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, {(.0974128 + .144195*ii)x11*x32*x53 + (- .189487 -
                                                           
                                                           
                                                           
                                                           
                                                           
     ------------------------------------------------------------------------
     .0881428*ii)x11*x32 + (- .0870473 + .364893*ii)x11*x53 + (.00136416 -
                                                                          
                                                                          
                                                                          
                                                                          
                                                                          
     ------------------------------------------------------------------------
     .0623296*ii)x32*x53 + (- .246128 - .0754413*ii)x11 + (- .0596382 -
                                                                       
                                                                       
                                                                       
                                                                       
                                                                       
     ------------------------------------------------------------------------
     .0998838*ii)x32 + (- .125354 + .154499*ii)x53 - .127946 - .088894*ii, (-
                                                                             
                                                                             
                                                                             
                                                                             
                                                                             
     ------------------------------------------------------------------------
     .61982 + .758775*ii)x11*x32*x53 + (.0357319 + .0620362*ii)x11*x32 + (-
                                                                           
                                                                           
                                                                           
                                                                           
                                                                           
     ------------------------------------------------------------------------
     .306751 + .598901*ii)x11*x53 + (- .404009 + .359386*ii)x32*x53 + (-
                                                                        
                                                                        
                                                                        
                                                                        
                                                                        
     ------------------------------------------------------------------------
     .13069 + .0737258*ii)x11 + (.0112032 + .0518096*ii)x32 + (- .254457 +
                                                                          
                                                                          
                                                                          
                                                                          
                                                                          
     ------------------------------------------------------------------------
     .305418*ii)x53 - .0845617 + .025317*ii, (.0456701 + .3873*ii)x11*x32*x53
                                                                             
                                                                             
                                                                             
                                                                             
                                                                             
     ------------------------------------------------------------------------
     + (- .269999 + .252977*ii)x11*x32 + (- .547104 - .144988*ii)x11*x53 + (-
                                                                             
                                                                             
                                                                             
                                                                             
                                                                             
     ------------------------------------------------------------------------
     .397825 + .389982*ii)x32*x53 + (- .727363 + .480574*ii)x11 + (- .295304
                                                                            
                                                                            
                                                                            
                                                                            
                                                                            
     ------------------------------------------------------------------------
     + .574006*ii)x32 + (- .838597 + .00177847*ii)x53 - .58481 + .893819*ii,
                                                                            
                                                                            
                                                                            
                                                                            
                                                                            
     ------------------------------------------------------------------------
     (- .117288 + .651256*ii)x11*x32*x53 + (- .0308358 + .392495*ii)x11*x32 +
                                                                             
                                                                             
                                                                             
                                                                             
                                                                             
     ------------------------------------------------------------------------
     (- .00600294 + .711293*ii)x11*x53 + (- .088248 + .532027*ii)x32*x53 + (-
                                                                             
                                                                             
                                                                             
                                                                             
                                                                             
     ------------------------------------------------------------------------
     .246078 + .35683*ii)x11 + (- .235293 + .283696*ii)x32 + (.529843 +
                                                                       
                                                                       
                                                                       
                                                                       
                                                                       
     ------------------------------------------------------------------------
     .646791*ii)x53 - .137649 + .227616*ii, (.291497 - .429926*ii)x11*x32*x53
                                                                             
                                                                             
                                                                             
                                                                             
                                                                             
     ------------------------------------------------------------------------
     + (- .10592 - .139228*ii)x11*x32 + (.585213 - .766222*ii)x11*x53 +
                                                                       
                                                                       
                                                                       
                                                                       
                                                                       
     ------------------------------------------------------------------------
     (.308052 - .323596*ii)x32*x53 + (- .222231 - .23133*ii)x11 + (-
                                                                    
                                                                    
                                                                    
                                                                    
                                                                    
     ------------------------------------------------------------------------
     .00845445 - .108167*ii)x32 + (.411001 - .602008*ii)x53 - .0519089 -
                                                                        
                                                                        
                                                                        
                                                                        
                                                                        
     ------------------------------------------------------------------------
     .207102*ii, (.446242 - .53358*ii)x11*x32*x53 + (- .458966 -
                                                                
