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

Synopsis

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 0.0180002s (cpu); 0.0180967s (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.