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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", Experimental Mathematics 21(1): 69-83 (2012) 

i1 : T = randomSd {2,3};
 
i2 : (S,solsS) = randomInitialPair T

                               2                                             
o2 = ({(.244218 - .220355*ii)x1  + (.539808 + .144395*ii)x1*x2 + (- .221394 -
     ------------------------------------------------------------------------
                   2                                                 
     .0613168*ii)x2  + (- .259397 - .00345748*ii)x1*x3 + (- .178951 -
     ------------------------------------------------------------------------
                                                   2            
     .107379*ii)x2*x3 + (- .0128909 - .144621*ii)x3 , (.359958 -
     ------------------------------------------------------------------------
                   3                           2                 
     .0342736*ii)x1  + (.221311 + .556399*ii)x1 x2 + (- .133948 +
     ------------------------------------------------------------------------
                     2                              3               
     .240825*ii)x1*x2  + (- .299729 - .0133971*ii)x2  + (- .119922 -
     ------------------------------------------------------------------------
                   2                                                   
     .0166779*ii)x1 x3 + (.132036 + .509053*ii)x1*x2*x3 + (- .0926582 +
     ------------------------------------------------------------------------
                   2                                  2               
     .0968547*ii)x2 x3 + (- .710775 + .256295*ii)x1*x3  + (- .104174 +
     ------------------------------------------------------------------------
                     2                          3
     .202058*ii)x2*x3  + (.170022 - .20222*ii)x3 }, {{-.710384+.284524*ii,
     ------------------------------------------------------------------------
     .183054-.427437*ii, .40779-.178596*ii}})

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

o3 = {{-.526105-.010808*ii, -.10453-.322525*ii, .60848-.487749*ii}}

o3 : List

See also

Ways to use randomInitialPair :

For the programmer

The object randomInitialPair is a method function.