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kGonalNodalCurves :: criticalBettiNumber

criticalBettiNumber -- computes the critical Betti number

Synopsis

Description

Computes the Artinian reduction of the ideal of a canonical curve and the critical Koszul map. Afterwars we compute the critical Betti number via Koszul cohomology. The M2 package extrasForTheKernel provides a function that computes the artinian reduction.

i1 : (k,g,n)=(4,8,1000);
i2 : I=idealOfNodalCurve(k,g,n);

               ZZ
o2 : Ideal of ----[t , t , t , t , t , t , t , t ]
              1009  0   1   2   3   4   5   6   7
i3 : time criticalBettiNumber(I)
     -- used 0.086942 seconds

o3 = 4
i4 : time criticalBettiNumber(k,g,n)
     -- used 0.818156 seconds

o4 = 4
i5 : time betti res I
     -- used 2.62404 seconds

            0  1  2  3  4  5 6
o5 = total: 1 15 39 50 39 15 1
         0: 1  .  .  .  .  . .
         1: . 15 35 25  4  . .
         2: .  .  4 25 35 15 .
         3: .  .  .  .  .  . 1

o5 : BettiTally

See also

Ways to use criticalBettiNumber :

  • criticalBettiNumber(Ideal)
  • criticalBettiNumber(ZZ,ZZ,ZZ)