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, {(.216361 - .613506*ii)x11*x32*x53 + (.187405 - 1.37134*ii)x11*x32 +
                                                                             
                                                                             
                                                                             
                                                                             
                                                                             
     ------------------------------------------------------------------------
     (.178547 - .256943*ii)x11*x53 + (.355105 - .506401*ii)x32*x53 + (-
                                                                       
                                                                       
                                                                       
                                                                       
                                                                       
     ------------------------------------------------------------------------
     .203614 - .857139*ii)x11 + (.424188 - 1.01442*ii)x32 + (.227266 -
                                                                      
                                                                      
                                                                      
                                                                      
                                                                      
     ------------------------------------------------------------------------
     .196895*ii)x53 - .0149183 - .707629*ii, (- .508746 +
                                                         
                                                         
                                                         
                                                         
                                                         
     ------------------------------------------------------------------------
     .119905*ii)x11*x32*x53 + (- .431144 - .45175*ii)x11*x32 + (.182234 -
                                                                         
                                                                         
                                                                         
                                                                         
                                                                         
     ------------------------------------------------------------------------
     .0523411*ii)x11*x53 + (- .453237 + .301075*ii)x32*x53 + (- .025834 -
                                                                         
                                                                         
                                                                         
                                                                         
                                                                         
     ------------------------------------------------------------------------
     .0799124*ii)x11 + (- .580011 - .0398863*ii)x32 + (.177192 +
                                                                
                                                                
                                                                
                                                                
                                                                
     ------------------------------------------------------------------------
     .0783813*ii)x53 - .0584618 + .274931*ii, (- .398064 -
                                                          
                                                          
                                                          
                                                          
                                                          
     ------------------------------------------------------------------------
     .252809*ii)x11*x32*x53 + (- .0408957 - .0204884*ii)x11*x32 + (- .356582
                                                                            
                                                                            
                                                                            
                                                                            
                                                                            
     ------------------------------------------------------------------------
     - .556671*ii)x11*x53 + (- .382129 + .349706*ii)x32*x53 + (.0519173 -
                                                                         
                                                                         
                                                                         
                                                                         
                                                                         
     ------------------------------------------------------------------------
     .376203*ii)x11 + (- .163574 + .166152*ii)x32 + (- .490616 -
                                                                
                                                                
                                                                
                                                                
                                                                
     ------------------------------------------------------------------------
     .252289*ii)x53 - .151662 - .19142*ii, (.139634 - .433477*ii)x11*x32*x53
                                                                            
                                                                            
                                                                            
                                                                            
                                                                            
     ------------------------------------------------------------------------
     + (.390348 - .331972*ii)x11*x32 + (.19351 - .737023*ii)x11*x53 +
                                                                     
                                                                     
                                                                     
                                                                     
                                                                     
     ------------------------------------------------------------------------
     (.167152 - .163974*ii)x32*x53 + (.566124 - .496194*ii)x11 + (.0669203 -
                                                                            
                                                                            
                                                                            
                                                                            
                                                                            
     ------------------------------------------------------------------------
     .183605*ii)x32 + (.168188 - .49878*ii)x53 + .203747 - .369785*ii,
                                                                      
                                                                      
                                                                      
                                                                      
                                                                      
     ------------------------------------------------------------------------
     (.316142 + .589702*ii)x11*x32*x53 + (- .308459 + .559398*ii)x11*x32 +
                                                                          
                                                                          
                                                                          
                                                                          
                                                                          
     ------------------------------------------------------------------------
     (.139228 + .598624*ii)x11*x53 + (.342809 + .548178*ii)x32*x53 + (-
                                                                       
                                                                       
                                                                       
                                                                       
                                                                       
     ------------------------------------------------------------------------
     .336507 + .472101*ii)x11 + (- .162927 + .588781*ii)x32 + (.105877 +
                                                                        
                                                                        
                                                                        
                                                                        
                                                                        
     ------------------------------------------------------------------------
     .568758*ii)x53 - .288059 + .415737*ii, (- .678 - .840209*ii)x11*x32*x53
                                                                            
                                                                            
                                                                            
                                                                            
                                                                            
