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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, {(- .0399744 - .0145143*ii)x11*x32*x53 + (.0926769 +
                                                             
                                                             
                                                             
                                                             
                                                             
     ------------------------------------------------------------------------
     .354494*ii)x11*x32 + (- .632386 + .186907*ii)x11*x53 + (.0228595 +
                                                                       
                                                                       
                                                                       
                                                                       
                                                                       
     ------------------------------------------------------------------------
     .0537889*ii)x32*x53 + (.406348 + .234116*ii)x11 + (- .0652501 -
                                                                    
                                                                    
                                                                    
                                                                    
                                                                    
     ------------------------------------------------------------------------
     .0138565*ii)x32 + (- .249868 + .134704*ii)x53 + .211821 - .165463*ii,
                                                                          
                                                                          
                                                                          
                                                                          
                                                                          
     ------------------------------------------------------------------------
     (.0933272 - .373609*ii)x11*x32*x53 + (.264606 - .401113*ii)x11*x32 + (-
                                                                            
                                                                            
                                                                            
                                                                            
                                                                            
     ------------------------------------------------------------------------
     .0939123 - .679424*ii)x11*x53 + (.0455688 - .0119688*ii)x32*x53 +
                                                                      
                                                                      
                                                                      
                                                                      
                                                                      
     ------------------------------------------------------------------------
     (.0451169 - .683975*ii)x11 + (.0388899 + .0672329*ii)x32 + (- .110409 -
                                                                            
                                                                            
                                                                            
                                                                            
                                                                            
     ------------------------------------------------------------------------
     .0867227*ii)x53 - .341856 - .148787*ii, (- .590604 +
                                                         
                                                         
                                                         
                                                         
                                                         
     ------------------------------------------------------------------------
     .0241807*ii)x11*x32*x53 + (- .13432 - .00692575*ii)x11*x32 + (.0566638 -
                                                                             
                                                                             
                                                                             
                                                                             
                                                                             
     ------------------------------------------------------------------------
     .0743429*ii)x11*x53 + (- .497876 - .197278*ii)x32*x53 + (.39268 -
                                                                      
                                                                      
                                                                      
                                                                      
                                                                      
     ------------------------------------------------------------------------
     .106231*ii)x11 + (- .0559863 - .0344225*ii)x32 + (.207618 +
                                                                
                                                                
                                                                
                                                                
                                                                
     ------------------------------------------------------------------------
     .0018821*ii)x53 + .546447 + .0849719*ii, (- .163197 +
                                                          
                                                          
                                                          
                                                          
                                                          
     ------------------------------------------------------------------------
     .856396*ii)x11*x32*x53 + (- .12002 + .6028*ii)x11*x32 + (- .0789951 +
                                                                          
                                                                          
                                                                          
                                                                          
                                                                          
     ------------------------------------------------------------------------
     .294668*ii)x11*x53 + (.494277 + .293229*ii)x32*x53 + (- .132923 +
                                                                      
                                                                      
                                                                      
                                                                      
                                                                      
     ------------------------------------------------------------------------
     .073211*ii)x11 + (.0697774 - .0225692*ii)x32 + (.268987 + .156267*ii)x53
                                                                             
                                                                             
                                                                             
                                                                             
                                                                             
     ------------------------------------------------------------------------
     - .120066 - .217474*ii, (- .0647381 - .530494*ii)x11*x32*x53 + (.244667
                                                                            
                                                                            
                                                                            
                                                                            
                                                                            
     ------------------------------------------------------------------------
     + .0388226*ii)x11*x32 + (- .071549 - .251294*ii)x11*x53 + (- .00247907 +
                                                                             
                                                                             
                                                                             
                                                                             
                                                                             
     ------------------------------------------------------------------------
     .0248108*ii)x32*x53 + (.21949 - .0809399*ii)x11 + (- .0359926 -
                                                                    
                                                                    
                                                                    
                                                                    
                                                                    
     ------------------------------------------------------------------------
     .0103534*ii)x32 + (- .363356 + .0515771*ii)x53 + .00303043 - .137416*ii,
                                                                             
                                                                             
                                                                             
                                                                             
                                                                             
     ------------------------------------------------------------------------
     (.124577 + .254012*ii)x11*x32*x53 + (.430422 + .0947952*ii)x11*x32 +
                                                                         
