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# CurveClassRepresentativeM0nbar -- class implementing curves on the moduli space of stable n-pointed genus zero curves

## Description

This class represents curve classes in $ NS_1(\bar{M}_{0,n}) $. A curve class is just a linear combination of F-curves.

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

    i2 : curveClassRepresentativeM0nbar(5,L)

    o2 = CurveClassRepresentativeM0nbar{"CurveExpression" => HashTable{{{1, 2}, {3}, {4}, {5}} => 1}}
                                                                       {{1, 3}, {2}, {4}, {5}} => 1
                                        "NumberOfMarkedPoints" => 5

    o2 : CurveClassRepresentativeM0nbar

## Functions and methods returning an object of class CurveClassRepresentativeM0nbar:

- curveClassRepresentativeM0nbar -- creates an object of type CurveClassRepresentativeM0nbar
- KeelRelationAmongCurves -- write the Keel relation among F curves based on the input lists
- writeCurveInSingletonSpineBasis -- write a curve class in the singleton spine basis of curve

## Methods that use an object of class CurveClassRepresentativeM0nbar:

- CurveClassRepresentativeM0nbar + CurveClassRepresentativeM0nbar -- add two curve class representatives on M0nbar
- CurveClassRepresentativeM0nbar - CurveClassRepresentativeM0nbar -- subtract two curve class representatives on M0nbar
- `intersect(CurveClassRepresentativeM0nbar,DivisorClassRepresentativeM0nbar)` -- see intersect -- intersection number of a curve class and divisor class
- intersect(DivisorClassRepresentativeM0nbar,CurveClassRepresentativeM0nbar) -- intersection number of a divisor class and curve class
- `isEffectiveExpression(CurveClassRepresentativeM0nbar)` -- see isEffectiveExpression -- determines whether a curve class expression is effective
- `isEquivalent(CurveClassRepresentativeM0nbar,CurveClassRepresentativeM0nbar)` -- see isEquivalent -- check whether two curve class representatives are numerically equivalent
- `negativeSum(CurveClassRepresentativeM0nbar)` -- see negativeSum -- sum of the negative coefficients in CurveClassRepresentativeM0nbar
- Number * CurveClassRepresentativeM0nbar -- multiply a curve class representatives on M0nbar by a scalar
- `permute(List,CurveClassRepresentativeM0nbar)` -- see permute -- compute the image of a curve class representative under a permutation of the marked points
- `seekEffectiveExpression(CurveClassRepresentativeM0nbar)` -- see seekEffectiveExpression -- seeks to write a curve class as an effective sum of F-curves
- tex(CurveClassRepresentativeM0nbar) -- convert to TeX format
- `writeCurveInDualNonadjacentBasis(CurveClassRepresentativeM0nbar)` -- see writeCurveInDualNonadjacentBasis -- write a curve in the basis dual to the nonadjacent basis
- `writeCurveInSingletonSpineBasis(CurveClassRepresentativeM0nbar)` -- see writeCurveInSingletonSpineBasis -- write a curve class in the singleton spine basis of curve

## For the programmer

The object CurveClassRepresentativeM0nbar is a type, with ancestor classes HashTable < Thing.

The source of this document is in /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/M0nbar.m2:1296:0.