isEquivalent -- check whether two curve class representatives are numerically equivalent

Synopsis

Usage:

isEquivalent(C1,C2)
Inputs:
- C1, an instance of the type CurveClassRepresentativeM0nbar,
- C2, an instance of the type CurveClassRepresentativeM0nbar,
Outputs:
- b, a Boolean value,

This function checks whether two curve class representatives C1 and C2 are equivalent.

To do so, it checks whether the vector of intersection numbers with the nonadjacent basis of divisors is the same for C1 and C2.

i1 : L1={ {{{1,2},{3},{4},{5}},1}, {{{1,3},{2},{4},{5}},1}};

i2 : C1=curveClassRepresentativeM0nbar(5,L1);

i3 : L2={ {{{1},{2},{3},{4,5}},-1}, {{{1},{2,5},{3},{4}},1}, {{{1,4},{2},{3},{5}},1},{{{1,3},{2},{4},{5}},1}};

i4 : C2=curveClassRepresentativeM0nbar(5,L2);

i5 : isEquivalent(C1,C2)

o5 = true

isEquivalent(CurveClassRepresentativeM0nbar,CurveClassRepresentativeM0nbar)
isEquivalent(DivisorClassRepresentativeM0nbar,DivisorClassRepresentativeM0nbar) -- check whether two divisor class representatives are numerically equivalent