pureFree -- computes a GL(V)-equivariant map whose resolution is pure, or the reduction mod p of such a map

• Usage:

  pureFree(d, P)

• Inputs:
  • d, a list, a list of degrees (increasing numbers)
  • P, a polynomial ring, a polynomial ring over a field K in n variables
• Outputs:
  • a matrix, A map whose cokernel has Betti diagram with degree sequence d if K has characteristic 0. If K has positive characteristic p, then the corresponding map is calculated over QQ and is lifted to a ZZ-form which is then reduced mod p.

i1 : betti res coker pureFree({0,1,2,4}, QQ[a,b,c]) -- degree sequence {0,1,2,4}

            0 1 2 3
o1 = total: 3 8 6 1
         0: 3 8 6 .
         1: . . . 1

o1 : BettiTally

i2 : betti res coker pureFree({0,1,2,4}, ZZ/2[a,b,c]) -- same map, but reduced mod 2

            0 1 2 3
o2 = total: 3 8 6 1
         0: 3 8 6 .
         1: . . . 1

o2 : BettiTally

i3 : betti res coker pureFree({0,1,2,4}, GF(4)[a,b,c]) -- can also use non prime fields

            0 1 2 3
o3 = total: 3 8 6 1
         0: 3 8 6 .
         1: . . . 1

o3 : BettiTally