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

## 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 .