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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 = ({(.222659 + .285057*ii)x1  + (- .230978 - .255439*ii)x1*x2 + (-
     ------------------------------------------------------------------------
                             2                                              
     .0318812 - .143146*ii)x2  + (.238687 + .0363986*ii)x1*x3 + (.00250744 +
     ------------------------------------------------------------------------
                                                  2              
     .0319789*ii)x2*x3 + (.0636681 - .250148*ii)x3 , (- .115046 +
     ------------------------------------------------------------------------
                  3                             2                 
     .212553*ii)x1  + (- .549332 + .574838*ii)x1 x2 + (- .461487 +
     ------------------------------------------------------------------------
                     2                              3             
     .278778*ii)x1*x2  + (- .0980768 - .386501*ii)x2  + (.159485 -
     ------------------------------------------------------------------------
                  2                                                
     .150016*ii)x1 x3 + (.170516 - .175911*ii)x1*x2*x3 + (.222683 -
     ------------------------------------------------------------------------
                 2                                  2              
     .24313*ii)x2 x3 + (- .543767 - .361312*ii)x1*x3  + (.0534635 -
     ------------------------------------------------------------------------
                      2                            3
     .0255507*ii)x2*x3  + (.0677818 + .103969*ii)x3 }, {{.262218-.296047*ii,
     ------------------------------------------------------------------------
     .514231-.54485*ii, .508003+.155679*ii}})

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

o3 = {{-.102878-.661891*ii, .242614-.118155*ii, .562138+.403108*ii}}

o3 : List

Ways to use randomInitialPair :