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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 = ({(.0457587 + .102751*ii)x1  + (- .294777 - .229327*ii)x1*x2 + (.143054
     ------------------------------------------------------------------------
                    2                                              
     + .278298*ii)x2  + (.0901467 + .0572922*ii)x1*x3 + (.0320494 +
     ------------------------------------------------------------------------
                                                  2              
     .144536*ii)x2*x3 + (- .156671 + .249596*ii)x3 , (- .087342 +
     ------------------------------------------------------------------------
                   3                            2               
     .0353853*ii)x1  + (.0092192 + .247169*ii)x1 x2 + (.121168 +
     ------------------------------------------------------------------------
                      2                             3               
     .0609829*ii)x1*x2  + (- .101181 - .367891*ii)x2  + (- .811562 +
     ------------------------------------------------------------------------
                  2                                               
     .301746*ii)x1 x3 + (.363217 - .60587*ii)x1*x2*x3 + (.116789 +
     ------------------------------------------------------------------------
                   2                                  2               
     .0232736*ii)x2 x3 + (.0933641 + .0887622*ii)x1*x3  + (- .400967 -
     ------------------------------------------------------------------------
                     2                             3
     .177193*ii)x2*x3  + (- .182152 + .303843*ii)x3 }, {{-.184086-.548176*ii,
     ------------------------------------------------------------------------
     -.679251-.344294*ii, .20856-.205423*ii}})

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

o3 = {{.177423-.13744*ii, -.670797-.236137*ii, .004536-.666245*ii}}

o3 : List

See also

Ways to use randomInitialPair :