# pureResES -- constructs the Eisenbud--Schreyer pure resolution of a given type

## Synopsis

• Usage:
pureResES(d,kk)
• Inputs:
• Outputs:

## Description

Given a degree sequence $d$, this function returns the pure resolution of type $d$ constructed in by Eisenbud and Schreyer in Section 5 of Betti numbers of graded modules and cohomology of vector bundles''. The function operates by resolving the output of pureResES1(d,kk).

 i1 : d={0,2,4,5}; i2 : FF=pureResES(d,ZZ/32003) ZZ 3 ZZ 10 ZZ 15 ZZ 8 o2 = (-----[x ..x ]) <-- (-----[x ..x ]) <-- (-----[x ..x ]) <-- (-----[x ..x ]) <-- 0 32003 0 2 32003 0 2 32003 0 2 32003 0 2 4 0 1 2 3 o2 : ChainComplex i3 : betti FF 0 1 2 3 o3 = total: 3 10 15 8 0: 3 . . . 1: . 10 . . 2: . . 15 8 o3 : BettiTally