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

                               2                                      
o2 = ({(.276494 - .105206*ii)x1  + (- .184426 + .0398379*ii)x1*x2 + (-
     ------------------------------------------------------------------------
                             2                                              
     .174679 - .0287153*ii)x2  + (.0356446 + .346006*ii)x1*x3 + (- .203986 -
     ------------------------------------------------------------------------
                                                  2            
     .0674766*ii)x2*x3 + (- .18798 + .273941*ii)x3 , (.135702 +
     ------------------------------------------------------------------------
                   3                           2                 
     .0968467*ii)x1  + (.704967 - .328874*ii)x1 x2 + (- .194347 -
     ------------------------------------------------------------------------
                     2                               3                
     .249648*ii)x1*x2  + (- .00968765 - .174135*ii)x2  + (- .0205947 +
     ------------------------------------------------------------------------
                   2                                               
     .0334841*ii)x1 x3 + (.89372 + .925361*ii)x1*x2*x3 + (.239665 -
     ------------------------------------------------------------------------
                  2                                 2               
     .344769*ii)x2 x3 + (.0461709 + .150503*ii)x1*x3  + (- .240124 -
     ------------------------------------------------------------------------
                     2                            3
     .516674*ii)x2*x3  + (.138986 - .0434084*ii)x3 }, {{.29709-.757518*ii,
     ------------------------------------------------------------------------
     -.123767+.0204291*ii, .53444-.19116*ii}})

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

o3 = {{.276153-.451767*ii, -.052369-.685801*ii, .478372-.133199*ii}}

o3 : List

Ways to use randomInitialPair :