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BooleanGB :: BooleanGB

BooleanGB -- Compute Groebner Basis in a Boolean Ring

Description

gbBoolean is a fast Groebner Basis computation done bitwise instead of symbolically when working over the quotient ring F2/J where J is the ideal generated by X2 - X .
i1 : n = 3;
i2 : R = ZZ/2[vars(0)..vars(n-1)];
i3 : J = apply( gens R, x -> x^2 + x);
i4 : QR = R/J;
i5 : I = ideal(a+b,b);

o5 : Ideal of QR
i6 : gbBoolean I

o6 = ideal (b, a)

o6 : Ideal of QR
i7 : gens gb I

o7 = | b a |

              1        2
o7 : Matrix QR  <--- QR

Caveat

gbBoolean assumes the quotient ring, regardless of the ring in which the ideal was generated.

R = ZZ/2[x]

gbBoolean ideal(x3)

Authors

Version

This documentation describes version 1.0 of BooleanGB.

Source code

The source code from which this documentation is derived is in the file BooleanGB.m2.

Exports

  • Functions and commands