biBasis -- constructs a reduced Boolean Gröbner basis for the given Ideal, if the second argument is true (default), and reduced Boolean Pommaret basis otherwise.

Synopsis

• Usage:

  biBasis(I, toGroebner => true)

• Inputs:
  • I, an ideal
• Optional inputs:
  • toGroebner => ..., default value true
• Outputs:
  • P, an ideal

Description

i1 : R = ZZ/2[x, y, MonomialOrder => GRevLex]

o1 = R

o1 : PolynomialRing

i2 : I = ideal(x*y + x + 1)

o2 = ideal(x*y + x + 1)

o2 : Ideal of R

i3 : P = biBasis(I, toGroebner => true)

o3 = ideal (x + 1, y)

o3 : Ideal of R

Caveat

• biBasis assumes coefficient Ring of the given Ideal is ZZ/2
• biBasis always treats the given Ideal as a Boolean one
• biBasis assumes the following monomials orders: Lex, GLex, GRevLex

See also

• gb -- compute a Gröbner basis
• gbBoolean -- Compute Groebner Basis for Ideals in Boolean Polynomial Quotient Ring