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NumericalAlgebraicGeometry :: goodInitialPair(List)

goodInitialPair(List) -- make an intial pair conjectured to be good by Shub and Smale

Synopsis

Description

Generates a start system S that is conjectured to have good complexity when used in linear homotopy with target system T leading to one solution. For more details see: C. Beltran and A. Leykin, "Certified numerical homotopy tracking", arXiv:0911.1783

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

                                 2
o2 = ({1.41421x1*x3, 1.73205x2*x3 }, {{0, 0, 1}})

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

o3 = {{.0312266+.0428244*ii, .191842+.67014*ii, .680368+.219998*ii}}

o3 : List

See also