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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}});
PHCv2.4.27 released 2016-10-16

the input data for phc -e : 
5
6
[ 2 4 6 ]^3;
0
0
0
/var/folders/11/t6mmkf11455d4nt0fn639c6h0000gn/T/M2-12050-0/3PHCout
0
y
y
0
0
0

writing data to file /var/folders/11/t6mmkf11455d4nt0fn639c6h0000gn/T/M2-12050-0/2PHCip
running phc -e, session output to /var/folders/11/t6mmkf11455d4nt0fn639c6h0000gn/T/M2-12050-0/4PHCses
                writing output to /var/folders/11/t6mmkf11455d4nt0fn639c6h0000gn/T/M2-12050-0/3PHCout
opening output file /var/folders/11/t6mmkf11455d4nt0fn639c6h0000gn/T/M2-12050-0/5PHCsolutions
i2 : (R, pols, sols, fixedFlags, movedFlag, solutionPlanes) = parseTriplet(f, p, s)

writing data to file /var/folders/11/t6mmkf11455d4nt0fn639c6h0000gn/T/M2-12050-0/6PHCinp
running phc -o, writing output to /var/folders/11/t6mmkf11455d4nt0fn639c6h0000gn/T/M2-12050-0/7PHCout

writing data to file /var/folders/11/t6mmkf11455d4nt0fn639c6h0000gn/T/M2-12050-0/9PHCipt
writing solutions to /var/folders/11/t6mmkf11455d4nt0fn639c6h0000gn/T/M2-12050-0/10PHCsolsrunning phc -z ...
the dimension : 6
the number of flags : 1

o2 = (R, {(- .0637142 + .222804*ii)x11*x32*x53 + (- .122741 +
                                                             
                                                             
                                                             
                                                             
                                                             
     ------------------------------------------------------------------------
     .140085*ii)x11*x32 + (.0971287 - .0832819*ii)x11*x53 + (.0111046 +
                                                                       
                                                                       
                                                                       
                                                                       
                                                                       
     ------------------------------------------------------------------------
     .111655*ii)x32*x53 + (- .0595241 + .0247224*ii)x11 + (- .0639824 +
                                                                       
                                                                       
                                                                       
                                                                       
                                                                       
     ------------------------------------------------------------------------
     .0828664*ii)x32 + (.0571559 - .154274*ii)x53 - .0875404 - .0111559*ii,
                                                                           
                                                                           
                                                                           
                                                                           
                                                                           
     ------------------------------------------------------------------------
     (.0400078 + .0353146*ii)x11*x32*x53 + (.0355667 + .0333899*ii)x11*x32 +
                                                                            
                                                                            
                                                                            
                                                                            
                                                                            
     ------------------------------------------------------------------------
     (- .0667066 + .146754*ii)x11*x53 + (- .000655815 + .0353306*ii)x32*x53 +
                                                                             
                                                                             
                                                                             
                                                                             
                                                                             
     ------------------------------------------------------------------------
     (.021134 + .113585*ii)x11 + (- .0124953 + .0472244*ii)x32 + (- .118738 +
                                                                             
                                                                             
                                                                             
                                                                             
                                                                             
     ------------------------------------------------------------------------
     .047703*ii)x53 - .0530505 + .0865391*ii, (.00284061 +
                                                          
                                                          
                                                          
                                                          
                                                          
     ------------------------------------------------------------------------
     .00288975*ii)x11*x32*x53 + (.000123071 - .00813135*ii)x11*x32 + (-
                                                                       
                                                                       
                                                                       
                                                                       
                                                                       
     ------------------------------------------------------------------------
     .0506458 + .00860547*ii)x11*x53 + (- .000764226 + .00989542*ii)x32*x53 +
                                                                             
                                                                             
                                                                             
                                                                             
                                                                             
     ------------------------------------------------------------------------
     (- .117889 - .0376117*ii)x11 + (.00811209 - .0018769*ii)x32 + (.00895064
                                                                             
                                                                             
                                                                             
                                                                             
                                                                             
     ------------------------------------------------------------------------
     + .0012129*ii)x53 - .031609 - .0947396*ii, (- .040393 -
                                                            
                                                            
                                                            
                                                            
                                                            
     ------------------------------------------------------------------------
     .0321375*ii)x11*x32*x53 + (- .00586067 - .0371427*ii)x11*x32 + (-
                                                                      
                                                                      
                                                                      
                                                                      
                                                                      
     ------------------------------------------------------------------------
     .0199123 + .00363433*ii)x11*x53 + (.0122616 - .0569594*ii)x32*x53 +
                                                                        
                                                                        
                                                                        
                                                                        
                                                                        
     ------------------------------------------------------------------------
     (.0495545 - .0561337*ii)x11 + (.0349853 - .0245071*ii)x32 + (- .0250363
                                                                            
                                                                            
                                                                            
                                                                            
                                                                            
     ------------------------------------------------------------------------
     + .0357151*ii)x53 + .0556534 + .0380411*ii, (.0680587 +
                                                            
                                                            
                                                            
                                                            
                                                            
