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

Synopsis

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, {(.208692 + 1.03965*ii)x11*x32*x53 + (.405301 + .197189*ii)x11*x32 +
                                                                             
                                                                             
                                                                             
                                                                             
                                                                             
     ------------------------------------------------------------------------
     (.566151 + .487787*ii)x11*x53 + (- .209197 + .468217*ii)x32*x53 +
                                                                      
                                                                      
                                                                      
                                                                      
                                                                      
     ------------------------------------------------------------------------
     (.312468 + .303249*ii)x11 + (- .0604092 - .0194041*ii)x32 + (.23684 +
                                                                          
                                                                          
                                                                          
                                                                          
                                                                          
     ------------------------------------------------------------------------
     .252038*ii)x53 - .0591918 + .101699*ii, (- .463283 -
                                                         
                                                         
                                                         
                                                         
                                                         
     ------------------------------------------------------------------------
     .240783*ii)x11*x32*x53 + (- .458021 + .0439516*ii)x11*x32 + (- .407911 -
                                                                             
                                                                             
                                                                             
                                                                             
                                                                             
     ------------------------------------------------------------------------
     .347409*ii)x11*x53 + (.306426 - .453088*ii)x32*x53 + (- .712326 +
                                                                      
                                                                      
                                                                      
                                                                      
                                                                      
     ------------------------------------------------------------------------
     .220682*ii)x11 + (- .202248 - .483313*ii)x32 + (.0203615 -
                                                               
                                                               
                                                               
                                                               
                                                               
     ------------------------------------------------------------------------
     .380034*ii)x53 - .544592 - .206127*ii, (- .561299 -
                                                        
                                                        
                                                        
                                                        
                                                        
     ------------------------------------------------------------------------
     .376592*ii)x11*x32*x53 + (.0107828 - .36624*ii)x11*x32 + (.166971 -
                                                                        
                                                                        
                                                                        
                                                                        
                                                                        
     ------------------------------------------------------------------------
     .449345*ii)x11*x53 + (- .393243 - .431221*ii)x32*x53 + (.699459 -
                                                                      
                                                                      
                                                                      
                                                                      
                                                                      
     ------------------------------------------------------------------------
     .374566*ii)x11 + (- .05748 - .258966*ii)x32 + (.248463 - .408062*ii)x53
                                                                            
                                                                            
                                                                            
                                                                            
                                                                            
     ------------------------------------------------------------------------
     + .518536 - .16739*ii, (- .40362 + .263607*ii)x11*x32*x53 + (- .680842 -
                                                                             
                                                                             
                                                                             
                                                                             
                                                                             
     ------------------------------------------------------------------------
     .459741*ii)x11*x32 + (- .283004 - .21073*ii)x11*x53 + (- .329091 +
                                                                       
                                                                       
                                                                       
                                                                       
                                                                       
     ------------------------------------------------------------------------
     .191945*ii)x32*x53 + (- .208371 - .65307*ii)x11 + (- .695681 -
                                                                   
                                                                   
                                                                   
                                                                   
                                                                   
     ------------------------------------------------------------------------
     .421961*ii)x32 + (- .323339 - .169246*ii)x53 - .251152 - .718577*ii, (-
                                                                            
                                                                            
                                                                            
                                                                            
                                                                            
     ------------------------------------------------------------------------
     .00437712 + .0530547*ii)x11*x32*x53 + (- .761652 + .146076*ii)x11*x32 +
                                                                            
                                                                            
                                                                            
                                                                            
                                                                            
     ------------------------------------------------------------------------
     (- .106439 + .109494*ii)x11*x53 + (- .36773 - .0415626*ii)x32*x53 + (-
                                                                           
                                                                           
                                                                           
                                                                           
                                                                           
     ------------------------------------------------------------------------
     .776877 + .551073*ii)x11 + (- .276157 - .298111*ii)x32 + (- .245764 +
                                                                          
                                                                          
                                                                          
                                                                          
                                                                          
     ------------------------------------------------------------------------
     .0300706*ii)x53 - .453972 + .283598*ii, (.135972 +
                                                       
                                                       
                                                       
                                                       
                                                       
