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NumericalSchubertCalculus :: parseTriplet

parseTriplet -- Parses a flag, system, and solutions (the output from LRtriple) into Macaulay2 objects.

Synopsis

Description

The parseTriplet allows to process the output of LRtriple.

i1 : (f, p, s) = LRtriple(6,matrix{{3, 2, 4, 6}});
PHCv2.4.77 released 2020-06-12

the input data for phc -e : 
5
6
[ 2 4 6 ]^3;
0
0
0
/var/folders/11/t6mmkf11455d4nt0fn639c6h0000gn/T/M2-95741-0/3PHCout
0
y
y
0
0
0

writing data to file /var/folders/11/t6mmkf11455d4nt0fn639c6h0000gn/T/M2-95741-0/2PHCip
running phc -e, session output to /var/folders/11/t6mmkf11455d4nt0fn639c6h0000gn/T/M2-95741-0/4PHCses
                writing output to /var/folders/11/t6mmkf11455d4nt0fn639c6h0000gn/T/M2-95741-0/3PHCout
opening output file /var/folders/11/t6mmkf11455d4nt0fn639c6h0000gn/T/M2-95741-0/5PHCsolutions
i2 : (R, pols, sols, fixedFlags, movedFlag, solutionPlanes) = parseTriplet(f, p, s)

writing data to file /var/folders/11/t6mmkf11455d4nt0fn639c6h0000gn/T/M2-95741-0/6PHCinp
running phc -o, writing output to /var/folders/11/t6mmkf11455d4nt0fn639c6h0000gn/T/M2-95741-0/7PHCout

writing data to file /var/folders/11/t6mmkf11455d4nt0fn639c6h0000gn/T/M2-95741-0/9PHCipt
writing solutions to /var/folders/11/t6mmkf11455d4nt0fn639c6h0000gn/T/M2-95741-0/10PHCsolsrunning phc -z ...
the dimension : 6
the number of flags : 1

o2 = (R, {(.0505666 - .372908*ii)x11*x32*x53 + (- .125667 -
                                                           
                                                           
                                                           
                                                           
                                                           
     ------------------------------------------------------------------------
     .174698*ii)x11*x32 + (.528492 + .176064*ii)x11*x53 + (- .277893 +
                                                                      
                                                                      
                                                                      
                                                                      
                                                                      
     ------------------------------------------------------------------------
     .393632*ii)x32*x53 + (.0389869 - .00332626*ii)x11 + (- .109694 +
                                                                     
                                                                     
                                                                     
                                                                     
                                                                     
     ------------------------------------------------------------------------
     .0282635*ii)x32 + (.15019 + .820056*ii)x53 + .0164399 + .185572*ii,
                                                                        
                                                                        
                                                                        
                                                                        
                                                                        
     ------------------------------------------------------------------------
     (.896403 - .000681142*ii)x11*x32*x53 + (.409548 + .398442*ii)x11*x32 +
                                                                           
                                                                           
                                                                           
                                                                           
                                                                           
     ------------------------------------------------------------------------
     (.482779 - .0684926*ii)x11*x53 + (.258711 - .101017*ii)x32*x53 +
                                                                     
                                                                     
                                                                     
                                                                     
                                                                     
     ------------------------------------------------------------------------
     (.0403049 + .353834*ii)x11 + (.0405762 + .0899132*ii)x32 + (.0145131 +
                                                                           
                                                                           
                                                                           
                                                                           
                                                                           
     ------------------------------------------------------------------------
     .040717*ii)x53 - .198072 + .182235*ii, (.217296 +
                                                      
                                                      
                                                      
                                                      
                                                      
     ------------------------------------------------------------------------
     .0668906*ii)x11*x32*x53 + (.0947249 - .0899528*ii)x11*x32 + (.261708 +
                                                                           
                                                                           
                                                                           
                                                                           
                                                                           
     ------------------------------------------------------------------------
     .169341*ii)x11*x53 + (.121374 + .0318812*ii)x32*x53 + (.0949904 -
                                                                      
                                                                      
                                                                      
                                                                      
                                                                      
     ------------------------------------------------------------------------
     .522245*ii)x11 + (- .0117734 - .0989531*ii)x32 + (.0539452 -
                                                                 
                                                                 
                                                                 
                                                                 
                                                                 
     ------------------------------------------------------------------------
     .0543458*ii)x53 - .2895 - .446488*ii, (.31649 - .580124*ii)x11*x32*x53 +
                                                                             
                                                                             
                                                                             
                                                                             
                                                                             
     ------------------------------------------------------------------------
     (- .221582 - .372767*ii)x11*x32 + (- .601742 - .292868*ii)x11*x53 +
                                                                        
                                                                        
                                                                        
                                                                        
                                                                        
     ------------------------------------------------------------------------
     (.18458 - .260165*ii)x32*x53 + (- .961014 - .00832047*ii)x11 + (-
                                                                      
                                                                      
                                                                      
                                                                      
                                                                      
     ------------------------------------------------------------------------
     .117815 - .0868351*ii)x32 + (- .526892 - .16218*ii)x53 - .806895 +
                                                                       
                                                                       
                                                                       
                                                                       
                                                                       
     ------------------------------------------------------------------------
     .148308*ii, (.27086 - .388616*ii)x11*x32*x53 + (- .148643 -
                                                                
