nonadjacentBasis -- computes the nonadjacent basis of divisors on M0nbar

Synopsis

Usage:

nonadjacentBasis n
Inputs:
- n, an integer,
Outputs:
- a list,

Description

The nonadjacent basis is described in Carr, A polygonal presentation of $Pic(\bar{M}_{0,n})$, arXiv:0911.2649.

i1 : B5=nonadjacentBasis(5)

o1 = {DivisorClassRepresentativeM0nbar{"DivisorExpression" => HashTable{{1,
                                       "NumberOfMarkedPoints" => 5         
     ------------------------------------------------------------------------
     3} => 1}}, DivisorClassRepresentativeM0nbar{"DivisorExpression" =>
                                                 "NumberOfMarkedPoints"
     ------------------------------------------------------------------------
     HashTable{{1, 4} => 1}},
     => 5                    
     ------------------------------------------------------------------------
     DivisorClassRepresentativeM0nbar{"DivisorExpression" => HashTable{{2, 4}
                                      "NumberOfMarkedPoints" => 5            
     ------------------------------------------------------------------------
     => 1}}, DivisorClassRepresentativeM0nbar{"DivisorExpression" =>
                                              "NumberOfMarkedPoints"
     ------------------------------------------------------------------------
     HashTable{{2, 5} => 1}},
     => 5                    
     ------------------------------------------------------------------------
     DivisorClassRepresentativeM0nbar{"DivisorExpression" => HashTable{{3, 5}
                                      "NumberOfMarkedPoints" => 5
     ------------------------------------------------------------------------
     => 1}}}

o1 : List

i2 : print toString B5
{new DivisorClassRepresentativeM0nbar from {DivisorExpression => new HashTable from {{1, 3} => 1}, NumberOfMarkedPoints => 5}, new DivisorClassRepresentativeM0nbar from {DivisorExpression => new HashTable from {{1, 4} => 1}, NumberOfMarkedPoints => 5}, new DivisorClassRepresentativeM0nbar from {DivisorExpression => new HashTable from {{2, 4} => 1}, NumberOfMarkedPoints => 5}, new DivisorClassRepresentativeM0nbar from {DivisorExpression => new HashTable from {{2, 5} => 1}, NumberOfMarkedPoints => 5}, new DivisorClassRepresentativeM0nbar from {DivisorExpression => new HashTable from {{3, 5} => 1}, NumberOfMarkedPoints => 5}}

i3 : B6=nonadjacentBasis(6)

o3 = {DivisorClassRepresentativeM0nbar{"DivisorExpression" => HashTable{{1,
                                       "NumberOfMarkedPoints" => 6         
     ------------------------------------------------------------------------
     3} => 1}}, DivisorClassRepresentativeM0nbar{"DivisorExpression" =>
                                                 "NumberOfMarkedPoints"
     ------------------------------------------------------------------------
     HashTable{{1, 4} => 1}},
     => 6                    
     ------------------------------------------------------------------------
     DivisorClassRepresentativeM0nbar{"DivisorExpression" => HashTable{{1, 5}
                                      "NumberOfMarkedPoints" => 6            
     ------------------------------------------------------------------------
     => 1}}, DivisorClassRepresentativeM0nbar{"DivisorExpression" =>
                                              "NumberOfMarkedPoints"
     ------------------------------------------------------------------------
     HashTable{{2, 4} => 1}},
     => 6                    
     ------------------------------------------------------------------------
     DivisorClassRepresentativeM0nbar{"DivisorExpression" => HashTable{{2, 5}
                                      "NumberOfMarkedPoints" => 6            
     ------------------------------------------------------------------------
     => 1}}, DivisorClassRepresentativeM0nbar{"DivisorExpression" =>
                                              "NumberOfMarkedPoints"
     ------------------------------------------------------------------------
     HashTable{{2, 6} => 1}},
     => 6                    
     ------------------------------------------------------------------------
     DivisorClassRepresentativeM0nbar{"DivisorExpression" => HashTable{{3, 5}
                                      "NumberOfMarkedPoints" => 6            
     ------------------------------------------------------------------------
     => 1}}, DivisorClassRepresentativeM0nbar{"DivisorExpression" =>
                                              "NumberOfMarkedPoints"
     ------------------------------------------------------------------------
     HashTable{{3, 6} => 1}},
     => 6                    
     ------------------------------------------------------------------------
     DivisorClassRepresentativeM0nbar{"DivisorExpression" => HashTable{{4, 6}
                                      "NumberOfMarkedPoints" => 6            
     ------------------------------------------------------------------------
     => 1}}, DivisorClassRepresentativeM0nbar{"DivisorExpression" =>
                                              "NumberOfMarkedPoints"
     ------------------------------------------------------------------------
     HashTable{{1, 2, 4} => 1}},
     => 6                       
     ------------------------------------------------------------------------
     DivisorClassRepresentativeM0nbar{"DivisorExpression" => HashTable{{1, 2,
                                      "NumberOfMarkedPoints" => 6            
     ------------------------------------------------------------------------
     5} => 1}}, DivisorClassRepresentativeM0nbar{"DivisorExpression" =>
                                                 "NumberOfMarkedPoints"
     ------------------------------------------------------------------------
     HashTable{{1, 3, 4} => 1}},
     => 6                       
     ------------------------------------------------------------------------
     DivisorClassRepresentativeM0nbar{"DivisorExpression" => HashTable{{1, 3,
                                      "NumberOfMarkedPoints" => 6            
     ------------------------------------------------------------------------
     5} => 1}}, DivisorClassRepresentativeM0nbar{"DivisorExpression" =>
                                                 "NumberOfMarkedPoints"
     ------------------------------------------------------------------------
     HashTable{{1, 3, 6} => 1}},
     => 6                       
     ------------------------------------------------------------------------
     DivisorClassRepresentativeM0nbar{"DivisorExpression" => HashTable{{1, 4,
                                      "NumberOfMarkedPoints" => 6            
     ------------------------------------------------------------------------
     5} => 1}}, DivisorClassRepresentativeM0nbar{"DivisorExpression" =>
                                                 "NumberOfMarkedPoints"
     ------------------------------------------------------------------------
     HashTable{{1, 4, 6} => 1}}}
     => 6

