Given the relative canonical resolution of C on a normalized scroll P(E), the function computes a (possibly non-minimal) free resolution of C in Pg-1 by an iterated mapping cone construction. For gonality k=3,4 the iterated mapping cone is always minimal. In these cases "iteratedCone" is much faster (for g >9) than computing the resolution via the resolution command.
i1 : (g,k,n) = (8,5,1000) o1 = (8, 5, 1000) o1 : Sequence |
i2 : e = balancedPartition(k-1,g-k+1)
o2 = {1, 1, 1, 1}
o2 : List
|
i3 : Ican = canCurveWithFixedScroll(g,k,n);
ZZ
o3 : Ideal of ----[t , t , t , t , t , t , t , t ]
1009 0 1 2 3 4 5 6 7
|
i4 : betti res(Ican,DegreeLimit=>1)
0 1 2 3
o4 = total: 1 15 35 21
0: 1 . . .
1: . 15 35 21
o4 : BettiTally
|
i5 : Jcan = curveOnScroll(Ican,g,k);
ZZ
o5 : Ideal of ----[pp , pp , pp , pp , v, w]
1009 0 1 2 3
|
i6 : betti(resX = resCurveOnScroll(Jcan,g,2))
0 1 2 3
o6 = total: 1 5 5 1
0: 1 . . .
1: . . . .
2: . 4 1 .
3: . 1 4 .
4: . . . .
5: . . . 1
o6 : BettiTally
|
i7 : betti(resC = iteratedCone(resX,e))
0 1 2 3 4 5 6
o7 = total: 1 15 41 54 41 15 1
0: 1 . . . . . .
1: . 15 35 27 6 . .
2: . . 6 27 35 15 .
3: . . . . . . 1
o7 : BettiTally
|