                                                                         
                                                                         
                                                                         
                                                                         
     ------------------------------------------------------------------------
     (.432935 - .140885*ii)x11*x53 + (- .153941 - .0356372*ii)x32*x53 +
                                                                       
                                                                       
                                                                       
                                                                       
                                                                       
     ------------------------------------------------------------------------
     (.6925 - .164863*ii)x11 + (- .0791601 - .0121276*ii)x32 + (.130397 -
                                                                         
                                                                         
                                                                         
                                                                         
                                                                         
     ------------------------------------------------------------------------
     .488438*ii)x53 + .0622165 - .376375*ii}, {{-.222837+.0578575*ii,
                                                                     
                                                                     
                                                                     
                                                                     
                                                                     
     ------------------------------------------------------------------------
     -.283529-1.74632*ii, -.170237+.574751*ii}, {.313108+.0647815*ii,
                                                                     
                                                                     
                                                                     
                                                                     
                                                                     
     ------------------------------------------------------------------------
     1.55934+3.57986*ii, -.119638-.243962*ii}}, {| -.408248+3.70074e-17ii
                                                 | -.254463-.319242ii    
                                                 | -.379006-.151728ii    
                                                 | .148242-.380383ii     
                                                 | -.400969+.0767495ii   
                                                 | .34486-.218491ii      
     ------------------------------------------------------------------------
     .295782-.557811ii   -.123338-.130106ii  -.443403-.43011ii   
     -.277722-.0337416ii -.15377+.281621ii   .287922-.0364758ii  
     -.310281+.0181191ii -.414435+.0695857ii .155757-.124855ii   
     -.154992-.218188ii  .665036+.134935ii   -.224407-.00485309ii
     .437341-.302059ii   .157632+.2603ii     .322701+.575512ii   
     .0124012-.268702ii  -.310116+.197611ii  .0692093-.0616366ii 
     ------------------------------------------------------------------------
     .101776-.0720625ii  -.0339506+.0651831ii |}, | 1  1  1  1  1  1 |, {|
     .171133-.455241ii   -.0427233+.574042ii  |   | -1 -1 -1 -1 -1 0 |   |
     -.370187+.597805ii  -.149512-.059328ii   |   | 1  1  1  1  0  0 |   |
     -.131206+.363686ii  -.0506159+.314321ii  |   | -1 -1 -1 0  0  0 |   |
     -.0364793+.110345ii .0844233-.0473268ii  |   | 1  1  0  0  0  0 |   |
     .209126+.2163ii     .724911-.033938ii    |   | -1 0  0  0  0  0 |   |
     ------------------------------------------------------------------------
     -.222837+.0578575ii 0                  0                  |, |
     1                   0                  0                  |  |
     0                   -.283529-1.74632ii 0                  |  |
     0                   1                  0                  |  |
     0                   0                  -.170237+.574751ii |  |
     0                   0                  1                  |  |
     ------------------------------------------------------------------------
     .313108+.0647815ii 0                 0                  |})
     1                  0                 0                  |
     0                  1.55934+3.57986ii 0                  |
     0                  1                 0                  |
     0                  0                 -.119638-.243962ii |
     0                  0                 1                  |

o2 : Sequence
i3 : vars(R)

o3 = | x11 x32 x53 |

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

o4 = {Point{cache => CacheTable{...3...}                              
            Coordinates => {-.222837+.0578575*ii, -.283529-1.74632*ii,
     ------------------------------------------------------------------------
                         }, Point{cache => CacheTable{...3...}        
     -.170237+.574751*ii}         Coordinates => {.313108+.0647815*ii,
     ------------------------------------------------------------------------
                                             }}
     1.55934+3.57986*ii, -.119638-.243962*ii}
i5 : peek solutionPlanes

o5 = {Matrix{cache => CacheTable{}                                               }, Matrix{cache => CacheTable{}                                             }}
             RawMatrix => -.222837+.0578575i 0                 0                           RawMatrix => .313108+.0647815i 0                0                 
                          1                  0                 0                                        1                 0                0                 
                          0                  -.283529-1.74632i 0                                        0                 1.55934+3.57986i 0                 
                          0                  1                 0                                        0                 1                0                 
                          0                  0                 -.170237+.574751i                        0                 0                -.119638-.243962i 
                          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.