weightVectorsRealizingSAGBI -- The main function for detecting SAGBI bases

• Usage:

  S = weightVectorsRealizingSAGBI Q

• Inputs:
  • Q, a list, of polynomials in the same ring
• Optional inputs:
  • Verbose (missing documentation) => ..., default value false,
• Outputs:
  • S, a list, (possibly empty) containing weight vectors for which Q forms a SAGBI basis

i1 : S1 = QQ[x,y,z, MonomialOrder=>Lex];

i2 : Q1 = {z, z*x, z*y, z*x*(x^2+y^2),z*y*(x^2+y^2)};

i3 : weightVectorsRealizingSAGBI Q1

o3 = {{2, 1, 1}, {1, 2, 1}}

o3 : List

i4 : S2 = QQ[x, MonomialOrder=>Lex];

i5 : Q2 = {x^4+x^3, x^2+x, x^3 + x^2};

i6 : weightVectorsRealizingSAGBI Q2

o6 = {{1}}

o6 : List

i7 : S3 = QQ[x,y, MonomialOrder=>Lex];

i8 : Q3 = {x+y, x*y, x*y^2};

i9 : weightVectorsRealizingSAGBI Q3

o9 = {}

o9 : List