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NumericalAlgebraicGeometry :: endGameCauchy

endGameCauchy -- Cauchy end game for getting a better approximation of a singular solution

Synopsis

Description

Refines an approximation of a (singular) solution to a polynomial system which was obtained via homotopy continuation. This method is used for posprocessing in the blackbox solver implemented in solveSystem.

i1 : CC[x,y]

o1 = CC  [x..y]
       53

o1 : PolynomialRing
i2 : T = {(x-2)^3,y-x+x^2-x^3}

       3     2               3    2
o2 = {x  - 6x  + 12x - 8, - x  + x  - x + y}

o2 : List
i3 : sols = solveSystem(T,PostProcess=>false);
i4 : p0 = first sols;
i5 : peek p0

o5 = Point{Coordinates => {2.01079-.011783*ii, 434.14+1247.66*ii}}
           H => GateHomotopy{...12...}
           LastIncrement => 5.72205e-7
           LastT => .999999
           NumberOfSteps => 26
           SolutionStatus => MinStepFailure
i6 : t'end = 1

o6 = 1
i7 : p = endGameCauchy(p0#"H",t'end,p0)

o7 = p

o7 : Point

See also

Ways to use endGameCauchy :

For the programmer

The object endGameCauchy is a method function with options.