oiRes -- compute an OI-resolution

Synopsis

Usage:

oiRes(L, n)
Inputs:
- L, a list,
- n, an integer,
Optional inputs:
- Strategy => ..., default value Minimize
- TopNonminimal => ..., default value false
- Verbose => ..., default value false
Outputs:
- an instance of the type OIResolution,

Description

Computes an OI-resolution of the submodule generated by L out to homological degree n. If L consists of homogeneous elements, then the resulting resolution will be graded and minimal out to homological degree $n-1$. The Verbose option must be either true or false, depending on whether one wants debug information printed.

The Strategy option has the following permissible values:

Strategy => FastNonminimal for no post-processing of the Gröbner basis computed at each step
Strategy => Minimize to minimize the Gröbner basis after it is computed at each step; see minimizeOIGB
Strategy => Reduce to reduce the Gröbner basis after it is computed at each step; see reduceOIGB

The TopNonminimal option must be either true or false, depending on whether one wants the Gröbner basis in homological degree $n-1$ to be minimized. Therefore, use TopNonminimal => true for no minimization of the basis in degree $n-1$.

i1 : P = makePolynomialOIAlgebra(2, x, QQ);

i2 : F = makeFreeOIModule(e, {1,1}, P);

i3 : installGeneratorsInWidth(F, 2);

i4 : b = x_(1,2)*x_(1,1)*e_(2,{2},1)+x_(2,2)*x_(2,1)*e_(2,{1},2);

i5 : time oiRes({b}, 2, TopNonminimal => true)
 -- used 0.494127s (cpu); 0.354347s (thread); 0s (gc)

o5 = 0: (e0, {2}, {-2})
     1: (e1, {4}, {-4})
     2: (e2, {4, 5, 5, 5, 5, 5}, {-4, -5, -5, -5, -5, -5})

o5 : OIResolution

Ways to use oiRes :

oiRes(List,ZZ)

For the programmer

The object oiRes is a method function with options.