%% This is a brief intro to use of the TeX/LaTeX package "xypic",
%% whose principal use is to make diagrams and arrows.
%
%% To invoke the package, at the top of your document have lines

\input xy
\xyoption{all}

%% FYI, contrary to old documentation, the $X_Y$-pic homepage is NOT
%% 
%% $$\hbox{http://www.ens-lyon.fr/${}\,^~$}krisrose/Xy-pic.html}$$

%% The main function of this package is to create arrows of various
%% styles and shapes among entries in a "matrix". In plain TeX, for
%% example, entries are TeX expressions, separated by &'s, with \cr
%% (carriage returns) for end-of-lines. The xypic package creates
%% _arrows_ among the entries, by appending \ar (with modifiers) to
%% various of the matrix entries. As an example, 

$$\xymatrix{
A & B\ar[d] & C \cr
D\ar[ur] & E & F\ar[ull]\ar[ul] \cr
}
$$

%% (when TeX'd) creates a math-displayed matrix with entries A,B,C in
%% the top row, and D,E,F in the lower row. The arrow \ar[d] attached
%% to B goes Down. The arrow \ar[ur] attached to D, which means an
%% arrow to go Up+Right. The \ar[ull] 
%% arrow attached to the entry F goes Up+Left+Left, and the _second_
%% arrow, \ar[ul], attached to F goes Up+Left. The Up/Down and
%% Right/Left indications inside the brackets are the _hop_.

%% Arrow styles can be changed as \ar@{style}[hop]
%%
%% where "style" can be =>  .>  :>  ~>  --> - + or empty
%% The hop descriptor comes _after_ the style change.

$$\xymatrix{
A & B\ar@{.>}[d] & C \cr
D\ar[ur] & E & F\ar@{-->}[ull]\ar@{=}[ul] \cr
}
$$

%% Labels on arrows: syntax is
%%
%%   \ar@{style}[hop]^{toplabel}_{lowerlabel}
%%
%% That is, the label comes _last_.
%%
%% For centering/balancing of the label _on_the_arrow_, use minus -
%% after the ^ or _ 

%% E.g., the following is bad, as it is without centering

$$\xymatrix{
A \ar@{-}[r] \ar@{-}[d] \ar@{-->}[dr]
 & B \ar@{-}[d]
\cr
C \ar@{->}[r]^{a}_{b} & {A\times B\times C \times D} 
}
$$

%% repaired, with centering

$$\xymatrix{
A \ar@{-}[r] \ar@{-}[d] \ar@{-->}[dr]
 & B \ar@{-}[d]
\cr
C \ar@{->}[r]^-{a}_-{b} & {A\times B\times C \times D} 
}
$$

%% Breaks: \ar[r]|f inserts an f _in_ the arrow:

$$\xymatrix{
A \ar@{-}[r] \ar@{-}[d] \ar@{-->}[dr]|g
 & B \ar@{->}[d]
\cr
C \ar@{->}[r]|f & D 
}
$$

%% a break with no label is simply "\hole", as in

$$
\xymatrix{
A \ar@{=>}[r]|\hole & B \cr
}$$

%% Curving in arrow style, @/curvingstyle/, namely @/^/, @/_/

$$
\xymatrix{
A \ar@/^/[r] & B\ar@/^/[l] \cr
}$$

%% Can insert a dimension as an _amount_ to curve up or down

$$
\xymatrix{
A \ar@/^/[r]\ar@/^1pc/[r] & B\ar@/^/[l] \cr
}$$

%% Boxes around entries:

%% *+[F]{B} acts on "B" by making a box around it

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