writeCurveInSingletonSpineBasis(ZZ,List) -- write a curve class in the singleton spine basis of curve

Synopsis

Function: writeCurveInSingletonSpineBasis
Usage:

writeCurveInSingletonSpineBasis(n,L)
Inputs:
- n, an integer,
- L, a list,
Outputs:
- C2, an instance of the type CurveClassRepresentativeM0nbar,

Description

This function writes a curve class in the singleton spine basis of curves. The input is the number of marked points n, and a list of the intersection numbers with the nonadjacent basis of divisors.

Recall that the singleton spine basis of curves is only defined on $\bar{M}_{0,n}$ if $n \geq 7$.

i1 : L= { {{1,2},{3,4},{5,6},{7,8}}=>1 };

i2 : C=curveClassRepresentativeM0nbar(8,L);

i3 : v=writeCurveInDualNonadjacentBasis(C);

i4 : writeCurveInSingletonSpineBasis(8,v)

o4 = CurveClassRepresentativeM0nbar{"CurveExpression" => HashTable{{{1, 2}, {3, 4}, {5}, {6, 7, 8}} => 1 }}
                                                                   {{1, 3, 4, 5, 6}, {2}, {7}, {8}} => -1
                                                                   {{1, 3, 4, 5, 8}, {2}, {6}, {7}} => 1
                                                                   {{1, 3, 4, 7, 8}, {2}, {5}, {6}} => -1
                                                                   {{1, 8}, {2}, {3, 4, 5}, {6, 7}} => 1
                                                                   {{1}, {2, 3, 4, 5}, {6}, {7, 8}} => 1
                                                                   {{1}, {2, 3, 4, 7, 8}, {5}, {6}} => -1
                                                                   {{1}, {2}, {3, 4, 5, 6, 7}, {8}} => 1
                                                                   {{1}, {2}, {3, 4, 5, 6}, {7, 8}} => -1
                                                                   {{1}, {2}, {3, 4, 6, 7, 8}, {5}} => 1
                                                                   {{1}, {2}, {3, 4, 7, 8}, {5, 6}} => -1
                                    "NumberOfMarkedPoints" => 8

o4 : CurveClassRepresentativeM0nbar

Ways to use this method: