24\^3, m4\ r12\^3\ r14\^2 + m2\ r23\^2\ r34\^3, \(-m4\)\ r12\^3 - m1\ r34\^3 + 2\ m1\ r12\^3\ r34\^3 + 2\ m2\ r12\^3\ r34\^3 + 2\ m3\ r12\^3\ r34\^3 + 2\ m4\ r12\^3\ r34\^3, \(-m3\)\ r12\^3 - m2\ r34\^3 + 2\ m1\ r12\^3\ r34\^3 + 2\ m2\ r12\^3\ r34\^3 + 2\ m3\ r12\^3\ r34\^3 + 2\ m4\ r12\^3\ r34\^3, m3\ r12\^3\ r23\^2 + m1\ r14\^2\ r34\^3, m2\ r13\^3\ r23\^2 + m1\ r14\^2\ r24\^3, 1 - r12\^3 - r34\^3, 1 - r12\^3 - r34\^3, \(-\((r13 + r24)\)\)\ \((r13\^2 - r13\ r24 + r24\^2)\)}\)], "Output"], Cell[BoxData[ \({\(-\((m2 + m3)\)\)\ \((m3 + m4)\), m1 + m2 + m3 + m4}\)], "Output"], Cell[BoxData[ \({\(-m3\)\ r12\^3\ r13\^3 + m3\ r12\ r13\^5 - m3\ r12\ r13\^3\ r23\^2 - m3\ r12\^3\ r23\^3 - m3\ r12\ r13\^2\ r23\^3 - 2\ m1\ r13\^3\ r23\^3 - 2\ m2\ r13\^3\ r23\^3 + 2\ m1\ r12\^3\ r13\^3\ r23\^3 + 2\ m2\ r12\^3\ r13\^3\ r23\^3 + 2\ m3\ r12\^3\ r13\^3\ r23\^3 + 2\ m4\ r12\^3\ r13\^3\ r23\^3 + m3\ r12\ r23\^5, m2\ r12\^5\ r13 - m2\ r12\^3\ r13\^3 - m2\ r12\^3\ r13\ r23\^2 - 2\ m1\ r12\^3\ r23\^3 - 2\ m3\ r12\^3\ r23\^3 - m2\ r12\^2\ r13\ r23\^3 - m2\ r13\^3\ r23\^3 + 2\ m1\ r12\^3\ r13\^3\ r23\^3 + 2\ m2\ r12\^3\ r13\^3\ r23\^3 + 2\ m3\ r12\^3\ r13\^3\ r23\^3 + 2\ m4\ r12\^3\ r13\^3\ r23\^3 + m2\ r13\ r23\^5, \(-2\)\ m2\ r12\^3\ r13\^3 - 2\ m3\ r12\^3\ r13\^3 + m1\ r12\^5\ r23 - m1\ r12\^3\ r13\^2\ r23 - m1\ r12\^2\ r13\^3\ r23 + m1\ r13\^5\ r23 - m1\ r12\^3\ r23\^3 - m1\ r13\^3\ r23\^3 + 2\ m1\ r12\^3\ r13\^3\ r23\^3 + 2\ m2\ r12\^3\ r13\^3\ r23\^3 + 2\ m3\ r12\^3\ r13\^3\ r23\^3 + 2\ m4\ r12\^3\ r13\^3\ r23\^3, m2\ r13\^3\ r24\^2 + m3\ r12\^3\ r34\^2, \(-m3\)\ r12\^3\ r24\^2 - m1\ r23\^3\ r24\^2 + 2\ m1\ r12\^3\ r23\^3\ r24\^2 + 2\ m2\ r12\^3\ r23\^3\ r24\^2 + 2\ m3\ r12\^3\ r23\^3\ r24\^2 + 2\ m4\ r12\^3\ r23\^3\ r24\^2 + m3\ r12\^3\ r34\^2, m2\ r13\^3\ r24\^2 - m2\ r13\^3\ r34\^2 - m1\ r23\^3\ r34\^2 + 2\ m1\ r13\^3\ r23\^3\ r34\^2 + 2\ m2\ r13\^3\ r23\^3\ r34\^2 + 2\ m3\ r13\^3\ r23\^3\ r34\^2 + 2\ m4\ r13\^3\ r23\^3\ r34\^2, \((r12 - r23)\)\ \((r12\^2 + r12\ r23 + r23\^2)\), \((r12 - r13)\)\ \((r12\^2 + r12\ r13 + r13\^2)\), \((r13 - r23)\)\ \((r13\^2 + r13\ r23 + r23\^2)\)}\)], "Output"], Cell[BoxData[ \({m4, \(-m1\) - m2 - m3}\)], "Output"], Cell[BoxData[ \({2\ \((\(-m1\) - m2 + m1\ r12\^3 + m2\ r12\^3 + m3\ r12\^3 + m4\ r12\^3)\), m4\ r12\^3\ r14\^2 + m2\ r23\^2\ r34\^3, \(-m4\)\ r12\^3 - m1\ r34\^3 + 2\ m1\ r12\^3\ r34\^3 + 2\ m2\ r12\^3\ r34\^3 + 2\ m3\ r12\^3\ r34\^3 + 2\ m4\ r12\^3\ r34\^3, \(-m3\)\ r12\^3 - m2\ r34\^3 + 2\ m1\ r12\^3\ r34\^3 + 2\ m2\ r12\^3\ r34\^3 + 2\ m3\ r12\^3\ r34\^3 + 2\ m4\ r12\^3\ r34\^3, m3\ r12\^3\ r23\^2 + m1\ r14\^2\ r34\^3, 2\ \((\(-m3\) - m4 + m1\ r34\^3 + m2\ r34\^3 + m3\ r34\^3 + m4\ r34\^3)\), 1 - r12\^3 - r34\^3, 1 - r12\^3 - r34\^3, \(-\((r13 + r24)\)\)\ \((r13\^2 - r13\ r24 + r24\^2)\)}\)], "Output"], Cell[BoxData[ \({\(-m3\) - m4, m1 + m2}\)], "Output"] }, Open ]], Cell["\<\ Now for the facets. The results for all of the facets except 22 ,33 involve simple sums of masses. We leave out 48 until the next cell because the Groebner basis computation is time consuming. \ \>", "Text"], Cell[CellGroupData[{ Cell[BoxData[{ \(\(red\ = \ ReducedSystem[{25}, nontrivialfacets, acdzeqs] // Factor;\)\), "\[IndentingNewLine]", \(red\ = Map[CleanUp[#, vars4bp] &, red]\), "\[IndentingNewLine]", \(\(\(GroebnerBasis[red~Join~{nzeq}, {m1, m2, m3, m4}, vars4bp] // Factor\)\(\[IndentingNewLine]\) \)\), "\[IndentingNewLine]", \(\(red\ = \ ReducedSystem[{29}, nontrivialfacets, acdzeqs] // Factor;\)\), "\n", \(red\ = Map[CleanUp[#, vars4bp] &, red]\), "\n", \(\(\(GroebnerBasis[red~Join~{nzeq}, {m1, m2, m3, m4}, vars4bp] // Factor\)\(\[IndentingNewLine]\) \)\), "\[IndentingNewLine]", \(\(red\ = \ ReducedSystem[{36}, nontrivialfacets, acdzeqs] // Factor;\)\), "\n", \(red\ = Map[CleanUp[#, vars4bp] &, red]\), "\n", \(GroebnerBasis[red~Join~{nzeq}, {m1, m2, m3, m4}, vars4bp] // Factor\)}], "Input"], Cell[BoxData[ \({\(-m3\)\ r12\^3\ r13\^3 + m3\ r12\ r13\^5 - m3\ r12\ r13\^3\ r23\^2 - m3\ r12\^3\ r23\^3 - m3\ r12\ r13\^2\ r23\^3 - 2\ m1\ r13\^3\ r23\^3 - 2\ m2\ r13\^3\ r23\^3 + 2\ m1\ r12\^3\ r13\^3\ r23\^3 + 2\ m2\ r12\^3\ r13\^3\ r23\^3 + 2\ m3\ r12\^3\ r13\^3\ r23\^3 + 2\ m4\ r12\^3\ r13\^3\ r23\^3 + m3\ r12\ r23\^5, m2\ r12\^5\ r13 - m2\ r12\^3\ r13\^3 - m2\ r12\^3\ r13\ r23\^2 - 2\ m1\ r12\^3\ r23\^3 - 2\ m3\ r12\^3\ r23\^3 - m2\ r12\^2\ r13\ r23\^3 - m2\ r13\^3\ r23\^3 + 2\ m1\ r12\^3\ r13\^3\ r23\^3 + 2\ m2\ r12\^3\ r13\^3\ r23\^3 + 2\ m3\ r12\^3\ r13\^3\ r23\^3 + 2\ m4\ r12\^3\ r13\^3\ r23\^3 + m2\ r13\ r23\^5, \(-2\)\ m2\ r12\^3\ r13\^3 - 2\ m3\ r12\^3\ r13\^3 + m1\ r12\^5\ r23 - m1\ r12\^3\ r13\^2\ r23 - m1\ r12\^2\ r13\^3\ r23 + m1\ r13\^5\ r23 - m1\ r12\^3\ r23\^3 - m1\ r13\^3\ r23\^3 + 2\ m1\ r12\^3\ r13\^3\ r23\^3 + 2\ m2\ r12\^3\ r13\^3\ r23\^3 + 2\ m3\ r12\^3\ r13\^3\ r23\^3 + 2\ m4\ r12\^3\ r13\^3\ r23\^3, \(-m3\)\ r12\^3\ r14\^2 - m2\ r13\^3\ r14\^2 + 2\ m1\ r12\^3\ r13\^3\ r14\^2 + 2\ m2\ r12\^3\ r13\^3\ r14\^2 + 2\ m3\ r12\^3\ r13\^3\ r14\^2 + 2\ m4\ r12\^3\ r13\^3\ r14\^2 + m2\ r13\^3\ r24\^2 + m3\ r12\^3\ r34\^2, m1\ r14\^2\ r23\^3 - m3\ r12\^3\ r24\^2 - m1\ r23\^3\ r24\^2 + 2\ m1\ r12\^3\ r23\^3\ r24\^2 + 2\ m2\ r12\^3\ r23\^3\ r24\^2 + 2\ m3\ r12\^3\ r23\^3\ r24\^2 + 2\ m4\ r12\^3\ r23\^3\ r24\^2 + m3\ r12\^3\ r34\^2, m1\ r14\^2\ r23\^3 + m2\ r13\^3\ r24\^2 - m2\ r13\^3\ r34\^2 - m1\ r23\^3\ r34\^2 + 2\ m1\ r13\^3\ r23\^3\ r34\^2 + 2\ m2\ r13\^3\ r23\^3\ r34\^2 + 2\ m3\ r13\^3\ r23\^3\ r34\^2 + 2\ m4\ r13\^3\ r23\^3\ r34\^2, \((r12 - r23)\)\ \((r12\^2 + r12\ r23 + r23\^2)\), \((r12 - r13)\)\ \((r12\^2 + r12\ r13 + r13\^2)\), \((r13 - r23)\)\ \((r13\^2 + r13\ r23 + r23\^2)\)}\)], "Output"], Cell[BoxData[ \({m4\^2, \(-\((m1 + m2 + m3)\)\)\ m4, \(-\((m1 + m2 + m3)\)\^2\)}\)], "Output"], Cell[BoxData[ \({m3\ r14\^3\ r23\^2 + m4\ r13\^3\ r24\^2, m2\ r14\^3\ r23\^2 + m4\ r12\^3\ r34\^2, \(-m1\)\ r12\^3 - m1\ r13\^3 + 2\ m1\ r12\^3\ r13\^3 + 2\ m2\ r12\^3\ r13\^3 + 2\ m3\ r12\^3\ r13\^3 + 2\ m4\ r12\^3\ r13\^3, m2\ r13\^3\ r24\^2 + m3\ r12\^3\ r34\^2, \(-m1\)\ r12\^3 - m1\ r14\^3 + 2\ m1\ r12\^3\ r14\^3 + 2\ m2\ r12\^3\ r14\^3 + 2\ m3\ r12\^3\ r14\^3 + 2\ m4\ r12\^3\ r14\^3, \(-m1\)\ r13\^3 - m1\ r14\^3 + 2\ m1\ r13\^3\ r14\^3 + 2\ m2\ r13\^3\ r14\^3 + 2\ m3\ r13\^3\ r14\^3 + 2\ m4\ r13\^3\ r14\^3, \((r12 - r14)\)\ \((r12\^2 + r12\ r14 + r14\^2)\), \((r12 - r13)\)\ \((r12\^2 + r12\ r13 + r13\^2)\), \((r13 - r14)\)\ \((r13\^2 + r13\ r14 + r14\^2)\)}\)], "Output"], Cell[BoxData[ \({m4, m3, m2}\)], "Output"], Cell[BoxData[ \({\(-m3\)\ r12\^3\ r13\^3\ r14\^3 + m3\ r12\ r13\^5\ r14\^3 - m3\ r12\ r13\^3\ r14\^3\ r23\^2 - m3\ r12\^3\ r14\^3\ r23\^3 - m3\ r12\ r13\^2\ r14\^3\ r23\^3 - 2\ m1\ r13\^3\ r14\^3\ r23\^3 - 2\ m2\ r13\^3\ r14\^3\ r23\^3 + 2\ m1\ r12\^3\ r13\^3\ r14\^3\ r23\^3 + 2\ m2\ r12\^3\ r13\^3\ r14\^3\ r23\^3 + 2\ m3\ r12\^3\ r13\^3\ r14\^3\ r23\^3 + 2\ m4\ r12\^3\ r13\^3\ r14\^3\ r23\^3 + m3\ r12\ r14\^3\ r23\^5 + m4\ r12\ r13\^3\ r23\^3\ r24\^2, m2\ r12\^5\ r13\ r14\^3 - m2\ r12\^3\ r13\^3\ r14\^3 - m2\ r12\^3\ r13\ r14\^3\ r23\^2 - 2\ m1\ r12\^3\ r14\^3\ r23\^3 - 2\ m3\ r12\^3\ r14\^3\ r23\^3 - m2\ r12\^2\ r13\ r14\^3\ r23\^3 - m2\ r13\^3\ r14\^3\ r23\^3 + 2\ m1\ r12\^3\ r13\^3\ r14\^3\ r23\^3 + 2\ m2\ r12\^3\ r13\^3\ r14\^3\ r23\^3 + 2\ m3\ r12\^3\ r13\^3\ r14\^3\ r23\^3 + 2\ m4\ r12\^3\ r13\^3\ r14\^3\ r23\^3 + m2\ r13\ r14\^3\ r23\^5 + m4\ r12\^3\ r13\ r23\^3\ r34\^2, \(-2\)\ m2\ r12\^3\ r13\^3 - 2\ m3\ r12\^3\ r13\^3 + m1\ r12\^5\ r23 - m1\ r12\^3\ r13\^2\ r23 - m1\ r12\^2\ r13\^3\ r23 + m1\ r13\^5\ r23 - m1\ r12\^3\ r23\^3 - m1\ r13\^3\ r23\^3 + 2\ m1\ r12\^3\ r13\^3\ r23\^3 + 2\ m2\ r12\^3\ r13\^3\ r23\^3 + 2\ m3\ r12\^3\ r13\^3\ r23\^3 + 2\ m4\ r12\^3\ r13\^3\ r23\^3, m2\ r13\^3\ r24\^2 + m3\ r12\^3\ r34\^2, \(-m3\)\ r12\^3\ r24\^2 - m1\ r23\^3\ r24\^2 + 2\ m1\ r12\^3\ r23\^3\ r24\^2 + 2\ m2\ r12\^3\ r23\^3\ r24\^2 + 2\ m3\ r12\^3\ r23\^3\ r24\^2 + 2\ m4\ r12\^3\ r23\^3\ r24\^2 + m3\ r12\^3\ r34\^2, m2\ r13\^3\ r24\^2 - m2\ r13\^3\ r34\^2 - m1\ r23\^3\ r34\^2 + 2\ m1\ r13\^3\ r23\^3\ r34\^2 + 2\ m2\ r13\^3\ r23\^3\ r34\^2 + 2\ m3\ r13\^3\ r23\^3\ r34\^2 + 2\ m4\ r13\^3\ r23\^3\ r34\^2, \((r12 - r23)\)\ \((r12\^2 + r12\ r23 + r23\^2)\), \((r12 - r13)\)\ \((r12\^2 + r12\ r13 + r13\^2)\), \((r13 - r23)\)\ \((r13\^2 + r13\ r23 + r23\^2)\)}\)], "Output"], Cell[BoxData[ \({m4, m1 + m2 + m3}\)], "Output"] }, Open ]], Cell["\<\ Facet 48 leads to a similar condition but the Groebner basis computation is faster using Macaulay 2. (All of the previous computations were checked with Macaulay 2.) The Macaulay computation was done using the ring R = QQ[r12,r13,r14,r23,r24,r34,m1,m2,m3,m4,MonomialOrder=>Eliminate 6] We simply record the equations and the resulting Groebner basis here. \ \>", "Text"], Cell[CellGroupData[{ Cell[BoxData[{ \(\(red\ = \ ReducedSystem[{48}, nontrivialfacets, acdzeqs] // Factor;\)\), "\n", \(\(red\ = Map[CleanUp[#, vars4bp] &, red];\)\), "\[IndentingNewLine]", \(red48\ = \ red~Join~{nzeq}\), "\n", \(gb48 = {m3 + m4, \ m1 + m2 + m3 + m4}\)}], "Input"], Cell[BoxData[ \({m4\ r12\ r13\^3\ r14\^2 - 2\ m1\ r13\^3\ r24\^3 - 2\ m2\ r13\^3\ r24\^3 + 2\ m1\ r12\^3\ r13\^3\ r24\^3 + 2\ m2\ r12\^3\ r13\^3\ r24\^3 + 2\ m3\ r12\^3\ r13\^3\ r24\^3 + 2\ m4\ r12\^3\ r13\^3\ r24\^3 + m3\ r12\ r23\^2\ r24\^3, m4\ r12\^3\ r14\^2 + m2\ r23\^2\ r34\^3, \(-m4\)\ r12\^3 - m1\ r34\^3 + 2\ m1\ r12\^3\ r34\^3 + 2\ m2\ r12\^3\ r34\^3 + 2\ m3\ r12\^3\ r34\^3 + 2\ m4\ r12\^3\ r34\^3, \(-m3\)\ r12\^3 - m2\ r34\^3 + 2\ m1\ r12\^3\ r34\^3 + 2\ m2\ r12\^3\ r34\^3 + 2\ m3\ r12\^3\ r34\^3 + 2\ m4\ r12\^3\ r34\^3, m3\ r12\^3\ r23\^2 + m1\ r14\^2\ r34\^3, \(-2\)\ m3\ r13\^3\ r24\^3 - 2\ m4\ r13\^3\ r24\^3 + m2\ r13\^3\ r23\^2\ r34 + m1\ r14\^2\ r24\^3\ r34 + 2\ m1\ r13\^3\ r24\^3\ r34\^3 + 2\ m2\ r13\^3\ r24\^3\ r34\^3 + 2\ m3\ r13\^3\ r24\^3\ r34\^3 + 2\ m4\ r13\^3\ r24\^3\ r34\^3, 1 - r12\^3 - r34\^3, 1 - r12\^3 - r34\^3, \(-\((r13 + r24)\)\)\ \((r13\^2 - r13\ r24 + r24\^2)\), \(-1\) + r12\ r13\ r14\ r23\ r24\ r34}\)], "Output"], Cell[BoxData[ \({m3 + m4, m1 + m2 + m3 + m4}\)], "Output"] }, Open ]], Cell["\<\ Facets 22 and 33 were also analyzed with Macaulay 2. We give the equations and the Groebner bases here. Here is facet 22. The mass polynomial \ is quadratic and it can vanish for some positive values of the masses. This means that for those masses, the reduced system with the normalization condition may be solved. \ \>", "Text"], Cell[CellGroupData[{ Cell[BoxData[{ \(\(red\ = \ ReducedSystem[{22}, nontrivialfacets, acdzeqs] // Factor;\)\), "\n", \(\(red\ = Map[CleanUp[#, vars4bp] &, red];\)\), "\[IndentingNewLine]", \(red22\ = \ red~Join~{nzeq}\), "\n", \(gb22 = {m2\ m3 - m1\ m4}\), "\[IndentingNewLine]", \(\)}], "Input"], Cell[BoxData[ \({m4\ r13\^3\ r14\^2 + m3\ r23\^2\ r24\^3, m4\ r12\^3\ r14\^2 + m2\ r23\^2\ r34\^3, \(-m4\)\ r12\^3\ r13\^3\ r24\^3 - m4\ r12\^3\ r13\^3\ r34\^3 - m1\ r12\^3\ r24\^3\ r34\^3 - m1\ r13\^3\ r24\^3\ r34\^3 + 2\ m1\ r12\^3\ r13\^3\ r24\^3\ r34\^3 + 2\ m2\ r12\^3\ r13\^3\ r24\^3\ r34\^3 + 2\ m3\ r12\^3\ r13\^3\ r24\^3\ r34\^3 + 2\ m4\ r12\^3\ r13\^3\ r24\^3\ r34\^3, \(-m3\)\ r12\^3\ r13\^3\ \ r24\^3 - m2\ r12\^3\ r13\^3\ r34\^3 - m3\ r12\^3\ r24\^3\ r34\^3 - m2\ r13\^3\ r24\^3\ r34\^3 + 2\ m1\ r12\^3\ r13\^3\ r24\^3\ r34\^3 + 2\ m2\ r12\^3\ r13\^3\ r24\^3\ r34\^3 + 2\ m3\ r12\^3\ r13\^3\ r24\^3\ r34\^3 + 2\ m4\ r12\^3\ r13\^3\ r24\^3\ r34\^3, m3\ r12\^3\ r23\^2 + m1\ r14\^2\ r34\^3, m2\ r13\^3\ r23\^2 + m1\ r14\^2\ r24\^3, 1 - r12\^3 - r34\^3, r13\^3\ r24\^3 - r12\^3\ r13\^3\ r24\^3 - r12\^3\ r34\^3 + r12\^3\ r13\^3\ r34\^3 + r12\^3\ r24\^3\ r34\^3 - r13\^3\ r24\^3\ r34\^3, 1 - r13\^3 - r24\^3, \(-1\) + r12\ r13\ r14\ r23\ r24\ r34}\)], "Output"], Cell[BoxData[ \({m2\ m3 - m1\ m4}\)], "Output"] }, Open ]], Cell["Here is facet 33", "Text"], Cell[CellGroupData[{ Cell[BoxData[{ \(\(red\ = \ ReducedSystem[{33}, nontrivialfacets, acdzeqs] // Factor;\)\), "\n", \(\(red\ = Map[CleanUp[#, vars4bp] &, red];\)\), "\[IndentingNewLine]", \(red33\ = \ red~Join~{nzeq}\), "\[IndentingNewLine]", \(gbnewton33 = {m1^8 m3^11 - m1^7 m2*m3^11 + m1^6 m2^2 m3^11 + 2 m1^5 m2^3 m3^11 - 2 m1^4 m2^4 m3^11 + 2 m1^3 m2^5 m3^11 + m1^2 m2^6 m3^11 - m1*m2^7 m3^11 + m2^8 m3^11 + 2 m1^8 m3^10 m4 - 2 m1^7 m2*m3^10 m4 + 2 m1^6 m2^2 m3^10 m4 + 4 m1^5 m2^3 m3^10 m4 - 4 m1^4 m2^4 m3^10 m4 + 4 m1^3 m2^5 m3^10 m4 + 2 m1^2 m2^6 m3^10 m4 - 2 m1*m2^7 m3^10 m4 + 2 m2^8 m3^10 m4 + m1^8 m3^9 m4^2 - m1^7 m2*m3^9 m4^2 + m1^6 m2^2 m3^9 m4^2 + 2 m1^5 m2^3 m3^9 m4^2 - 2 m1^4 m2^4 m3^9 m4^2 + 2 m1^3 m2^5 m3^9 m4^2 + m1^2 m2^6 m3^9 m4^2 - m1*m2^7 m3^9 m4^2 + m2^8 m3^9 m4^2 + 3 m1^8 m3^8 m4^3 - 3 m1^7 m2*m3^8 m4^3 + 3 m1^6 m2^2 m3^8 m4^3 - 10 m1^5 m2^3 m3^8 m4^3 + 10 m1^4 m2^4 m3^8 m4^3 - 10 m1^3 m2^5 m3^8 m4^3 + 3 m1^2 m2^6 m3^8 m4^3 - 3 m1*m2^7 m3^8 m4^3 + 3 m2^8 m3^8 m4^3 + 6 m1^8 m3^7 m4^4 - 6 m1^7 m2*m3^7 m4^4 + 6 m1^6 m2^2 m3^7 m4^4 - 20 m1^5 m2^3 m3^7 m4^4 + 20 m1^4 m2^4 m3^7 m4^4 - 20 m1^3 m2^5 m3^7 m4^4 + 6 m1^2 m2^6 m3^7 m4^4 - 6 m1*m2^7 m3^7 m4^4 + 6 m2^8 m3^7 m4^4 + 3 m1^8 m3^6 m4^5 - 3 m1^7 m2*m3^6 m4^5 + 3 m1^6 m2^2 m3^6 m4^5 - 10 m1^5 m2^3 m3^6 m4^5 + 10 m1^4 m2^4 m3^6 m4^5 - 10 m1^3 m2^5 m3^6 m4^5 + 3 m1^2 m2^6 m3^6 m4^5 - 3 m1*m2^7 m3^6 m4^5 + 3 m2^8 m3^6 m4^5 + 3 m1^8 m3^5 m4^6 - 3 m1^7 m2*m3^5 m4^6 + 3 m1^6 m2^2 m3^5 m4^6 - 10 m1^5 m2^3 m3^5 m4^6 + 10 m1^4 m2^4 m3^5 m4^6 - 10 m1^3 m2^5 m3^5 m4^6 + 3 m1^2 m2^6 m3^5 m4^6 - 3 m1*m2^7 m3^5 m4^6 + 3 m2^8 m3^5 m4^6 + 6 m1^8 m3^4 m4^7 - 6 m1^7 m2*m3^4 m4^7 + 6 m1^6 m2^2 m3^4 m4^7 - 20 m1^5 m2^3 m3^4 m4^7 + 20 m1^4 m2^4 m3^4 m4^7 - 20 m1^3 m2^5 m3^4 m4^7 + 6 m1^2 m2^6 m3^4 m4^7 - 6 m1*m2^7 m3^4 m4^7 + 6 m2^8 m3^4 m4^7 + 3 m1^8 m3^3 m4^8 - 3 m1^7 m2*m3^3 m4^8 + 3 m1^6 m2^2 m3^3 m4^8 - 10 m1^5 m2^3 m3^3 m4^8 + 10 m1^4 m2^4 m3^3 m4^8 - 10 m1^3 m2^5 m3^3 m4^8 + 3 m1^2 m2^6 m3^3 m4^8 - 3 m1*m2^7 m3^3 m4^8 + 3 m2^8 m3^3 m4^8 + m1^8 m3^2 m4^9 - m1^7 m2*m3^2 m4^9 + m1^6 m2^2 m3^2 m4^9 + 2 m1^5 m2^3 m3^2 m4^9 - 2 m1^4 m2^4 m3^2 m4^9 + 2 m1^3 m2^5 m3^2 m4^9 + m1^2 m2^6 m3^2 m4^9 - m1*m2^7 m3^2 m4^9 + m2^8 m3^2 m4^9 + 2 m1^8 m3*m4^10 - 2 m1^7 m2*m3*m4^10 + 2 m1^6 m2^2 m3*m4^10 + 4 m1^5 m2^3 m3*m4^10 - 4 m1^4 m2^4 m3*m4^10 + 4 m1^3 m2^5 m3*m4^10 + 2 m1^2 m2^6 m3*m4^10 - 2 m1*m2^7 m3*m4^10 + 2 m2^8 m3*m4^10 + m1^8 m4^11 - m1^7 m2*m4^11 + m1^6 m2^2 m4^11 + 2 m1^5 m2^3 m4^11 - 2 m1^4 m2^4 m4^11 + 2 m1^3 m2^5 m4^11 + m1^2 m2^6 m4^11 - m1*m2^7 m4^11 + m2^8 m4^11, \n m1^9 m3^10 + 3 m1^6 m2^3 m3^10 + 3 m1^3 m2^6 m3^10 + m2^9 m3^10 + m1^9 m3^9 m4 + 3 m1^6 m2^3 m3^9 m4 + 3 m1^3 m2^6 m3^9 m4 + m2^9 m3^9 m4 + 3 m1^9 m3^7 m4^3 - 7 m1^6 m2^3 m3^7 m4^3 - 7 m1^3 m2^6 m3^7 m4^3 + 3 m2^9 m3^7 m4^3 + 3 m1^9 m3^6 m4^4 - 7 m1^6 m2^3 m3^6 m4^4 - 7 m1^3 m2^6 m3^6 m4^4 + 3 m2^9 m3^6 m4^4 + 3 m1^9 m3^4 m4^6 - 7 m1^6 m2^3 m3^4 m4^6 - 7 m1^3 m2^6 m3^4 m4^6 + 3 m2^9 m3^4 m4^6 + 3 m1^9 m3^3 m4^7 - 7 m1^6 m2^3 m3^3 m4^7 - 7 m1^3 m2^6 m3^3 m4^7 + 3 m2^9 m3^3 m4^7 + m1^9 m3*m4^9 + 3 m1^6 m2^3 m3*m4^9 + 3 m1^3 m2^6 m3*m4^9 + m2^9 m3*m4^9 + m1^9 m4^10 + 3 m1^6 m2^3 m4^10 + 3 m1^3 m2^6 m4^10 + m2^9 m4^10, \n m1^10 m3^9 + m1^9 m2*m3^9 + 3 m1^7 m2^3 m3^9 + 3 m1^6 m2^4 m3^9 + 3 m1^4 m2^6 m3^9 + 3 m1^3 m2^7 m3^9 + m1*m2^9 m3^9 + m2^10 m3^9 + 3 m1^10 m3^6 m4^3 + 3 m1^9 m2*m3^6 m4^3 - 7 m1^7 m2^3 m3^6 m4^3 - 7 m1^6 m2^4 m3^6 m4^3 - 7 m1^4 m2^6 m3^6 m4^3 - 7 m1^3 m2^7 m3^6 m4^3 + 3 m1*m2^9 m3^6 m4^3 + 3 m2^10 m3^6 m4^3 + 3 m1^10 m3^3 m4^6 + 3 m1^9 m2*m3^3 m4^6 - 7 m1^7 m2^3 m3^3 m4^6 - 7 m1^6 m2^4 m3^3 m4^6 - 7 m1^4 m2^6 m3^3 m4^6 - 7 m1^3 m2^7 m3^3 m4^6 + 3 m1*m2^9 m3^3 m4^6 + 3 m2^10 m3^3 m4^6 + m1^10 m4^9 + m1^9 m2*m4^9 + 3 m1^7 m2^3 m4^9 + 3 m1^6 m2^4 m4^9 + 3 m1^4 m2^6 m4^9 + 3 m1^3 m2^7 m4^9 + m1*m2^9 m4^9 + m2^10 m4^9, \n m1^11 m3^8 + 2 m1^10 m2*m3^8 + m1^9 m2^2 m3^8 + 3 m1^8 m2^3 m3^8 + 6 m1^7 m2^4 m3^8 + 3 m1^6 m2^5 m3^8 + 3 m1^5 m2^6 m3^8 + 6 m1^4 m2^7 m3^8 + 3 m1^3 m2^8 m3^8 + m1^2 m2^9 m3^8 + 2 m1*m2^10 m3^8 + m2^11 m3^8 - m1^11 m3^7 m4 - 2 m1^10 m2*m3^7 m4 - m1^9 m2^2 m3^7 m4 - 3 m1^8 m2^3 m3^7 m4 - 6 m1^7 m2^4 m3^7 m4 - 3 m1^6 m2^5 m3^7 m4 - 3 m1^5 m2^6 m3^7 m4 - 6 m1^4 m2^7 m3^7 m4 - 3 m1^3 m2^8 m3^7 m4 - m1^2 m2^9 m3^7 m4 - 2 m1*m2^10 m3^7 m4 - m2^11 m3^7 m4 + m1^11 m3^6 m4^2 + 2 m1^10 m2*m3^6 m4^2 + m1^9 m2^2 m3^6 m4^2 + 3 m1^8 m2^3 m3^6 m4^2 + 6 m1^7 m2^4 m3^6 m4^2 + 3 m1^6 m2^5 m3^6 m4^2 + 3 m1^5 m2^6 m3^6 m4^2 + 6 m1^4 m2^7 m3^6 m4^2 + 3 m1^3 m2^8 m3^6 m4^2 + m1^2 m2^9 m3^6 m4^2 + 2 m1*m2^10 m3^6 m4^2 + m2^11 m3^6 m4^2 + 2 m1^11 m3^5 m4^3 + 4 m1^10 m2*m3^5 m4^3 + 2 m1^9 m2^2 m3^5 m4^3 - 10 m1^8 m2^3 m3^5 m4^3 - 20 m1^7 m2^4 m3^5 m4^3 - 10 m1^6 m2^5 m3^5 m4^3 - 10 m1^5 m2^6 m3^5 m4^3 - 20 m1^4 m2^7 m3^5 m4^3 - 10 m1^3 m2^8 m3^5 m4^3 + 2 m1^2 m2^9 m3^5 m4^3 + 4 m1*m2^10 m3^5 m4^3 + 2 m2^11 m3^5 m4^3 - 2 m1^11 m3^4 m4^4 - 4 m1^10 m2*m3^4 m4^4 - 2 m1^9 m2^2 m3^4 m4^4 + 10 m1^8 m2^3 m3^4 m4^4 + 20 m1^7 m2^4 m3^4 m4^4 + 10 m1^6 m2^5 m3^4 m4^4 + 10 m1^5 m2^6 m3^4 m4^4 + 20 m1^4 m2^7 m3^4 m4^4 + 10 m1^3 m2^8 m3^4 m4^4 - 2 m1^2 m2^9 m3^4 m4^4 - 4 m1*m2^10 m3^4 m4^4 - 2 m2^11 m3^4 m4^4 + 2 m1^11 m3^3 m4^5 + 4 m1^10 m2*m3^3 m4^5 + 2 m1^9 m2^2 m3^3 m4^5 - 10 m1^8 m2^3 m3^3 m4^5 - 20 m1^7 m2^4 m3^3 m4^5 - 10 m1^6 m2^5 m3^3 m4^5 - 10 m1^5 m2^6 m3^3 m4^5 - 20 m1^4 m2^7 m3^3 m4^5 - 10 m1^3 m2^8 m3^3 m4^5 + 2 m1^2 m2^9 m3^3 m4^5 + 4 m1*m2^10 m3^3 m4^5 + 2 m2^11 m3^3 m4^5 + m1^11 m3^2 m4^6 + 2 m1^10 m2*m3^2 m4^6 + m1^9 m2^2 m3^2 m4^6 + 3 m1^8 m2^3 m3^2 m4^6 + 6 m1^7 m2^4 m3^2 m4^6 + 3 m1^6 m2^5 m3^2 m4^6 + 3 m1^5 m2^6 m3^2 m4^6 + 6 m1^4 m2^7 m3^2 m4^6 + 3 m1^3 m2^8 m3^2 m4^6 + m1^2 m2^9 m3^2 m4^6 + 2 m1*m2^10 m3^2 m4^6 + m2^11 m3^2 m4^6 - m1^11 m3*m4^7 - 2 m1^10 m2*m3*m4^7 - m1^9 m2^2 m3*m4^7 - 3 m1^8 m2^3 m3*m4^7 - 6 m1^7 m2^4 m3*m4^7 - 3 m1^6 m2^5 m3*m4^7 - 3 m1^5 m2^6 m3*m4^7 - 6 m1^4 m2^7 m3*m4^7 - 3 m1^3 m2^8 m3*m4^7 - m1^2 m2^9 m3*m4^7 - 2 m1*m2^10 m3*m4^7 - m2^11 m3*m4^7 + m1^11 m4^8 + 2 m1^10 m2*m4^8 + m1^9 m2^2 m4^8 + 3 m1^8 m2^3 m4^8 + 6 m1^7 m2^4 m4^8 + 3 m1^6 m2^5 m4^8 + 3 m1^5 m2^6 m4^8 + 6 m1^4 m2^7 m4^8 + 3 m1^3 m2^8 m4^8 + m1^2 m2^9 m4^8 + 2 m1*m2^10 m4^8 + m2^11 m4^8} // Factor\)}], "Input"], Cell[BoxData[ \({2\ \((\(-m1\) - m2 + m1\ r12\^3 + m2\ r12\^3 + m3\ r12\^3 + m4\ r12\^3)\), \(-m4\)\ r12\^3\ r13\^2 + m4\ r12\^3\ r14\^2 - m2\ r13\^2\ r34\^3 + 2\ m1\ r12\^3\ r13\^2\ r34\^3 + 2\ m2\ r12\^3\ r13\^2\ r34\^3 + 2\ m3\ r12\^3\ r13\^2\ r34\^3 + 2\ m4\ r12\^3\ r13\^2\ r34\^3 + m2\ r23\^2\ r34\^3, \(-m4\)\ r12\^3\ r23\^2 + m4\ r12\^3\ r24\^2 + m1\ r13\^2\ r34\^3 - m1\ r23\^2\ r34\^3 + 2\ m1\ r12\^3\ r23\^2\ r34\^3 + 2\ m2\ r12\^3\ r23\^2\ r34\^3 + 2\ m3\ r12\^3\ r23\^2\ r34\^3 + 2\ m4\ r12\^3\ r23\^2\ r34\^3, m3\ r12\^3\ r13\^2 - m3\ r12\^3\ r14\^2 - m2\ r14\^2\ r34\^3 + 2\ m1\ r12\^3\ r14\^2\ r34\^3 + 2\ m2\ r12\^3\ r14\^2\ r34\^3 + 2\ m3\ r12\^3\ r14\^2\ r34\^3 + 2\ m4\ r12\^3\ r14\^2\ r34\^3 + m2\ r24\^2\ r34\^3, m3\ r12\^3\ r23\^2 - m3\ r12\^3\ r24\^2 + m1\ r14\^2\ r34\^3 - m1\ r24\^2\ r34\^3 + 2\ m1\ r12\^3\ r24\^2\ r34\^3 + 2\ m2\ r12\^3\ r24\^2\ r34\^3 + 2\ m3\ r12\^3\ r24\^2\ r34\^3 + 2\ m4\ r12\^3\ r24\^2\ r34\^3, 2\ \((\(-m3\) - m4 + m1\ r34\^3 + m2\ r34\^3 + m3\ r34\^3 + m4\ r34\^3)\), 1 - r12\^3 - r34\^3, 1 - r12\^3 - r34\^3, \(-r13\^3\)\ r14\^3\ r23\^3 + r13\^3\ r14\^3\ r24\^3 + r13\^3\ r23\^3\ r24\^3 - r14\^3\ r23\^3\ r24\^3, \(-1\) + r12\ r13\ r14\ r23\ r24\ r34}\)], "Output"], Cell[BoxData[ \({\((m1\^2 - m1\ m2 + m2\^2)\)\ \((m3 + m4)\)\^3\ \((m3\^2 - m3\ m4 + m4\^2)\)\ \((m1\^6\ m3\^6 + 2\ m1\^3\ m2\^3\ m3\^6 + m2\^6\ m3\^6 + 2\ m1\^6\ m3\^3\ m4\^3 - 12\ m1\^3\ m2\^3\ m3\^3\ m4\^3 + 2\ m2\^6\ m3\^3\ m4\^3 + m1\^6\ m4\^6 + 2\ m1\^3\ m2\^3\ m4\^6 + m2\^6\ m4\^6)\), \((m1 + m2)\)\ \((m1\^2 - m1\ m2 + m2\^2)\)\ \((m3 + m4)\)\^2\ \((m3\^2 - m3\ m4 + m4\^2)\)\ \((m1\^6\ m3\^6 + 2\ m1\^3\ m2\^3\ m3\^6 + m2\^6\ m3\^6 + 2\ m1\^6\ m3\^3\ m4\^3 - 12\ m1\^3\ m2\^3\ m3\^3\ m4\^3 + 2\ m2\^6\ m3\^3\ m4\^3 + m1\^6\ m4\^6 + 2\ m1\^3\ m2\^3\ m4\^6 + m2\^6\ m4\^6)\), \((m1 + m2)\)\^2\ \((m1\^2 - m1\ m2 + m2\^2)\)\ \((m3 + m4)\)\ \((m3\^2 - m3\ m4 + m4\^2)\)\ \((m1\^6\ m3\^6 + 2\ m1\^3\ m2\^3\ m3\^6 + m2\^6\ m3\^6 + 2\ m1\^6\ m3\^3\ m4\^3 - 12\ m1\^3\ m2\^3\ m3\^3\ m4\^3 + 2\ m2\^6\ m3\^3\ m4\^3 + m1\^6\ m4\^6 + 2\ m1\^3\ m2\^3\ m4\^6 + m2\^6\ m4\^6)\), \((m1 + m2)\)\^3\ \((m1\^2 - m1\ m2 + m2\^2)\)\ \((m3\^2 - m3\ m4 + m4\^2)\)\ \((m1\^6\ m3\^6 + 2\ m1\^3\ m2\^3\ m3\^6 + m2\^6\ m3\^6 + 2\ m1\^6\ m3\^3\ m4\^3 - 12\ m1\^3\ m2\^3\ m3\^3\ m4\^3 + 2\ m2\^6\ m3\^3\ m4\^3 + m1\^6\ m4\^6 + 2\ m1\^3\ m2\^3\ m4\^6 + m2\^6\ m4\^6)\)}\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(\((m3 + m4)\)^2*\((m3^3 + m4^3)\) // Factor\)], "Input"], Cell[BoxData[ \(\((m3 + m4)\)\^3\ \((m3\^2 - m3\ m4 + m4\^2)\)\)], "Output"] }, Open ]], Cell["\<\ The Groebner basis gb33 contains 4 mass polynomials but they are all multiples of the polynomial Q below. All 4 of these polynomials are divisors of the mass polynomial (m1 + m2)^2(m3 + m4)^2 (m1^3+m2^3) (m3^3+m4^3) Q Therefore this mass polynomial is in the ideal generated by the reduced system as claimed in the paper. The following cell displays Q and shows that it can be written in the form of \ equation (19) in the paper. \ \>", "Text"], Cell[CellGroupData[{ Cell[BoxData[{ \(\(Q = \((m1\^6\ m3\^6 + 2\ m1\^3\ m2\^3\ m3\^6 + m2\^6\ m3\^6 + 2\ m1\^6\ m3\^3\ m4\^3 - 12\ m1\^3\ m2\^3\ m3\^3\ m4\^3 + 2\ m2\^6\ m3\^3\ m4\^3 + m1\^6\ m4\^6 + 2\ m1\^3\ m2\^3\ m4\^6 + m2\^6\ m4\^6)\);\)\), "\[IndentingNewLine]", \(Qeq19\ = \ \((m1^3 - m2^3)\)^2 \((m3^3 - m4^3)\)^2 + 4 \((m1^3 - m2^3)\)^2*m3^3*m4^3 + 4 \((m3^3 - m4^3)\)^2*m1^3*m2^3\), "\[IndentingNewLine]", \(Q - Qeq19 // Expand\)}], "Input"], Cell[BoxData[ \(4\ \((m1\^3 - m2\^3)\)\^2\ m3\^3\ m4\^3 + 4\ m1\^3\ m2\^3\ \((m3\^3 - m4\^3)\)\^2 + \((m1\^3 - m2\^3)\)\^2\ \((m3\ \^3 - m4\^3)\)\^2\)], "Output"], Cell[BoxData[ \(0\)], "Output"] }, Open ]], Cell["\<\ This polynomial also has positive roots, so the facets 22 and 33 will be analyzed further in the next section. \ \>", "Text"] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell["Exceptional Cases", "Section"], Cell["\<\ In this section we will show that there do not exist Puiseux series solutions of orders which are positive multiples of the normal vectors a22 = \ ( 0, 0, -1, -1, 0 , 0) or a33 = (0, -1, -1, -1, -1, 0 ) \ \>", "Text"], Cell[CellGroupData[{ Cell["Facet 22", "Subsection"], Cell["\<\ If m1 m4 - m2 m3 is not zero, the reduced equations for this facet have no solutions in the algebraic torus. So there can be no Puiseux series solution in this