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ThinSincereQuivers :: AsSubquiver

AsSubquiver

Description

option for subquiver representation. Applying AsSubquiver = true insures that the matrix representation of the subquiver is the same size as the matrix original quiver. If false, then the subquiver is returned as a standalone quiver represented by only the vertices and arrows comprising the subquiver.

i1 : subquivers(bipartiteQuiver(2, 2), Format=>"quiver", AsSubquiver=>true)

o1 = {ToricQuiver{flow => {1, 0, 0, 0}                  },
                  IncidenceMatrix => | -1 -1 0  0  |      
                                     | 0  0  -1 -1 |      
                                     | 1  0  1  0  |      
                                     | 0  1  0  1  |      
                  Q0 => {0, 1, 2, 3}                      
                  Q1 => {{0, 2}, {0, 3}, {1, 2}, {1, 3}}  
                  weights => {-1, 0, 1, 0}                
     ------------------------------------------------------------------------
     ToricQuiver{flow => {0, 1, 0, 0}                  },
                 IncidenceMatrix => | -1 -1 0  0  |      
                                    | 0  0  -1 -1 |      
                                    | 1  0  1  0  |      
                                    | 0  1  0  1  |      
                 Q0 => {0, 1, 2, 3}                      
                 Q1 => {{0, 2}, {0, 3}, {1, 2}, {1, 3}}  
                 weights => {-1, 0, 0, 1}                
     ------------------------------------------------------------------------
     ToricQuiver{flow => {0, 0, 1, 0}                  },
                 IncidenceMatrix => | -1 -1 0  0  |      
                                    | 0  0  -1 -1 |      
                                    | 1  0  1  0  |      
                                    | 0  1  0  1  |      
                 Q0 => {0, 1, 2, 3}                      
                 Q1 => {{0, 2}, {0, 3}, {1, 2}, {1, 3}}  
                 weights => {0, -1, 1, 0}                
     ------------------------------------------------------------------------
     ToricQuiver{flow => {0, 0, 0, 1}                  },
                 IncidenceMatrix => | -1 -1 0  0  |      
                                    | 0  0  -1 -1 |      
                                    | 1  0  1  0  |      
                                    | 0  1  0  1  |      
                 Q0 => {0, 1, 2, 3}                      
                 Q1 => {{0, 2}, {0, 3}, {1, 2}, {1, 3}}  
                 weights => {0, -1, 0, 1}                
     ------------------------------------------------------------------------
     ToricQuiver{flow => {1, 1, 0, 0}                  },
                 IncidenceMatrix => | -1 -1 0  0  |      
                                    | 0  0  -1 -1 |      
                                    | 1  0  1  0  |      
                                    | 0  1  0  1  |      
                 Q0 => {0, 1, 2, 3}                      
                 Q1 => {{0, 2}, {0, 3}, {1, 2}, {1, 3}}  
                 weights => {-2, 0, 1, 1}                
     ------------------------------------------------------------------------
     ToricQuiver{flow => {1, 0, 1, 0}                  },
                 IncidenceMatrix => | -1 -1 0  0  |      
                                    | 0  0  -1 -1 |      
                                    | 1  0  1  0  |      
                                    | 0  1  0  1  |      
                 Q0 => {0, 1, 2, 3}                      
                 Q1 => {{0, 2}, {0, 3}, {1, 2}, {1, 3}}  
                 weights => {-1, -1, 2, 0}               
     ------------------------------------------------------------------------
     ToricQuiver{flow => {0, 1, 1, 0}                  },
                 IncidenceMatrix => | -1 -1 0  0  |      
                                    | 0  0  -1 -1 |      
                                    | 1  0  1  0  |      