                                                                
                                                                
                                                                
                                                                
     ------------------------------------------------------------------------
     .0818857*ii)x11*x32 + (.150742 - .736321*ii)x11*x53 + (.516006 -
                                                                     
                                                                     
                                                                     
                                                                     
                                                                     
     ------------------------------------------------------------------------
     .149701*ii)x32*x53 + (- .637962 + .0141713*ii)x11 + (- .150928 -
                                                                     
                                                                     
                                                                     
                                                                     
                                                                     
     ------------------------------------------------------------------------
     .168794*ii)x32 + (.310708 - .407201*ii)x53 - .347673 - .0414695*ii},
                                                                         
                                                                         
                                                                         
                                                                         
                                                                         
     ------------------------------------------------------------------------
     {{-.319529-1.18258*ii, -1.85139-.070020*ii, .075946+.124476*ii},
                                                                     
                                                                     
                                                                     
                                                                     
                                                                     
     ------------------------------------------------------------------------
     {-.460917+.167376*ii, -.918775+.638221*ii, -.237557+.630409*ii}}, {|
                                                                        |
                                                                        |
                                                                        |
                                                                        |
                                                                        |
     ------------------------------------------------------------------------
     -.408248           -.0925739-.262832ii -.2668+.33232ii    
     -.316268+.258149ii -.271646-.0420575ii .192221-.22208ii   
     .267331+.308546ii  .254066+.222019ii   -.323311+.0557395ii
     .330814-.239226ii  -.567437+.112578ii  -.20093+.516663ii  
     .353908-.203509ii  -.1518+.37281ii     .0446458-.316299ii 
     .322424-.250419ii  -.0780662-.479754ii .334892-.320892ii  
     ------------------------------------------------------------------------
     -.705335-.0453254ii -.254638+.0213078ii  -.0938777+.0201134ii |}, | 1 
     .246474-.273622ii   -.563032-.00176807ii .310571+.34989ii     |   | -1
     -.189207+.128629ii  .0226163-.519704ii   .349197+.408617ii    |   | 1 
     .157866-.255905ii   .0789903+.099837ii   .0138981+.290781ii   |   | -1
     -.253651+.147937ii  -.515825-.0835412ii  -.456426+.040755ii   |   | 1 
     -.368349+.0130775ii .20694+.122508ii     .236048+.36407ii     |   | -1
     ------------------------------------------------------------------------
     1  1  1  1  1 |, {| -.319529-1.18258ii 0                  
     -1 -1 -1 -1 0 |   | 1                  0                  
     1  1  1  0  0 |   | 0                  -1.85139-.0700203ii
     -1 -1 0  0  0 |   | 0                  1                  
     1  0  0  0  0 |   | 0                  0                  
     0  0  0  0  0 |   | 0                  0                  
     ------------------------------------------------------------------------
     0                 |, | -.460917+.167376ii 0                 
     0                 |  | 1                  0                 
     0                 |  | 0                  -.918775+.638221ii
     0                 |  | 0                  1                 
     .075946+.124476ii |  | 0                  0                 
     1                 |  | 0                  0                 
     ------------------------------------------------------------------------
     0                  |})
     0                  |
     0                  |
     0                  |
     -.237557+.630409ii |
     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 => {-.319529-1.18258*ii, -1.85139-.070020*ii,
     ------------------------------------------------------------------------
                        }, Point{cache => CacheTable{...3...}        
     .075946+.124476*ii}         Coordinates => {-.460917+.167376*ii,
     ------------------------------------------------------------------------
                                              }}
     -.918775+.638221*ii, -.237557+.630409*ii}

i5 : peek solutionPlanes

o5 = {Matrix{cache => CacheTable{}                                             }, Matrix{cache => CacheTable{}                                              }}
             RawMatrix => -.319529-1.18258i 0                 0                          RawMatrix => -.460917+.167376i 0                 0                 
                          1                 0                 0                                       1                 0                 0                 
                          0                 -1.85139-.070020i 0                                       0                 -.918775+.638221i 0                 
                          0                 1                 0                                       0                 1                 0                 
                          0                 0                 .075946+.124476i                        0                 0                 -.237557+.630409i 
                          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.