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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 = ({(- .314372 + .0392749*ii)x1  + (.00385674 - .139033*ii)x1*x2 + (-
     ------------------------------------------------------------------------
                             2                                             
     .0801079 + .416285*ii)x2  + (.188799 + .108803*ii)x1*x3 + (- .257663 -
     ------------------------------------------------------------------------
                                                2                           3
     .120384*ii)x2*x3 + (.253294 - .203649*ii)x3 , (.111945 - .0625955*ii)x1 
     ------------------------------------------------------------------------
                               2                                2            
     + (.531324 + .680264*ii)x1 x2 + (.331017 + .175939*ii)x1*x2  + (.0224039
     ------------------------------------------------------------------------
                       3                             2               
     + .000549852*ii)x2  + (- .0153557 + .10055*ii)x1 x3 + (.011116 +
     ------------------------------------------------------------------------
                                                  2               
     .8072*ii)x1*x2*x3 + (.0499787 - .496494*ii)x2 x3 + (.398291 +
     ------------------------------------------------------------------------
                     2                               2              
     .172305*ii)x1*x3  + (.0998109 + .126745*ii)x2*x3  + (.0627651 -
     ------------------------------------------------------------------------
                  3
     .101109*ii)x3 }, {{.19227+.118765*ii, .588638-.227785*ii,
     ------------------------------------------------------------------------
     .680858-.29492*ii}})

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

o3 = {{-.534799-.37252*ii, .403545-.0084163*ii, .616895-.178158*ii}}

o3 : List

Ways to use randomInitialPair :