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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 = ({(.117765 + .20139*ii)x1  + (- .064886 + .235737*ii)x1*x2 + (.102524 -
     ------------------------------------------------------------------------
                   2                                             
     .0181962*ii)x2  + (.386384 + .321668*ii)x1*x3 + (- .270519 -
     ------------------------------------------------------------------------
                                                    2             
     .0294082*ii)x2*x3 + (- .0529597 + .377956*ii)x3 , (.0646637 +
     ------------------------------------------------------------------------
                   3                            2                   
     .0677821*ii)x1  + (- .24129 + .268954*ii)x1 x2 + (- .00978836 -
     ------------------------------------------------------------------------
                     2                               3                
     .127702*ii)x1*x2  + (- .100928 - .00509582*ii)x2  + (- .0137247 +
     ------------------------------------------------------------------------
                   2                                                
     .0526324*ii)x1 x3 + (- .2307 - .301016*ii)x1*x2*x3 + (.484787 +
     ------------------------------------------------------------------------
                 2                                  2             
     .26749*ii)x2 x3 + (.0607759 - .0122979*ii)x1*x3  + (.109101 -
     ------------------------------------------------------------------------
                     2                              3
     .303935*ii)x2*x3  + (- .129845 + .0908601*ii)x3 },
     ------------------------------------------------------------------------
     {{-.885954+.279789*ii, .0144428-.219626*ii, .258144+.147385*ii}})

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

o3 = {{-.715333+.243949*ii, -.150414-.271706*ii, -.172434+.550097*ii}}

o3 : List

See also

Ways to use randomInitialPair :