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NumericalAlgebraicGeometry :: randomInitialPair

randomInitialPair -- a random initial pair

Synopsis

Description

Generates a start system S that has an equal chance of reaching any of the solutions of the target system T. For more details see: C. Beltran and A. Leykin, "Certified numerical homotopy tracking", arXiv:0911.1783

i1 : T = randomSd {2,3};
i2 : (S,solsS) = randomInitialPair T

                                    2                                 
o2 = ({(- .476038 + .000789694*ii)x1  + (- .19571 + .198643*ii)x1*x2 +
     ------------------------------------------------------------------------
                                2                                            
     (.0393046 - .00669864*ii)x2  + (.225441 - .0382109*ii)x1*x3 + (- .141844
     ------------------------------------------------------------------------
                                                    2            
     - .0349976*ii)x2*x3 + (.283961 + .0594359*ii)x3 , (.119455 +
     ------------------------------------------------------------------------
                  3                             2                 
     .116729*ii)x1  + (- .226172 + .420067*ii)x1 x2 + (- .727034 -
     ------------------------------------------------------------------------
                     2                            3             
     .017203*ii)x1*x2  + (.265775 - .0886812*ii)x2  + (.140467 +
     ------------------------------------------------------------------------
                   2                                                    
     .0365211*ii)x1 x3 + (- .641322 - .126218*ii)x1*x2*x3 + (.00751692 +
     ------------------------------------------------------------------------
                  2                                  2              
     .249693*ii)x2 x3 + (- .313471 + .275676*ii)x1*x3  + (.0837198 +
     ------------------------------------------------------------------------
                     2                             3
     .266264*ii)x2*x3  + (- .232453 - .177339*ii)x3 },
     ------------------------------------------------------------------------
     {{-.0887717-.0992099*ii, .241133-.854278*ii, .440741-.0094608*ii}})

o2 : Sequence
i3 : M = track(S,T,solsS,gamma=>0.6+0.8*ii,Software=>M2)

o3 = {{-.609326+.657661*ii, -.02753-.170872*ii, .281581-.294891*ii}}

o3 : List

See also

Ways to use randomInitialPair :