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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. For more details see: C. Beltran and A. Leykin, "Certified numerical homotopy tracking", arXiv:0911.1783

i1 : T = randomSd {2,3};
i2 : (S,solsS) = randomInitialPair T

                               2                                            
o2 = ({(.131679 + .149331*ii)x1  + (.150508 + .0823828*ii)x1*x2 + (.218325 -
     ------------------------------------------------------------------------
                  2                                             
     .178537*ii)x2  + (- .433866 - .647397*ii)x1*x3 + (.257253 -
     ------------------------------------------------------------------------
                                                    2                      3
     .178349*ii)x2*x3 + (- .0719741 - .0288617*ii)x3 , (.0858 - .2157*ii)x1 
     ------------------------------------------------------------------------
                               2                                 2           
     + (.247188 + .144628*ii)x1 x2 + (.136729 - .0482212*ii)x1*x2  + (.316642
     ------------------------------------------------------------------------
                    3                             2               
     + .141111*ii)x2  + (- .266772 - .397955*ii)x1 x3 + (.171725 -
     ------------------------------------------------------------------------
                                                     2               
     .793097*ii)x1*x2*x3 + (- .020319 + .126177*ii)x2 x3 + (.101579 +
     ------------------------------------------------------------------------
                     2                              2              
     .137638*ii)x1*x3  + (.319486 - .373667*ii)x2*x3  + (.0121629 -
     ------------------------------------------------------------------------
                  3
     .107636*ii)x3 }, {{.0948926+.355015*ii, -.27722-.768798*ii,
     ------------------------------------------------------------------------
     .436121+.0828112*ii}})

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

o3 = {{-.612685-.156773*ii, .0452-.417235*ii, .651078+.002879*ii}}

o3 : List

See also

Ways to use randomInitialPair :