o3 : List

i4 : print toString B6
{new DivisorClassRepresentativeM0nbar from {DivisorExpression => new HashTable from {{1, 3} => 1}, NumberOfMarkedPoints => 6}, new DivisorClassRepresentativeM0nbar from {DivisorExpression => new HashTable from {{1, 4} => 1}, NumberOfMarkedPoints => 6}, new DivisorClassRepresentativeM0nbar from {DivisorExpression => new HashTable from {{1, 5} => 1}, NumberOfMarkedPoints => 6}, new DivisorClassRepresentativeM0nbar from {DivisorExpression => new HashTable from {{2, 4} => 1}, NumberOfMarkedPoints => 6}, new DivisorClassRepresentativeM0nbar from {DivisorExpression => new HashTable from {{2, 5} => 1}, NumberOfMarkedPoints => 6}, new DivisorClassRepresentativeM0nbar from {DivisorExpression => new HashTable from {{2, 6} => 1}, NumberOfMarkedPoints => 6}, new DivisorClassRepresentativeM0nbar from {DivisorExpression => new HashTable from {{3, 5} => 1}, NumberOfMarkedPoints => 6}, new DivisorClassRepresentativeM0nbar from {DivisorExpression => new HashTable from {{3, 6} => 1}, NumberOfMarkedPoints => 6}, new DivisorClassRepresentativeM0nbar from {DivisorExpression => new HashTable from {{4, 6} => 1}, NumberOfMarkedPoints => 6}, new DivisorClassRepresentativeM0nbar from {DivisorExpression => new HashTable from {{1, 2, 4} => 1}, NumberOfMarkedPoints => 6}, new DivisorClassRepresentativeM0nbar from {DivisorExpression => new HashTable from {{1, 2, 5} => 1}, NumberOfMarkedPoints => 6}, new DivisorClassRepresentativeM0nbar from {DivisorExpression => new HashTable from {{1, 3, 4} => 1}, NumberOfMarkedPoints => 6}, new DivisorClassRepresentativeM0nbar from {DivisorExpression => new HashTable from {{1, 3, 5} => 1}, NumberOfMarkedPoints => 6}, new DivisorClassRepresentativeM0nbar from {DivisorExpression => new HashTable from {{1, 3, 6} => 1}, NumberOfMarkedPoints => 6}, new DivisorClassRepresentativeM0nbar from {DivisorExpression => new HashTable from {{1, 4, 5} => 1}, NumberOfMarkedPoints => 6}, new DivisorClassRepresentativeM0nbar from {DivisorExpression => new HashTable from {{1, 4, 6} => 1}, NumberOfMarkedPoints => 6}}

Ways to use nonadjacentBasis :

nonadjacentBasis(ZZ)

For the programmer

The object nonadjacentBasis is a method function.