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# resCurveOnScroll -- Computes the relative canonical resolution

- Usage:
    `resX=resCurveOnScroll(Jcan,g,l)`
    `resX=resCurveOnScroll(Jcan,g)`
- Inputs:
  - Jcan, an ideal, the ideal of a genus g curve with a degree k line bundle in terms of generators on the scroll
  - g, an integer, the genus of C
  - l, an integer, the length limit of the resolution
- Outputs:
  - resX, a chain complex, the relative canonical resolution

## Description

This function computes the relative canonical resolution by picking syzygies of correct degree in each step until the length limit is reached.

    i1 : (g,k,n) = (8,5,1000);

    i2 : Ican = canCurveWithFixedScroll(g,k,n);

                   ZZ
    o2 : Ideal of ----[t ..t ]
                  1009  0   7

    i3 : Jcan = curveOnScroll(Ican,g,k);

                   ZZ
    o3 : Ideal of ----[pp ..pp , v..w]
                  1009   0    3

    i4 : resX = resCurveOnScroll(Jcan,g,2);

    i5 : betti resX

                0 1 2 3
    o5 = total: 1 5 5 1
             0: 1 . . .
             1: . . . .
             2: . 4 1 .
             3: . 1 4 .
             4: . . . .
             5: . . . 1

    o5 : BettiTally

## See also

- curveOnScroll -- Computes the ideal of a canonical curve on a normalized scroll in terms of generators of the scroll

## Ways to use resCurveOnScroll:

- `resCurveOnScroll(Ideal,ZZ)`
- `resCurveOnScroll(Ideal,ZZ,ZZ)`

## For the programmer

The object resCurveOnScroll is a method function.

The source of this document is in /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/RelativeCanonicalResolution.m2:604:0.