     ------------------------------------------------------------------------
     + (- .174243 - .596519*ii)x11*x32 + (- .325555 - .127327*ii)x11*x53 + (-
                                                                             
                                                                             
                                                                             
                                                                             
                                                                             
     ------------------------------------------------------------------------
     .393406 - .663198*ii)x32*x53 + (- .270956 - .0504107*ii)x11 + (.0676485
                                                                            
                                                                            
                                                                            
                                                                            
                                                                            
     ------------------------------------------------------------------------
     - .144988*ii)x32 + (- .248206 - .0675478*ii)x53 - .134934 + .187279*ii},
                                                                             
                                                                             
                                                                             
                                                                             
                                                                             
     ------------------------------------------------------------------------
     {{-.900457-.104624*ii, -.423713-.341403*ii, -2.20778-3.14411*ii},
                                                                      
                                                                      
                                                                      
                                                                      
                                                                      
     ------------------------------------------------------------------------
     {-.585259+1.2745*ii, -.757855+.232022*ii, -.572686-.54932*ii}}, {|
                                                                      |
                                                                      |
                                                                      |
                                                                      |
                                                                      |
     ------------------------------------------------------------------------
     -.408248+1.85037e-17ii .309379-.187496ii  -.00832942-.11344ii
     -.406896-.0331957ii    -.343576-.046882ii .0324266-.359624ii 
     .0323597-.406964ii     .0575577-.336367ii -.806143+.0122043ii
     -.136451+.38477ii      .0302204-.411918ii -.164381+.0150739ii
     -.0240377-.40754ii     .267937+.0770943ii .11597+.278586ii   
     -.355968+.199884ii     .198555+.587098ii  -.288511+.0715476ii
     ------------------------------------------------------------------------
     .041552-.308596ii   -.348464+.378022ii -.111598+.561948ii  |}, | 1  1 
     .377913+.485983ii   -.003682-.262137ii .250706+.26857ii    |   | -1 -1
     .108692+.143333ii   .0628639+.120515ii -.0575872-.112745ii |   | 1  1 
     -.37308+.017015ii   -.41156-.551847ii  -.0908257-.117688ii |   | -1 -1
     -.135778+.0973918ii -.383009-.066007ii .692965-.0732571ii  |   | 1  1 
     -.383477+.420991ii  .0417492+.147493ii -.11437+.00163494ii |   | -1 0 
     ------------------------------------------------------------------------
     1  1  1  1 |, {| -.900457-.104624ii 0                 
     -1 -1 -1 0 |   | 1                  0                 
     1  1  0  0 |   | 0                  -.423713-.341403ii
     -1 0  0  0 |   | 0                  1                 
     0  0  0  0 |   | 0                  0                 
     0  0  0  0 |   | 0                  0                 
     ------------------------------------------------------------------------
     0                  |, | -.585259+1.2745ii 0                 
     0                  |  | 1                 0                 
     0                  |  | 0                 -.757855+.232022ii
     0                  |  | 0                 1                 
     -2.20778-3.14411ii |  | 0                 0                 
     1                  |  | 0                 0                 
     ------------------------------------------------------------------------
     0                 |})
     0                 |
     0                 |
     0                 |
     -.572686-.54932ii |
     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 => {-.900457-.104624*ii, -.423713-.341403*ii,
     ------------------------------------------------------------------------
                         }, Point{cache => CacheTable{...3...}       
     -2.20778-3.14411*ii}         Coordinates => {-.585259+1.2745*ii,
     ------------------------------------------------------------------------
                                             }}
     -.757855+.232022*ii, -.572686-.54932*ii}

i5 : peek solutionPlanes

o5 = {Matrix{cache => CacheTable{}                                              }, Matrix{cache => CacheTable{}                                            }}
             RawMatrix => -.900457-.104624i 0                 0                           RawMatrix => -.585259+1.2745i 0                 0                
                          1                 0                 0                                        1                0                 0                
                          0                 -.423713-.341403i 0                                        0                -.757855+.232022i 0                
                          0                 1                 0                                        0                1                 0                
                          0                 0                 -2.20778-3.14411i                        0                0                 -.572686-.54932i 
                          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.