Tigers OX Server Manual

Edition : auto generated by oxgentexi on October 23, 2017

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1 TIGERS Functions

This chapter describes interface functions for tigers ox server ox_sm1_tigers.


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1.0.1 tigers.tigers

tigers.tigers(a|proc=a)

:: It asks the tigers server of the descriptor number p to enumerate all Grobner bases associated to the toric variaty defined by the matrix a.

return

List

p

Number

a

List

[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]]]

In this example, all reduced Grobner bases for the toric ideal associated to the matrix A are stored in S. There are eight distinct Grobner bases of 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].


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