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# isOIGB -- check if a list of elements of a free OI-module forms a Gröbner basis

- Usage:
    `isOIGB L`
- Inputs:
  - L, a list,
- Optional inputs:
  - Verbose => ..., default value false
- Outputs:
  - a Boolean value,

## Description

Checks if a L forms a Gröbner basis for the submodule it generates. The Verbose option must be either true or false, depending on whether one wants debug information printed.

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

    i2 : F = makeFreeOIModule(e, {1,1,2}, P);

    i3 : installGeneratorsInWidth(F, 1);

    i4 : installGeneratorsInWidth(F, 2);

    i5 : installGeneratorsInWidth(F, 3);

    i6 : use F_1; b1 = x_(1,1)*e_(1,{1},1)+x_(2,1)*e_(1,{1},2);

    i8 : 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);

    i10 : isOIGB {b1, b2}

    o10 = false

    i11 : time B = oiGB {b1, b2}
     -- used 0.0238363s (cpu); 0.0238368s (thread); 0s (gc)

    o11 = {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

    o11 : List

    i12 : isOIGB B

    o12 = true

## Ways to use isOIGB:

- `isOIGB(List)`

## For the programmer

The object isOIGB is a method function with options.

The source of this document is in /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/OIGroebnerBases.m2:2555:0.