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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 = ({(.0842415 + .170057*ii)x1  + (- .0579991 - .0234819*ii)x1*x2 +
     ------------------------------------------------------------------------
                             2                                             
     (.132173 + .376237*ii)x2  + (.138124 + .0142108*ii)x1*x3 + (.0861771 +
     ------------------------------------------------------------------------
                                                 2               
     .120823*ii)x2*x3 + (.0728894 + .022701*ii)x3 , (- .0501426 -
     ------------------------------------------------------------------------
                  3                            2                 
     .365549*ii)x1  + (.0335431 + .212138*ii)x1 x2 + (- .408275 +
     ------------------------------------------------------------------------
                    2                             3             
     .22927*ii)x1*x2  + (- .127156 - .150453*ii)x2  + (.503155 +
     ------------------------------------------------------------------------
                 2                                                  
     .46393*ii)x1 x3 + (- .535227 + .360827*ii)x1*x2*x3 + (.453678 -
     ------------------------------------------------------------------------
                  2                                2             
     .151293*ii)x2 x3 + (.544331 + .178048*ii)x1*x3  + (.285791 +
     ------------------------------------------------------------------------
                     2                              3
     .215745*ii)x2*x3  + (- .0193141 - .109708*ii)x3 },
     ------------------------------------------------------------------------
     {{-.579301+.249349*ii, -.207203-.301352*ii, .680673-.071925*ii}})

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

o3 = {{-.100446+.005905*ii, -.032560-.809001*ii, .356608-.455152*ii}}

o3 : List

Ways to use randomInitialPair :