     ------------------------------------------------------------------------
     .588926*ii)x11*x32*x53 + (.6076 - .200541*ii)x11*x32 + (- .283696 +
                                                                        
                                                                        
                                                                        
                                                                        
                                                                        
     ------------------------------------------------------------------------
     .172472*ii)x11*x53 + (.14003 + .618682*ii)x32*x53 + (.622696 -
                                                                   
                                                                   
                                                                   
                                                                   
                                                                   
     ------------------------------------------------------------------------
     .0521078*ii)x11 + (.487289 - .0181031*ii)x32 + (- .174105 +
                                                                
                                                                
                                                                
                                                                
                                                                
     ------------------------------------------------------------------------
     .19223*ii)x53 + .516146 + .110568*ii}, {{-.821212-.037818*ii,
                                                                  
                                                                  
                                                                  
                                                                  
                                                                  
     ------------------------------------------------------------------------
     -.569987-.018055*ii, .112781-1.49632*ii}, {-.674526-.501588*ii,
                                                                    
                                                                    
                                                                    
                                                                    
                                                                    
     ------------------------------------------------------------------------
     -.461876-.739848*ii, -.224144+.66624*ii}}, {| -.408248+1.85037e-17ii
                                                 | .35285+.205337ii      
                                                 | .180223+.366314ii     
                                                 | -.112231+.392519ii    
                                                 | -.386429-.131678ii    
                                                 | .379266-.151075ii     
     ------------------------------------------------------------------------
     .0119294+.502626ii   -.186934+.620316ii   .122167-.151345ii 
     -.383343-.127677ii   .230949+.244268ii    .0430535+.174629ii
     -.342457+.00934968ii .0827073+.0851401ii  -.196086-.478639ii
     -.313814+.130817ii   -.28829-.368183ii    -.150923-.316389ii
     -.0511755-.330575ii  -.0730288+.0544028ii -.677879+.188118ii
     .00236316-.488989ii  -.275102+.387978ii   .151215-.147044ii 
     ------------------------------------------------------------------------
     -.207192+.198433ii  .0258732+.200046ii |}, | 1  1  1  1  1  1 |, {|
     -.232673-.232934ii  .278648+.581968ii  |   | -1 -1 -1 -1 -1 0 |   |
     -.422701-.037308ii  -.261099-.431386ii |   | 1  1  1  1  0  0 |   |
     .382436+.28813ii    .28168+.259944ii   |   | -1 -1 -1 0  0  0 |   |
     -.293505+.0889841ii .344844-.0724727ii |   | 1  1  0  0  0  0 |   |
     .118466+.540239ii   .0999718-.087378ii |   | -1 0  0  0  0  0 |   |
     ------------------------------------------------------------------------
     -.821212-.0378182ii 0                  0                 |, |
     1                   0                  0                 |  |
     0                   -.569987-.018055ii 0                 |  |
     0                   1                  0                 |  |
     0                   0                  .112781-1.49632ii |  |
     0                   0                  1                 |  |
     ------------------------------------------------------------------------
     -.674526-.501588ii 0                  0                 |})
     1                  0                  0                 |
     0                  -.461876-.739848ii 0                 |
     0                  1                  0                 |
     0                  0                  -.224144+.66624ii |
     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 => {-.821212-.037818*ii, -.569987-.018055*ii,
     ------------------------------------------------------------------------
                        }, Point{cache => CacheTable{...3...}        
     .112781-1.49632*ii}         Coordinates => {-.674526-.501588*ii,
     ------------------------------------------------------------------------
                                             }}
     -.461876-.739848*ii, -.224144+.66624*ii}

i5 : peek solutionPlanes

o5 = {Matrix{cache => CacheTable{}                                             }, Matrix{cache => CacheTable{}                                             }}
             RawMatrix => -.821212-.037818i 0                 0                          RawMatrix => -.674526-.501588i 0                 0                
                          1                 0                 0                                       1                 0                 0                
                          0                 -.569987-.018055i 0                                       0                 -.461876-.739848i 0                
                          0                 1                 0                                       0                 1                 0                
                          0                 0                 .112781-1.49632i                        0                 0                 -.224144+.66624i 
                          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.