# oiGB -- compute a Gröbner basis for a submodule of a free OI-module

## Synopsis

• Usage:
oiGB L
• Inputs:
• Optional inputs:
• Strategy => ..., default value Minimize
• Verbose => ..., default value false
• Outputs:

## Description

Given a list of elements L belonging to a free OI-module $\mathbf{F}$, this method computes a Gröbner basis for the submodule generated by L with respect to the monomial order of $\mathbf{F}$. 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:

 i1 : P = makePolynomialOIAlgebra(2, x, QQ); i2 : F = makeFreeOIModule(e, {1,1,2}, P); i3 : installGeneratorsInWidth(F, 1); i4 : installGeneratorsInWidth(F, 2); i5 : use F_1; b1 = x_(1,1)*e_(1,{1},1)+x_(2,1)*e_(1,{1},2); i7 : use F_2; b2 = x_(1,2)*x_(1,1)*e_(2,{2},2)+x_(2,2)*x_(2,1)*e_(2,{1,2},3); i9 : time oiGB {b1, b2} -- used 0.0503653s (cpu); 0.0526917s (thread); 0s (gc) o9 = {x e + x e , x x e + x x e , 1,1 1,{1},1 2,1 1,{1},2 1,2 1,1 2,{2},2 2,2 2,1 2,{1, 2},3 ------------------------------------------------------------------------ x x x e - x x x e } 2,3 2,2 1,1 3,{2, 3},3 2,3 2,1 1,2 3,{1, 3},3 o9 : List

• oiGB(List)

## For the programmer

The object oiGB is .