standardPairs MonomialIdeal -- finds the standard pairs of a monomial ideal

standardPairs MonomialIdeal -- finds the standard pairs of a monomial ideal

Synopsis:

Usage: L = standardPairs I

Function: standardPairs

Input:

I, an instance of class MonomialIdeal: a monomial ideal

Output:

L, an instance of class Thing: a list of the standard pairs of I

A standard pair of a monomial ideal I is a pair {x^a,l} where m is a monomial and l is a subset of the variables subject to the following three conditions:

m is supported on the complement of l.
for all monomials n supported on l the monomial m * n does not belong to I.
for all monomials n supported on l there exists b_j >= 0 such that m x_j^b_j n lies in I.

i1 : QQ[x,y,z,w];

i2 : I = monomialIdeal(y^2, y*w, y*z, x*w^2)



                     2               2

o2 = monomialIdeal (y , y*z, y*w, x*w )



o2 : MonomialIdeal of QQ [x, y, z, w]

i3 : standardPairs I



o3 = {{1, {z, w}}, {1, {z, x}}, {w, {z, x}}, {y, {x}}}



o3 : List

The standard pairs are computed with algorithm 3.2.5 in Groebner Deformations of Hypergeometric Differential Equations, by Mutsumi Saito, Bernd Sturmfels and Nobuki Takayama; Algorithms and Computation in Mathematics, Volume 6, Springer-Verlag, 2000.

Implemented by Greg Smith.

Code:

     -- ../../../Macaulay2/m2/monideal.m2:347
     standardPairs MonomialIdeal := (I) -> standardPairs(I,Delta I)