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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}}  
                  synonym => toric quiver                 
                  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}}  
                 synonym => toric quiver                 
                 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}}  
                 synonym => toric quiver                 
                 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}}  
                 synonym => toric quiver                 
                 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}}  
                 synonym => toric quiver                 
                 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}}  
                 synonym => toric quiver                 
                 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}}  
                 synonym => toric quiver                 
                 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}}  
                 synonym => toric quiver                 
                 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}}  
                 synonym => toric quiver                 
                 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}}  
                 synonym => toric quiver                 
                 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}}  
                 synonym => toric quiver                 
                 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}}  
                 synonym => toric quiver                 
                 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}}  
                 synonym => toric quiver                 
                 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}}
                 synonym => toric quiver
                 weights => {-1, -2, 1, 2}

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

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

o2 : List

See also

Functions with optional argument named AsSubquiver :

For the programmer

The object AsSubquiver is a symbol.