BooleanGB is a package to compute Groebner Bases in lexicographic order for polynomial ideals in the quotient ring * F_{2}[x_{1}, ..., x_{n}]/J*, where J is the ideal generated by field polynomials

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 |

BooleanGB always assumes that the ideal is in the Boolean quotient ring, i.e., * F_{2}[x_{1}, ..., x_{n}] / <x_{1}^{2}-x_{1}, ..., x_{n}^{2}-x_{n} >*, regardless of the ring in which the ideal was generated. Thus, any ideal in the base ring is promoted to the quotient ring automatically, even if the quotient ring has not been defined.

- Mike Stillman
- Elizabeth Arnold

- Functions and commands
- gbBoolean, see gbBoolean(Ideal) -- Compute Groebner Basis for Ideals in Boolean Polynomial Quotient Ring