# oiRes -- compute an OI-resolution

## Synopsis

• Usage:
oiRes(L, n)
• Inputs:
• Optional inputs:
• Strategy => ..., default value Minimize
• TopNonminimal => ..., default value false
• Verbose => ..., default value false
• Outputs:

## 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 .