case. We may assume without loss of generality that m4 = 1; therefore we begin with the full system so equations with mass substitutions m4 = 1 and m1 m4 = m2 m3 \ \>", "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(eqs22\ = \ acdzeqs /. {m4 \[Rule] 1, m1 \[Rule] m2*m3}\)], "Input"], Cell[BoxData[ \({\(-r12\^3\)\ r13\^3\ r14\^3\ r23\^3 + r12\ r13\^3\ r14\^5\ r23\^3 - r12\ r13\^3\ r14\^3\ r23\^3\ r24\^2 - m3\ r12\^3\ r13\^3\ r14\^3\ r24\^3 + m3\ r12\ r13\^5\ r14\^3\ r24\^3 - m3\ r12\ r13\^3\ r14\^3\ r23\^2\ r24\^3 - r12\^3\ r13\^3\ r23\^3\ r24\^3 - r12\ r13\^3\ r14\^2\ r23\^3\ r24\^3 - m3\ r12\^3\ r14\^3\ r23\^3\ r24\^3 - m3\ r12\ r13\^2\ r14\^3\ r23\^3\ r24\^3 - 2\ m2\ r13\^3\ r14\^3\ r23\^3\ r24\^3 - 2\ m2\ m3\ r13\^3\ r14\^3\ r23\^3\ r24\^3 + 2\ r12\^3\ r13\^3\ r14\^3\ r23\^3\ r24\^3 + 2\ m2\ r12\^3\ r13\^3\ r14\^3\ r23\^3\ r24\^3 + 2\ m3\ r12\^3\ r13\^3\ r14\^3\ r23\^3\ r24\^3 + 2\ m2\ m3\ r12\^3\ r13\^3\ r14\^3\ r23\^3\ r24\^3 + m3\ r12\ r14\^3\ r23\^5\ r24\^3 + r12\ r13\^3\ r23\^3\ r24\^5, \(-r12\^3\)\ r13\^3\ r14\^3\ r23\^3 + r12\^3\ r13\ r14\^5\ r23\^3 - r12\^3\ r13\ r14\^3\ r23\^3\ r34\^2 + m2\ r12\^5\ r13\ r14\^3\ r34\^3 - m2\ r12\^3\ r13\^3\ r14\^3\ r34\^3 - m2\ r12\^3\ r13\ r14\^3\ r23\^2\ r34\^3 - r12\^3\ r13\^3\ r23\^3\ r34\^3 - r12\^3\ r13\ r14\^2\ r23\^3\ r34\^3 - 2\ m3\ r12\^3\ r14\^3\ r23\^3\ r34\^3 - 2\ m2\ m3\ r12\^3\ r14\^3\ r23\^3\ r34\^3 - m2\ r12\^2\ r13\ r14\^3\ r23\^3\ r34\^3 - m2\ r13\^3\ r14\^3\ r23\^3\ r34\^3 + 2\ r12\^3\ r13\^3\ r14\^3\ r23\^3\ r34\^3 + 2\ m2\ r12\^3\ r13\^3\ r14\^3\ r23\^3\ r34\^3 + 2\ m3\ r12\^3\ r13\^3\ r14\^3\ r23\^3\ r34\^3 + 2\ m2\ m3\ r12\^3\ r13\^3\ r14\^3\ r23\^3\ r34\^3 + m2\ r13\ r14\^3\ r23\^5\ r34\^3 + r12\^3\ r13\ r23\^3\ r34\^5, \(-r12\^3\)\ r13\^3\ r23\^3\ r24\^3 + r12\^3\ r13\^3\ r23\ r24\^5 - r12\^3\ r13\^3\ r23\ r24\^3\ r34\^2 - r12\^3\ r13\^3\ r23\^3\ r34\^3 - r12\^3\ r13\^3\ r23\ r24\^2\ r34\^3 - 2\ m2\ r12\^3\ r13\^3\ r24\^3\ r34\^3 - 2\ m3\ r12\^3\ r13\^3\ r24\^3\ r34\^3 + m2\ m3\ r12\^5\ r23\ r24\^3\ r34\^3 - m2\ m3\ r12\^3\ r13\^2\ r23\ r24\^3\ r34\^3 - m2\ m3\ r12\^2\ r13\^3\ r23\ r24\^3\ r34\^3 + m2\ m3\ r13\^5\ r23\ r24\^3\ r34\^3 - m2\ m3\ r12\^3\ r23\^3\ r24\^3\ r34\^3 - m2\ m3\ r13\^3\ r23\^3\ r24\^3\ r34\^3 + 2\ r12\^3\ r13\^3\ r23\^3\ r24\^3\ r34\^3 + 2\ m2\ r12\^3\ r13\^3\ r23\^3\ r24\^3\ r34\^3 + 2\ m3\ r12\^3\ r13\^3\ r23\^3\ r24\^3\ r34\^3 + 2\ m2\ m3\ r12\^3\ r13\^3\ r23\^3\ r24\^3\ r34\^3 + r12\^3\ r13\^3\ r23\ r34\^5, m3\ r12\^3\ r13\^5\ r14\ r24\^3 - m3\ r12\^3\ r13\^3\ r14\^3\ r24\^3 - m3\ r12\^3\ r13\^3\ r14\ r24\^3\ r34\^2 + m2\ r12\^5\ r13\^3\ r14\ r34\^3 - m2\ r12\^3\ r13\^3\ r14\^3\ r34\^3 - m2\ r12\^3\ r13\^3\ r14\ r24\^2\ r34\^3 - 2\ r12\^3\ r13\^3\ r24\^3\ r34\^3 - 2\ m2\ m3\ r12\^3\ r13\^3\ r24\^3\ r34\^3 - m3\ r12\^3\ r13\^2\ r14\ r24\^3\ r34\^3 - m2\ r12\^2\ r13\^3\ r14\ r24\^3\ r34\^3 - m3\ r12\^3\ r14\^3\ r24\^3\ r34\^3 - m2\ r13\^3\ r14\^3\ r24\^3\ r34\^3 + 2\ r12\^3\ r13\^3\ r14\^3\ r24\^3\ r34\^3 + 2\ m2\ r12\^3\ r13\^3\ r14\^3\ r24\^3\ r34\^3 + 2\ m3\ r12\^3\ r13\^3\ r14\^3\ r24\^3\ r34\^3 + 2\ m2\ m3\ r12\^3\ r13\^3\ r14\^3\ r24\^3\ r34\^3 + m2\ r13\^3\ r14\ r24\^5\ r34\^3 + m3\ r12\^3\ r14\ r24\^3\ r34\^5, m3\ r12\^3\ r14\^3\ r23\^5\ r24 - m3\ r12\^3\ r14\^3\ r23\^3\ r24\^3 - m3\ r12\^3\ r14\^3\ r23\^3\ r24\ r34\^2 - 2\ r12\^3\ r14\^3\ r23\^3\ r34\^3 - 2\ m2\ r12\^3\ r14\^3\ r23\^3\ r34\^3 - m3\ r12\^3\ r14\^3\ r23\^2\ r24\ r34\^3 + m2\ m3\ r12\^5\ r23\^3\ r24\ r34\^3 - m2\ m3\ r12\^3\ r14\^2\ r23\^3\ r24\ r34\^3 - m2\ m3\ r12\^2\ r14\^3\ r23\^3\ r24\ r34\^3 + m2\ m3\ r14\^5\ r23\^3\ r24\ r34\^3 - m3\ r12\^3\ r14\^3\ r24\^3\ r34\^3 - m2\ m3\ r12\^3\ r23\^3\ r24\^3\ r34\^3 - m2\ m3\ r14\^3\ r23\^3\ r24\^3\ r34\^3 + 2\ r12\^3\ r14\^3\ r23\^3\ r24\^3\ r34\^3 + 2\ m2\ r12\^3\ r14\^3\ r23\^3\ r24\^3\ r34\^3 + 2\ m3\ r12\^3\ r14\^3\ r23\^3\ r24\^3\ r34\^3 + 2\ m2\ m3\ r12\^3\ r14\^3\ r23\^3\ r24\^3\ r34\^3 + m3\ r12\^3\ r14\^3\ r24\ r34\^5, \(-2\)\ r13\^3\ r14\^3\ r23\^3\ \ r24\^3 - 2\ m3\ r13\^3\ r14\^3\ r23\^3\ r24\^3 + m2\ r13\^3\ r14\^3\ r23\^5\ r34 - m2\ r13\^3\ r14\^3\ r23\^3\ r24\^2\ r34 - m2\ r13\^3\ r14\^3\ r23\^2\ r24\^3\ r34 + m2\ m3\ r13\^5\ r23\^3\ r24\^3\ r34 - m2\ m3\ r13\^3\ r14\^2\ r23\^3\ r24\^3\ r34 - m2\ m3\ r13\^2\ r14\^3\ r23\^3\ r24\^3\ r34 + m2\ m3\ r14\^5\ r23\^3\ r24\^3\ r34 + m2\ r13\^3\ r14\^3\ r24\^5\ r34 - m2\ r13\^3\ r14\^3\ r23\^3\ r34\^3 - m2\ r13\^3\ r14\^3\ r24\^3\ r34\^3 - m2\ m3\ r13\^3\ r23\^3\ r24\^3\ r34\^3 - m2\ m3\ r14\^3\ r23\^3\ r24\^3\ r34\^3 + 2\ r13\^3\ r14\^3\ r23\^3\ r24\^3\ r34\^3 + 2\ m2\ r13\^3\ r14\^3\ r23\^3\ r24\^3\ r34\^3 + 2\ m3\ r13\^3\ r14\^3\ r23\^3\ r24\^3\ r34\^3 + 2\ m2\ m3\ r13\^3\ r14\^3\ r23\^3\ r24\^3\ r34\^3, r14\^3\ r23\^3 - r12\^3\ r14\^3\ r23\^3 - r12\^3\ r34\^3 + r12\^3\ r14\^3\ r34\^3 + r12\^3\ r23\^3\ r34\^3 - r14\^3\ r23\^3\ r34\^3, r13\^3\ r24\^3 - r12\^3\ r13\^3\ r24\^3 - r12\^3\ r34\^3 + r12\^3\ r13\^3\ r34\^3 + r12\^3\ r24\^3\ r34\^3 - r13\^3\ r24\^3\ r34\^3, r14\^3\ r23\^3 - r13\^3\ r14\^3\ r23\^3 - r13\^3\ r24\^3 + r13\^3\ r14\^3\ r24\^3 + r13\^3\ r23\^3\ r24\^3 - r14\^3\ r23\^3\ r24\^3}\)], "Output"] }, Open ]], Cell["\<\ Make a change of variables corresponding to the normal vector alpha22=(0,0,-1,-1,0,0). After this substitution, we will be looking for series solutions for all variables starting with the power t^0, except r14 will be gone (without loss of generality, we can look for a Puiseux solution with r14 = 1/t) \ \>", "Text"], Cell[CellGroupData[{ Cell[BoxData[{ \(sub0\ = \ {r14 \[Rule] 1/t, r23 \[Rule] r23/t}\), "\[IndentingNewLine]", \(eqs221 = \(eqs22 /. sub0 // Factor\) // Numerator\)}], "Input"], Cell[BoxData[ \({r14 \[Rule] 1\/t, r23 \[Rule] r23\/t}\)], "Output"], Cell[BoxData[ \({r12\ r13\^3\ r23\^3 + m3\ r12\ r23\^5\ r24\^3 - r12\^3\ r13\^3\ r23\^3\ t\^2 - r12\ r13\^3\ r23\^3\ r24\^2\ t\^2 - m3\ r12\^3\ r23\^3\ r24\^3\ t\^2 - m3\ r12\ r13\^2\ r23\^3\ r24\^3\ t\^2 - 2\ m2\ r13\^3\ r23\^3\ r24\^3\ t\^2 - 2\ m2\ m3\ r13\^3\ r23\^3\ r24\^3\ t\^2 + 2\ r12\^3\ r13\^3\ r23\^3\ r24\^3\ t\^2 + 2\ m2\ r12\^3\ r13\^3\ r23\^3\ r24\^3\ t\^2 + 2\ m3\ r12\^3\ r13\^3\ r23\^3\ r24\^3\ t\^2 + 2\ m2\ m3\ r12\^3\ r13\^3\ r23\^3\ r24\^3\ t\^2 - m3\ r12\ r13\^3\ r23\^2\ r24\^3\ t\^3 - r12\ r13\^3\ r23\^3\ r24\^3\ t\^3 - m3\ r12\^3\ r13\^3\ r24\^3\ t\^5 + m3\ r12\ r13\^5\ r24\^3\ t\^5 - r12\^3\ r13\^3\ r23\^3\ r24\^3\ t\^5 + r12\ r13\^3\ r23\^3\ r24\^5\ t\^5, r12\^3\ r13\ r23\^3 + m2\ r13\ r23\^5\ r34\^3 - r12\^3\ r13\^3\ r23\^3\ t\^2 - r12\^3\ r13\ r23\^3\ r34\^2\ t\^2 - 2\ m3\ r12\^3\ r23\^3\ r34\^3\ t\^2 - 2\ m2\ m3\ r12\^3\ r23\^3\ r34\^3\ t\^2 - m2\ r12\^2\ r13\ r23\^3\ r34\^3\ t\^2 - m2\ r13\^3\ r23\^3\ r34\^3\ t\^2 + 2\ r12\^3\ r13\^3\ r23\^3\ r34\^3\ t\^2 + 2\ m2\ r12\^3\ r13\^3\ r23\^3\ r34\^3\ t\^2 + 2\ m3\ r12\^3\ r13\^3\ r23\^3\ r34\^3\ t\^2 + 2\ m2\ m3\ r12\^3\ r13\^3\ r23\^3\ r34\^3\ t\^2 - m2\ r12\^3\ r13\ r23\^2\ r34\^3\ t\^3 - r12\^3\ r13\ r23\^3\ r34\^3\ t\^3 + m2\ r12\^5\ r13\ r34\^3\ t\^5 - m2\ r12\^3\ r13\^3\ r34\^3\ t\^5 - r12\^3\ r13\^3\ r23\^3\ r34\^3\ t\^5 + r12\^3\ r13\ r23\^3\ r34\^5\ t\^5, \(-r12\^3\)\ r13\^3\ r23\^3\ \ r24\^3 - r12\^3\ r13\^3\ r23\^3\ r34\^3 - m2\ m3\ r12\^3\ r23\^3\ r24\^3\ r34\^3 - m2\ m3\ r13\^3\ r23\^3\ r24\^3\ r34\^3 + 2\ r12\^3\ r13\^3\ r23\^3\ r24\^3\ r34\^3 + 2\ m2\ r12\^3\ r13\^3\ r23\^3\ r24\^3\ r34\^3 + 2\ m3\ r12\^3\ r13\^3\ r23\^3\ r24\^3\ r34\^3 + 2\ m2\ m3\ r12\^3\ r13\^3\ r23\^3\ r24\^3\ r34\^3 + r12\^3\ r13\^3\ r23\ r24\^5\ t\^2 - r12\^3\ r13\^3\ r23\ r24\^3\ r34\^2\ t\^2 - r12\^3\ r13\^3\ r23\ r24\^2\ r34\^3\ t\^2 + m2\ m3\ r12\^5\ r23\ r24\^3\ r34\^3\ t\^2 - m2\ m3\ r12\^3\ r13\^2\ r23\ r24\^3\ r34\^3\ t\^2 - m2\ m3\ r12\^2\ r13\^3\ r23\ r24\^3\ r34\^3\ t\^2 + m2\ m3\ r13\^5\ r23\ r24\^3\ r34\^3\ t\^2 + r12\^3\ r13\^3\ r23\ r34\^5\ t\^2 - 2\ m2\ r12\^3\ r13\^3\ r24\^3\ r34\^3\ t\^3 - 2\ m3\ r12\^3\ r13\^3\ r24\^3\ r34\^3\ t\^3, \(-m3\)\ r12\^3\ r13\^3\ \ r24\^3 - m2\ r12\^3\ r13\^3\ r34\^3 - m3\ r12\^3\ r24\^3\ r34\^3 - m2\ r13\^3\ r24\^3\ r34\^3 + 2\ r12\^3\ r13\^3\ r24\^3\ r34\^3 + 2\ m2\ r12\^3\ r13\^3\ r24\^3\ r34\^3 + 2\ m3\ r12\^3\ r13\^3\ r24\^3\ r34\^3 + 2\ m2\ m3\ r12\^3\ r13\^3\ r24\^3\ r34\^3 + m3\ r12\^3\ r13\^5\ r24\^3\ t\^2 - m3\ r12\^3\ r13\^3\ r24\^3\ r34\^2\ t\^2 + m2\ r12\^5\ r13\^3\ r34\^3\ t\^2 - m2\ r12\^3\ r13\^3\ r24\^2\ r34\^3\ t\^2 - m3\ r12\^3\ r13\^2\ r24\^3\ r34\^3\ t\^2 - m2\ r12\^2\ r13\^3\ r24\^3\ r34\^3\ t\^2 + m2\ r13\^3\ r24\^5\ r34\^3\ t\^2 + m3\ r12\^3\ r24\^3\ r34\^5\ t\^2 - 2\ r12\^3\ r13\^3\ r24\^3\ r34\^3\ t\^3 - 2\ m2\ m3\ r12\^3\ r13\^3\ r24\^3\ r34\^3\ t\^3, m3\ r12\^3\ r23\^5\ r24 + m2\ m3\ r23\^3\ r24\ r34\^3 - m3\ r12\^3\ r23\^3\ r24\^3\ t\^2 - m3\ r12\^3\ r23\^3\ r24\ r34\^2\ t\^2 - 2\ r12\^3\ r23\^3\ r34\^3\ t\^2 - 2\ m2\ r12\^3\ r23\^3\ r34\^3\ t\^2 - m2\ m3\ r12\^2\ r23\^3\ r24\ r34\^3\ t\^2 - m2\ m3\ r23\^3\ r24\^3\ r34\^3\ t\^2 + 2\ r12\^3\ r23\^3\ r24\^3\ r34\^3\ t\^2 + 2\ m2\ r12\^3\ r23\^3\ r24\^3\ r34\^3\ t\^2 + 2\ m3\ r12\^3\ r23\^3\ r24\^3\ r34\^3\ t\^2 + 2\ m2\ m3\ r12\^3\ r23\^3\ r24\^3\ r34\^3\ t\^2 - m3\ r12\^3\ r23\^2\ r24\ r34\^3\ t\^3 - m2\ m3\ r12\^3\ r23\^3\ r24\ r34\^3\ t\^3 + m2\ m3\ r12\^5\ r23\^3\ r24\ r34\^3\ t\^5 - m3\ r12\^3\ r24\^3\ r34\^3\ t\^5 - m2\ m3\ r12\^3\ r23\^3\ r24\^3\ r34\^3\ t\^5 + m3\ r12\^3\ r24\ r34\^5\ t\^5, m2\ r13\^3\ r23\^5\ r34 + m2\ m3\ r23\^3\ r24\^3\ r34 - 2\ r13\^3\ r23\^3\ r24\^3\ t\^2 - 2\ m3\ r13\^3\ r23\^3\ r24\^3\ t\^2 - m2\ r13\^3\ r23\^3\ r24\^2\ r34\ t\^2 - m2\ m3\ r13\^2\ r23\^3\ r24\^3\ r34\ t\^2 - m2\ r13\^3\ r23\^3\ r34\^3\ t\^2 - m2\ m3\ r23\^3\ r24\^3\ r34\^3\ t\^2 + 2\ r13\^3\ r23\^3\ r24\^3\ r34\^3\ t\^2 + 2\ m2\ r13\^3\ r23\^3\ r24\^3\ r34\^3\ t\^2 + 2\ m3\ r13\^3\ r23\^3\ r24\^3\ r34\^3\ t\^2 + 2\ m2\ m3\ r13\^3\ r23\^3\ r24\^3\ r34\^3\ t\^2 - m2\ r13\^3\ r23\^2\ r24\^3\ r34\ t\^3 - m2\ m3\ r13\^3\ r23\^3\ r24\^3\ r34\ t\^3 + m2\ m3\ r13\^5\ r23\^3\ r24\^3\ r34\ t\^5 + m2\ r13\^3\ r24\^5\ r34\ t\^5 - m2\ r13\^3\ r24\^3\ r34\^3\ t\^5 - m2\ m3\ r13\^3\ r23\^3\ r24\^3\ r34\^3\ t\^5, r23\^3 - r12\^3\ r23\^3 - r23\^3\ r34\^3 + r12\^3\ r34\^3\ t\^3 + r12\^3\ r23\^3\ r34\^3\ t\^3 - r12\^3\ r34\^3\ t\^6, r13\^3\ r24\^3 - r12\^3\ r13\^3\ r24\^3 - r12\^3\ r34\^3 + r12\^3\ r13\^3\ r34\^3 + r12\^3\ r24\^3\ r34\^3 - r13\^3\ r24\^3\ r34\^3, r23\^3 - r13\^3\ r23\^3 - r23\^3\ r24\^3 + r13\^3\ r24\^3\ t\^3 + r13\^3\ r23\^3\ r24\^3\ t\^3 - r13\^3\ r24\^3\ t\^6}\)], "Output"] }, Open ]], Cell["\<\ Here are the lowest order terms in t. The order 0 terms are equivalent to the reduced system red22. There are no terms at order 1. We truncate the equations above order 3 since the other terms will not be relevant. \ \>", "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(\(\(F0\ = \ eqs221 /. t \[Rule] 0 // Factor\[IndentingNewLine] F1\ = \ Coefficient[eqs221, t] // Factor\[IndentingNewLine] F2\ = \ Coefficient[eqs221, t^2] // Factor\[IndentingNewLine] F3\ = \ Coefficient[eqs221, t^3] // Factor\[IndentingNewLine] \(F\ = \ F0\ + \ t*F1\ + \ t^2*F2\ + \ t^3*F3;\)\)\(\ \)\)\)], "Input"], Cell[BoxData[ \({r12\ r23\^3\ \((r13\^3 + m3\ r23\^2\ r24\^3)\), r13\ r23\^3\ \((r12\^3 + m2\ r23\^2\ r34\^3)\), r23\^3\ \((\(-r12\^3\)\ r13\^3\ r24\^3 - r12\^3\ r13\^3\ r34\^3 - m2\ m3\ r12\^3\ r24\^3\ r34\^3 - m2\ m3\ r13\^3\ r24\^3\ r34\^3 + 2\ r12\^3\ r13\^3\ r24\^3\ r34\^3 + 2\ m2\ r12\^3\ r13\^3\ r24\^3\ r34\^3 + 2\ m3\ r12\^3\ r13\^3\ r24\^3\ r34\^3 + 2\ m2\ m3\ r12\^3\ r13\^3\ r24\^3\ r34\^3)\), \(-m3\)\ r12\^3\ \ r13\^3\ r24\^3 - m2\ r12\^3\ r13\^3\ r34\^3 - m3\ r12\^3\ r24\^3\ r34\^3 - m2\ r13\^3\ r24\^3\ r34\^3 + 2\ r12\^3\ r13\^3\ r24\^3\ r34\^3 + 2\ m2\ r12\^3\ r13\^3\ r24\^3\ r34\^3 + 2\ m3\ r12\^3\ r13\^3\ r24\^3\ r34\^3 + 2\ m2\ m3\ r12\^3\ r13\^3\ r24\^3\ r34\^3, m3\ r23\^3\ r24\ \((r12\^3\ r23\^2 + m2\ r34\^3)\), m2\ r23\^3\ \((r13\^3\ r23\^2 + m3\ r24\^3)\)\ r34, \(-r23\^3\)\ \((\(-1\) + r12\^3 + r34\^3)\), r13\^3\ r24\^3 - r12\^3\ r13\^3\ r24\^3 - r12\^3\ r34\^3 + r12\^3\ r13\^3\ r34\^3 + r12\^3\ r24\^3\ r34\^3 - r13\^3\ r24\^3\ r34\^3, \(-r23\^3\)\ \((\(-1\) + r13\^3 + r24\^3)\)}\)], "Output"], Cell[BoxData[ \({0, 0, 0, 0, 0, 0, 0, 0, 0}\)], "Output"], Cell[BoxData[ \({r23\^3\ \((\(-r12\^3\)\ r13\^3 - r12\ r13\^3\ r24\^2 - m3\ r12\^3\ r24\^3 - m3\ r12\ r13\^2\ r24\^3 - 2\ m2\ r13\^3\ r24\^3 - 2\ m2\ m3\ r13\^3\ r24\^3 + 2\ r12\^3\ r13\^3\ r24\^3 + 2\ m2\ r12\^3\ r13\^3\ r24\^3 + 2\ m3\ r12\^3\ r13\^3\ r24\^3 + 2\ m2\ m3\ r12\^3\ r13\^3\ r24\^3)\), r23\^3\ \((\(-r12\^3\)\ r13\^3 - r12\^3\ r13\ r34\^2 - 2\ m3\ r12\^3\ r34\^3 - 2\ m2\ m3\ r12\^3\ r34\^3 - m2\ r12\^2\ r13\ r34\^3 - m2\ r13\^3\ r34\^3 + 2\ r12\^3\ r13\^3\ r34\^3 + 2\ m2\ r12\^3\ r13\^3\ r34\^3 + 2\ m3\ r12\^3\ r13\^3\ r34\^3 + 2\ m2\ m3\ r12\^3\ r13\^3\ r34\^3)\), r23\ \((r12\^3\ r13\^3\ r24\^5 - r12\^3\ r13\^3\ r24\^3\ r34\^2 - r12\^3\ r13\^3\ r24\^2\ r34\^3 + m2\ m3\ r12\^5\ r24\^3\ r34\^3 - m2\ m3\ r12\^3\ r13\^2\ r24\^3\ r34\^3 - m2\ m3\ r12\^2\ r13\^3\ r24\^3\ r34\^3 + m2\ m3\ r13\^5\ r24\^3\ r34\^3 + r12\^3\ r13\^3\ r34\^5)\), m3\ r12\^3\ r13\^5\ r24\^3 - m3\ r12\^3\ r13\^3\ r24\^3\ r34\^2 + m2\ r12\^5\ r13\^3\ r34\^3 - m2\ r12\^3\ r13\^3\ r24\^2\ r34\^3 - m3\ r12\^3\ r13\^2\ r24\^3\ r34\^3 - m2\ r12\^2\ r13\^3\ r24\^3\ r34\^3 + m2\ r13\^3\ r24\^5\ r34\^3 + m3\ r12\^3\ r24\^3\ r34\^5, r23\^3\ \((\(-m3\)\ r12\^3\ r24\^3 - m3\ r12\^3\ r24\ r34\^2 - 2\ r12\^3\ r34\^3 - 2\ m2\ r12\^3\ r34\^3 - m2\ m3\ r12\^2\ r24\ r34\^3 - m2\ m3\ r24\^3\ r34\^3 + 2\ r12\^3\ r24\^3\ r34\^3 + 2\ m2\ r12\^3\ r24\^3\ r34\^3 + 2\ m3\ r12\^3\ r24\^3\ r34\^3 + 2\ m2\ m3\ r12\^3\ r24\^3\ r34\^3)\), r23\^3\ \((\(-2\)\ r13\^3\ r24\^3 - 2\ m3\ r13\^3\ r24\^3 - m2\ r13\^3\ r24\^2\ r34 - m2\ m3\ r13\^2\ r24\^3\ r34 - m2\ r13\^3\ r34\^3 - m2\ m3\ r24\^3\ r34\^3 + 2\ r13\^3\ r24\^3\ r34\^3 + 2\ m2\ r13\^3\ r24\^3\ r34\^3 + 2\ m3\ r13\^3\ r24\^3\ r34\^3 + 2\ m2\ m3\ r13\^3\ r24\^3\ r34\^3)\), 0, 0, 0}\)], "Output"], Cell[BoxData[ \({\(-r12\)\ r13\^3\ r23\^2\ \((m3 + r23)\)\ r24\^3, \(-r12\^3\)\ r13\ r23\^2\ \((m2 + r23)\)\ r34\^3, \(-2\)\ \((m2 + m3)\)\ r12\^3\ r13\^3\ r24\^3\ r34\^3, \(-2\)\ \((1 + m2\ m3)\)\ r12\^3\ r13\^3\ r24\^3\ r34\^3, \(-m3\)\ r12\^3\ \ r23\^2\ \((1 + m2\ r23)\)\ r24\ r34\^3, \(-m2\)\ r13\^3\ r23\^2\ \((1 + m3\ r23)\)\ r24\^3\ r34, r12\^3\ \((1 + r23)\)\ \((1 - r23 + r23\^2)\)\ r34\^3, 0, r13\^3\ \((1 + r23)\)\ \((1 - r23 + r23\^2)\)\ r24\^3}\)], "Output"] }, Open ]], Cell["\<\ Solve the reduced system for the leading order terms of a Puiseux solution. We begin by \"cleaning up\" the equautions (eliminating factors of \ the indicated variables). \ \>", "Text"], Cell[CellGroupData[{ Cell[BoxData[{ \(\(allvars\ = \ {r12, r13, r14, r23, r24, r34, m1, m2, m3, m4};\)\), "\[IndentingNewLine]", \(F00 = \ Map[CleanUp[#, allvars] &, F0]\)}], "Input"], Cell[BoxData[ \({r13\^3 + m3\ r23\^2\ r24\^3, r12\^3 + m2\ r23\^2\ r34\^3, \(-r12\^3\)\ r13\^3\ r24\^3 - r12\^3\ r13\^3\ r34\^3 - m2\ m3\ r12\^3\ r24\^3\ r34\^3 - m2\ m3\ r13\^3\ r24\^3\ r34\^3 + 2\ r12\^3\ r13\^3\ r24\^3\ r34\^3 + 2\ m2\ r12\^3\ r13\^3\ r24\^3\ r34\^3 + 2\ m3\ r12\^3\ r13\^3\ r24\^3\ r34\^3 + 2\ m2\ m3\ r12\^3\ r13\^3\ r24\^3\ r34\^3, \(-m3\)\ r12\^3\ r13\^3\ \ r24\^3 - m2\ r12\^3\ r13\^3\ r34\^3 - m3\ r12\^3\ r24\^3\ r34\^3 - m2\ r13\^3\ r24\^3\ r34\^3 + 2\ r12\^3\ r13\^3\ r24\^3\ r34\^3 + 2\ m2\ r12\^3\ r13\^3\ r24\^3\ r34\^3 + 2\ m3\ r12\^3\ r13\^3\ r24\^3\ r34\^3 + 2\ m2\ m3\ r12\^3\ r13\^3\ r24\^3\ r34\^3, r12\^3\ r23\^2 + m2\ r34\^3, r13\^3\ r23\^2 + m3\ r24\^3, 1 - r12\^3 - r34\^3, r13\^3\ r24\^3 - r12\^3\ r13\^3\ r24\^3 - r12\^3\ r34\^3 + r12\^3\ r13\^3\ r34\^3 + r12\^3\ r24\^3\ r34\^3 - r13\^3\ r24\^3\ r34\^3, 1 - r13\^3 - r24\^3}\)], "Output"] }, Open ]], Cell["\<\ The first two equations are uniquely solveable for r13^3 and r12^3. We make these substitutions. \ \>", "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(\(\(F001\ = \ Map[CleanUp[#, allvars] &, F00 /. {r13^3 \[Rule] \(-m3\)*r23^2*r24^3, r12^3 \[Rule] \(-m2\)*r23^2*r34^3}] // Factor\)\(\[IndentingNewLine]\) \)\)], "Input"], Cell[BoxData[ \({0, 0, m3\ r24\^3 - r23\^2\ r24\^3 + m2\ r34\^3 - r23\^2\ r34\^3 + 2\ r23\^2\ r24\^3\ r34\^3 + 2\ m2\ r23\^2\ r24\^3\ r34\^3 + 2\ m3\ r23\^2\ r24\^3\ r34\^3 + 2\ m2\ m3\ r23\^2\ r24\^3\ r34\^3, r24\^3 - m3\ r23\^2\ r24\^3 + r34\^3 - m2\ r23\^2\ r34\^3 + 2\ r23\^2\ r24\^3\ r34\^3 + 2\ m2\ r23\^2\ r24\^3\ r34\^3 + 2\ m3\ r23\^2\ r24\^3\ r34\^3 + 2\ m2\ m3\ r23\^2\ r24\^3\ r34\^3, \(-\((\(-1\) + r23)\)\)\ \((1 + r23)\)\ \((1 + r23\^2)\), \(-\((\(-1\) + r23)\)\)\ \((1 + r23)\)\ \((1 + r23\^2)\), 1 - r34\^3 + m2\ r23\^2\ r34\^3, \(-m3\)\ r24\^6 + m3\ r24\^6\ r34\^3 - m2\ m3\ r23\^2\ r24\^6\ r34\^3 + m2\ r34\^6 - m2\ r24\^3\ r34\^6 + m2\ m3\ r23\^2\ r24\^3\ r34\^6, 1 - r24\^3 + m3\ r23\^2\ r24\^3}\)], "Output"] }, Open ]], Cell["\<\ Equations 5 and 6 now force us to take r23 = 1, -1 , i or -i. First we show that the cases r23 = 1, -1 are impossible for positive masses In each case we can find a solution only if m2 + m3 = 0. \ \>", "Text"], Cell[CellGroupData[{ Cell[BoxData[{ \(F001 /. r23 \[Rule] 1 // Factor\), "\[IndentingNewLine]", \(\(% /. {r34^3 \[Rule] 1/\((1 - m2)\), r24^3 \[Rule] 1/\((1 - m3)\)} // Factor\) // Numerator\), "\[IndentingNewLine]", \(F001 /. r23 \[Rule] \(-1\) // Factor\), "\[IndentingNewLine]", \(\(% /. {r34^3 \[Rule] 1/\((1 - m2)\), r24^3 \[Rule] 1/\((1 - m3)\)} // Factor\) // Numerator\), "\[IndentingNewLine]", \(\)}], "Input"], Cell[BoxData[ \({0, 0, \(-r24\^3\) + m3\ r24\^3 - r34\^3 + m2\ r34\^3 + 2\ r24\^3\ r34\^3 + 2\ m2\ r24\^3\ r34\^3 + 2\ m3\ r24\^3\ r34\^3 + 2\ m2\ m3\ r24\^3\ r34\^3, r24\^3 - m3\ r24\^3 + r34\^3 - m2\ r34\^3 + 2\ r24\^3\ r34\^3 + 2\ m2\ r24\^3\ r34\^3 + 2\ m3\ r24\^3\ r34\^3 + 2\ m2\ m3\ r24\^3\ r34\^3, 0, 0, 1 - r34\^3 + m2\ r34\^3, \(-m3\)\ r24\^6 + m3\ r24\^6\ r34\^3 - m2\ m3\ r24\^6\ r34\^3 + m2\ r34\^6 - m2\ r24\^3\ r34\^6 + m2\ m3\ r24\^3\ r34\^6, 1 - r24\^3 + m3\ r24\^3}\)], "Output"], Cell[BoxData[ \({0, 0, 4\ \((m2 + m3)\), 4\ \((1 + m2\ m3)\), 0, 0, 0, 0, 0}\)], "Output"], Cell[BoxData[ \({0, 0, \(-r24\^3\) + m3\ r24\^3 - r34\^3 + m2\ r34\^3 + 2\ r24\^3\ r34\^3 + 2\ m2\ r24\^3\ r34\^3 + 2\ m3\ r24\^3\ r34\^3 + 2\ m2\ m3\ r24\^3\ r34\^3, r24\^3 - m3\ r24\^3 + r34\^3 - m2\ r34\^3 + 2\ r24\^3\ r34\^3 + 2\ m2\ r24\^3\ r34\^3 + 2\ m3\ r24\^3\ r34\^3 + 2\ m2\ m3\ r24\^3\ r34\^3, 0, 0, 1 - r34\^3 + m2\ r34\^3, \(-m3\)\ r24\^6 + m3\ r24\^6\ r34\^3 - m2\ m3\ r24\^6\ r34\^3 + m2\ r34\^6 - m2\ r24\^3\ r34\^6 + m2\ m3\ r24\^3\ r34\^6, 1 - r24\^3 + m3\ r24\^3}\)], "Output"], Cell[BoxData[ \({0, 0, 4\ \((m2 + m3)\), 4\ \((1 + m2\ m3)\), 0, 0, 0, 0, 0}\)], "Output"] }, Open ]], Cell["\<\ On the other hand, the cases r23 = i and r23 = -i are possible. \ \>", "Text"], Cell[CellGroupData[{ Cell[BoxData[{ \(F001 /. r23 \[Rule] I // Factor\), "\[IndentingNewLine]", \(\(% /. {r34^3 \[Rule] 1/\((1 + m2)\), r24^3 \[Rule] 1/\((1 + m3)\)} // Factor\) // Numerator\), "\[IndentingNewLine]", \(F001 /. r23 \[Rule] \(-I\) // Factor\), "\[IndentingNewLine]", \(\(% /. {r34^3 \[Rule] 1/\((1 + m2)\), r24^3 \[Rule] 1/\((1 + m3)\)} // Factor\) // Numerator\)}], "Input"], Cell[BoxData[ \({0, 0, r24\^3 + m3\ r24\^3 + r34\^3 + m2\ r34\^3 - 2\ r24\^3\ r34\^3 - 2\ m2\ r24\^3\ r34\^3 - 2\ m3\ r24\^3\ r34\^3 - 2\ m2\ m3\ r24\^3\ r34\^3, r24\^3 + m3\ r24\^3 + r34\^3 + m2\ r34\^3 - 2\ r24\^3\ r34\^3 - 2\ m2\ r24\^3\ r34\^3 - 2\ m3\ r24\^3\ r34\^3 - 2\ m2\ m3\ r24\^3\ r34\^3, 0, 0, 1 - r34\^3 - m2\ r34\^3, \(-m3\)\ r24\^6 + m3\ r24\^6\ r34\^3 + m2\ m3\ r24\^6\ r34\^3 + m2\ r34\^6 - m2\ r24\^3\ r34\^6 - m2\ m3\ r24\^3\ r34\^6, 1 - r24\^3 - m3\ r24\^3}\)], "Output"], Cell[BoxData[ \({0, 0, 0, 0, 0, 0, 0, 0, 0}\)], "Output"], Cell[BoxData[ \({0, 0, r24\^3 + m3\ r24\^3 + r34\^3 + m2\ r34\^3 - 2\ r24\^3\ r34\^3 - 2\ m2\ r24\^3\ r34\^3 - 2\ m3\ r24\^3\ r34\^3 - 2\ m2\ m3\ r24\^3\ r34\^3, r24\^3 + m3\ r24\^3 + r34\^3 + m2\ r34\^3 - 2\ r24\^3\ r34\^3 - 2\ m2\ r24\^3\ r34\^3 - 2\ m3\ r24\^3\ r34\^3 - 2\ m2\ m3\ r24\^3\ r34\^3, 0, 0, 1 - r34\^3 - m2\ r34\^3, \(-m3\)\ r24\^6 + m3\ r24\^6\ r34\^3 + m2\ m3\ r24\^6\ r34\^3 + m2\ r34\^6 - m2\ r24\^3\ r34\^6 - m2\ m3\ r24\^3\ r34\^6, 1 - r24\^3 - m3\ r24\^3}\)], "Output"], Cell[BoxData[ \({0, 0, 0, 0, 0, 0, 0, 0, 0}\)], "Output"] }, Open ]], Cell["\<\ Here is a substitution valid for all relevant solutions of the reduced system. \ \>", "Text"], Cell[CellGroupData[{ Cell[BoxData[{ \(sub1 = {r12^3 \[Rule] m2/\((1 + m2)\), r34^3 \[Rule] 1/\((1 + m2)\), r13^3 \[Rule] m3/\((1 + m3)\), r24^3 \[Rule] 1/\((1 + m3)\), r23^2 \[Rule] \(-1\), r23^3 \[Rule] \(-r23\), r23^4 \[Rule] 1, r12^5 \[Rule] m2*r12^2/\((1 + m2)\), r34^5 \[Rule] r34^2/\((1 + m2)\), r13^5 \[Rule] m3*r13^2/\((1 + m3)\), r24^5 \[Rule] r24^2/\((1 + m3)\)}\), "\[IndentingNewLine]", \(F00 /. sub1 // Factor\)}], "Input"], Cell[BoxData[ \({r12\^3 \[Rule] m2\/\(1 + m2\), r34\^3 \[Rule] 1\/\(1 + m2\), r13\^3 \[Rule] m3\/\(1 + m3\), r24\^3 \[Rule] 1\/\(1 + m3\), r23\^2 \[Rule] \(-1\), r23\^3 \[Rule] \(-r23\), r23\^4 \[Rule] 1, r12\^5 \[Rule] \(m2\ r12\^2\)\/\(1 + m2\), r34\^5 \[Rule] r34\^2\/\(1 + m2\), r13\^5 \[Rule] \(m3\ r13\^2\)\/\(1 + m3\), r24\^5 \[Rule] r24\^2\/\(1 + m3\)}\)], "Output"], Cell[BoxData[ \({0, 0, 0, 0, 0, 0, 0, 0, 0}\)], "Output"] }, Open ]], Cell["\<\ We want to show that the solution of the reduced system does not really determine a continuum of solutions by showing that the Puiseux series solutions cannot be continued to higher order terms. To do this we have to do some rescalings and substitutions. We have a system F(x,t) = F0(x) + t^2 F2(x) + t^3 F3(x) + ... where x =( r12 ,r13, r23 ,r24, r34 ) and r14 = 1/t . We also have a solution x0 of F0(x0) = 0 (the reduced equations). We use the implicit function theorem to see that any Puiseux solution x = x0 + o(t) must be a power series in t. It suffices to show that the 9 x 5 matrix DF0(x0) has rank 5. We single out a 5 x 5 submatrix and take its determinant, making the substition corresponding to the solutions of the reduced system. \ \>", "Text"], Cell[CellGroupData[{ Cell[BoxData[{ \(grad[f_]\ := \ {D[f, r12], D[f, r13], D[f, r23], D[f, r24], D[f, r34]}\), "\[IndentingNewLine]", \(\(DF0\ = \ Map[grad, F0] /. sub1 // Factor;\)\), "\[IndentingNewLine]", \(DF0 // MatrixForm\), "\[IndentingNewLine]", \(\((\(Det[DF0[\([{1, 2, 4, 5, 7}]\)]] /. sub1 // Factor\) // Numerator)\) /. sub1\)}], "Input"], Cell[BoxData[ TagBox[ RowBox[{"(", "\[NoBreak]", GridBox[{ { "0", \(3\ r12\ r13\^2\ r23\^3\), \(\(2\ m3\ r12\ r23\^4\)\/\(1 \ + m3\)\), \(3\ m3\ r12\ r23\^5\ r24\^2\), "0"}, {\(3\ r12\^2\ r13\ r23\^3\), "0", \(\(2\ m2\ r13\ r23\^4\)\/\(1 + m2\)\), "0", \(3\ m2\ r13\ r23\^5\ r34\^2\)}, {\(\(3\ m3\^2\ r12\^2\ r23\^3\)\/\((1 + m3)\)\^2\), \(\(3\ m2\^2\ \ r13\^2\ r23\^3\)\/\((1 + m2)\)\^2\), "0", \(\(3\ m2\ m3\ r23\^3\ r24\^2\)\/\((1 + m2)\)\^2\), \(\(3\ \ m2\ m3\ r23\^3\ r34\^2\)\/\((1 + m3)\)\^2\)}, {\(\(3\ m3\ r12\^2\)\/\((1 + m3)\)\^2\), \(\(3\ m2\ \ r13\^2\)\/\((1 + m2)\)\^2\), "0", \(\(3\ m2\^2\ m3\ r24\^2\)\/\((1 + m2)\)\^2\), \(\(3\ m2\ \ m3\^2\ r34\^2\)\/\((1 + m3)\)\^2\)}, {\(3\ m3\ r12\^2\ r23\^5\ r24\), "0", \(\(2\ m2\ m3\ r23\^4\ r24\)\/\(1 + m2\)\), "0", \(3\ m2\ m3\ r23\^3\ r24\ r34\^2\)}, { "0", \(3\ m2\ r13\^2\ r23\^5\ r34\), \(\(2\ m2\ m3\ r23\^4\ r34\ \)\/\(1 + m3\)\), \(3\ m2\ m3\ r23\^3\ r24\^2\ r34\), "0"}, {\(\(-3\)\ r12\^2\ r23\^3\), "0", "0", "0", \(\(-3\)\ r23\^3\ r34\^2\)}, {\(-\(\(3\ m3\ r12\^2\)\/\((1 + m3)\)\^2\)\), \(\(3\ m2\ r13\^2\)\ \/\((1 + m2)\)\^2\), "0", \(\(3\ m2\ r24\^2\)\/\((1 + m2)\)\^2\), \(-\(\(3\ m3\ \ r34\^2\)\/\((1 + m3)\)\^2\)\)}, {"0", \(\(-3\)\ r13\^2\ r23\^3\), "0", \(\(-3\)\ r23\^3\ r24\^2\), "0"} }], "\[NoBreak]", ")"}], Function[ BoxForm`e$, MatrixForm[ BoxForm`e$]]]], "Output"], Cell[BoxData[ \(162\ m2\^3\ \((1 + m2)\)\ m3\^3\ \((\(-1\) + r23)\)\ r23\^13\ \((1 + r23)\)\ r34\^2\)], "Output"] }, Open ]], Cell["\<\ Since r23 is not 1 or -1 and since the masses are positive, this determinant is nonzero. Knowing that our Puiseux solution is a power series and that the first order term in our equation is F1=0, we are justified in setting x = x0 + t^2 u+ t^3 \ v + ... . We will derive the (linear) equations for u and v \ \>", "Text"], Cell[CellGroupData[{ Cell[BoxData[{ \(\(Ft\ = \ F /. {r12 \[Rule] r12 + t^2*u12 + t^3*v12, r13 \[Rule] r13 + t^2*u13 + t^3*v13, r23 \[Rule] r23 + t^2*u23 + t^3*v23, r24 \[Rule] r24 + t^2*u24 + t^3*v24, r34 \[Rule] r34 + t^2*u34 + t^3*v34};\)\), "\[IndentingNewLine]", \(Ft0\ = \ \((Ft /. t \[Rule] 0 // Factor)\) /. sub1 // Factor\), "\[IndentingNewLine]", \(Ft1\ = \ Coefficient[Ft, t] /. sub1 // Factor\), "\[IndentingNewLine]", \(Ft2\ = \ Coefficient[Ft, t^2] /. sub1 // Factor\), "\[IndentingNewLine]", \(Ft3\ = \ Coefficient[Ft, t^3] /. sub1 // Factor\)}], "Input"], Cell[BoxData[ \({0, 0, 0, 0, 0, 0, 0, 0, 0}\)], "Output"], Cell[BoxData[ \({0, 0, 0, 0, 0, 0, 0, 0, 0}\)], "Output"], Cell[BoxData[ \({\(1\/\(\((1 + m2)\)\ \((1 + m3)\)\)\) \((r23\^3\ \((\(-2\)\ m2\ m3 - m3\ r12\ r13\^2 - m2\ m3\ r12\ r13\^2 - m3\ r12\ r24\^2 - m2\ m3\ r12\ r24\^2 + 3\ r12\ r13\^2\ u13 + 3\ m2\ r12\ r13\^2\ u13 + 3\ m3\ r12\ r13\^2\ u13 + 3\ m2\ m3\ r12\ r13\^2\ u13 + 2\ m3\ r12\ r23\ u23 + 2\ m2\ m3\ r12\ r23\ u23 - 3\ m3\ r12\ r24\^2\ u24 - 3\ m2\ m3\ r12\ r24\^2\ u24 - 3\ m3\^2\ r12\ r24\^2\ u24 - 3\ m2\ m3\^2\ r12\ r24\^2\ u24)\))\), \(1\/\(\((1 + m2)\)\ \((1 + m3)\)\)\) \((r23\^3\ \((\(-2\)\ m2\ m3 - m2\ r12\^2\ r13 - m2\ m3\ r12\^2\ r13 - m2\ r13\ r34\^2 - m2\ m3\ r13\ r34\^2 + 3\ r12\^2\ r13\ u12 + 3\ m2\ r12\^2\ r13\ u12 + 3\ m3\ r12\^2\ r13\ u12 + 3\ m2\ m3\ r12\^2\ r13\ u12 + 2\ m2\ r13\ r23\ u23 + 2\ m2\ m3\ r13\ r23\ u23 - 3\ m2\ r13\ r34\^2\ u34 - 3\ m2\^2\ r13\ r34\^2\ u34 - 3\ m2\ m3\ r13\ r34\^2\ u34 - 3\ m2\^2\ m3\ r13\ r34\^2\ u34)\))\), \(1\/\(\((1 + m2)\)\^2\ \ \((1 + m3)\)\^2\)\) \((r23\ \((m2\^2\ m3\ r12\^2 - m2\ m3\^2\ r12\^2 - m2\^2\ m3\ r13\^2 + m2\ m3\^2\ r13\^2 + m2\^2\ m3\ r24\^2 - m2\ m3\^2\ r24\^2 - m2\^2\ m3\ r34\^2 + m2\ m3\^2\ r34\^2 + 3\ m3\^2\ r12\^2\ r23\^2\ u12 + 6\ m2\ m3\^2\ r12\^2\ r23\^2\ u12 + 3\ m2\^2\ m3\^2\ r12\^2\ r23\^2\ u12 + 3\ m2\^2\ r13\^2\ r23\^2\ u13 + 6\ m2\^2\ m3\ r13\^2\ r23\^2\ u13 + 3\ m2\^2\ m3\^2\ r13\^2\ r23\^2\ u13 + 3\ m2\ m3\ r23\^2\ r24\^2\ u24 + 6\ m2\ m3\^2\ r23\^2\ r24\^2\ u24 + 3\ m2\ m3\^3\ r23\^2\ r24\^2\ u24 + 3\ m2\ m3\ r23\^2\ r34\^2\ u34 + 6\ m2\^2\ m3\ r23\^2\ r34\^2\ u34 + 3\ m2\^3\ m3\ r23\^2\ r34\^2\ u34)\))\), \(1\/\(\((1 + \ m2)\)\^2\ \((1 + m3)\)\^2\)\) \((\(-m2\)\ m3\ r12\^2 + m2\^2\ m3\^2\ r12\^2 - m2\ m3\ r13\^2 + m2\^2\ m3\^2\ r13\^2 + m2\ m3\ r24\^2 - m2\^2\ m3\^2\ r24\^2 + m2\ m3\ r34\^2 - m2\^2\ m3\^2\ r34\^2 + 3\ m3\ r12\^2\ u12 + 6\ m2\ m3\ r12\^2\ u12 + 3\ m2\^2\ m3\ r12\^2\ u12 + 3\ m2\ r13\^2\ u13 + 6\ m2\ m3\ r13\^2\ u13 + 3\ m2\ m3\^2\ r13\^2\ u13 + 3\ m2\^2\ m3\ r24\^2\ u24 + 6\ m2\^2\ m3\^2\ r24\^2\ u24 + 3\ m2\^2\ m3\^3\ r24\^2\ u24 + 3\ m2\ m3\^2\ r34\^2\ u34 + 6\ m2\^2\ m3\^2\ r34\^2\ u34 + 3\ m2\^3\ m3\^2\ r34\^2\ u34)\), \(1\/\(\((1 + m2)\)\ \((1 + m3)\)\)\) \((m3\ r23\^3\ \((\(-2\)\ m2 - m2\ r12\^2\ r24 - m2\ m3\ r12\^2\ r24 - m2\ r24\ r34\^2 - m2\ m3\ r24\ r34\^2 - 3\ r12\^2\ r24\ u12 - 3\ m2\ r12\^2\ r24\ u12 - 3\ m3\ r12\^2\ r24\ u12 - 3\ m2\ m3\ r12\^2\ r24\ u12 + 2\ m2\ r23\ r24\ u23 + 2\ m2\ m3\ r23\ r24\ u23 + 3\ m2\ r24\ r34\^2\ u34 + 3\ m2\^2\ r24\ r34\^2\ u34 + 3\ m2\ m3\ r24\ r34\^2\ u34 + 3\ m2\^2\ m3\ r24\ r34\^2\ u34)\))\), \(1\/\(\((1 + m2)\)\ \((1 + m3)\)\)\) \((m2\ r23\^3\ \((\(-2\)\ m3 - m3\ r13\^2\ r34 - m2\ m3\ r13\^2\ r34 - m3\ r24\^2\ r34 - m2\ m3\ r24\^2\ r34 - 3\ r13\^2\ r34\ u13 - 3\ m2\ r13\^2\ r34\ u13 - 3\ m3\ r13\^2\ r34\ u13 - 3\ m2\ m3\ r13\^2\ r34\ u13 + 2\ m3\ r23\ r34\ u23 + 2\ m2\ m3\ r23\ r34\ u23 + 3\ m3\ r24\^2\ r34\ u24 + 3\ m2\ m3\ r24\^2\ r34\ u24 + 3\ m3\^2\ r24\^2\ r34\ u24 + 3\ m2\ m3\^2\ r24\^2\ r34\ u24)\))\), \(-3\)\ r23\^3\ \ \((r12\^2\ u12 + r34\^2\ u34)\), \(-\(\(1\/\(\((1 + m2)\)\^2\ \((1 + m3)\)\^2\)\) \ \((3\ \((m3\ r12\^2\ u12 + 2\ m2\ m3\ r12\^2\ u12 + m2\^2\ m3\ r12\^2\ u12 - m2\ r13\^2\ u13 - 2\ m2\ m3\ r13\^2\ u13 - m2\ m3\^2\ r13\^2\ u13 - m2\ r24\^2\ u24 - 2\ m2\ m3\ r24\^2\ u24 - m2\ m3\^2\ r24\^2\ u24 + m3\ r34\^2\ u34 + 2\ m2\ m3\ r34\^2\ u34 + m2\^2\ m3\ r34\^2\ u34)\))\)\)\), \(-3\)\ r23\^3\ \((r13\^2\ \ u13 + r24\^2\ u24)\)}\)], "Output"], Cell[BoxData[ \({\(-\(\(1\/\((1 + m3)\)\^2\) \((r12\ \((\(-m3\^2\) - m3\ r23 - 3\ r13\^2\ r23\^3\ v13 - 6\ m3\ r13\^2\ r23\^3\ v13 - 3\ m3\^2\ r13\^2\ r23\^3\ v13 - 2\ m3\ r23\^4\ v23 - 2\ m3\^2\ r23\^4\ v23 + 3\ m3\ r23\^3\ r24\^2\ v24 + 6\ m3\^2\ r23\^3\ r24\^2\ v24 + 3\ m3\^3\ r23\^3\ r24\^2\ v24)\))\)\)\), \(-\(\(1\/\((1 + \ m2)\)\^2\) \((r13\ \((\(-m2\^2\) - m2\ r23 - 3\ r12\^2\ r23\^3\ v12 - 6\ m2\ r12\^2\ r23\^3\ v12 - 3\ m2\^2\ r12\^2\ r23\^3\ v12 - 2\ m2\ r23\^4\ v23 - 2\ m2\^2\ r23\^4\ v23 + 3\ m2\ r23\^3\ r34\^2\ v34 + 6\ m2\^2\ r23\^3\ r34\^2\ v34 + 3\ m2\^3\ r23\^3\ r34\^2\ v34)\))\)\)\), \(1\/\(\((1 + \ m2)\)\^2\ \((1 + m3)\)\^2\)\) \((\(-2\)\ m2\^2\ m3 - 2\ m2\ m3\^2 + 3\ m3\^2\ r12\^2\ r23\^3\ v12 + 6\ m2\ m3\^2\ r12\^2\ r23\^3\ v12 + 3\ m2\^2\ m3\^2\ r12\^2\ r23\^3\ v12 + 3\ m2\^2\ r13\^2\ r23\^3\ v13 + 6\ m2\^2\ m3\ r13\^2\ r23\^3\ v13 + 3\ m2\^2\ m3\^2\ r13\^2\ r23\^3\ v13 + 3\ m2\ m3\ r23\^3\ r24\^2\ v24 + 6\ m2\ m3\^2\ r23\^3\ r24\^2\ v24 + 3\ m2\ m3\^3\ r23\^3\ r24\^2\ v24 + 3\ m2\ m3\ r23\^3\ r34\^2\ v34 + 6\ m2\^2\ m3\ r23\^3\ r34\^2\ v34 + 3\ m2\^3\ m3\ r23\^3\ r34\^2\ v34)\), \(1\/\(\((1 + m2)\)\^2\ \ \((1 + m3)\)\^2\)\) \((\(-2\)\ m2\ m3 - 2\ m2\^2\ m3\^2 + 3\ m3\ r12\^2\ v12 + 6\ m2\ m3\ r12\^2\ v12 + 3\ m2\^2\ m3\ r12\^2\ v12 + 3\ m2\ r13\^2\ v13 + 6\ m2\ m3\ r13\^2\ v13 + 3\ m2\ m3\^2\ r13\^2\ v13 + 3\ m2\^2\ m3\ r24\^2\ v24 + 6\ m2\^2\ m3\^2\ r24\^2\ v24 + 3\ m2\^2\ m3\^3\ r24\^2\ v24 + 3\ m2\ m3\^2\ r34\^2\ v34 + 6\ m2\^2\ m3\^2\ r34\^2\ v34 + 3\ m2\^3\ m3\^2\ r34\^2\ v34)\), \(1\/\((1 + m2)\)\^2\) \((m3\ \ r24\ \((m2 + m2\^2\ r23 - 3\ r12\^2\ r23\^3\ v12 - 6\ m2\ r12\^2\ r23\^3\ v12 - 3\ m2\^2\ r12\^2\ r23\^3\ v12 + 2\ m2\ r23\^4\ v23 + 2\ m2\^2\ r23\^4\ v23 + 3\ m2\ r23\^3\ r34\^2\ v34 + 6\ m2\^2\ r23\^3\ r34\^2\ v34 + 3\ m2\^3\ r23\^3\ r34\^2\ v34)\))\), \(1\/\((1 + m3)\)\^2\) \ \((m2\ r34\ \((m3 + m3\^2\ r23 - 3\ r13\^2\ r23\^3\ v13 - 6\ m3\ r13\^2\ r23\^3\ v13 - 3\ m3\^2\ r13\^2\ r23\^3\ v13 + 2\ m3\ r23\^4\ v23 + 2\ m3\^2\ r23\^4\ v23 + 3\ m3\ r23\^3\ r24\^2\ v24 + 6\ m3\^2\ r23\^3\ r24\^2\ v24 + 3\ m3\^3\ r23\^3\ r24\^2\ v24)\))\), \(-\(\(1\/\((1 + \ m2)\)\^2\) \((\(-m2\) - m2\ r23\^3 + 3\ r12\^2\ r23\^3\ v12 + 6\ m2\ r12\^2\ r23\^3\ v12 + 3\ m2\^2\ r12\^2\ r23\^3\ v12 + 3\ r23\^3\ r34\^2\ v34 + 6\ m2\ r23\^3\ r34\^2\ v34 + 3\ m2\^2\ r23\^3\ r34\^2\ v34)\)\)\), \(-\(\(1\/\(\((1 + \ m2)\)\^2\ \((1 + m3)\)\^2\)\) \((3\ \((m3\ r12\^2\ v12 + 2\ m2\ m3\ r12\^2\ v12 + m2\^2\ m3\ r12\^2\ v12 - m2\ r13\^2\ v13 - 2\ m2\ m3\ r13\^2\ v13 - m2\ m3\^2\ r13\^2\ v13 - m2\ r24\^2\ v24 - 2\ m2\ m3\ r24\^2\ v24 - m2\ m3\^2\ r24\^2\ v24 + m3\ r34\^2\ v34 + 2\ m2\ m3\ r34\^2\ v34 + m2\^2\ m3\ r34\^2\ v34)\))\)\)\), \(-\(\(1\/\((1 + m3)\)\^2\ \) \((\(-m3\) - m3\ r23\^3 + 3\ r13\^2\ r23\^3\ v13 + 6\ m3\ r13\^2\ r23\^3\ v13 + 3\ m3\^2\ r13\^2\ r23\^3\ v13 + 3\ r23\^3\ r24\^2\ v24 + 6\ m3\ r23\^3\ r24\^2\ v24 + 3\ m3\^2\ r23\^3\ r24\^2\ v24)\)\)\)}\)], "Output"] }, Open ]], Cell["\<\ Look at the t^2 terms which are linear in the new variable uij. Solve five of the equations to find the uij. It turns out (for some reason) that the resulting solution works for all nine equations. \ \>", "Text"], Cell[CellGroupData[{ Cell[BoxData[{ \(Ft2\ = \ Numerator[Ft2]\), "\[IndentingNewLine]", \(\(Ft2five\ = \ Ft2[\([{1, 2, 4, 5, 7}]\)];\)\), "\[IndentingNewLine]", \(\(\(usol\ = \ \(Solve[ Ft2five \[Equal] {0, 0, 0, 0, 0}, {u12, u13, u23, u24, u34}]\)[\([1]\)] /. sub1 // FullSimplify\)\(\[IndentingNewLine]\) \)\), "\[IndentingNewLine]", \(\((Ft2 /. usol // Factor)\) /. sub1 // Simplify\)}], "Input"], Cell[BoxData[ \({r23\^3\ \((\(-2\)\ m2\ m3 - m3\ r12\ r13\^2 - m2\ m3\ r12\ r13\^2 - m3\ r12\ r24\^2 - m2\ m3\ r12\ r24\^2 + 3\ r12\ r13\^2\ u13 + 3\ m2\ r12\ r13\^2\ u13 + 3\ m3\ r12\ r13\^2\ u13 + 3\ m2\ m3\ r12\ r13\^2\ u13 + 2\ m3\ r12\ r23\ u23 + 2\ m2\ m3\ r12\ r23\ u23 - 3\ m3\ r12\ r24\^2\ u24 - 3\ m2\ m3\ r12\ r24\^2\ u24 - 3\ m3\^2\ r12\ r24\^2\ u24 - 3\ m2\ m3\^2\ r12\ r24\^2\ u24)\), r23\^3\ \((\(-2\)\ m2\ m3 - m2\ r12\^2\ r13 - m2\ m3\ r12\^2\ r13 - m2\ r13\ r34\^2 - m2\ m3\ r13\ r34\^2 + 3\ r12\^2\ r13\ u12 + 3\ m2\ r12\^2\ r13\ u12 + 3\ m3\ r12\^2\ r13\ u12 + 3\ m2\ m3\ r12\^2\ r13\ u12 + 2\ m2\ r13\ r23\ u23 + 2\ m2\ m3\ r13\ r23\ u23 - 3\ m2\ r13\ r34\^2\ u34 - 3\ m2\^2\ r13\ r34\^2\ u34 - 3\ m2\ m3\ r13\ r34\^2\ u34 - 3\ m2\^2\ m3\ r13\ r34\^2\ u34)\), r23\ \((m2\^2\ m3\ r12\^2 - m2\ m3\^2\ r12\^2 - m2\^2\ m3\ r13\^2 + m2\ m3\^2\ r13\^2 + m2\^2\ m3\ r24\^2 - m2\ m3\^2\ r24\^2 - m2\^2\ m3\ r34\^2 + m2\ m3\^2\ r34\^2 + 3\ m3\^2\ r12\^2\ r23\^2\ u12 + 6\ m2\ m3\^2\ r12\^2\ r23\^2\ u12 + 3\ m2\^2\ m3\^2\ r12\^2\ r23\^2\ u12 + 3\ m2\^2\ r13\^2\ r23\^2\ u13 + 6\ m2\^2\ m3\ r13\^2\ r23\^2\ u13 + 3\ m2\^2\ m3\^2\ r13\^2\ r23\^2\ u13 + 3\ m2\ m3\ r23\^2\ r24\^2\ u24 + 6\ m2\ m3\^2\ r23\^2\ r24\^2\ u24 + 3\ m2\ m3\^3\ r23\^2\ r24\^2\ u24 + 3\ m2\ m3\ r23\^2\ r34\^2\ u34 + 6\ m2\^2\ m3\ r23\^2\ r34\^2\ u34 + 3\ m2\^3\ m3\ r23\^2\ r34\^2\ u34)\), \(-m2\)\ m3\ r12\^2 + m2\^2\ m3\^2\ r12\^2 - m2\ m3\ r13\^2 + m2\^2\ m3\^2\ r13\^2 + m2\ m3\ r24\^2 - m2\^2\ m3\^2\ r24\^2 + m2\ m3\ r34\^2 - m2\^2\ m3\^2\ r34\^2 + 3\ m3\ r12\^2\ u12 + 6\ m2\ m3\ r12\^2\ u12 + 3\ m2\^2\ m3\ r12\^2\ u12 + 3\ m2\ r13\^2\ u13 + 6\ m2\ m3\ r13\^2\ u13 + 3\ m2\ m3\^2\ r13\^2\ u13 + 3\ m2\^2\ m3\ r24\^2\ u24 + 6\ m2\^2\ m3\^2\ r24\^2\ u24 + 3\ m2\^2\ m3\^3\ r24\^2\ u24 + 3\ m2\ m3\^2\ r34\^2\ u34 + 6\ m2\^2\ m3\^2\ r34\^2\ u34 + 3\ m2\^3\ m3\^2\ r34\^2\ u34, m3\ r23\^3\ \((\(-2\)\ m2 - m2\ r12\^2\ r24 - m2\ m3\ r12\^2\ r24 - m2\ r24\ r34\^2 - m2\ m3\ r24\ r34\^2 - 3\ r12\^2\ r24\ u12 - 3\ m2\ r12\^2\ r24\ u12 - 3\ m3\ r12\^2\ r24\ u12 - 3\ m2\ m3\ r12\^2\ r24\ u12 + 2\ m2\ r23\ r24\ u23 + 2\ m2\ m3\ r23\ r24\ u23 + 3\ m2\ r24\ r34\^2\ u34 + 3\ m2\^2\ r24\ r34\^2\ u34 + 3\ m2\ m3\ r24\ r34\^2\ u34 + 3\ m2\^2\ m3\ r24\ r34\^2\ u34)\), m2\ r23\^3\ \((\(-2\)\ m3 - m3\ r13\^2\ r34 - m2\ m3\ r13\^2\ r34 - m3\ r24\^2\ r34 - m2\ m3\ r24\^2\ r34 - 3\ r13\^2\ r34\ u13 - 3\ m2\ r13\^2\ r34\ u13 - 3\ m3\ r13\^2\ r34\ u13 - 3\ m2\ m3\ r13\^2\ r34\ u13 + 2\ m3\ r23\ r34\ u23 + 2\ m2\ m3\ r23\ r34\ u23 + 3\ m3\ r24\^2\ r34\ u24 + 3\ m2\ m3\ r24\^2\ r34\ u24 + 3\ m3\^2\ r24\^2\ r34\ u24 + 3\ m2\ m3\^2\ r24\^2\ r34\ u24)\), \(-3\)\ r23\^3\ \((r12\^2\ u12 \ + r34\^2\ u34)\), \(-3\)\ \((m3\ r12\^2\ u12 + 2\ m2\ m3\ r12\^2\ u12 + m2\^2\ m3\ r12\^2\ u12 - m2\ r13\^2\ u13 - 2\ m2\ m3\ r13\^2\ u13 - m2\ m3\^2\ r13\^2\ u13 - m2\ r24\^2\ u24 - 2\ m2\ m3\ r24\^2\ u24 - m2\ m3\^2\ r24\^2\ u24 + m3\ r34\^2\ u34 + 2\ m2\ m3\ r34\^2\ u34 + m2\^2\ m3\ r34\^2\ u34)\), \(-3\)\ r23\^3\ \((r13\^2\ u13 + r24\^2\ u24)\)}\)], "Output"], Cell[BoxData[ \({u13 \[Rule] \(-\(\((m3\ \((\(-2\)\ m2\^2\ \((1 + m3)\)\^2\ r13\ r24 + \ \((1 + m2)\)\ \((1 + m3)\)\ \((\(-1\) + m2 + 2\ m2\ m3)\)\ r12\^3\ r13\ r24 + \((1 + m2)\)\ r12\ \((\((1 + m2)\)\ m3\ r24 - \((1 + m2)\)\ \((1 + m3)\)\ r13\^3\ r24 - \((\(-1\) + m2 + 2\ m2\ m3)\)\ r13\ \((\(-1\) + \((1 + m3)\)\ r24\^3)\) + \((1 + m2)\)\ \((1 + m3)\)\ r13\ r24\ r34\^2)\))\))\)/\((3\ \((1 + \ m2)\)\^2\ \((1 + m3)\)\^3\ r12\ r13\^3\ r24)\)\)\), u24 \[Rule] \((\(-2\)\ m2\ \((1 + m3)\)\^2\ r13\ r24 - \((1 + m2)\)\ \((1 + m3)\)\ \((\(-2\) + \((\(-1\) + m2)\)\ m3)\)\ r12\^3\ r13\ r24 + \((1 + m2)\)\ r12\ \((\((1 + m2)\)\ m3\^2\ r24 - \((1 + m2)\)\ m3\ \((1 + m3)\)\ r13\^3\ r24 + \((\(-2\) + \((\(-1\) + m2)\)\ m3)\)\ r13\ \((\(-1\) + \((1 + m3)\)\ r24\^3)\) + \((1 + m2)\)\ m3\ \((1 + m3)\)\ r13\ r24\ r34\^2)\))\)/\((3\ \((1 + m2)\)\^2\ \ \((1 + m3)\)\^3\ r12\ r13\ r24\^3)\), u23 \[Rule] \(m3\ r24 + r13\ \((1 + \((1 + m3)\)\ r24\ \((r12\^2 + \ r34\^2)\))\)\)\/\(2\ \((1 + m3)\)\ r13\ r23\ r24\), u12 \[Rule] \(m2\ \((\(-r13\) + m3\ r24)\)\)\/\(3\ \((1 + m2)\)\^2\ \ \((1 + m3)\)\ r12\^2\ r13\ r24\), u34 \[Rule] \(m2\ \((r13 - m3\ r24)\)\)\/\(3\ \((1 + m2)\)\^2\ \((1 + \ m3)\)\ r13\ r24\ r34\^2\)}\)], "Output"], Cell[BoxData[ \({0, 0, 0, 0, 0, 0, 0, 0, 0}\)], "Output"] }, Open ]], Cell["\<\ Now make a substitution to go on to the next order. This gives linear equations for the vij. We find the augmented matrix of this system of \ nine equations and five unknowns. \ \>", "Text"], Cell[CellGroupData[{ Cell[BoxData[{ \(\(Ft3u\ = \(Ft3 /. usol // Factor\) // Numerator;\)\), "\[IndentingNewLine]", \(augv[f_]\ := \ {Coefficient[f, v12], Coefficient[f, v13], Coefficient[f, v23], Coefficient[f, v24], Coefficient[f, v34], f /. {v12 \[Rule] 0, v13 \[Rule] 0, v23 \[Rule] 0, v24 \[Rule] 0, v34 \[Rule] 0}}\), "\[IndentingNewLine]", \(\(Ft3umatrix\ = \ Map[augv, Ft3u] /. sub1 // Factor;\)\), "\[IndentingNewLine]", \(Ft3umatrix // MatrixForm\)}], "Input"], Cell[BoxData[ TagBox[ RowBox[{"(", "\[NoBreak]", GridBox[{ { "0", \(\(-3\)\ \((1 + m3)\)\^2\ r12\ r13\^2\ r23\), \(2\ m3\ \ \((1 + m3)\)\ r12\), \(3\ m3\ \((1 + m3)\)\^2\ r12\ r23\ r24\^2\), "0", \(m3\ r12\ \((m3 + r23)\)\)}, {\(\(-3\)\ \((1 + m2)\)\^2\ r12\^2\ r13\ r23\), "0", \(2\ m2\ \((1 + m2)\)\ r13\), "0", \(3\ m2\ \((1 + m2)\)\^2\ r13\ r23\ r34\^2\), \(m2\ r13\ \ \((m2 + r23)\)\)}, {\(\(-3\)\ \((1 + m2)\)\^2\ m3\^2\ r12\^2\ r23\), \(\(-3\)\ m2\^2\ \ \((1 + m3)\)\^2\ r13\^2\ r23\), "0", \(\(-3\)\ m2\ m3\ \((1 + m3)\)\^2\ r23\ r24\^2\), \(\(-3\)\ \ m2\ \((1 + m2)\)\^2\ m3\ r23\ r34\^2\), \(\(-2\)\ m2\ m3\ \((m2 + m3)\)\)}, {\(3\ \((1 + m2)\)\^2\ m3\ r12\^2\), \(3\ m2\ \((1 + m3)\)\^2\ \ r13\^2\), "0", \(3\ m2\^2\ m3\ \((1 + m3)\)\^2\ r24\^2\), \(3\ m2\ \((1 + \ m2)\)\^2\ m3\^2\ r34\^2\), \(\(-2\)\ m2\ m3\ \((1 + m2\ m3)\)\)}, {\(3\ \((1 + m2)\)\^2\ m3\ r12\^2\ r23\ r24\), "0", \(2\ m2\ \((1 + m2)\)\ m3\ r24\), "0", \(\(-3\)\ m2\ \((1 + m2)\)\^2\ m3\ r23\ r24\ r34\^2\), \ \(m2\ m3\ \((1 + m2\ r23)\)\ r24\)}, { "0", \(3\ m2\ \((1 + m3)\)\^2\ r13\^2\ r23\ r34\), \(2\ m2\ m3\ \ \((1 + m3)\)\ r34\), \(\(-3\)\ m2\ m3\ \((1 + m3)\)\^2\ r23\ r24\^2\ r34\), "0", \(m2\ m3\ \((1 + m3\ r23)\)\ r34\)}, {\(3\ \((1 + m2)\)\^2\ r12\^2\ r23\), "0", "0", "0", \(3\ \((1 + m2)\)\^2\ r23\ r34\^2\), \(\(-m2\)\ \((\(-1\) \ + r23)\)\)}, {\(\(-3\)\ \((1 + m2)\)\^2\ m3\ r12\^2\), \(3\ m2\ \((1 + \ m3)\)\^2\ r13\^2\), "0", \(3\ m2\ \((1 + m3)\)\^2\ r24\^2\), \(\(-3\)\ \((1 + m2)\)\ \^2\ m3\ r34\^2\), "0"}, {"0", \(3\ \((1 + m3)\)\^2\ r13\^2\ r23\), "0", \(3\ \((1 + m3)\)\^2\ r23\ r24\^2\), "0", \(\(-m3\)\ \((\(-1\) + r23)\)\)} }], "\[NoBreak]", ")"}], Function[ BoxForm`e$, MatrixForm[ BoxForm`e$]]]], "Output"] }, Open ]], Cell["\<\ The resulting augmented matrix has rank six which shows that the system is inconsistent. \ \>", "Text"], Cell[CellGroupData[{ Cell[BoxData[{ \(\(\((\(Det[Ft3umatrix[\([{1, 2, 3, 4, 5, 7}]\)]] /. sub1 // Factor\) // Numerator)\);\)\), "\[IndentingNewLine]", \(% /. sub1 // Factor\)}], "Input"], Cell[BoxData[ \(\(-324\)\ m2\^4\ \((1 + m2)\)\^7\ m3\^4\ \((1 + m3)\)\^3\ r23\ \((1 + r23)\)\ r34\^2\)], "Output"] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell["Facet 33", "Subsection"], Cell["\<\ If the mass polynomials for the reduced equations do not vanish then we are done. Since we are assuming positive masses, the only way for these polynomials to vanish is to have Q = 0 and this implies that m1= m2 and \ m3= m4. So without loss of generality, we may begin with the equations and the mass substitutions m1=m2 and m3 = m4 = 1. \ \>", "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(eqs33\ = \ acdzeqs /. {m4 \[Rule] 1, m3 \[Rule] 1, m2 -> m1}\)], "Input"], Cell[BoxData[ \({\(-r12\^3\)\ r13\^3\ r14\^3\ r23\^3 + r12\ r13\^3\ r14\^5\ r23\^3 - r12\ r13\^3\ r14\^3\ r23\^3\ r24\^2 - r12\^3\ r13\^3\ r14\^3\ r24\^3 + r12\ r13\^5\ r14\^3\ r24\^3 - r12\ r13\^3\ r14\^3\ r23\^2\ r24\^3 - r12\^3\ r13\^3\ r23\^3\ r24\^3 - r12\ r13\^3\ r14\^2\ r23\^3\ r24\^3 - r12\^3\ r14\^3\ r23\^3\ r24\^3 - r12\ r13\^2\ r14\^3\ r23\^3\ r24\^3 - 4\ m1\ r13\^3\ r14\^3\ r23\^3\ r24\^3 + 4\ r12\^3\ r13\^3\ r14\^3\ r23\^3\ r24\^3 + 4\ m1\ r12\^3\ r13\^3\ r14\^3\ r23\^3\ r24\^3 + r12\ r14\^3\ r23\^5\ r24\^3 + r12\ r13\^3\ r23\^3\ r24\^5, \(-r12\^3\)\ r13\^3\ r14\^3\ r23\^3 + r12\^3\ r13\ r14\^5\ r23\^3 - r12\^3\ r13\ r14\^3\ r23\^3\ r34\^2 + m1\ r12\^5\ r13\ r14\^3\ r34\^3 - m1\ r12\^3\ r13\^3\ r14\^3\ r34\^3 - m1\ r12\^3\ r13\ r14\^3\ r23\^2\ r34\^3 - r12\^3\ r13\^3\ r23\^3\ r34\^3 - r12\^3\ r13\ r14\^2\ r23\^3\ r34\^3 - 2\ r12\^3\ r14\^3\ r23\^3\ r34\^3 - 2\ m1\ r12\^3\ r14\^3\ r23\^3\ r34\^3 - m1\ r12\^2\ r13\ r14\^3\ r23\^3\ r34\^3 - m1\ r13\^3\ r14\^3\ r23\^3\ r34\^3 + 4\ r12\^3\ r13\^3\ r14\^3\ r23\^3\ r34\^3 + 4\ m1\ r12\^3\ r13\^3\ r14\^3\ r23\^3\ r34\^3 + m1\ r13\ r14\^3\ r23\^5\ r34\^3 + r12\^3\ r13\ r23\^3\ r34\^5, \(-r12\^3\)\ r13\^3\ r23\^3\ r24\^3 + r12\^3\ r13\^3\ r23\ r24\^5 - r12\^3\ r13\^3\ r23\ r24\^3\ r34\^2 - r12\^3\ r13\^3\ r23\^3\ r34\^3 - r12\^3\ r13\^3\ r23\ r24\^2\ r34\^3 - 2\ r12\^3\ r13\^3\ r24\^3\ r34\^3 - 2\ m1\ r12\^3\ r13\^3\ r24\^3\ r34\^3 + m1\ r12\^5\ r23\ r24\^3\ r34\^3 - m1\ r12\^3\ r13\^2\ r23\ r24\^3\ r34\^3 - m1\ r12\^2\ r13\^3\ r23\ r24\^3\ r34\^3 + m1\ r13\^5\ r23\ r24\^3\ r34\^3 - m1\ r12\^3\ r23\^3\ r24\^3\ r34\^3 - m1\ r13\^3\ r23\^3\ r24\^3\ r34\^3 + 4\ r12\^3\ r13\^3\ r23\^3\ r24\^3\ r34\^3 + 4\ m1\ r12\^3\ r13\^3\ r23\^3\ r24\^3\ r34\^3 + r12\^3\ r13\^3\ r23\ r34\^5, r12\^3\ r13\^5\ r14\ r24\^3 - r12\^3\ r13\^3\ r14\^3\ r24\^3 - r12\^3\ r13\^3\ r14\ r24\^3\ r34\^2 + m1\ r12\^5\ r13\^3\ r14\ r34\^3 - m1\ r12\^3\ r13\^3\ r14\^3\ r34\^3 - m1\ r12\^3\ r13\^3\ r14\ r24\^2\ r34\^3 - 2\ r12\^3\ r13\^3\ r24\^3\ r34\^3 - 2\ m1\ r12\^3\ r13\^3\ r24\^3\ r34\^3 - r12\^3\ r13\^2\ r14\ r24\^3\ r34\^3 - m1\ r12\^2\ r13\^3\ r14\ r24\^3\ r34\^3 - r12\^3\ r14\^3\ r24\^3\ r34\^3 - m1\ r13\^3\ r14\^3\ r24\^3\ r34\^3 + 4\ r12\^3\ r13\^3\ r14\^3\ r24\^3\ r34\^3 + 4\ m1\ r12\^3\ r13\^3\ r14\^3\ r24\^3\ r34\^3 + m1\ r13\^3\ r14\ r24\^5\ r34\^3 + r12\^3\ r14\ r24\^3\ r34\^5, r12\^3\ r14\^3\ r23\^5\ r24 - r12\^3\ r14\^3\ r23\^3\ r24\^3 - r12\^3\ r14\^3\ r23\^3\ r24\ r34\^2 - 2\ r12\^3\ r14\^3\ r23\^3\ r34\^3 - 2\ m1\ r12\^3\ r14\^3\ r23\^3\ r34\^3 - r12\^3\ r14\^3\ r23\^2\ r24\ r34\^3 + m1\ r12\^5\ r23\^3\ r24\ r34\^3 - m1\ r12\^3\ r14\^2\ r23\^3\ r24\ r34\^3 - m1\ r12\^2\ r14\^3\ r23\^3\ r24\ r34\^3 + m1\ r14\^5\ r23\^3\ r24\ r34\^3 - r12\^3\ r14\^3\ r24\^3\ r34\^3 - m1\ r12\^3\ r23\^3\ r24\^3\ r34\^3 - m1\ r14\^3\ r23\^3\ r24\^3\ r34\^3 + 4\ r12\^3\ r14\^3\ r23\^3\ r24\^3\ r34\^3 + 4\ m1\ r12\^3\ r14\^3\ r23\^3\ r24\^3\ r34\^3 + r12\^3\ r14\^3\ r24\ r34\^5, \(-4\)\ r13\^3\ r14\^3\ r23\^3\ r24\^3 + m1\ r13\^3\ r14\^3\ r23\^5\ r34 - m1\ r13\^3\ r14\^3\ r23\^3\ r24\^2\ r34 - m1\ r13\^3\ r14\^3\ r23\^2\ r24\^3\ r34 + m1\ r13\^5\ r23\^3\ r24\^3\ r34 - m1\ r13\^3\ r14\^2\ r23\^3\ r24\^3\ r34 - m1\ r13\^2\ r14\^3\ r23\^3\ r24\^3\ r34 + m1\ r14\^5\ r23\^3\ r24\^3\ r34 + m1\ r13\^3\ r14\^3\ r24\^5\ r34 - m1\ r13\^3\ r14\^3\ r23\^3\ r34\^3 - m1\ r13\^3\ r14\^3\ r24\^3\ r34\^3 - m1\ r13\^3\ r23\^3\ r24\^3\ r34\^3 - m1\ r14\^3\ r23\^3\ r24\^3\ r34\^3 + 4\ r13\^3\ r14\^3\ r23\^3\ r24\^3\ r34\^3 + 4\ m1\ r13\^3\ r14\^3\ r23\^3\ r24\^3\ r34\^3, r14\^3\ r23\^3 - r12\^3\ r14\^3\ r23\^3 - r12\^3\ r34\^3 + r12\^3\ r14\^3\ r34\^3 + r12\^3\ r23\^3\ r34\^3 - r14\^3\ r23\^3\ r34\^3, r13\^3\ r24\^3 - r12\^3\ r13\^3\ r24\^3 - r12\^3\ r34\^3 + r12\^3\ r13\^3\ r34\^3 + r12\^3\ r24\^3\ r34\^3 - r13\^3\ r24\^3\ r34\^3, r14\^3\ r23\^3 - r13\^3\ r14\^3\ r23\^3 - r13\^3\ r24\^3 + r13\^3\ r14\^3\ r24\^3 + r13\^3\ r23\^3\ r24\^3 - r14\^3\ r23\^3\ r24\^3}\)], "Output"] }, Open ]], Cell["\<\ Make a change of variables corresponding to the normal vector alpha33=(0,-1,-1,-1,-1,0). After this substitution, we will be looking for series solutions for all variables starting with the power t^0, except r13 will be gone (without loss of generality, we can look for a Puiseux solution with r13 = 1/t) \ \>", "Text"], Cell[CellGroupData[{ Cell[BoxData[{ \(sub0\ = \ {r13 \[Rule] 1/t, r14 \[Rule] r14/t, r23 \[Rule] r23/t, r24 \[Rule] r24/t}\), "\[IndentingNewLine]", \(eqs331 = \(eqs33 /. sub0 // Factor\) // Numerator\)}], "Input"], Cell[BoxData[ \({r13 \[Rule] 1\/t, r14 \[Rule] r14\/t, r23 \[Rule] r23\/t, r24 \[Rule] r24\/t}\)], "Output"], Cell[BoxData[ \({\(-4\)\ m1\ r14\^3\ r23\^3\ r24\^3 + 4\ r12\^3\ r14\^3\ r23\^3\ r24\^3 + 4\ m1\ r12\^3\ r14\^3\ r23\^3\ r24\^3 + r12\ r14\^5\ r23\^3\ t - r12\ r14\^3\ r23\^3\ r24\^2\ t + r12\ r14\^3\ r24\^3\ t - r12\ r14\^3\ r23\^2\ r24\^3\ t - r12\ r14\^2\ r23\^3\ r24\^3\ t - r12\ r14\^3\ r23\^3\ r24\^3\ t + r12\ r14\^3\ r23\^5\ r24\^3\ t + r12\ r23\^3\ r24\^5\ t - r12\^3\ r14\^3\ r23\^3\ t\^3 - r12\^3\ r14\^3\ r24\^3\ t\^3 - r12\^3\ r23\^3\ r24\^3\ t\^3 - r12\^3\ r14\^3\ r23\^3\ r24\^3\ t\^3, \(-r12\^3\)\ r14\^3\ r23\^3 + r12\^3\ r14\^5\ r23\^3 - m1\ r14\^3\ r23\^3\ r34\^3 + 4\ r12\^3\ r14\^3\ r23\^3\ r34\^3 + 4\ m1\ r12\^3\ r14\^3\ r23\^3\ r34\^3 + m1\ r14\^3\ r23\^5\ r34\^3 - r12\^3\ r14\^3\ r23\^3\ r34\^2\ t\^2 - m1\ r12\^2\ r14\^3\ r23\^3\ r34\^3\ t\^2 - m1\ r12\^3\ r14\^3\ r34\^3\ t\^3 - m1\ r12\^3\ r14\^3\ r23\^2\ r34\^3\ t\^3 - r12\^3\ r23\^3\ r34\^3\ t\^3 - r12\^3\ r14\^2\ r23\^3\ r34\^3\ t\^3 - 2\ r12\^3\ r14\^3\ r23\^3\ r34\^3\ t\^3 - 2\ m1\ r12\^3\ r14\^3\ r23\^3\ r34\^3\ t\^3 + m1\ r12\^5\ r14\^3\ r34\^3\ t\^5 + r12\^3\ r23\^3\ r34\^5\ t\^5, \(-r12\^3\)\ r23\^3\ r24\^3 + r12\^3\ r23\ r24\^5 + m1\ r23\ r24\^3\ r34\^3 - m1\ r23\^3\ r24\^3\ r34\^3 + 4\ r12\^3\ r23\^3\ r24\^3\ r34\^3 + 4\ m1\ r12\^3\ r23\^3\ r24\^3\ r34\^3 - r12\^3\ r23\ r24\^3\ r34\^2\ t\^2 - m1\ r12\^2\ r23\ r24\^3\ r34\^3\ t\^2 - r12\^3\ r23\^3\ r34\^3\ t\^3 - r12\^3\ r23\ r24\^2\ r34\^3\ t\^3 - 2\ r12\^3\ r24\^3\ r34\^3\ t\^3 - 2\ m1\ r12\^3\ r24\^3\ r34\^3\ t\^3 - m1\ r12\^3\ r23\ r24\^3\ r34\^3\ t\^3 - m1\ r12\^3\ r23\^3\ r24\^3\ r34\^3\ t\^3 + m1\ r12\^5\ r23\ r24\^3\ r34\^3\ t\^5 + r12\^3\ r23\ r34\^5\ t\^5, r12\^3\ r14\ r24\^3 - r12\^3\ r14\^3\ r24\^3 - m1\ r14\^3\ r24\^3\ r34\^3 + 4\ r12\^3\ r14\^3\ r24\^3\ r34\^3 + 4\ m1\ r12\^3\ r14\^3\ r24\^3\ r34\^3 + m1\ r14\ r24\^5\ r34\^3 - r12\^3\ r14\ r24\^3\ r34\^2\ t\^2 - m1\ r12\^2\ r14\ r24\^3\ r34\^3\ t\^2 - m1\ r12\^3\ r14\^3\ r34\^3\ t\^3 - m1\ r12\^3\ r14\ r24\^2\ r34\^3\ t\^3 - 2\ r12\^3\ r24\^3\ r34\^3\ t\^3 - 2\ m1\ r12\^3\ r24\^3\ r34\^3\ t\^3 - r12\^3\ r14\ r24\^3\ r34\^3\ t\^3 - r12\^3\ r14\^3\ r24\^3\ r34\^3\ t\^3 + m1\ r12\^5\ r14\ r34\^3\ t\^5 + r12\^3\ r14\ r24\^3\ r34\^5\ t\^5, r12\^3\ r14\^3\ r23\^5\ r24 - r12\^3\ r14\^3\ r23\^3\ r24\^3 + m1\ r14\^5\ r23\^3\ r24\ r34\^3 - m1\ r14\^3\ r23\^3\ r24\^3\ r34\^3 + 4\ r12\^3\ r14\^3\ r23\^3\ r24\^3\ r34\^3 + 4\ m1\ r12\^3\ r14\^3\ r23\^3\ r24\^3\ r34\^3 - r12\^3\ r14\^3\ r23\^3\ r24\ r34\^2\ t\^2 - m1\ r12\^2\ r14\^3\ r23\^3\ r24\ r34\^3\ t\^2 - 2\ r12\^3\ r14\^3\ r23\^3\ r34\^3\ t\^3 - 2\ m1\ r12\^3\ r14\^3\ r23\^3\ r34\^3\ t\^3 - r12\^3\ r14\^3\ r23\^2\ r24\ r34\^3\ t\^3 - m1\ r12\^3\ r14\^2\ r23\^3\ r24\ r34\^3\ t\^3 - r12\^3\ r14\^3\ r24\^3\ r34\^3\ t\^3 - m1\ r12\^3\ r23\^3\ r24\^3\ r34\^3\ t\^3 + m1\ r12\^5\ r23\^3\ r24\ r34\^3\ t\^5 + r12\^3\ r14\^3\ r24\ r34\^5\ t\^5, \(-4\)\ r14\^3\ r23\^3\ r24\^3 + 4\ r14\^3\ r23\^3\ r24\^3\ r34\^3 + 4\ m1\ r14\^3\ r23\^3\ r24\^3\ r34\^3 + m1\ r14\^3\ r23\^5\ r34\ t - m1\ r14\^3\ r23\^3\ r24\^2\ r34\ t - m1\ r14\^3\ r23\^2\ r24\^3\ r34\ t + m1\ r23\^3\ r24\^3\ r34\ t - m1\ r14\^2\ r23\^3\ r24\^3\ r34\ t - m1\ r14\^3\ r23\^3\ r24\^3\ r34\ t + m1\ r14\^5\ r23\^3\ r24\^3\ r34\ t + m1\ r14\^3\ r24\^5\ r34\ t - m1\ r14\^3\ r23\^3\ r34\^3\ t\^3 - m1\ r14\^3\ r24\^3\ r34\^3\ t\^3 - m1\ r23\^3\ r24\^3\ r34\^3\ t\^3 - m1\ r14\^3\ r23\^3\ r24\^3\ r34\^3\ t\^3, r14\^3\ r23\^3 - r12\^3\ r14\^3\ r23\^3 - r14\^3\ r23\^3\ r34\^3 + r12\^3\ r14\^3\ r34\^3\ t\^3 + r12\^3\ r23\^3\ r34\^3\ t\^3 - r12\^3\ r34\^3\ t\^6, r24\^3 - r12\^3\ r24\^3 - r24\^3\ r34\^3 + r12\^3\ r34\^3\ t\^3 + r12\^3\ r24\^3\ r34\^3\ t\^3 - r12\^3\ r34\^3\ t\^6, \(-r14\^3\)\ r23\^3 + r14\^3\ r24\^3 + r23\^3\ r24\^3 - r14\^3\ r23\^3\ r24\^3 + r14\^3\ r23\^3\ t\^3 - r24\^3\ t\^3}\)], "Output"] }, Open ]], Cell["\<\ Here are the lowest order terms in t. The order 0 terms are equivalent to the reduced system red33. \ \>", "Text"], Cell[CellGroupData[{ Cell[BoxData[{ \(F0\ = \ eqs331 /. t \[Rule] 0 // Factor\), "\[IndentingNewLine]", \(F1\ = \ Coefficient[eqs331, t] // Factor\), "\[IndentingNewLine]", \(F2\ = \ Coefficient[eqs331, t^2] // Factor\), "\[IndentingNewLine]", \(F3\ = \ Coefficient[eqs331, t^3] // Factor\), "\[IndentingNewLine]", \(\(F\ = \ F0\ + \ t*F1\ + \ t^2*F2\ + \ t^3*F3;\)\)}], "Input"], Cell[BoxData[ \({4\ \((\(-m1\) + r12\^3 + m1\ r12\^3)\)\ r14\^3\ r23\^3\ r24\^3, r14\^3\ r23\^3\ \((\(-r12\^3\) + r12\^3\ r14\^2 - m1\ r34\^3 + 4\ r12\^3\ r34\^3 + 4\ m1\ r12\^3\ r34\^3 + m1\ r23\^2\ r34\^3)\), r23\ r24\^3\ \((\(-r12\^3\)\ r23\^2 + r12\^3\ r24\^2 + m1\ r34\^3 - m1\ r23\^2\ r34\^3 + 4\ r12\^3\ r23\^2\ r34\^3 + 4\ m1\ r12\^3\ r23\^2\ r34\^3)\), r14\ r24\^3\ \((r12\^3 - r12\^3\ r14\^2 - m1\ r14\^2\ r34\^3 + 4\ r12\^3\ r14\^2\ r34\^3 + 4\ m1\ r12\^3\ r14\^2\ r34\^3 + m1\ r24\^2\ r34\^3)\), r14\^3\ r23\^3\ r24\ \((r12\^3\ r23\^2 - r12\^3\ r24\^2 + m1\ r14\^2\ r34\^3 - m1\ r24\^2\ r34\^3 + 4\ r12\^3\ r24\^2\ r34\^3 + 4\ m1\ r12\^3\ r24\^2\ r34\^3)\), 4\ r14\^3\ r23\^3\ r24\^3\ \((\(-1\) + r34\^3 + m1\ r34\^3)\), \(-r14\^3\)\ r23\^3\ \((\(-1\) + r12\^3 + r34\^3)\), \(-r24\^3\)\ \((\(-1\) + r12\^3 + r34\^3)\), \(-r14\^3\)\ r23\^3 + r14\^3\ r24\^3 + r23\^3\ r24\^3 - r14\^3\ r23\^3\ r24\^3}\)], "Output"], Cell[BoxData[ \({r12\ \((r14\^5\ r23\^3 - r14\^3\ r23\^3\ r24\^2 + r14\^3\ r24\^3 - r14\^3\ r23\^2\ r24\^3 - r14\^2\ r23\^3\ r24\^3 - r14\^3\ r23\^3\ r24\^3 + r14\^3\ r23\^5\ r24\^3 + r23\^3\ r24\^5)\), 0, 0, 0, 0, m1\ \((r14\^3\ r23\^5 - r14\^3\ r23\^3\ r24\^2 - r14\^3\ r23\^2\ r24\^3 + r23\^3\ r24\^3 - r14\^2\ r23\^3\ r24\^3 - r14\^3\ r23\^3\ r24\^3 + r14\^5\ r23\^3\ r24\^3 + r14\^3\ r24\^5)\)\ r34, 0, 0, 0}\)], "Output"], Cell[BoxData[ \({0, \(-r12\^2\)\ r14\^3\ r23\^3\ r34\^2\ \((r12 + m1\ r34)\), \(-r12\^2\)\ r23\ r24\^3\ r34\^2\ \((r12 + m1\ r34)\), \(-r12\^2\)\ r14\ r24\^3\ r34\^2\ \((r12 + m1\ r34)\), \(-r12\^2\)\ r14\^3\ r23\^3\ r24\ r34\^2\ \((r12 + m1\ r34)\), 0, 0, 0, 0}\)], "Output"], Cell[BoxData[ \({\(-r12\^3\)\ \((r14\^3\ r23\^3 + r14\^3\ r24\^3 + r23\^3\ r24\^3 + r14\^3\ r23\^3\ r24\^3)\), \(-r12\^3\)\ \((m1\ r14\^3 + m1\ r14\^3\ r23\^2 + r23\^3 + r14\^2\ r23\^3 + 2\ r14\^3\ r23\^3 + 2\ m1\ r14\^3\ r23\^3)\)\ r34\^3, \(-r12\^3\)\ \((r23\^3 + r23\ r24\^2 + 2\ r24\^3 + 2\ m1\ r24\^3 + m1\ r23\ r24\^3 + m1\ r23\^3\ r24\^3)\)\ r34\^3, \(-r12\^3\)\ \((m1\ r14\^3 + m1\ r14\ r24\^2 + 2\ r24\^3 + 2\ m1\ r24\^3 + r14\ r24\^3 + r14\^3\ r24\^3)\)\ r34\^3, \(-r12\^3\)\ \((2\ r14\^3\ r23\^3 + 2\ m1\ r14\^3\ r23\^3 + r14\^3\ r23\^2\ r24 + m1\ r14\^2\ r23\^3\ r24 + r14\^3\ r24\^3 + m1\ r23\^3\ r24\^3)\)\ r34\^3, \(-m1\)\ \((r14\^3\ r23\^3 + r14\^3\ r24\^3 + r23\^3\ r24\^3 + r14\^3\ r23\^3\ r24\^3)\)\ r34\^3, r12\^3\ \((r14 + r23)\)\ \((r14\^2 - r14\ r23 + r23\^2)\)\ r34\^3, r12\^3\ \((1 + r24)\)\ \((1 - r24 + r24\^2)\)\ r34\^3, \((r14\ r23 - r24)\)\ \((r14\^2\ r23\^2 + r14\ r23\ r24 + r24\^2)\)}\)], "Output"] }, Open ]], Cell["Solve the reduced system. ", "Text"], Cell["\<\ Solve the reduced system for the leading order terms of a Puiseux solution. We begin by \"cleaning up\" the equautions (eliminating factors of \ the indicated variables). \ \>", "Text"], Cell[CellGroupData[{ Cell[BoxData[{ \(\(allvars\ = \ {r12, r13, r14, r23, r24, r34, m1, m2, m3, m4};\)\), "\[IndentingNewLine]", \(F00 = \ Map[CleanUp[#, allvars] &, F0]\)}], "Input"], Cell[BoxData[ \({4\ \((\(-m1\) + r12\^3 + m1\ r12\^3)\), \(-r12\^3\) + r12\^3\ r14\^2 - m1\ r34\^3 + 4\ r12\^3\ r34\^3 + 4\ m1\ r12\^3\ r34\^3 + m1\ r23\^2\ r34\^3, \(-r12\^3\)\ r23\^2 + r12\^3\ r24\^2 + m1\ r34\^3 - m1\ r23\^2\ r34\^3 + 4\ r12\^3\ r23\^2\ r34\^3 + 4\ m1\ r12\^3\ r23\^2\ r34\^3, r12\^3 - r12\^3\ r14\^2 - m1\ r14\^2\ r34\^3 + 4\ r12\^3\ r14\^2\ r34\^3 + 4\ m1\ r12\^3\ r14\^2\ r34\^3 + m1\ r24\^2\ r34\^3, r12\^3\ r23\^2 - r12\^3\ r24\^2 + m1\ r14\^2\ r34\^3 - m1\ r24\^2\ r34\^3 + 4\ r12\^3\ r24\^2\ r34\^3 + 4\ m1\ r12\^3\ r24\^2\ r34\^3, 4\ \((\(-1\) + r34\^3 + m1\ r34\^3)\), 1 - r12\^3 - r34\^3, 1 - r12\^3 - r34\^3, \(-r14\^3\)\ r23\^3 + r14\^3\ r24\^3 + r23\^3\ r24\^3 - r14\^3\ r23\^3\ r24\^3}\)], "Output"] }, Open ]], Cell["\<\ Equations 1 and 5 are uniquely solveable for r12^3 and r34^3. We make these substitutions. \ \>", "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(F001\ = \ Map[CleanUp[#, allvars] &, F00 /. {r34^3 \[Rule] 1/\((1 + m1)\), r12^3 \[Rule] m1/\((1 + m1)\)}] // Factor\)], "Input"], Cell[BoxData[ \({0, \(2 + r14\^2 + r23\^2\)\/\(1 + m1\), \(1 + 2\ r23\^2 + \ r24\^2\)\/\(1 + m1\), \(1 + 2\ r14\^2 + r24\^2\)\/\(1 + m1\), \(r14\^2 + \ r23\^2 + 2\ r24\^2\)\/\(1 + m1\), 0, 0, 0, \(-r14\^3\)\ r23\^3 + r14\^3\ r24\^3 + r23\^3\ r24\^3 - r14\^3\ r23\^3\ r24\^3}\)], "Output"] }, Open ]], Cell["\<\ The second equation gives us r23^2 = -2 - r14^2, after which we are forced to choose r24=1 or -1. First consider r24 = 1 (which means r23^2 = - 3). The result forces us to a contradictary value of r23 -- thus r24 = 1 is impossible \ \>", "Text"], Cell[CellGroupData[{ Cell[BoxData[{ \(F002\ = \ Map[CleanUp[#, allvars] &, F001 /. {r23^2 \[Rule] \(-2\) - r14^2, r23^3 \[Rule] r23*\((\(-2\) - r14^2)\)}] // Factor\), "\[IndentingNewLine]", \(Map[CleanUp[#, allvars] &, F002 /. {r24 \[Rule] 1}] // Factor\), "\[IndentingNewLine]", \(Map[CleanUp[#, allvars] &, % /. {r14 \[Rule] I}] // Factor\)}], "Input"], Cell[BoxData[ \({0, 0, \(-\(\(3 + 2\ r14\^2 - r24\^2\)\/\(1 + m1\)\)\), \(1 + 2\ r14\^2 + r24\^2\)\/\(1 + m1\), \(2\ \ \((\(-1\) + r24)\)\ \((1 + r24)\)\)\/\(1 + m1\), 0, 0, 0, 2\ r14\^3\ r23 + r14\^5\ r23 + r14\^3\ r24\^3 - 2\ r23\ r24\^3 - r14\^2\ r23\ r24\^3 + 2\ r14\^3\ r23\ r24\^3 + r14\^5\ r23\ r24\^3}\)], "Output"], Cell[BoxData[ \({0, 0, \(-\(\(2\ \((1 + r14\^2)\)\)\/\(1 + m1\)\)\), \(2\ \((1 + r14\^2)\)\)\/\(1 + m1\), 0, 0, 0, 0, r14\^3 - 2\ r23 - r14\^2\ r23 + 4\ r14\^3\ r23 + 2\ r14\^5\ r23}\)], "Output"], Cell[BoxData[ \({0, 0, 0, 0, 0, 0, 0, 0, \(-\[ImaginaryI]\) - \((1 + 2\ \[ImaginaryI])\)\ r23}\)], "Output"] }, Open ]], Cell["\<\ Now we try r24 = -1. We are forced to pick r14 = -r23 = i or r14 = -r23 = - i \ \>", "Text"], Cell[CellGroupData[{ Cell[BoxData[{ \(Map[CleanUp[#, allvars] &, F002 /. {r24 \[Rule] \(-1\)}] // Factor\), "\[IndentingNewLine]", \(Map[CleanUp[#, allvars] &, % /. {r14 \[Rule] I}] // Factor\), "\[IndentingNewLine]", \(\(\(Map[CleanUp[#, allvars] &, % /. {r23 \[Rule] \(-I\)}] // Factor\)\(\[IndentingNewLine]\) \)\), "\[IndentingNewLine]", \(Map[CleanUp[#, allvars] &, F002 /. {r24 \[Rule] \(-1\)}] // Factor\), "\[IndentingNewLine]", \(Map[CleanUp[#, allvars] &, % /. {r14 \[Rule] \(-I\)}] // Factor\), "\[IndentingNewLine]", \(Map[CleanUp[#, allvars] &, % /. {r23 \[Rule] I}] // Factor\)}], "Input"], Cell[BoxData[ \({0, 0, \(-\(\(2\ \((1 + r14\^2)\)\)\/\(1 + m1\)\)\), \(2\ \((1 + r14\^2)\)\)\/\(1 + m1\), 0, 0, 0, 0, \(-r14\^3\) + 2\ r23 + r14\^2\ r23}\)], "Output"], Cell[BoxData[ \({0, 0, 0, 0, 0, 0, 0, 0, \[ImaginaryI] + r23}\)], "Output"], Cell[BoxData[ \({0, 0, 0, 0, 0, 0, 0, 0, 0}\)], "Output"], Cell[BoxData[ \({0, 0, \(-\(\(2\ \((1 + r14\^2)\)\)\/\(1 + m1\)\)\), \(2\ \((1 + r14\^2)\)\)\/\(1 + m1\), 0, 0, 0, 0, \(-r14\^3\) + 2\ r23 + r14\^2\ r23}\)], "Output"], Cell[BoxData[ \({0, 0, 0, 0, 0, 0, 0, 0, \(-\[ImaginaryI]\) + r23}\)], "Output"], Cell[BoxData[ \({0, 0, 0, 0, 0, 0, 0, 0, 0}\)], "Output"] }, Open ]], Cell["\<\ Here is the solution of the reduced system with r14 = -I and r23= I. The other case is similar. \ \>", "Text"], Cell[CellGroupData[{ Cell[BoxData[{ \(\(\(sub1 = {r34^3 \[Rule] 1/\((1 + m1)\), r12^3 \[Rule] m1/\((1 + m1)\), r14 \[Rule] \(-I\), r23 \[Rule] I, r24 \[Rule] \(-1\)}\)\(\[IndentingNewLine]\) \)\), "\[IndentingNewLine]", \(F00 /. sub1 // Factor\)}], "Input"], Cell[BoxData[ \({r34\^3 \[Rule] 1\/\(1 + m1\), r12\^3 \[Rule] m1\/\(1 + m1\), r14 \[Rule] \(-\[ImaginaryI]\), r23 \[Rule] \[ImaginaryI], r24 \[Rule] \(-1\)}\)], "Output"], Cell[BoxData[ \({0, 0, 0, 0, 0, 0, 0, 0, 0}\)], "Output"] }, Open ]], Cell["\<\ We want to show that the solution of the reduced system does not really determine a continuum of solutions by showing that the Puiseux series solutions cannot be continued to higher order terms. To do this we have to do some rescalings and substitutions. We have a system F(x,t) = F0(x) + t^2 F2(x) + t^3 F3(x) + ... where x =( r12 ,r14, r23 ,r24, r34 ) and r13 = 1/t . We also have a solution x0 of F0(x0) = 0 (the reduced equations). We use the implicit function theorem to see that any Puiseux solution x = x0 + o(t) must be a power series in t. It suffices to show that the 9 x 5 matrix DF0(x0) has rank 5. We single out a 5 x 5 submatrix and take its determinant, making the substition corresponding to the solutions of the reduced system. \ \>", "Text"], Cell[CellGroupData[{ Cell[BoxData[{ \(grad[f_]\ := \ {D[f, r12], D[f, r14], D[f, r23], D[f, r24], D[f, r34]}\), "\[IndentingNewLine]", \(\(DF0\ = \ Map[grad, F0] /. sub1 // Factor;\)\), "\[IndentingNewLine]", \(DF0 // MatrixForm\), "\[IndentingNewLine]", \(\((\(Det[DF0[\([{1, 2, 5, 6, 9}]\)]] /. sub1 // Factor\) // Numerator)\) /. sub1\)}], "Input"], Cell[BoxData[ TagBox[ RowBox[{"(", "\[NoBreak]", GridBox[{ {\(\(-12\)\ \((1 + m1)\)\ r12\^2\), "0", "0", "0", "0"}, {\(6\ r12\^2\), \(-\(\(2\ \[ImaginaryI]\ m1\)\/\(1 + m1\)\)\), \(\(2\ \[ImaginaryI]\ m1\)\/\(1 + m1\)\), "0", \(6\ m1\ r34\^2\)}, {\(6\ \[ImaginaryI]\ r12\^2\), "0", \(\(4\ m1\)\/\(1 + m1\)\), \(\(2\ \[ImaginaryI]\ m1\)\/\(1 + m1\)\), \(6\ \[ImaginaryI]\ m1\ r34\^2\)}, {\(\(-6\)\ \[ImaginaryI]\ r12\^2\), \(\(4\ m1\)\/\(1 + m1\)\), "0", \(-\(\(2\ \[ImaginaryI]\ m1\)\/\(1 + m1\)\)\), \(\(-6\)\ \[ImaginaryI]\ m1\ r34\^2\)}, {\(\(-6\)\ r12\^2\), \(\(2\ \[ImaginaryI]\ m1\)\/\(1 + m1\)\), \(-\(\(2\ \[ImaginaryI]\ m1\)\/\(1 + m1\)\)\), \(\(4\ m1\)\/\(1 + m1\)\), \(\(-6\)\ m1\ r34\^2\)}, {"0", "0", "0", "0", \(\(-12\)\ \((1 + m1)\)\ r34\^2\)}, {\(\(-3\)\ r12\^2\), "0", "0", "0", \(\(-3\)\ r34\^2\)}, {\(3\ r12\^2\), "0", "0", "0", \(3\ r34\^2\)}, {"0", "3", "3", \(-3\), "0"} }], "\[NoBreak]", ")"}], Function[ BoxForm`e$, MatrixForm[ BoxForm`e$]]]], "Output"], Cell[BoxData[ \(\(-6912\)\ \[ImaginaryI]\ m1\^2\ r12\^2\ r34\^2\)], "Output"] }, Open ]], Cell["For some reason, it turns out that F1 vanishes at x0", "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(F1 /. sub1 // Factor\)], "Input"], Cell[BoxData[ \({0, 0, 0, 0, 0, 0, 0, 0, 0}\)], "Output"] }, Open ]], Cell[BoxData[{ \(\(Ft\ = \ F /. {r12 \[Rule] r12 + t^2*u12 + t^3*v12, r13 \[Rule] r13 + t^2*u13 + t^3*v13, r23 \[Rule] r23 + t^2*u23 + t^3*v23, r24 \[Rule] r24 + t^2*u24 + t^3*v24, r34 \[Rule] r34 + t^2*u34 + t^3*v34};\)\), "\[IndentingNewLine]", \(Ft0\ = \ \((Ft /. t \[Rule] 0 // Factor)\) /. sub1 // Factor\), "\[IndentingNewLine]", \(Ft1\ = \ Coefficient[Ft, t] /. sub1 // Factor\), "\[IndentingNewLine]", \(Ft2\ = \ Coefficient[Ft, t^2] /. sub1 // Factor\), "\[IndentingNewLine]", \(Ft3\ = \ Coefficient[Ft, t^3] /. sub1 // Factor\)}], "Input"], Cell["\<\ Knowing this, we are justified in setting x = x0 + t^2 u+ t^3 v + ... . We will derive the equations for u and v \ \>", "Text"], Cell[CellGroupData[{ Cell[BoxData[{ \(\(Ft\ = \ F /. {r12 \[Rule] r12 + t^2*u12 + t^3*v12, r14 \[Rule] r14 + t^2*u14 + t^3*v14, r23 \[Rule] r23 + t^2*u23 + t^3*v23, r24 \[Rule] r24 + t^2*u24 + t^3*v24, r34 \[Rule] r34 + t^2*u34 + t^3*v34};\)\), "\[IndentingNewLine]", \(Ft0\ = \ \((Ft /. t \[Rule] 0 // Factor)\) /. sub1 // Factor\), "\[IndentingNewLine]", \(Ft1\ = \ Coefficient[Ft, t] /. sub1 // Factor\), "\[IndentingNewLine]", \(Ft2\ = \ Coefficient[Ft, t^2] /. sub1 // Factor\), "\[IndentingNewLine]", \(Ft3\ = \ Coefficient[Ft, t^3] /. sub1 // Factor\)}], "Input"], Cell[BoxData[ \({0, 0, 0, 0, 0, 0, 0, 0, 0}\)], "Output"], Cell[BoxData[ \({0, 0, 0, 0, 0, 0, 0, 0, 0}\)], "Output"], Cell[BoxData[ \({\(-12\)\ \((1 + m1)\)\ r12\^2\ u12, \(-\(\(1\/\(1 + m1\)\) \((r12\^3\ r34\^2 + m1\ r12\^3\ r34\^2 + m1\ r12\^2\ r34\^3 + m1\^2\ r12\^2\ r34\^3 - 6\ r12\^2\ u12 - 6\ m1\ r12\^2\ u12 + 2\ \[ImaginaryI]\ m1\ u14 - 2\ \[ImaginaryI]\ m1\ u23 - 6\ m1\ r34\^2\ u34 - 6\ m1\^2\ r34\^2\ u34)\)\)\), \(1\/\(1 + m1\)\) \((\[ImaginaryI]\ r12\^3\ r34\^2 + \[ImaginaryI]\ m1\ \ r12\^3\ r34\^2 + \[ImaginaryI]\ m1\ r12\^2\ r34\^3 + \[ImaginaryI]\ m1\^2\ \ r12\^2\ r34\^3 + 6\ \[ImaginaryI]\ r12\^2\ u12 + 6\ \[ImaginaryI]\ m1\ r12\^2\ u12 + 4\ m1\ u23 + 2\ \[ImaginaryI]\ m1\ u24 + 6\ \[ImaginaryI]\ m1\ r34\^2\ u34 + 6\ \[ImaginaryI]\ m1\^2\ r34\^2\ u34)\), \(1\/\(1 + m1\)\) \((\(-\[ImaginaryI]\)\ r12\^3\ r34\^2 - \[ImaginaryI]\ \ m1\ r12\^3\ r34\^2 - \[ImaginaryI]\ m1\ r12\^2\ r34\^3 - \[ImaginaryI]\ m1\^2\ \ r12\^2\ r34\^3 - 6\ \[ImaginaryI]\ r12\^2\ u12 - 6\ \[ImaginaryI]\ m1\ r12\^2\ u12 + 4\ m1\ u14 - 2\ \[ImaginaryI]\ m1\ u24 - 6\ \[ImaginaryI]\ m1\ r34\^2\ u34 - 6\ \[ImaginaryI]\ m1\^2\ r34\^2\ u34)\), \(1\/\(1 + m1\)\) \((r12\^3\ r34\^2 + m1\ r12\^3\ r34\^2 + m1\ r12\^2\ r34\^3 + m1\^2\ r12\^2\ r34\^3 - 6\ r12\^2\ u12 - 6\ m1\ r12\^2\ u12 + 2\ \[ImaginaryI]\ m1\ u14 - 2\ \[ImaginaryI]\ m1\ u23 + 4\ m1\ u24 - 6\ m1\ r34\^2\ u34 - 6\ m1\^2\ r34\^2\ u34)\), \(-12\)\ \((1 + m1)\)\ r34\^2\ u34, \(-3\)\ \((r12\^2\ u12 + r34\^2\ u34)\), 3\ \((r12\^2\ u12 + r34\^2\ u34)\), 3\ \((u14 + u23 - u24)\)}\)], "Output"], Cell[BoxData[ \({\(-2\)\ r12\ \((\((\(-2\) + \[ImaginaryI])\)\ u14 - \((2 - \ \[ImaginaryI])\)\ u23 + \((2 + \[ImaginaryI])\)\ u24 + 6\ r12\ v12 + 6\ m1\ r12\ v12)\), \(1\/\(1 + m1\)\) \((2\ \((\(-m1\) + 3\ r12\^2\ v12 + 3\ m1\ r12\^2\ v12 - \[ImaginaryI]\ m1\ v14 + \[ImaginaryI]\ \ m1\ v23 + 3\ m1\ r34\^2\ v34 + 3\ m1\^2\ r34\^2\ v34)\))\), \(1\/\(1 + m1\)\) \((2\ \((m1 + 3\ \[ImaginaryI]\ r12\^2\ v12 + 3\ \[ImaginaryI]\ m1\ r12\^2\ v12 + 2\ m1\ v23 + \[ImaginaryI]\ m1\ v24 + 3\ \[ImaginaryI]\ m1\ r34\^2\ v34 + 3\ \[ImaginaryI]\ m1\^2\ r34\^2\ v34)\))\), \(1\/\(1 + m1\)\) \((2\ \((m1 - 3\ \[ImaginaryI]\ r12\^2\ v12 - 3\ \[ImaginaryI]\ m1\ r12\^2\ v12 + 2\ m1\ v14 - \[ImaginaryI]\ m1\ v24 - 3\ \[ImaginaryI]\ m1\ r34\^2\ v34 - 3\ \[ImaginaryI]\ m1\^2\ r34\^2\ v34)\))\), \(-\(\(1\/\(1 + m1\)\) \((2\ \((m1 + 3\ r12\^2\ v12 + 3\ m1\ r12\^2\ v12 - \[ImaginaryI]\ m1\ v14 + \[ImaginaryI]\ \ m1\ v23 - 2\ m1\ v24 + 3\ m1\ r34\^2\ v34 + 3\ m1\^2\ r34\^2\ v34)\))\)\)\), \(-2\)\ r34\ \((\((\(-2\) \ - \[ImaginaryI])\)\ m1\ u14 - \((2 + \[ImaginaryI])\)\ m1\ u23 + \((2 - \ \[ImaginaryI])\)\ m1\ u24 + 6\ r34\ v34 + 6\ m1\ r34\ v34)\), \(-3\)\ \((r12\^2\ v12 + r34\^2\ v34)\), 3\ \((r12\^2\ v12 + r34\^2\ v34)\), 2 + 3\ v14 + 3\ v23 - 3\ v24}\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[{ \(Ft2\ = \ Numerator[Ft2]\), "\[IndentingNewLine]", \(\(Ft2five\ = \ Ft2[\([{1, 2, 5, 6, 9}]\)];\)\), "\[IndentingNewLine]", \(\(\(usol\ = \ \(Solve[ Ft2five \[Equal] {0, 0, 0, 0, 0}, {u12, u14, u23, u24, u34}]\)[\([1]\)] /. sub1 // FullSimplify\)\(\[IndentingNewLine]\) \)\), "\[IndentingNewLine]", \(\((Ft2 /. usol // Factor)\) /. sub1 // Simplify\)}], "Input"], Cell[BoxData[ \({\(-12\)\ \((1 + m1)\)\ r12\^2\ u12, \(-r12\^3\)\ r34\^2 - m1\ r12\^3\ r34\^2 - m1\ r12\^2\ r34\^3 - m1\^2\ r12\^2\ r34\^3 + 6\ r12\^2\ u12 + 6\ m1\ r12\^2\ u12 - 2\ \[ImaginaryI]\ m1\ u14 + 2\ \[ImaginaryI]\ m1\ u23 + 6\ m1\ r34\^2\ u34 + 6\ m1\^2\ r34\^2\ u34, \[ImaginaryI]\ r12\^3\ r34\^2 + \[ImaginaryI]\ \ m1\ r12\^3\ r34\^2 + \[ImaginaryI]\ m1\ r12\^2\ r34\^3 + \[ImaginaryI]\ m1\^2\ \ r12\^2\ r34\^3 + 6\ \[ImaginaryI]\ r12\^2\ u12 + 6\ \[ImaginaryI]\ m1\ r12\^2\ u12 + 4\ m1\ u23 + 2\ \[ImaginaryI]\ m1\ u24 + 6\ \[ImaginaryI]\ m1\ r34\^2\ u34 + 6\ \[ImaginaryI]\ m1\^2\ r34\^2\ u34, \(-\[ImaginaryI]\)\ r12\^3\ r34\ \^2 - \[ImaginaryI]\ m1\ r12\^3\ r34\^2 - \[ImaginaryI]\ m1\ r12\^2\ r34\^3 - \ \[ImaginaryI]\ m1\^2\ r12\^2\ r34\^3 - 6\ \[ImaginaryI]\ r12\^2\ u12 - 6\ \[ImaginaryI]\ m1\ r12\^2\ u12 + 4\ m1\ u14 - 2\ \[ImaginaryI]\ m1\ u24 - 6\ \[ImaginaryI]\ m1\ r34\^2\ u34 - 6\ \[ImaginaryI]\ m1\^2\ r34\^2\ u34, r12\^3\ r34\^2 + m1\ r12\^3\ r34\^2 + m1\ r12\^2\ r34\^3 + m1\^2\ r12\^2\ r34\^3 - 6\ r12\^2\ u12 - 6\ m1\ r12\^2\ u12 + 2\ \[ImaginaryI]\ m1\ u14 - 2\ \[ImaginaryI]\ m1\ u23 + 4\ m1\ u24 - 6\ m1\ r34\^2\ u34 - 6\ m1\^2\ r34\^2\ u34, \(-12\)\ \((1 + m1)\)\ r34\^2\ u34, \(-3\)\ \((r12\^2\ u12 + r34\^2\ u34)\), 3\ \((r12\^2\ u12 + r34\^2\ u34)\), 3\ \((u14 + u23 - u24)\)}\)], "Output"], Cell[BoxData[ \({u24 \[Rule] 0, u14 \[Rule] 1\/4\ \[ImaginaryI]\ \((r12\^2 + r34\^2)\), u23 \[Rule] \(-\(1\/4\)\)\ \[ImaginaryI]\ \((r12\^2 + r34\^2)\), u12 \[Rule] 0, u34 \[Rule] 0}\)], "Output"], Cell[BoxData[ \({0, 0, 0, 0, 0, 0, 0, 0, 0}\)], "Output"] }, Open ]], Cell["\<\ Now make a substitution to go on to the next order. This gives linear equations for the vij. We find the augmented matrix of this system of \ nine equations and five unknowns. \ \>", "Text"], Cell[CellGroupData[{ Cell[BoxData[{ \(\(Ft3u\ = \(Ft3 /. usol // Factor\) // Numerator;\)\), "\[IndentingNewLine]", \(augv[f_]\ := \ {Coefficient[f, v12], Coefficient[f, v14], Coefficient[f, v23], Coefficient[f, v24], Coefficient[f, v34], f /. {v12 \[Rule] 0, v14 \[Rule] 0, v23 \[Rule] 0, v24 \[Rule] 0, v34 \[Rule] 0}}\), "\[IndentingNewLine]", \(\(Ft3umatrix\ = \ Map[augv, Ft3u] /. sub1 // Factor;\)\), "\[IndentingNewLine]", \(Ft3umatrix // MatrixForm\)}], "Input"], Cell[BoxData[ TagBox[ RowBox[{"(", "\[NoBreak]", GridBox[{ {\(\(-12\)\ \((1 + m1)\)\ r12\^2\), "0", "0", "0", "0", "0"}, {\(6\ \((1 + m1)\)\ r12\^2\), \(\(-2\)\ \[ImaginaryI]\ m1\), \(2\ \ \[ImaginaryI]\ m1\), "0", \(6\ m1\ \((1 + m1)\)\ r34\^2\), \(\(-2\)\ m1\)}, {\(6\ \[ImaginaryI]\ \((1 + m1)\)\ r12\^2\), "0", \(4\ m1\), \(2\ \[ImaginaryI]\ m1\), \(6\ \[ImaginaryI]\ \ m1\ \((1 + m1)\)\ r34\^2\), \(2\ m1\)}, {\(\(-6\)\ \[ImaginaryI]\ \((1 + m1)\)\ r12\^2\), \(4\ m1\), "0", \(\(-2\)\ \[ImaginaryI]\ m1\), \(\(-6\)\ \[ImaginaryI]\ m1\ \ \((1 + m1)\)\ r34\^2\), \(2\ m1\)}, {\(\(-6\)\ \((1 + m1)\)\ r12\^2\), \(2\ \[ImaginaryI]\ m1\), \(\(-2\)\ \ \[ImaginaryI]\ m1\), \(4\ m1\), \(\(-6\)\ m1\ \((1 + m1)\)\ r34\^2\), \(\(-2\)\ m1\)}, {"0", "0", "0", "0", \(\(-12\)\ \((1 + m1)\)\ r34\^2\), "0"}, {\(\(-3\)\ r12\^2\), "0", "0", "0", \(\(-3\)\ r34\^2\), "0"}, {\(3\ r12\^2\), "0", "0", "0", \(3\ r34\^2\), "0"}, {"0", "3", "3", \(-3\), "0", "2"} }], "\[NoBreak]", ")"}], Function[ BoxForm`e$, MatrixForm[ BoxForm`e$]]]], "Output"] }, Open ]], Cell["\<\ The resulting augmented matrix has rank six which shows that the system is inconsistent. \ \>", "Text"], Cell[CellGroupData[{ Cell[BoxData[{ \(\(\((\(Det[Ft3umatrix[\([{1, 2, 3, 5, 6, 9}]\)]] /. sub1 // Factor\) // Numerator)\);\)\), "\[IndentingNewLine]", \(% /. sub1 // Factor\)}], "Input"], Cell[BoxData[ \(18432\ \[ImaginaryI]\ m1\^3\ \((1 + m1)\)\^2\ r12\^2\ r34\^2\)], \ "Output"] }, Open ]] }, Closed]] }, Closed]] }, Open ]] }, FrontEndVersion->"5.0 for Macintosh", ScreenRectangle->{{0, 978}, {0, 746}}, WindowSize->{761, 639}, WindowMargins->{{0, Automatic}, {Automatic, 0}} ] (******************************************************************* Cached data follows. 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