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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 = ({(.241827 - .039734*ii)x1  + (.237479 + .128117*ii)x1*x2 + (- .188862 +
     ------------------------------------------------------------------------
                   2                                             
     .0278525*ii)x2  + (.284075 + .0234827*ii)x1*x3 + (.0301306 -
     ------------------------------------------------------------------------
                                                 2              
     .225598*ii)x2*x3 + (- .453088 + .27661*ii)x3 , (- .428215 +
     ------------------------------------------------------------------------
                  3                             2                
     .128252*ii)x1  + (- .149729 + .254179*ii)x1 x2 + (.0232859 +
     ------------------------------------------------------------------------
                       2                           3             
     .00926805*ii)x1*x2  + (.103315 - .131275*ii)x2  + (.190455 -
     ------------------------------------------------------------------------
                   2                                                     
     .0828241*ii)x1 x3 + (- .441265 - .0413784*ii)x1*x2*x3 + (- .481993 -
     ------------------------------------------------------------------------
                 2                                 2               
     .23217*ii)x2 x3 + (.0875953 + .373565*ii)x1*x3  + (- .491479 +
     ------------------------------------------------------------------------
                     2                            3
     .294727*ii)x2*x3  + (.132498 - .0516904*ii)x3 }, {{.492158-.57294*ii,
     ------------------------------------------------------------------------
     -.392147+.310414*ii, .290844-.307887*ii}})

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

o3 = {{.555192-.621841*ii, -.288697+.45985*ii, -.0726448+.0706445*ii}}

o3 : List

See also

Ways to use randomInitialPair :