# relativeResolution -- compute the relative resolution

## Synopsis

• Usage:
F = relativeResolution(a,b,k)
• Inputs:
• Outputs:
• F, , multi-graded chainComplex in the Cox ring

## Description

We compute the relative resolution of a resonance degenerate K3 in case of k resonance. The first step consists in chooses a prime field which has a k-th root of unity. We then follow section 4 of the paper equations and syzygies of K3 carpets and unions of scrolls.

 i1 : F = relativeResolution(5,4,3) ZZ 1 ZZ 9 ZZ 16 ZZ 9 ZZ 1 o1 = (--[s, t, u ..u , v ..v ]) <-- (--[s, t, u ..u , v ..v ]) <-- (--[s, t, u ..u , v ..v ]) <-- (--[s, t, u ..u , v ..v ]) <-- (--[s, t, u ..u , v ..v ]) 61 0 2 0 2 61 0 2 0 2 61 0 2 0 2 61 0 2 0 2 61 0 2 0 2 0 1 2 3 4 o1 : ChainComplex i2 : betti F 0 1 2 3 4 o2 = total: 1 9 16 9 1 0: 1 . . . . 1: . 1 . . . 2: . 7 8 1 . 3: . 1 8 7 . 4: . . . 1 . 5: . . . . 1 o2 : BettiTally