betti(GroebnerBasis) -- diagram of the degrees of a groebner basis

Synopsis

• Function: betti

• Usage:

  betti G

• Inputs:
  • G, a Gröbner basis
• Optional inputs:
  • Minimize => ..., default value false, minimal betti numbers of a non-minimal free resolution
  • Weights => ..., default value null,
• Outputs:
  • a Betti tally, a diagram showing the degrees of the generators of the source and target modules of the matrix of generators of G

Description

i1 : S = ZZ/10007[x,y];

i2 : G = gb ideal(x^3+y^3, x*y^4);

i3 : gens G

o3 = | x3+y3 xy4 y7 |

             1       3
o3 : Matrix S  <--- S

i4 : betti G

            0 1
o4 = total: 1 3
         0: 1 .
         1: . .
         2: . 1
         3: . .
         4: . 1
         5: . .
         6: . 1

o4 : BettiTally