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NumericalSchubertCalculus :: parseTriplet

parseTriplet -- Parses the output from LRtriple into Macaulay2 objects.

Synopsis

Description

parseTriplet processes the output of LRtriple for other methods in NumericalSchubertCalculus.

i1 : (f, p, s) = LRtriple(6,matrix{{3, 2, 4, 6}});
i2 : (R, pols, sols, fixedFlags, movedFlag, solutionPlanes) = parseTriplet(f, p, s)

o2 = (R, {(- .123979 - .271487*ii)x11*x32*x53 + (- .326265 -
                                                            
                                                            
                                                            
                                                            
                                                            
     ------------------------------------------------------------------------
     .0750385*ii)x11*x32 + (- .422918 - .62527*ii)x11*x53 + (- .234956 -
                                                                        
                                                                        
                                                                        
                                                                        
                                                                        
     ------------------------------------------------------------------------
     .401365*ii)x32*x53 + (- .344594 - .609603*ii)x11 + (- .164778 -
                                                                    
                                                                    
                                                                    
                                                                    
                                                                    
     ------------------------------------------------------------------------
     .325795*ii)x32 + (- .122029 - .60918*ii)x53 + .0277676 - .663013*ii, (-
                                                                            
                                                                            
                                                                            
                                                                            
                                                                            
     ------------------------------------------------------------------------
     .410612 + .10356*ii)x11*x32*x53 + (- .263909 - .00600623*ii)x11*x32 + (-
                                                                             
                                                                             
                                                                             
                                                                             
                                                                             
     ------------------------------------------------------------------------
     .118613 + .163312*ii)x11*x53 + (- .0578879 + .231125*ii)x32*x53 +
                                                                      
                                                                      
                                                                      
                                                                      
                                                                      
     ------------------------------------------------------------------------
     (.270738 + .138384*ii)x11 + (.058097 - .164926*ii)x32 + (- .130736 +
                                                                         
                                                                         
                                                                         
                                                                         
                                                                         
     ------------------------------------------------------------------------
     .297187*ii)x53 + .333229 + .199033*ii, (.0590851 -
                                                       
                                                       
                                                       
                                                       
                                                       
     ------------------------------------------------------------------------
     .0527586*ii)x11*x32*x53 + (- .592733 - .198671*ii)x11*x32 + (.388844 -
                                                                           
                                                                           
                                                                           
                                                                           
                                                                           
     ------------------------------------------------------------------------
     .218657*ii)x11*x53 + (.262764 + .0916954*ii)x32*x53 + (- .262339 -
                                                                       
                                                                       
                                                                       
                                                                       
                                                                       
     ------------------------------------------------------------------------
     .274718*ii)x11 + (- .0703037 + .394986*ii)x32 + (.316134 - .20821*ii)x53
                                                                             
                                                                             
                                                                             
                                                                             
                                                                             
     ------------------------------------------------------------------------
     + .10449 + .121338*ii, (- .604022 - .0807855*ii)x11*x32*x53 + (- .945342
                                                                             
                                                                             
                                                                             
                                                                             
                                                                             
     ------------------------------------------------------------------------
     + .0223748*ii)x11*x32 + (- .810129 - .0530349*ii)x11*x53 + (- .494493 +
                                                                            
                                                                            
                                                                            
                                                                            
                                                                            
     ------------------------------------------------------------------------
     .0880785*ii)x32*x53 + (- 1.14471 + .27124*ii)x11 + (- .747344 +
                                                                    
                                                                    
                                                                    
                                                                    
                                                                    
     ------------------------------------------------------------------------
     .230097*ii)x32 + (- .63818 + .212993*ii)x53 - .859404 + .543209*ii, (-
                                                                           
                                                                           
                                                                           
                                                                           
                                                                           
     ------------------------------------------------------------------------
     .156096 + .0208787*ii)x11*x32*x53 + (- .0799358 + .0288499*ii)x11*x32 +
                                                                            
                                                                            
                                                                            
                                                                            
                                                                            
     ------------------------------------------------------------------------
     (- .285308 - .133674*ii)x11*x53 + (.139971 + .271639*ii)x32*x53 + (-
                                                                         
                                                                         
                                                                         
                                                                         
                                                                         
     ------------------------------------------------------------------------
     .0666208 - .367066*ii)x11 + (.404026 + .277637*ii)x32 + (.0469196 +
                                                                        
                                                                        
                                                                        
                                                                        
                                                                        
     ------------------------------------------------------------------------
     .332916*ii)x53 + .350314 + .00343754*ii, (.570169 +
                                                        
                                                        
                                                        
                                                        
                                                        
     ------------------------------------------------------------------------
     .276346*ii)x11*x32*x53 + (.926786 + .641809*ii)x11*x32 + (.615267 +
                                                                        
