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

Usage:

(R, pols, sols, fixedFlags, movedFlag, solutionPlanes) = parseTriplet(f, p, s)
Inputs:
- f, a string, represents the fixed flag.
- p, a string, represents a polynomial system.
- s, a string, solutions to the polynomial system.
Optional inputs:
- Verbose => ..., default value false, request verbose feedback
Outputs:
- R, a ring, a polynomial ring with complex floating-point coefficients and in the variables used in the systems p.
- pols, a list, list of polynomial equations in the ring R.
- sols, a list, list of solutions of the system pols.
- fixedFlags, a list, list of the fixed flags, as matrices of complex numbers.
- movedFlag, a list, the moved flag, the flag not listed here is the identity matrix.
- solutionPlanes, a list, list of complex matrices which store the solution planes.

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, {(.715829 + .0336859*ii)x11*x32*x53 + (.457733 + .258275*ii)x11*x32
                                                                            
                                                                            
                                                                            
                                                                            
                                                                            
     ------------------------------------------------------------------------
     + (.856551 + .0451894*ii)x11*x53 + (.145242 + .299281*ii)x32*x53 +
                                                                       
                                                                       
                                                                       
                                                                       
                                                                       
     ------------------------------------------------------------------------
     (.211503 + .186344*ii)x11 + (.0286656 + .0995057*ii)x32 + (.403136 +
                                                                         
                                                                         
                                                                         
                                                                         
                                                                         
     ------------------------------------------------------------------------
     .330517*ii)x53 + .0647637 - .00804137*ii, (.0497902 +
                                                          
                                                          
                                                          
                                                          
                                                          
     ------------------------------------------------------------------------
     .494378*ii)x11*x32*x53 + (.349746 + .402567*ii)x11*x32 + (- .262908 +
                                                                          
                                                                          
                                                                          
                                                                          
                                                                          
     ------------------------------------------------------------------------
     .267251*ii)x11*x53 + (.338123 + .00434827*ii)x32*x53 + (- .00376092 +
                                                                          
                                                                          
                                                                          
                                                                          
                                                                          
     ------------------------------------------------------------------------
     .518353*ii)x11 + (.259149 + .155435*ii)x32 + (- .0127329 -
                                                               
                                                               
                                                               
                                                               
                                                               
     ------------------------------------------------------------------------
     .118095*ii)x53 - .092796 + .348257*ii, (- .305985 -
                                                        
                                                        
                                                        
                                                        
                                                        
     ------------------------------------------------------------------------
     .329839*ii)x11*x32*x53 + (- .367691 - .364995*ii)x11*x32 + (- .0364914 -
                                                                             
                                                                             
                                                                             
                                                                             
                                                                             
     ------------------------------------------------------------------------
     .368785*ii)x11*x53 + (.291177 - .619311*ii)x32*x53 + (- .295162 -
                                                                      
                                                                      
                                                                      
                                                                      
                                                                      
     ------------------------------------------------------------------------
     .231133*ii)x11 + (.330354 - .469959*ii)x32 + (.321302 - .462339*ii)x53 +
                                                                             
                                                                             
                                                                             
                                                                             
                                                                             
     ------------------------------------------------------------------------
     .0524065 - .374358*ii, (- .194859 - .449462*ii)x11*x32*x53 + (- .158581
                                                                            
                                                                            
                                                                            
                                                                            
                                                                            
     ------------------------------------------------------------------------
     - .525124*ii)x11*x32 + (- .147465 - .151527*ii)x11*x53 + (- .350587 -
                                                                          
                                                                          
                                                                          
                                                                          
                                                                          
     ------------------------------------------------------------------------
     .0976366*ii)x32*x53 + (- .25603 + .28883*ii)x11 + (- .0159025 +
                                                                    
                                                                    
                                                                    
                                                                    
                                                                    
     ------------------------------------------------------------------------
     .0590783*ii)x32 + (- .23455 + .017331*ii)x53 - .0153894 + .600312*ii, (-
                                                                             
                                                                             
                                                                             
                                                                             
                                                                             
     ------------------------------------------------------------------------
     .272265 - .39208*ii)x11*x32*x53 + (- .45981 - .0272325*ii)x11*x32 +
                                                                        
                                                                        
                                                                        
                                                                        
                                                                        
     ------------------------------------------------------------------------
     (.0292487 - .311556*ii)x11*x53 + (.189648 - .394632*ii)x32*x53 + (-
                                                                        
                                                                        
                                                                        
                                                                        
                                                                        
     ------------------------------------------------------------------------
     .397236 - .250656*ii)x11 + (.0135332 - .538095*ii)x32 + (.288245 -
                                                                       
