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

## Synopsis

• Usage:
pureFree(d, P)
• Inputs:
• d, a list, a list of degrees (increasing numbers)
• P, , a polynomial ring over a field K in n variables
• Outputs:
• , 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.

## 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

• pieri -- computes a matrix representation for a Pieri inclusion of representations of a general linear group

## Ways to use pureFree :

• "pureFree(List,PolynomialRing)"

## For the programmer

The object pureFree is .