                                                                
                                                                
                                                                
                                                                
     ------------------------------------------------------------------------
     .325764*ii)x11*x32 + (- .140591 - .712519*ii)x11*x53 + (.1353 -
                                                                    
                                                                    
                                                                    
                                                                    
                                                                    
     ------------------------------------------------------------------------
     .125228*ii)x32*x53 + (- .200488 - .692699*ii)x11 + (.0474776 -
                                                                   
                                                                   
                                                                   
                                                                   
                                                                   
     ------------------------------------------------------------------------
     .111848*ii)x32 + (- .0645212 - .169015*ii)x53 + .0737699 - .353332*ii,
                                                                           
                                                                           
                                                                           
                                                                           
                                                                           
     ------------------------------------------------------------------------
     (- .33043 + .345645*ii)x11*x32*x53 + (.0413541 + .30404*ii)x11*x32 + (-
                                                                            
                                                                            
                                                                            
                                                                            
                                                                            
     ------------------------------------------------------------------------
     1.01938 - .394939*ii)x11*x53 + (- .364567 - .00518278*ii)x32*x53 + (-
                                                                          
                                                                          
                                                                          
                                                                          
                                                                          
     ------------------------------------------------------------------------
     .298548 + .0575488*ii)x11 + (- .10951 + .0433004*ii)x32 + (- 1.02662 -
                                                                           
                                                                           
                                                                           
                                                                           
                                                                           
     ------------------------------------------------------------------------
     .212574*ii)x53 - .370062 + .0614622*ii}, {{-.621452+.228377*ii,
                                                                    
                                                                    
                                                                    
                                                                    
                                                                    
     ------------------------------------------------------------------------
     -1.16425+.167051*ii, -.878379+.407896*ii}, {-.176021-.0627266*ii,
                                                                      
                                                                      
                                                                      
                                                                      
                                                                      
     ------------------------------------------------------------------------
     -4.1371+1.43564*ii, -.199739-.115337*ii}}, {| -.408248           
                                                 | .204879+.353117ii  
                                                 | -.401354+.0747127ii
                                                 | .352781+.205456ii  
                                                 | -.144098+.381972ii 
                                                 | -.0412063+.406163ii
     ------------------------------------------------------------------------
     -.413842-.0469354ii .386427+.243254ii  -.371244+.0945682ii
     -.413005+.110599ii  .340641+.364115ii  .0510064-.328813ii 
     .106752+.372231ii   -.318647-.111914ii -.0272795-.126731ii
     -.175324-.350758ii  -.286006-.28689ii  -.644613-.0357934ii
     -.124183-.397823ii  .0897318-.297226ii .227378+.421381ii  
     .0758723+.400705ii  -.299659+.280231ii -.255512+.119807ii 
     ------------------------------------------------------------------------
     .139375+.24491ii    -.181156+.438609ii |}, | 1  1  1  1  1  1 |, {|
     .0923877-.13612ii   .0387858-.512469ii |   | -1 -1 -1 -1 -1 0 |   |
     .521333+.305745ii   -.273507-.335324ii |   | 1  1  1  1  0  0 |   |
     .194689+.158011ii   .170999-.0808673ii |   | -1 -1 -1 0  0  0 |   |
     -.206446+.0672331ii -.462802-.269565ii |   | 1  1  0  0  0  0 |   |
     -.606808+.223684ii  .020777+.019108ii  |   | -1 0  0  0  0  0 |   |
     ------------------------------------------------------------------------
     -.621452+.228377ii 0                  0                  |, |
     1                  0                  0                  |  |
     0                  -1.16425+.167051ii 0                  |  |
     0                  1                  0                  |  |
     0                  0                  -.878379+.407896ii |  |
     0                  0                  1                  |  |
     ------------------------------------------------------------------------
     -.176021-.0627266ii 0                 0                  |})
     1                   0                 0                  |
     0                   -4.1371+1.43564ii 0                  |
     0                   1                 0                  |
     0                   0                 -.199739-.115337ii |
     0                   0                 1                  |

o2 : Sequence
i3 : vars(R)

o3 = | x11 x32 x53 |

             1       3
o3 : Matrix R  <--- R
i4 : peek sols

o4 = {Point{ConditionNumber => 3.8432                                                     }, Point{ConditionNumber => 15.873                                                     }}
            Coordinates => {-.621452+.228377*ii, -1.16425+.167051*ii, -.878379+.407896*ii}         Coordinates => {-.176021-.0627266*ii, -4.1371+1.43564*ii, -.199739-.115337*ii}
            LastT => 1                                                                             LastT => 1
            SolutionStatus => Regular                                                              SolutionStatus => Regular
i5 : peek solutionPlanes

o5 = {Matrix{cache => CacheTable{}                                              }, Matrix{cache => CacheTable{}                                              }}
             RawMatrix => -.621452+.228377i 0                 0                           RawMatrix => -.176021-.0627266i 0                0                 
                          1                 0                 0                                        1                  0                0                 
                          0                 -1.16425+.167051i 0                                        0                  -4.1371+1.43564i 0                 
                          0                 1                 0                                        0                  1                0                 
                          0                 0                 -.878379+.407896i                        0                  0                -.199739-.115337i 
                          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 :

For the programmer

The object parseTriplet is a method function.