                                                                       
                                                                       
                                                                       
                                                                       
     ------------------------------------------------------------------------
     .243552*ii)x53 + .028189 - .484208*ii, (- .151925 +
                                                        
                                                        
                                                        
                                                        
                                                        
     ------------------------------------------------------------------------
     .751089*ii)x11*x32*x53 + (.0688338 + .113934*ii)x11*x32 + (- .0845156 -
                                                                            
                                                                            
                                                                            
                                                                            
                                                                            
     ------------------------------------------------------------------------
     .0802866*ii)x11*x53 + (- .0804406 - .0121712*ii)x32*x53 + (.346709 -
                                                                         
                                                                         
                                                                         
                                                                         
                                                                         
     ------------------------------------------------------------------------
     .358877*ii)x11 + (.215196 + .206336*ii)x32 + (.107845 - .425532*ii)x53 +
                                                                             
                                                                             
                                                                             
                                                                             
                                                                             
     ------------------------------------------------------------------------
     .64849 - .164007*ii}, {{-.752972-.310158*ii, -.597223+.030587*ii,
                                                                      
                                                                      
                                                                      
                                                                      
                                                                      
     ------------------------------------------------------------------------
     -6.31534-9.62019*ii}, {.497486-.64303*ii, -2.0059-4.23251*ii,
                                                                  
                                                                  
                                                                  
                                                                  
                                                                  
     ------------------------------------------------------------------------
     -.834296+.080017*ii}}, {| -.408248            .0454048+.243002ii 
                             | .180198+.366327ii   -.496459-.0429053ii
                             | -.0994839+.395941ii .160476-.181288ii  
                             | -.351037+.208422ii  .23495-.189381ii   
                             | -.0306783-.407094ii .122745-.639474ii  
                             | .0043376+.408225ii  .287407+.185189ii  
     ------------------------------------------------------------------------
     .315504+.275247ii   .457873+.161921ii    .164518-.0432516ii 
     .157733+.328072ii   -.112513-.483762ii   -.0911291-.185647ii
     -.522784-.0796383ii -.171775+.201718ii   -.404138-.0392353ii
     .194586+.344384ii   -.647223+.0348297ii  .369394+.123977ii  
     .420796+.0355418ii  -.0116837-.0540883ii -.449459+.0323838ii
     .275486-.0430262ii  .13663+.0735615ii    -.295208+.566916ii 
     ------------------------------------------------------------------------
     -.17455-.549224ii    |}, | 1  1  1  1  1  1 |, {| -.752972-.310158ii
     .290578-.280392ii    |   | -1 -1 -1 -1 -1 0 |   | 1                 
     -.164562-.482624ii   |   | 1  1  1  1  0  0 |   | 0                 
     -.0864361+.0799902ii |   | -1 -1 -1 0  0  0 |   | 0                 
     .0124057-.157255ii   |   | 1  1  0  0  0  0 |   | 0                 
     .442565+.10103ii     |   | -1 0  0  0  0  0 |   | 0                 
     ------------------------------------------------------------------------
     0                   0                  |, | .497486-.64303ii
     0                   0                  |  | 1               
     -.597223+.0305871ii 0                  |  | 0               
     1                   0                  |  | 0               
     0                   -6.31534-9.62019ii |  | 0               
     0                   1                  |  | 0               
     ------------------------------------------------------------------------
     0                 0                   |})
     0                 0                   |
     -2.0059-4.23251ii 0                   |
     1                 0                   |
     0                 -.834296+.0800166ii |
     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 => {-.752972-.310158*ii, -.597223+.030587*ii,
     ------------------------------------------------------------------------
                         }, Point{cache => CacheTable{...3...}      
     -6.31534-9.62019*ii}         Coordinates => {.497486-.64303*ii,
     ------------------------------------------------------------------------
                                             }}
     -2.0059-4.23251*ii, -.834296+.080017*ii}

i5 : peek solutionPlanes

o5 = {Matrix{cache => CacheTable{}                                                   }, Matrix{cache => CacheTable{}                                                }}
             RawMatrix => -0.752972-0.310158i 0                    0                           RawMatrix => 0.497486-0.64303i 0                0                    
                          1                   0                    0                                        1                 0                0                    
                          0                   -0.597223+0.0305871i 0                                        0                 -2.0059-4.23251i 0                    
                          0                   1                    0                                        0                 1                0                    
                          0                   0                    -6.31534-9.62019i                        0                 0                -0.834296+0.0800166i 
                          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:

parseTriplet(String,String,String)

For the programmer

The object parseTriplet is a method function with options.

The source of this document is in NumericalSchubertCalculus/PHCpack-LRhomotopies-doc.m2:184:0.