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NumericalAlgebraicGeometry :: Certified

Certified -- a value for the option Predictor that triggers certified tracking

Description

Tells basic functions, e.g., track, to use soft certification described in

C. Beltran and A. Leykin, "Certified numerical homotopy tracking", arXiv:0911.1783

The code for robust certification is not incorporated in this package at the moment; the location of this stand-alone code is in the references of

C. Beltran and A. Leykin, "Robust certified numerical homotopy tracking", arXiv:1105.5992

The functions related to this paper are:

i1 : R = CC[x,y,z];
i2 : S = {x^2-z^2,y^2-z^2};
i3 : T = {x^2+y^2-z^2, x*y};
i4 : solsS = {(1,-1,1),(1,1,1)};
i5 : track(S,T,solsS,Predictor=>Certified,Normalize=>true)

o5 = {{.00000107266, -.70712, .70712}, {.707125, -1.48993e-7, .707107}}

o5 : List

For the programmer

The object Certified is a symbol.