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# FcurvesOfGivenShape -- a list of the F-curves with the given shape

## Description

Given four positive integers $a$, $b$, $c$, $d$ with $a+b+c+d=n$, this function lists the F-curves $F_{I_1,I_2,I_3,I_4}$ with $\#I_1=a$, $\#I_2=b$, $\#I_3=c$, $\#I_4=d$.

 i1 : FcurvesOfGivenShape(2,2,1,1) o1 = {CurveClassRepresentativeM0nbar{"CurveExpression" => HashTable{{{1, 2}, "NumberOfMarkedPoints" => 6 ------------------------------------------------------------------------ {3, 4}, {5}, {6}} => 1}}, ------------------------------------------------------------------------ CurveClassRepresentativeM0nbar{"CurveExpression" => HashTable{{{1, 2}, "NumberOfMarkedPoints" => 6 ------------------------------------------------------------------------ {3, 5}, {4}, {6}} => 1}}, ------------------------------------------------------------------------ CurveClassRepresentativeM0nbar{"CurveExpression" => HashTable{{{1, 2}, "NumberOfMarkedPoints" => 6 ------------------------------------------------------------------------ {3, 6}, {4}, {5}} => 1}}, ------------------------------------------------------------------------ CurveClassRepresentativeM0nbar{"CurveExpression" => HashTable{{{1, 2}, "NumberOfMarkedPoints" => 6 ------------------------------------------------------------------------ {3}, {4, 5}, {6}} => 1}}, ------------------------------------------------------------------------ CurveClassRepresentativeM0nbar{"CurveExpression" => HashTable{{{1, 2}, "NumberOfMarkedPoints" => 6 ------------------------------------------------------------------------ {3}, {4, 6}, {5}} => 1}}, ------------------------------------------------------------------------ CurveClassRepresentativeM0nbar{"CurveExpression" => HashTable{{{1, 2}, "NumberOfMarkedPoints" => 6 ------------------------------------------------------------------------ {3}, {4}, {5, 6}} => 1}}, ------------------------------------------------------------------------ CurveClassRepresentativeM0nbar{"CurveExpression" => HashTable{{{1, 3}, "NumberOfMarkedPoints" => 6 ------------------------------------------------------------------------ {2, 4}, {5}, {6}} => 1}}, ------------------------------------------------------------------------ CurveClassRepresentativeM0nbar{"CurveExpression" => HashTable{{{1, 3}, "NumberOfMarkedPoints" => 6 ------------------------------------------------------------------------ {2, 5}, {4}, {6}} => 1}}, ------------------------------------------------------------------------ CurveClassRepresentativeM0nbar{"CurveExpression" => HashTable{{{1, 3}, "NumberOfMarkedPoints" => 6 ------------------------------------------------------------------------ {2, 6}, {4}, {5}} => 1}}, ------------------------------------------------------------------------ CurveClassRepresentativeM0nbar{"CurveExpression" => HashTable{{{1, 3}, "NumberOfMarkedPoints" => 6 ------------------------------------------------------------------------ {2}, {4, 5}, {6}} => 1}}, ------------------------------------------------------------------------ CurveClassRepresentativeM0nbar{"CurveExpression" => HashTable{{{1, 3}, "NumberOfMarkedPoints" => 6 ------------------------------------------------------------------------ {2}, {4, 6}, {5}} => 1}}, ------------------------------------------------------------------------ CurveClassRepresentativeM0nbar{"CurveExpression" => HashTable{{{1, 3}, "NumberOfMarkedPoints" => 6 ------------------------------------------------------------------------ {2}, {4}, {5, 6}} => 1}}, ------------------------------------------------------------------------ CurveClassRepresentativeM0nbar{"CurveExpression" => HashTable{{{1, 4}, "NumberOfMarkedPoints" => 6 ------------------------------------------------------------------------ {2, 3}, {5}, {6}} => 1}}, ------------------------------------------------------------------------ CurveClassRepresentativeM0nbar{"CurveExpression" => HashTable{{{1, 4}, "NumberOfMarkedPoints" => 6 ------------------------------------------------------------------------ {2, 5}, {3}, {6}} => 1}}, ------------------------------------------------------------------------ CurveClassRepresentativeM0nbar{"CurveExpression" => HashTable{{{1, 