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D.4.25.1 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:
 
See also: Toric ideals; intprog_lib; toric_lib; toric_std.


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