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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 = ({(- .0699927 - .39041*ii)x1  + (- .354584 - .063796*ii)x1*x2 +
     ------------------------------------------------------------------------
                               2                                            
     (.0340547 + .0545397*ii)x2  + (.118722 - .409015*ii)x1*x3 + (.0390547 -
     ------------------------------------------------------------------------
                                                   2               
     .111298*ii)x2*x3 + (- .0193083 + .184755*ii)x3 , (.000425231 +
     ------------------------------------------------------------------------
                  3                           2                 
     .127014*ii)x1  + (.317607 - .173007*ii)x1 x2 + (- .108502 -
     ------------------------------------------------------------------------
                      2                                3             
     .0286033*ii)x1*x2  + (- .0963651 + .00625777*ii)x2  + (.379604 -
     ------------------------------------------------------------------------
                  2                                               
     .462476*ii)x1 x3 + (.17151 - 1.27561*ii)x1*x2*x3 + (.326776 +
     ------------------------------------------------------------------------
                   2                                2             
     .0529794*ii)x2 x3 + (.053649 + .250219*ii)x1*x3  + (.226767 +
     ------------------------------------------------------------------------
                     2                               3
     .082787*ii)x2*x3  + (- .239853 - .00643816*ii)x3 },
     ------------------------------------------------------------------------
     {{.234071+.0050390*ii, .369629+.150015*ii, .886114+.029276*ii}})

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

o3 = {{.406007-.0565181*ii, -.518031+.12682*ii, .735911+.077204*ii}}

o3 : List

See also

Ways to use randomInitialPair :