
D.4.29.1 toric_ideal
Procedure from library toric.lib (see toric_lib).
 Usage:
 toric_ideal(A,alg); A intmat, alg string
toric_ideal(A,alg,prsv); A intmat, alg string, prsv intvec
 Return:
 ideal: standard basis of the toric ideal of A
 Note:
 These procedures return the standard basis of the toric ideal of A
with respect to the term ordering in the current basering. Not all
term orderings are supported: The usual global term orderings may be
used, but no block orderings combining them.
One may call the procedure with several different algorithms:
 the algorithm of Conti/Traverso using elimination (ect),
 the algorithm of Pottier (pt),
 an algorithm of Bigatti/La Scala/Robbiano (blr),
 the algorithm of Hosten/Sturmfels (hs),
 the algorithm of DiBiase/Urbanke (du).
The argument `alg' should be the abbreviation for an algorithm as
above: ect, pt, blr, hs or du.
If `alg' is chosen to be `blr' or `hs', the algorithm needs a vector
with positive coefficients in the row space of A.
If no row of A contains only positive entries, one has to use the
second version of toric_ideal which takes such a vector as its third
argument.
For the mathematical background, see
Toric ideals and integer programming.
Example:
 LIB "toric.lib";
ring r=0,(x,y,z),dp;
// call with two arguments
intmat A[2][3]=1,1,0,0,1,1;
A;
==> 1,1,0,
==> 0,1,1
ideal I=toric_ideal(A,"du");
I;
==> I[1]=xzy
I=toric_ideal(A,"blr");
==> ? The chosen algorithm needs a positive vector in the row space of the\
matrix.
==> ? leaving toric.lib::toric_ideal_1
==> ? leaving toric.lib::toric_ideal
I;
==> I[1]=xzy
// call with three arguments
intvec prsv=1,2,1;
I=toric_ideal(A,"blr",prsv);
I;
==> I[1]=xzy
 See also:
Toric ideals;
intprog_lib;
toric_lib;
toric_std.