                                    | 0  1  0  1  |      
                 Q0 => {0, 1, 2, 3}                      
                 Q1 => {{0, 2}, {0, 3}, {1, 2}, {1, 3}}  
                 weights => {-1, -1, 1, 1}               
     ------------------------------------------------------------------------
     ToricQuiver{flow => {1, 0, 0, 1}                  },
                 IncidenceMatrix => | -1 -1 0  0  |      
                                    | 0  0  -1 -1 |      
                                    | 1  0  1  0  |      
                                    | 0  1  0  1  |      
                 Q0 => {0, 1, 2, 3}                      
                 Q1 => {{0, 2}, {0, 3}, {1, 2}, {1, 3}}  
                 weights => {-1, -1, 1, 1}               
     ------------------------------------------------------------------------
     ToricQuiver{flow => {0, 1, 0, 1}                  },
                 IncidenceMatrix => | -1 -1 0  0  |      
                                    | 0  0  -1 -1 |      
                                    | 1  0  1  0  |      
                                    | 0  1  0  1  |      
                 Q0 => {0, 1, 2, 3}                      
                 Q1 => {{0, 2}, {0, 3}, {1, 2}, {1, 3}}  
                 weights => {-1, -1, 0, 2}               
     ------------------------------------------------------------------------
     ToricQuiver{flow => {0, 0, 1, 1}                  },
                 IncidenceMatrix => | -1 -1 0  0  |      
                                    | 0  0  -1 -1 |      
                                    | 1  0  1  0  |      
                                    | 0  1  0  1  |      
                 Q0 => {0, 1, 2, 3}                      
                 Q1 => {{0, 2}, {0, 3}, {1, 2}, {1, 3}}  
                 weights => {0, -2, 1, 1}                
     ------------------------------------------------------------------------
     ToricQuiver{flow => {1, 1, 1, 0}                  },
                 IncidenceMatrix => | -1 -1 0  0  |      
                                    | 0  0  -1 -1 |      
                                    | 1  0  1  0  |      
                                    | 0  1  0  1  |      
                 Q0 => {0, 1, 2, 3}                      
                 Q1 => {{0, 2}, {0, 3}, {1, 2}, {1, 3}}  
                 weights => {-2, -1, 2, 1}               
     ------------------------------------------------------------------------
     ToricQuiver{flow => {1, 1, 0, 1}                  },
                 IncidenceMatrix => | -1 -1 0  0  |      
                                    | 0  0  -1 -1 |      
                                    | 1  0  1  0  |      
                                    | 0  1  0  1  |      
                 Q0 => {0, 1, 2, 3}                      
                 Q1 => {{0, 2}, {0, 3}, {1, 2}, {1, 3}}  
                 weights => {-2, -1, 1, 2}               
     ------------------------------------------------------------------------
     ToricQuiver{flow => {1, 0, 1, 1}                  },
                 IncidenceMatrix => | -1 -1 0  0  |      
                                    | 0  0  -1 -1 |      
                                    | 1  0  1  0  |      
                                    | 0  1  0  1  |      
                 Q0 => {0, 1, 2, 3}                      
                 Q1 => {{0, 2}, {0, 3}, {1, 2}, {1, 3}}  
                 weights => {-1, -2, 2, 1}               
     ------------------------------------------------------------------------
     ToricQuiver{flow => {0, 1, 1, 1}                  }}
                 IncidenceMatrix => | -1 -1 0  0  |
                                    | 0  0  -1 -1 |
                                    | 1  0  1  0  |
                                    | 0  1  0  1  |
                 Q0 => {0, 1, 2, 3}
                 Q1 => {{0, 2}, {0, 3}, {1, 2}, {1, 3}}
                 weights => {-1, -2, 1, 2}

