seekEffectiveExpression -- seeks to write a curve class as an effective sum of F-curves

Synopsis

Usage:

seekEffectiveExpression(C)
Inputs:
- C, an instance of the type CurveClassRepresentativeM0nbar,
Outputs:
- H, a hash table,

Description

This function seeks to write a curve class representative as an effective sum of F-curves. See Moon and Swinarski, "Subvarieties of $\bar{M}_{0,n}$ from group actions" for a description of the strategy used.

Important note: the strategy used by this function is not an algorithm because it is not guaranteed to terminate.

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

i2 : C1=curveClassRepresentativeM0nbar(5,L1);

i3 : seekEffectiveExpression(C1)
New sum of negative coefficients: 0
New curve expression: new CurveClassRepresentativeM0nbar from {CurveExpression => new HashTable from {{{1, 2}, {3}, {4}, {5}} => 1}, NumberOfMarkedPoints => 5}
Keel relations added: 
    F_{{1}, {2, 5}, {3}, {4}} - F_{{1, 2}, {3}, {4}, {5}} - F_{{1}, {2}, {3}, {4, 5}} + F_{{1, 4}, {2}, {3}, {5}}

o3 = HashTable{"CurveClassRepresentative" => CurveClassRepresentativeM0nbar{"CurveExpression" => HashTable{{{1, 2}, {3}, {4}, {5}} => 1}}}
                                                                            "NumberOfMarkedPoints" => 5
               "TotalPath" => {{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

o3 : HashTable

Ways to use seekEffectiveExpression:

seekEffectiveExpression(CurveClassRepresentativeM0nbar)

For the programmer

The object seekEffectiveExpression is a method function.