     ------------------------------------------------------------------------
     .0211643*ii)x11*x32*x53 + (.0325199 + .0458332*ii)x11*x32 + (- .00892008
                                                                             
                                                                             
                                                                             
                                                                             
                                                                             
     ------------------------------------------------------------------------
     + .0291568*ii)x11*x53 + (.0145271 + .0875449*ii)x32*x53 + (- .0627707 +
                                                                            
                                                                            
                                                                            
                                                                            
                                                                            
     ------------------------------------------------------------------------
     .0781898*ii)x11 + (- .0307314 + .0592439*ii)x32 + (.0196731 +
                                                                  
                                                                  
                                                                  
                                                                  
                                                                  
     ------------------------------------------------------------------------
     .00532361*ii)x53 - .0877325 + .00821034*ii, (- .0146501 +
                                                              
                                                              
                                                              
                                                              
                                                              
     ------------------------------------------------------------------------
     .0204081*ii)x11*x32*x53 + (- .0151978 + .00855551*ii)x11*x32 + (.0855858
                                                                             
                                                                             
                                                                             
                                                                             
                                                                             
     ------------------------------------------------------------------------
     + .122637*ii)x11*x53 + (- .0238161 - .0058264*ii)x32*x53 + (.0184607 +
                                                                           
                                                                           
                                                                           
                                                                           
                                                                           
     ------------------------------------------------------------------------
     .0988078*ii)x11 + (- .014684 - .0112081*ii)x32 + (- .0264726 +
                                                                   
                                                                   
                                                                   
                                                                   
                                                                   
     ------------------------------------------------------------------------
     .120082*ii)x53 - .0469397 + .080074*ii}, {{-.0194076-.479672*ii,
                                                                     
                                                                     
                                                                     
                                                                     
                                                                     
     ------------------------------------------------------------------------
     -1.50362+6.80773*ii, -.777358-.425202*ii}, {-.563473-1.00664*ii,
                                                                     
                                                                     
                                                                     
                                                                     
                                                                     
     ------------------------------------------------------------------------
     1.97344-2.9889*ii, -.435436-.411613*ii}}, {| -.829408-.558644i
                                                | .93765+.34758i   
                                                | -.913834-.406088i
                                                | .9083+.418319i   
                                                | -.988914+.148487i
                                                | .503797-.863822i 
     ------------------------------------------------------------------------
     -.888702-.458485i .96251-.271247i   .354919+.934897i .334607+.942358i 
     -.975508-.219965i .111481+.993767i  .209974+.977707i .810915+.585164i 
     -.069838-.997558i .895382-.445298i  .711254-.702936i .960655+.277743i 
     -.237522+.971382i -.999258-.038509i .629035-.777377i .531425-.847106i 
     .100099+.994978i  -.976359-.216154i .98822+.153039i  .962451-.271456i 
     -.960383-.278683i -.272569+.962136i .993257-.115931i -.580516-.814249i
     ------------------------------------------------------------------------
     -.998951-.045793i |}, | 1  1  1  1  1  1 |, {| -.0194076-.479672i
     .975683+.219188i  |   | -1 -1 -1 -1 -1 0 |   | 1                 
     .776939+.629576i  |   | 1  1  1  1  0  0 |   | 0                 
     -.65065-.759378i  |   | -1 -1 -1 0  0  0 |   | 0                 
     .118868+.99291i   |   | 1  1  0  0  0  0 |   | 0                 
     .975418+.220361i  |   | -1 0  0  0  0  0 |   | 0                 
     ------------------------------------------------------------------------
     0                 0                 |, | -.563473-1.00664i
     0                 0                 |  | 1                
     -1.50362+6.80773i 0                 |  | 0                
     1                 0                 |  | 0                
     0                 -.777358-.425202i |  | 0                
     0                 1                 |  | 0                
     ------------------------------------------------------------------------
     0               0                 |})
     0               0                 |
     1.97344-2.9889i 0                 |
     1               0                 |
     0               -.435436-.411613i |
     0               1                 |

o2 : Sequence
i3 : vars(R)

o3 = | x11 x32 x53 |

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

o4 = {Point{ConditionNumber => 1                                                           }, Point{ConditionNumber => 1                                                        }}
            Coordinates => {-.0194076-.479672*ii, -1.50362+6.80773*ii, -.777358-.425202*ii}         Coordinates => {-.563473-1.00664*ii, 1.97344-2.9889*ii, -.435436-.411613*ii}
            LastT => 1                                                                              LastT => 1
            SolutionStatus => Regular                                                               SolutionStatus => Regular
i5 : peek solutionPlanes

o5 = {Matrix{cache => CacheTable{}                                               }, Matrix{cache => CacheTable{}                                            }}
             RawMatrix => -.0194076-.479672i 0                 0                           RawMatrix => -.563473-1.00664i 0               0                 
                          1                  0                 0                                        1                 0               0                 
                          0                  -1.50362+6.80773i 0                                        0                 1.97344-2.9889i 0                 
                          0                  1                 0                                        0                 1               0                 
                          0                  0                 -.777358-.425202i                        0                 0               -.435436-.411613i 
                          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 :