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 $\PP^{ g-1}$
• Outputs:
  • I, an ideal, of a canonical curve $C$ of genus $g$

Description

i1 : setRandomSeed "alpha";

i2 : g=14;

i3 : FF=ZZ/10007;

i4 : R=FF[x_0..x_(g-1)];

i5 : time betti(I=(random canonicalCurve)(g,R))
     -- used 4.46869 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