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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 = ({(.172541 - .106523*ii)x1  + (- .395011 - .0712191*ii)x1*x2 + (.164344
     ------------------------------------------------------------------------
                    2                                             
     + .113528*ii)x2  + (.368785 + .423381*ii)x1*x3 + (- .192138 +
     ------------------------------------------------------------------------
                                                    2               
     .233684*ii)x2*x3 + (- .0844709 - .0552039*ii)x3 , (- .0284499 -
     ------------------------------------------------------------------------
                   3                             2               
     .0575512*ii)x1  + (- .306504 - .465409*ii)x1 x2 + (.211368 -
     ------------------------------------------------------------------------
                     2                           3              
     .256722*ii)x1*x2  + (.102875 - .206196*ii)x2  + (.0857799 +
     ------------------------------------------------------------------------
                  2                                                   
     .733009*ii)x1 x3 + (.150587 + .0946126*ii)x1*x2*x3 + (- .564702 -
     ------------------------------------------------------------------------
                  2                                  2               
     .144625*ii)x2 x3 + (- .188766 - .235963*ii)x1*x3  + (- .360614 -
     ------------------------------------------------------------------------
                     2                           3
     .248205*ii)x2*x3  + (.0263772 - .28106*ii)x3 }, {{.422782+.395301*ii,
     ------------------------------------------------------------------------
     -.064148+.603087*ii, .539027+.081326*ii}})

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

o3 = {{-.151856+.421269*ii, .551465-.055486*ii, .585503-.38661*ii}}

o3 : List

See also

Ways to use randomInitialPair :