betti(Module) -- show the degrees of the generators and relations of a module or a coherent sheaf

Synopsis

• Function: betti

• Usage:

  betti M

• Inputs:
  • M, a module, graded.
• 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 and the relations in the module M

Description

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

i2 : betti coker matrix{{x^3,x*y^2},{y*x^2,y^3}}

            0 1
o2 = total: 2 2
         0: 2 .
         1: . .
         2: . 2

o2 : BettiTally

i3 : betti coker map(S^{0,-1},,matrix{{x^2,y},{y^3,x^2}})

            0 1
o3 = total: 2 2
         0: 1 .
         1: 1 .
         2: . 1
         3: . 1

o3 : BettiTally