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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 = ({(.0195524 - .0871472*ii)x1  + (- .205215 - .164435*ii)x1*x2 + (.156114
     ------------------------------------------------------------------------
                     2                                              
     - .0892349*ii)x2  + (.333628 - .241044*ii)x1*x3 + (- .0598254 -
     ------------------------------------------------------------------------
                                                2                           3
     .0627657*ii)x2*x3 + (.12777 - .349031*ii)x3 , (.309921 + .0373362*ii)x1 
     ------------------------------------------------------------------------
                                   2                                   2     
     + (- .0913321 - .0679175*ii)x1 x2 + (- .00904196 + .10695*ii)x1*x2  + (-
     ------------------------------------------------------------------------
                           3                           2               
     .24844 + .067977*ii)x2  + (.254505 + .116747*ii)x1 x3 + (.416033 +
     ------------------------------------------------------------------------
                                                     2               
     .681028*ii)x1*x2*x3 + (- .177688 - .397113*ii)x2 x3 + (.123743 +
     ------------------------------------------------------------------------
                     2                                 2                
     .159915*ii)x1*x3  + (- .0946942 + .950308*ii)x2*x3  + (- .0234567 +
     ------------------------------------------------------------------------
                  3
     .119088*ii)x3 }, {{-.256068-.697362*ii, -.093810-.53965*ii,
     ------------------------------------------------------------------------
     .384692-.0102568*ii}})

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

o3 = {{.35256-.582399*ii, -.0612421-.358005*ii, -.392094-.500856*ii}}

o3 : List

See also

Ways to use randomInitialPair :