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PieriMaps :: pureFree

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

Synopsis

Description

The function translates the data of a degree sequence d for a desired pure free resolution into the data of a Pieri map according to the formula of Eisenbud-Fl\o ystad-Weyman and then applies the function pieri.
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

See also

Ways to use pureFree :