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M0nbar :: KeelRelationAmongCurves

KeelRelationAmongCurves -- write the Keel relation among F curves based on the input lists

Synopsis

Description

This function writes a Keel relation among curves. It is an expression supported on four F-curves that is equivalent to zero.

Specifically, let P = I1 ∪…∪I5 be a partition of {1,...,n} into five nonempty subsets. Then this function returns the curve class representative FI1,I2,I3,I4 ∪I5 + FI1 ∪I2, I3,I4,I5 - FI1, I4, I3, I2 ∪I5 - FI1 ∪I4, I3, I2, I5.

i1 : C1=KeelRelationAmongCurves({{1},{2},{3},{4},{5}})

o1 = CurveClassRepresentativeM0nbar{CurveExpression => HashTable{{{1, 2}, {3}, {4}, {5}} => 1 }}
                                                                 {{1, 4}, {2}, {3}, {5}} => -1
                                                                 {{1}, {2, 5}, {3}, {4}} => -1
                                                                 {{1}, {2}, {3}, {4, 5}} => 1
                                    NumberOfMarkedPoints => 5

o1 : CurveClassRepresentativeM0nbar
i2 : L={  };
i3 : C2=curveClassRepresentativeM0nbar(5,L);
i4 : isEquivalent(C1,C2)

o4 = true

Ways to use KeelRelationAmongCurves :