o1 : List
 
i2 : subquivers(bipartiteQuiver(2, 2), Format=>"quiver", AsSubquiver=>false)

o2 = {ToricQuiver{flow => {1}              }, ToricQuiver{flow => {1}       
                  IncidenceMatrix => | -1 |               IncidenceMatrix =>
                                     | 1  |                                 
                  Q0 => {0, 1}                            Q0 => {0, 1}      
                  Q1 => {{0, 1}}                          Q1 => {{0, 1}}    
                  weights => {-1, 1}                      weights => {-1, 1}
                                                                            
                                                                            
     ------------------------------------------------------------------------
           }, ToricQuiver{flow => {1}              },
     | -1 |               IncidenceMatrix => | -1 |  
     | 1  |                                  | 1  |  
                          Q0 => {0, 1}               
                          Q1 => {{0, 1}}             
                          weights => {-1, 1}         
                                                     
                                                     
     ------------------------------------------------------------------------
     ToricQuiver{flow => {1}              }, ToricQuiver{flow => {1, 1}    
                 IncidenceMatrix => | -1 |               IncidenceMatrix =>
                                    | 1  |                                 
                 Q0 => {0, 1}                                              
                 Q1 => {{0, 1}}                          Q0 => {0, 1, 2}   
                 weights => {-1, 1}                      Q1 => {{0, 1}, {0,
                                                         weights => {-2, 1,
                                                                           
     ------------------------------------------------------------------------
              }, ToricQuiver{flow => {1, 1}              },
     | -1 -1 |               IncidenceMatrix => | -1 0  |  
     | 1  0  |                                  | 0  -1 |  
     | 0  1  |                                  | 1  1  |  
                             Q0 => {0, 1, 2}               
     2}}                     Q1 => {{0, 2}, {1, 2}}        
     1}                      weights => {-1, -1, 2}        
                                                           
     ------------------------------------------------------------------------
     ToricQuiver{flow => {1, 1}              },
                 IncidenceMatrix => | -1 0  |  
                                    | 0  -1 |  
                                    | 0  1  |  
                                    | 1  0  |  
                 Q0 => {0, 1, 2, 3}            
                 Q1 => {{0, 3}, {1, 2}}        
                 weights => {-1, -1, 1, 1}     
     ------------------------------------------------------------------------
     ToricQuiver{flow => {1, 1}              },
                 IncidenceMatrix => | -1 0  |  
                                    | 0  -1 |  
                                    | 1  0  |  
                                    | 0  1  |  
                 Q0 => {0, 1, 2, 3}            
                 Q1 => {{0, 2}, {1, 3}}        
                 weights => {-1, -1, 1, 1}     
     ------------------------------------------------------------------------
     ToricQuiver{flow => {1, 1}              },
                 IncidenceMatrix => | -1 0  |  
                                    | 0  -1 |  
                                    | 1  1  |  
                 Q0 => {0, 1, 2}               
                 Q1 => {{0, 2}, {1, 2}}        
                 weights => {-1, -1, 2}        
                                               
     ------------------------------------------------------------------------
     ToricQuiver{flow => {1, 1}              },
                 IncidenceMatrix => | -1 -1 |  
                                    | 1  0  |  
                                    | 0  1  |  
                 Q0 => {0, 1, 2}               
                 Q1 => {{0, 1}, {0, 2}}        
                 weights => {-2, 1, 1}         
                                               
     ------------------------------------------------------------------------
     ToricQuiver{flow => {1, 1, 1}              },
                 IncidenceMatrix => | -1 -1 0  |  
                                    | 0  0  -1 |  
                                    | 1  0  1  |  
                                    | 0  1  0  |  
                 Q0 => {0, 1, 2, 3}               
                 Q1 => {{0, 2}, {0, 3}, {1, 2}}   
                 weights => {-2, -1, 2, 1}        
     ------------------------------------------------------------------------
     ToricQuiver{flow => {1, 1, 1}              },
                 IncidenceMatrix => | -1 -1 0  |  
                                    | 0  0  -1 |  
                                    | 1  0  0  |  
                                    | 0  1  1  |  
                 Q0 => {0, 1, 2, 3}               
                 Q1 => {{0, 2}, {0, 3}, {1, 3}}   
                 weights => {-2, -1, 1, 2}        
     ------------------------------------------------------------------------
     ToricQuiver{flow => {1, 1, 1}              },
                 IncidenceMatrix => | -1 0  0  |  
                                    | 0  -1 -1 |  
                                    | 1  1  0  |  
                                    | 0  0  1  |  
                 Q0 => {0, 1, 2, 3}               
                 Q1 => {{0, 2}, {1, 2}, {1, 3}}   
                 weights => {-1, -2, 2, 1}        
     ------------------------------------------------------------------------
     ToricQuiver{flow => {1, 1, 1}              }}
                 IncidenceMatrix => | -1 0  0  |
                                    | 0  -1 -1 |
                                    | 0  1  0  |
                                    | 1  0  1  |
                 Q0 => {0, 1, 2, 3}
                 Q1 => {{0, 3}, {1, 2}, {1, 3}}
                 weights => {-1, -2, 1, 2}

o2 : List

See also

Functions with optional argument named AsSubquiver :

For the programmer

The object AsSubquiver is a symbol.