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Added a manual for the tigers ox server.

/* $OpenXM: OpenXM/src/asir-contrib/packages/doc/tigers/tigers.oxw,v 1.1 2005/04/14 00:01:08 takayama Exp $


/*&C
@node TIGERS Functions,,, Top
*/
/*&en
@chapter TIGERS Functions

This chapter describes  interface functions for
tigers ox server @code{ox_sm1_tigers}.
*/
/*&ja
@chapter TIGERS $BH!?t(B

$B$3$N>O$G$O(B, 
tigers ox server @code{ox_sm1_tigers}
$B$K$?$$$9$k%$%s%?%U%'!<%9H!?t$r@bL@$9$k(B.
*/

/*&en
@menu
* tigers.tigers::
@end menu
@node tigers.tigers,,, TIGERS Functions
@subsection @code{tigers.tigers}
@findex tigers.tigers
@table @t
@item tigers.tigers(@var{a}|proc=@var{a})
::   It asks the @code{tigers} server of the descriptor number @var{p}
to enumerate all Grobner bases associated to the toric variaty
defined by the matrix @var{a}.
@end table

@table @var
@item return
List
@item p
Number
@item a
List
@end table

@itemize @bullet
@item  It asks the @code{tigers} server of the descriptor number @var{p}
to enumerate all Grobner bases associated to the toric variaty
defined by the matrix @var{a}.
@item
The system tigers is an expert system to enumerate
all Gr\"obner bases of affine toric ideals.
In other words, it can be used to determine the state polytope
of a given affine toric ideal.
As to a theoretical background, see the book @*
B.Sturmfels, Grobner bases and Convex Polytopes. @*
The original tigers is written by Birk Hubert.
The algorithm used in explained in the paper @*
B.Huber and R.Thomas, Computing Grobner Fans of Toric Ideals.
@end itemize
*/

/*&ja
@menu
* tigers.tigers::
@end menu
@node tigers.tigers,,, TIGERS Functions
@subsection @code{tigers.tigers}
@findex tigers.tigers
@table @t
@item tigers.tigers(@var{a}|proc=@var{a})
::   $B$3$NH!?t$O<1JL;R(B @var{p} $B$N(B tigers $B%5!<%P$K(B
$B9TNs(B @var{a} $B$KIU?o$7$?%H!<%j%C%/%$%G%"%k$N$9$Y$F$N%0%l%V%J4pDl$r(B
$B7W;;$7$F$/$l$k$h$&$K$?$N$`(B.
@end table

@table @var
@item $BLa$jCM(B
$B%j%9%H(B
@item p
$B?t(B
@item a
$B%j%9%H(B
@end table

@itemize @bullet
@item  
 $B$3$NH!?t$O<1JL;R(B @var{p} $B$N(B tigers $B%5!<%P$K(B
$B9TNs(B @var{a} $B$KIU?o$7$?%H!<%j%C%/%$%G%"%k$N$9$Y$F$N%0%l%V%J4pDl$r(B
$B7W;;$7$F$/$l$k$h$&$K$?$N$`(B.
@item
Tigers $B$O(B $B%"%U%#%s%H!<%j%C%/%$%G%"%k$N(B reduced $B%0%l%V%J4pDl$r(B
$B$9$Y$F?t$($"$2$k$?$a$N@lMQ$N%W%m%0%i%`$G$"$k(B.
$B$3$N%W%m%0%i%`$O(B, $B%"%U%#%s%H!<%j%C%/%$%G%"%k$N(B state polytope
$B$r$-$a$k$?$a$K;H$($k(B.
$BM}O@E*$J%P%C%/%0%i%&%s%I$K$D$$$F$O(B,
$BK\(B @*
B.Sturmfels, Grobner bases and Convex Polytopes @*
$B$r8+$h(B.
Tigers $B$O(B Birk Hubert $B$,:n<T$G$"$k(B.
$B$3$N%W%m%0%i%`$NMxMQ$7$F$$$k%"%k%4%j%:%`$O(B @*
B.Huber and R.Thomas, Computing Grobner Fans of Toric Ideals @*
$B$K@bL@$5$l$F$$$k(B.
@end itemize
*/

/*&C

@example
[395] A=[[1,1,1,1],[0,1,2,3]]$
[306] S=tigers.tigers(A)$
[307] length(S);
8
[308] S[0];
[[[1,0,1,0],[0,2,0,0]],[[1,0,0,1],[0,1,1,0]],[[0,1,0,1],[0,0,2,0]]]
[309] S[1];
[[[1,0,0,1],[0,1,1,0]],[[0,2,0,0],[1,0,1,0]],[[0,1,0,1],[0,0,2,0]]]

@end example

*/

/*&en
In this example, all reduced Grobner bases for the toric ideal
associated to the matrix @var{A} are stored in @var{S}.
There are eight distinct Grobner bases of @var{A}.
[[i_1, i_2, ...],[j_1, j_2, ...]] is a set of exponents of
two monomials and stands for a binomial.
For example,
the S[0] consists of @*
  x1 x3 - x2^2,   x1 x4 - x2 x3, x2 x4 - x3^2.  @*
<x1 x3, x1 x4, x2 x4> is the initial ideal of S[0].

*/
/*&ja
$B$3$NNc$G$O(B, @var{A} $B$KIU?o$7$?%"%U%#%s%H!<%j%C%/%$%G%"%k$N(B
$B$9$Y$F$N%0%l%V%J4pDl$,(B @var{S} $B$K3JG<$5$l$k(B.
$B$3$NNc$G$O(B, 8 $B8D$N%0%l%V%J4pDl$,$"$k(B.
[[i_1, i_2, ...],[j_1, j_2, ...]] $B$OFs$D$N%b%N%_%"%k$N(B
exponent $B$r$J$i$Y$?$b$N$G$"$j(B, 2 $B9`<0$r$"$i$o$9(B.
$B$?$H$($P(B,
S[0] $B$O<!$NB?9`<0$N=89g(B @*
  x1 x3 - x2^2,   x1 x4 - x2 x3, x2 x4 - x3^2  @*
$B$G$"$j(B,
<x1 x3, x1 x4, x2 x4> $B$,$=$N(B initial ideal $B$G$"$k(B.

*/