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, {(- .471646 - .9954*ii)x11*x32*x53 + (- .869072 - .43886*ii)x11*x32
                                                                            
                                                                            
                                                                            
                                                                            
                                                                            
     ------------------------------------------------------------------------
     + (- .642276 - .265166*ii)x11*x53 + (- .0603964 - .67823*ii)x32*x53 + (-
                                                                             
                                                                             
                                                                             
                                                                             
                                                                             
     ------------------------------------------------------------------------
     .570235 + .128313*ii)x11 + (- .326867 - .382885*ii)x32 + (- .372724 -
                                                                          
                                                                          
                                                                          
                                                                          
                                                                          
     ------------------------------------------------------------------------
     .222037*ii)x53 - .257401 + .0316447*ii, (.303734 +
                                                       
                                                       
                                                       
                                                       
                                                       
     ------------------------------------------------------------------------
     .744526*ii)x11*x32*x53 + (.226972 + .768298*ii)x11*x32 + (.58282 +
                                                                       
                                                                       
                                                                       
                                                                       
                                                                       
     ------------------------------------------------------------------------
     .162737*ii)x11*x53 + (.653127 + .0849658*ii)x32*x53 + (.495139 +
                                                                     
                                                                     
                                                                     
                                                                     
                                                                     
     ------------------------------------------------------------------------
     .229682*ii)x11 + (.394523 - .0167605*ii)x32 + (.732801 - .173069*ii)x53
                                                                            
                                                                            
                                                                            
                                                                            
                                                                            
     ------------------------------------------------------------------------
     + .533122 - .274907*ii, (- .18661 + .215089*ii)x11*x32*x53 + (- .309351
                                                                            
                                                                            
                                                                            
                                                                            
                                                                            
     ------------------------------------------------------------------------
     - .428333*ii)x11*x32 + (- .486815 + .161359*ii)x11*x53 + (- .108247 +
                                                                          
                                                                          
                                                                          
                                                                          
                                                                          
     ------------------------------------------------------------------------
     .194965*ii)x32*x53 + (- .104537 - 1.0865*ii)x11 + (- .218615 -
                                                                   
                                                                   
                                                                   
                                                                   
                                                                   
     ------------------------------------------------------------------------
     .108011*ii)x32 + (- .256078 + .0243888*ii)x53 - .0177934 - .584684*ii,
                                                                           
                                                                           
                                                                           
                                                                           
                                                                           
     ------------------------------------------------------------------------
     (.0273895 + .39522*ii)x11*x32*x53 + (- .214911 - .111125*ii)x11*x32 + (-
                                                                             
                                                                             
                                                                             
                                                                             
                                                                             
     ------------------------------------------------------------------------
     .196011 + .290367*ii)x11*x53 + (.128298 + .248982*ii)x32*x53 + (-
                                                                      
                                                                      
                                                                      
                                                                      
                                                                      
     ------------------------------------------------------------------------
     .0382901 - .376232*ii)x11 + (.0344195 - .0337692*ii)x32 + (- .109889 +
                                                                           
                                                                           
                                                                           
                                                                           
                                                                           
     ------------------------------------------------------------------------
     .131053*ii)x53 + .225794 - .302136*ii, (.590816 - .318487*ii)x11*x32*x53
                                                                             
                                                                             
                                                                             
                                                                             
                                                                             
     ------------------------------------------------------------------------
     + (.241664 + .375667*ii)x11*x32 + (.372265 - .302125*ii)x11*x53 +
                                                                      
                                                                      
                                                                      
                                                                      
                                                                      
     ------------------------------------------------------------------------
     (.282047 - .0565437*ii)x32*x53 + (.674057 + .0595601*ii)x11 + (.167211 +
                                                                             
                                                                             
                                                                             
                                                                             
                                                                             
     ------------------------------------------------------------------------
     .52667*ii)x32 + (.207793 - .0873171*ii)x53 + .553026 + .33979*ii, (-
                                                                         
                                                                         
                                                                         
                                                                         
                                                                         
     ------------------------------------------------------------------------
     .723798 - .592262*ii)x11*x32*x53 + (- .979458 - .326772*ii)x11*x32 + (-
                                                                            
                                                                            
                                                                            
                                                                            
                                                                            
