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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 = ({(- .110359 - .194593*ii)x1  + (.0103147 + .0308393*ii)x1*x2 +
     ------------------------------------------------------------------------
                               2                                            
     (.0613542 + .0869879*ii)x2  + (- .141272 - .256506*ii)x1*x3 + (.45725 +
     ------------------------------------------------------------------------
                                                  2            
     .58215*ii)x2*x3 + (- .0671545 + .131127*ii)x3 , (.120046 -
     ------------------------------------------------------------------------
                  3                           2                  
     .263297*ii)x1  + (.236374 - .115818*ii)x1 x2 + (- .0616236 +
     ------------------------------------------------------------------------
                     2                             3             
     .137308*ii)x1*x2  + (- .213451 + .132116*ii)x2  + (.289556 +
     ------------------------------------------------------------------------
                 2                                               
     .11695*ii)x1 x3 + (.519954 - .76456*ii)x1*x2*x3 + (.570718 +
     ------------------------------------------------------------------------
                  2                                    2               
     .573272*ii)x2 x3 + (- .0904212 - .0811905*ii)x1*x3  + (- .358862 +
     ------------------------------------------------------------------------
                     2                              3
     .253423*ii)x2*x3  + (- .0702156 + .198385*ii)x3 }, {{.602021-.21278*ii,
     ------------------------------------------------------------------------
     .733246-.231382*ii, .0317567-.0100139*ii}})

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

o3 = {{-.0719459+.0718583*ii, .507382-.227826*ii, .082090+.820719*ii}}

o3 : List

See also

Ways to use randomInitialPair :