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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 = ({(- .390938 + .208247*ii)x1  + (- .137414 - .31691*ii)x1*x2 + (.156126
     ------------------------------------------------------------------------
                    2                                             
     + .069641*ii)x2  + (- .624836 + .037332*ii)x1*x3 + (.452879 -
     ------------------------------------------------------------------------
                                                  2            
     .288967*ii)x2*x3 + (- .11305 + .0902642*ii)x3 , (.133272 +
     ------------------------------------------------------------------------
                   3                           2               
     .0844797*ii)x1  + (.373939 + .525036*ii)x1 x2 + (.201192 -
     ------------------------------------------------------------------------
                      2                             3              
     .0954665*ii)x1*x2  + (.0853534 + .0369937*ii)x2  + (.0257336 +
     ------------------------------------------------------------------------
                  2                                                  
     .131202*ii)x1 x3 + (.202234 + .395876*ii)x1*x2*x3 + (- .234545 -
     ------------------------------------------------------------------------
                   2                                    2              
     .0868499*ii)x2 x3 + (- .0444852 + .0777368*ii)x1*x3  + (.0671853 +
     ------------------------------------------------------------------------
                     2                            3
     .391457*ii)x2*x3  + (.140262 + .0176611*ii)x3 }, {{-.385349+.500237*ii,
     ------------------------------------------------------------------------
     -.425964-.101383*ii, .634462-.083689*ii}})

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

o3 = {{.0988707-.0236044*ii, -.736751-.051206*ii, .297822-.596276*ii}}

o3 : List

See also

Ways to use randomInitialPair :