getAPrymCanonicalCurve -- get a Prym canonical curve

We compute the ideal of a Prym canonical of genus g over a finite ground field by starting with a smooth anonical curve of genus 8 with two torsion. We add nodes and extend the two torsion untill we reach the desired genus. The curve of genus 8 has a plane modell of degree 7. Hence is somewhat special. The resulting curve get nodes by identifying random two points. The time reaching the curve of each intermediate genus will be printed reported.

i1 : betti(J=getAPrymCanonicalCurve(9,10^4))
     -- used 1.27913 seconds
     -- used 9.00296 seconds

            0  1
o1 = total: 1 12
         0: 1  .
         1: . 12

o1 : BettiTally

i2 : dim J, codim J, degree J, genus J

o2 = (2, 6, 16, 9)

o2 : Sequence