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BooleanGB :: gbBoolean(Ideal)

gbBoolean(Ideal) -- Compute Groebner Basis

Synopsis

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

o1 = 3
i2 : R = ZZ/2[vars(0)..vars(n-1)]

o2 = R

o2 : PolynomialRing
i3 : J = apply( gens R, x -> x^2 + x)

       2       2       2
o3 = {a  + a, b  + b, c  + c}

o3 : List
i4 : QR = R/J

o4 = QR

o4 : QuotientRing
i5 : I = ideal(a+b,b)

o5 = 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)

See also