     ------------------------------------------------------------------------
     .335332 - .569444*ii)x11*x53 + (- .469315 - .297852*ii)x32*x53 + (-
                                                                        
                                                                        
                                                                        
                                                                        
                                                                        
     ------------------------------------------------------------------------
     .897371 - .453343*ii)x11 + (- .610368 - .132587*ii)x32 + (- .114415 -
                                                                          
                                                                          
                                                                          
                                                                          
                                                                          
     ------------------------------------------------------------------------
     .317184*ii)x53 - .487613 - .267875*ii}, {{-.773649-.235132*ii,
                                                                   
                                                                   
                                                                   
                                                                   
                                                                   
     ------------------------------------------------------------------------
     -.685693+.132902*ii, 2.03196-.198652*ii}, {-.657506+.065900*ii,
                                                                    
                                                                    
                                                                    
                                                                    
                                                                    
     ------------------------------------------------------------------------
     -1.98322+1.12022*ii, -.838731+.4121*ii}}, {| -.408248-1.85037e-17ii
                                                | .180737-.366061ii     
                                                | .204436-.353373ii     
                                                | .404559+.054759ii     
                                                | .405591+.0465072ii    
                                                | .115491-.391572ii     
     ------------------------------------------------------------------------
     .346052-.235876ii  .346313-.221297ii    -.366469-.1354ii    
     -.335789+.120226ii .156047-.744019ii    -.0241166-.0405615ii
     -.236226-.281874ii -.170674+.00529615ii -.389476-.0297145ii 
     -.11808+.446968ii  .0949265+.270728ii   -.582255+.145386ii  
     .179121-.323089ii  -.252619+.0363794ii  .194702+.406084ii   
     .341526-.308728ii  -.250639+.117292ii   -.3062-.189305ii    
     ------------------------------------------------------------------------
     -.24813+.426481ii   .296902+.0692881ii |}, | 1  1  1  1  1  1 |, {|
     -.0778119-.250394ii .229291+.0682375ii |   | -1 -1 -1 -1 -1 0 |   |
     -.180344+.315664ii  -.599576+.157119ii |   | 1  1  1  1  0  0 |   |
     -.084651+.114781ii  .309664-.246811ii  |   | -1 -1 -1 0  0  0 |   |
     -.438495+.0295669ii .352732+.333672ii  |   | 1  1  0  0  0  0 |   |
     .504883-.295341ii   .266274+.0466155ii |   | -1 0  0  0  0  0 |   |
     ------------------------------------------------------------------------
     -.773649-.235132ii 0                  0                 |, |
     1                  0                  0                 |  |
     0                  -.685693+.132902ii 0                 |  |
     0                  1                  0                 |  |
     0                  0                  2.03196-.198652ii |  |
     0                  0                  1                 |  |
     ------------------------------------------------------------------------
     -.657506+.0659003ii 0                  0                |})
     1                   0                  0                |
     0                   -1.98322+1.12022ii 0                |
     0                   1                  0                |
     0                   0                  -.838731+.4121ii |
     0                   0                  1                |

o2 : Sequence

i3 : vars(R)

o3 = | x11 x32 x53 |

             1       3
o3 : Matrix R  <--- R

i4 : peek sols

o4 = {Point{ConditionNumber => 32.7011                                                   }, Point{ConditionNumber => 15.6446                                                  }}
            Coordinates => {-.773649-.235132*ii, -.685693+.132902*ii, 2.03196-.198652*ii}         Coordinates => {-.657506+.065900*ii, -1.98322+1.12022*ii, -.838731+.4121*ii}
            LastT => 1                                                                            LastT => 1
            SolutionStatus => Regular                                                             SolutionStatus => Regular

i5 : peek solutionPlanes

o5 = {Matrix{cache => CacheTable{}                                             }, Matrix{cache => CacheTable{}                                            }}
             RawMatrix => -.773649-.235132i 0                 0                          RawMatrix => -.657506+.065900i 0                 0               
                          1                 0                 0                                       1                 0                 0               
                          0                 -.685693+.132902i 0                                       0                 -1.98322+1.12022i 0               
                          0                 1                 0                                       0                 1                 0               
                          0                 0                 2.03196-.198652i                        0                 0                 -.838731+.4121i 
                          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.

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

Synopsis

Description

Ways to use parseTriplet :

For the programmer

Ways to use `parseTriplet` :