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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 = ({(- .00129308 + .326879*ii)x1  + (.0497884 + .165861*ii)x1*x2 +
     ------------------------------------------------------------------------
                              2                                       
     (.0522039 + .223317*ii)x2  + (- .0170559 + .0555133*ii)x1*x3 + (-
     ------------------------------------------------------------------------
                                                          2              
     .457688 + .281675*ii)x2*x3 + (.234124 - .148231*ii)x3 , (- .247619 -
     ------------------------------------------------------------------------
                  3                             2                  
     .321822*ii)x1  + (- .309321 + .155523*ii)x1 x2 + (- .0434789 -
     ------------------------------------------------------------------------
                     2                              3             
     .540447*ii)x1*x2  + (- .0994088 + .218636*ii)x2  + (.102522 +
     ------------------------------------------------------------------------
                  2                                                  
     .305542*ii)x1 x3 + (- .281117 - .261852*ii)x1*x2*x3 + (.253547 +
     ------------------------------------------------------------------------
                  2                                   2              
     .619293*ii)x2 x3 + (.00927199 - .0782913*ii)x1*x3  + (.0404045 -
     ------------------------------------------------------------------------
                      2                            3
     .0264106*ii)x2*x3  + (.0510345 + .175857*ii)x3 }, {{.597858-.054666*ii,
     ------------------------------------------------------------------------
     .119042+.2108*ii, .75254-.12105*ii}})

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

o3 = {{-.33437-.427851*ii, .019062+.678531*ii, .494112-.0150431*ii}}

o3 : List

Ways to use randomInitialPair :