4}, "NumberOfMarkedPoints" => 6 ------------------------------------------------------------------------ {2, 6}, {3}, {5}} => 1}}, ------------------------------------------------------------------------ CurveClassRepresentativeM0nbar{"CurveExpression" => HashTable{{{1, 4}, "NumberOfMarkedPoints" => 6 ------------------------------------------------------------------------ {2}, {3, 5}, {6}} => 1}}, ------------------------------------------------------------------------ CurveClassRepresentativeM0nbar{"CurveExpression" => HashTable{{{1, 4}, "NumberOfMarkedPoints" => 6 ------------------------------------------------------------------------ {2}, {3, 6}, {5}} => 1}}, ------------------------------------------------------------------------ CurveClassRepresentativeM0nbar{"CurveExpression" => HashTable{{{1, 4}, "NumberOfMarkedPoints" => 6 ------------------------------------------------------------------------ {2}, {3}, {5, 6}} => 1}}, ------------------------------------------------------------------------ CurveClassRepresentativeM0nbar{"CurveExpression" => HashTable{{{1, 5}, "NumberOfMarkedPoints" => 6 ------------------------------------------------------------------------ {2, 3}, {4}, {6}} => 1}}, ------------------------------------------------------------------------ CurveClassRepresentativeM0nbar{"CurveExpression" => HashTable{{{1, 5}, "NumberOfMarkedPoints" => 6 ------------------------------------------------------------------------ {2, 4}, {3}, {6}} => 1}}, ------------------------------------------------------------------------ CurveClassRepresentativeM0nbar{"CurveExpression" => HashTable{{{1, 5}, "NumberOfMarkedPoints" => 6 ------------------------------------------------------------------------ {2, 6}, {3}, {4}} => 1}}, ------------------------------------------------------------------------ CurveClassRepresentativeM0nbar{"CurveExpression" => HashTable{{{1, 5}, "NumberOfMarkedPoints" => 6 ------------------------------------------------------------------------ {2}, {3, 4}, {6}} => 1}}, ------------------------------------------------------------------------ CurveClassRepresentativeM0nbar{"CurveExpression" => HashTable{{{1, 5}, "NumberOfMarkedPoints" => 6 ------------------------------------------------------------------------ {2}, {3, 6}, {4}} => 1}}, ------------------------------------------------------------------------ CurveClassRepresentativeM0nbar{"CurveExpression" => HashTable{{{1, 5}, "NumberOfMarkedPoints" => 6 ------------------------------------------------------------------------ {2}, {3}, {4, 6}} => 1}}, ------------------------------------------------------------------------ CurveClassRepresentativeM0nbar{"CurveExpression" => HashTable{{{1, 6}, "NumberOfMarkedPoints" => 6 ------------------------------------------------------------------------ {2, 3}, {4}, {5}} => 1}}, ------------------------------------------------------------------------ CurveClassRepresentativeM0nbar{"CurveExpression" => HashTable{{{1, 6}, "NumberOfMarkedPoints" => 6 ------------------------------------------------------------------------ {2, 4}, {3}, {5}} => 1}}, ------------------------------------------------------------------------ CurveClassRepresentativeM0nbar{"CurveExpression" => HashTable{{{1, 6}, "NumberOfMarkedPoints" => 6 ------------------------------------------------------------------------ {2, 5}, {3}, {4}} => 1}}, ------------------------------------------------------------------------ CurveClassRepresentativeM0nbar{"CurveExpression" => HashTable{{{1, 6}, "NumberOfMarkedPoints" => 6 ------------------------------------------------------------------------ {2}, {3, 4}, {5}} => 1}}, ------------------------------------------------------------------------ CurveClassRepresentativeM0nbar{"CurveExpression" => HashTable{{{1, 6}, "NumberOfMarkedPoints" => 6 ------------------------------------------------------------------------ {2}, {3, 5}, {4}} => 1}}, ------------------------------------------------------------------------ CurveClassRepresentativeM0nbar{"CurveExpression" => HashTable{{{1, 6}, "NumberOfMarkedPoints" => 6 ------------------------------------------------------------------------ {2}, {3}, {4, 5}} => 