canonicalCurve -- Compute a random canonical curve of genus less or equal to 14

Synopsis

Usage:
I=(random canonicalCurve)(g,S)
Inputs:
- g, an integer, the genus
- R, a polynomial ring, homogeneous coordinate ring of ℙ^g-1
Outputs:
- I, an ideal, of a canonical curve C of genus g

Description

Compute a random canonical curve of genus g ≤ 14, based on the proofs of unirationality of M_g by Severi, Sernesi, Chang-Ran and Verra.

i1 : g=14;

i2 : FF=ZZ/10007;

i3 : R=FF[x_0..x_(g-1)];

i4 : setRandomSeed "alpha";

i5 : time betti(I=(random canonicalCurve)(g,R))
     -- used 19.8638 seconds

            0  1
o5 = total: 1 66
         0: 1  .
         1: . 66

o5 : BettiTally

i6 : genus I == g and degree I ==2*g-2

o6 = true

For the programmer

The object canonicalCurve is an object of class RandomObject.