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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 = ({(.0807171 - .0324063*ii)x1  + (- .0701887 + .260996*ii)x1*x2 + (-
     ------------------------------------------------------------------------
                             2                                              
     .0566058 + .262874*ii)x2  + (.236888 + .146104*ii)x1*x3 + (- .0262818 -
     ------------------------------------------------------------------------
                                                 2             
     .157465*ii)x2*x3 + (.063235 - .0182039*ii)x3 , (.0564269 -
     ------------------------------------------------------------------------
                  3                             2                 
     .293486*ii)x1  + (- .0731126 + .36913*ii)x1 x2 + (- .550251 -
     ------------------------------------------------------------------------
                    2                             3               
     .49837*ii)x1*x2  + (- .309545 - .186439*ii)x2  + (- .118174 -
     ------------------------------------------------------------------------
                   2                                                 
     .0661793*ii)x1 x3 + (- .10221 - .596309*ii)x1*x2*x3 + (.472465 +
     ------------------------------------------------------------------------
                  2                                2             
     .661514*ii)x2 x3 + (.020614 - .457607*ii)x1*x3  + (.201608 +
     ------------------------------------------------------------------------
                      2                             3
     .0566853*ii)x2*x3  + (- .108678 + .193677*ii)x3 },
     ------------------------------------------------------------------------
     {{-.157215-.316113*ii, .085476-.572296*ii, -.371611-.634376*ii}})

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

o3 = {{-.473001-.419122*ii, -.115124+.145642*ii, -.499917-.562338*ii}}

o3 : List

Ways to use randomInitialPair :