1}}, ------------------------------------------------------------------------ CurveClassRepresentativeM0nbar{"CurveExpression" => HashTable{{{1}, {2, "NumberOfMarkedPoints" => 6 ------------------------------------------------------------------------ 3}, {4, 5}, {6}} => 1}}, ------------------------------------------------------------------------ CurveClassRepresentativeM0nbar{"CurveExpression" => HashTable{{{1}, {2, "NumberOfMarkedPoints" => 6 ------------------------------------------------------------------------ 3}, {4, 6}, {5}} => 1}}, ------------------------------------------------------------------------ CurveClassRepresentativeM0nbar{"CurveExpression" => HashTable{{{1}, {2, "NumberOfMarkedPoints" => 6 ------------------------------------------------------------------------ 3}, {4}, {5, 6}} => 1}}, ------------------------------------------------------------------------ CurveClassRepresentativeM0nbar{"CurveExpression" => HashTable{{{1}, {2, "NumberOfMarkedPoints" => 6 ------------------------------------------------------------------------ 4}, {3, 5}, {6}} => 1}}, ------------------------------------------------------------------------ CurveClassRepresentativeM0nbar{"CurveExpression" => HashTable{{{1}, {2, "NumberOfMarkedPoints" => 6 ------------------------------------------------------------------------ 4}, {3, 6}, {5}} => 1}}, ------------------------------------------------------------------------ CurveClassRepresentativeM0nbar{"CurveExpression" => HashTable{{{1}, {2, "NumberOfMarkedPoints" => 6 ------------------------------------------------------------------------ 4}, {3}, {5, 6}} => 1}}, ------------------------------------------------------------------------ CurveClassRepresentativeM0nbar{"CurveExpression" => HashTable{{{1}, {2, "NumberOfMarkedPoints" => 6 ------------------------------------------------------------------------ 5}, {3, 4}, {6}} => 1}}, ------------------------------------------------------------------------ CurveClassRepresentativeM0nbar{"CurveExpression" => HashTable{{{1}, {2, "NumberOfMarkedPoints" => 6 ------------------------------------------------------------------------ 5}, {3, 6}, {4}} => 1}}, ------------------------------------------------------------------------ CurveClassRepresentativeM0nbar{"CurveExpression" => HashTable{{{1}, {2, "NumberOfMarkedPoints" => 6 ------------------------------------------------------------------------ 5}, {3}, {4, 6}} => 1}}, ------------------------------------------------------------------------ CurveClassRepresentativeM0nbar{"CurveExpression" => HashTable{{{1}, {2, "NumberOfMarkedPoints" => 6 ------------------------------------------------------------------------ 6}, {3, 4}, {5}} => 1}}, ------------------------------------------------------------------------ CurveClassRepresentativeM0nbar{"CurveExpression" => HashTable{{{1}, {2, "NumberOfMarkedPoints" => 6 ------------------------------------------------------------------------ 6}, {3, 5}, {4}} => 1}}, ------------------------------------------------------------------------ CurveClassRepresentativeM0nbar{"CurveExpression" => HashTable{{{1}, {2, "NumberOfMarkedPoints" => 6 ------------------------------------------------------------------------ 6}, {3}, {4, 5}} => 1}}, ------------------------------------------------------------------------ CurveClassRepresentativeM0nbar{"CurveExpression" => HashTable{{{1}, {2}, "NumberOfMarkedPoints" => 6 ------------------------------------------------------------------------ {3, 4}, {5, 6}} => 1}}, ------------------------------------------------------------------------ CurveClassRepresentativeM0nbar{"CurveExpression" => HashTable{{{1}, {2}, "NumberOfMarkedPoints" => 6 ------------------------------------------------------------------------ {3, 5}, {4, 6}} => 1}}, ------------------------------------------------------------------------ CurveClassRepresentativeM0nbar{"CurveExpression" => HashTable{{{1}, {2}, "NumberOfMarkedPoints" => 6 ------------------------------------------------------------------------ {3, 6}, {4, 5}} => 1}}} o1 : List

## Ways to use FcurvesOfGivenShape :

• FcurvesOfGivenShape(ZZ,ZZ,ZZ,ZZ)

## For the programmer

The object FcurvesOfGivenShape is .