                                                                        
                                                                        
                                                                        
                                                                        
     ------------------------------------------------------------------------
     .324858*ii)x11*x53 + (.226568 - .021962*ii)x32*x53 + (.894113 +
                                                                    
                                                                    
                                                                    
                                                                    
                                                                    
     ------------------------------------------------------------------------
     .577899*ii)x11 + (.495682 + .19942*ii)x32 + (.291287 + .0490962*ii)x53 +
                                                                             
                                                                             
                                                                             
                                                                             
                                                                             
     ------------------------------------------------------------------------
     .599831 + .333173*ii}, {{1.38342+.778213*ii, -1.524+.174085*ii,
                                                                    
                                                                    
                                                                    
                                                                    
                                                                    
     ------------------------------------------------------------------------
     -2.09881-1.01497*ii}, {-.698447+.616907*ii, .357546-2.83866*ii,
                                                                    
                                                                    
                                                                    
                                                                    
                                                                    
     ------------------------------------------------------------------------
     -1.73753+.381693*ii}}, {| -.408248             -.156865+.313224ii  
                             | .191795+.360391ii    -.482047-.00251531ii
                             | -.00743444+.408181ii -.246411+.167474ii  
                             | -.386121-.13258ii    .498836+.397221ii   
                             | .0840189+.399509ii   .200866+.204805ii   
                             | .359906-.192704ii    .234711-.110179ii   
     ------------------------------------------------------------------------
     -.246572+.390703ii  -.00885404+.342113ii .148187+.236107ii  
     .181545-.0791939ii  -.342212+.230809ii   .40371-.440726ii   
     -.53735+.0509626ii  .339208+.107659ii    .0213178+.102925ii 
     -.0589877-.11459ii  -.325278+.123365ii   .244871-.274962ii  
     -.347904-.474704ii  -.0953217-.456153ii  .0862683+.0565694ii
     -.0260519-.303826ii .273718+.415619ii    .539458+.341763ii  
     ------------------------------------------------------------------------
     .349923-.424145ii   |}, | 1  1  1  1  1  1 |, {| 1.38342+.778213ii
     .178044+.0492368ii  |   | -1 -1 -1 -1 -1 0 |   | 1                
     -.321027+.460941ii  |   | 1  1  1  1  0  0 |   | 0                
     -.0775372+.384056ii |   | -1 -1 -1 0  0  0 |   | 0                
     .239321-.345805ii   |   | 1  1  0  0  0  0 |   | 0                
     .1282+.0346971ii    |   | -1 0  0  0  0  0 |   | 0                
     ------------------------------------------------------------------------
     0                0                  |, | -.698447+.616907ii
     0                0                  |  | 1                 
     -1.524+.174085ii 0                  |  | 0                 
     1                0                  |  | 0                 
     0                -2.09881-1.01497ii |  | 0                 
     0                1                  |  | 0                 
     ------------------------------------------------------------------------
     0                 0                  |})
     0                 0                  |
     .357546-2.83866ii 0                  |
     1                 0                  |
     0                 -1.73753+.381693ii |
     0                 1                  |

o2 : Sequence
i3 : vars(R)

o3 = | x11 x32 x53 |

             1       3
o3 : Matrix R  <--- R
i4 : peek sols

o4 = {Point{ConditionNumber => 7.42942                                                 }, Point{ConditionNumber => 20.3583                                                   }}
            Coordinates => {1.38342+.778213*ii, -1.524+.174085*ii, -2.09881-1.01497*ii}         Coordinates => {-.698447+.616907*ii, .357546-2.83866*ii, -1.73753+.381693*ii}
            LastT => 1                                                                          LastT => 1
            SolutionStatus => Regular                                                           SolutionStatus => Regular
i5 : peek solutionPlanes

o5 = {Matrix{cache => CacheTable{}                                           }, Matrix{cache => CacheTable{}                                             }}
             RawMatrix => 1.38342+.778213i 0               0                           RawMatrix => -.698447+.616907i 0                0                 
                          1                0               0                                        1                 0                0                 
                          0                -1.524+.174085i 0                                        0                 .357546-2.83866i 0                 
                          0                1               0                                        0                 1                0                 
                          0                0               -2.09881-1.01497i                        0                 0                -1.73753+.381693i 
                          0                0               1                                        0                 0                1                 

             ring => CC                                                                ring => CC
                       53                                                                        53
                           3                                                                         3
             source => CC                                                              source => CC
                         53                                                                        53
                           6                                                                         6
             target => CC                                                              target => CC
                         53                                                                        53

Ways to use parseTriplet :

For the programmer

The object parseTriplet is a method function with options.