gfanIsMarkedGroebnerBasis -- checks if a list of polynomials are a Groebner basis

Synopsis

• Usage:

  B = gfanIsMarkedGroebnerBasis(M)

  B = gfanIsMarkedGroebnerBasis(L)

  B = gfanIsMarkedGroebnerBasis(I)

• Inputs:
  • M, a marked polynomial list,
  • L, a list,
  • I, an ideal,
• Outputs:
  • B, a Boolean value, true if input forms a Groebner basis

Description

i1 : QQ[x,y,z];

i2 : gfanIsMarkedGroebnerBasis({x^2+y, y^3+z})

o2 = true

i3 : gfanIsMarkedGroebnerBasis markedPolynomialList {{y,y^3}, {x^2+y, y^3+z}}

o3 = false

This program checks if a set of marked polynomials is a Groebner basis with respect to its marking. First it is checked if the markings are consistent with respect to a positive vector. Then Buchberger's S-criterion is checked. The output is boolean value.
Options: