# canonicalCarpet -- Carpet of given genus and Clifford index

## Synopsis

• Usage:
I = canonicalCarpet(g,cliff)
(I,xmat,ymat) = canonicalCarpet(g,cliff,Scrolls=>true)
• Inputs:
• g, an integer, desired genus
• cliff, an integer, desired clifford index
• Optional inputs:
• Characteristic => an integer, default value 32003, the characteristic of the ground field
• Scrolls => , default value false, if true return in addition the matrices defining the sections
• FineGrading => , default value false, if true then I is defined over the ring with $\ZZ^4$-grading
• Outputs:
• I, an ideal, ideal of the K3 Carpet of (sectional) genus g, Clifford index cliff

## Description

This is just a re-indexing of the carpet script: canonicalCarpet(g,cliff) = carpet(g-cliff-1, cliff). Here the natural choices for cliff are $1 \leq{} cliff \leq{} (g-1)//2$.