phc[deflationStep]  - solves a system of polynomial equations

Calling Sequence

     L = deflationStep(S, T)

Parameters

   S - a (possibly partial) list of isolated solutions of T
   T - a polynomial system

Return value

       L - the list of clusters corresponding to the isolated solutions respresented by tables with fields

               "points" - the list of points in the cluster (approximating an isolated solution x* );
               "corank" - the corank of the Jacobian of T  at x*.  

               "deflated system" - a system for which x*  has a lower  multiplicity than before;
               "multipliers" - the additional variables lambda[1], lambda[2],... of the deflated system.

Description

Examples

>    with(phc): setPHCloc("C:\\PHCmaple"):

>    T := makeSystem([x,y],[],[x^2+y-3, x+0.125*y^2-1.5]):

>    sols := solve(T):

>    printSolutions(T,sols); 

(1) [x = .99999-.92073e-5*I, y = 2.0000+.18414e-4*I]

(2) [x = -3.0, y = -6.0]

(3) [x = 1.0000+.22753e-4*I, y = 1.9999-.45505e-4*I]

(4) [x = 1.0000-.22139e-5*I, y = 2.0000+.44277e-5*I]

>    clusters := deflationStep(sols,T);

clusters := [TABLE([
clusters := [TABLE([
clusters := [TABLE([
clusters := [TABLE([
clusters := [TABLE([
clusters := [TABLE([

>    DT := clusters[2]["deflated system"]:

>    printSystem(DT); 

(1) x^2+y-3

(2) .125000000000000*y^2+x-1.50000000000000

(3) .412228143341983e-1*x*lambda[1]+1.99957512476485*I*x*lambda[1]-.787279070700346*x*lambda[2]-1.83852975630997*I*x*lambda[2]+.603601806251125*lambda[1]-.797285933332816*I*lambda[1]+.888433062978371*lambda[2]-.459006201054920*I*lambda[2]

(4) .150900451562781*y*lambda[1]-.199321483333204*I*y*lambda[1]+.222108265744593*y*lambda[2]-.114751550263730*I*y*lambda[2]+.206114071670992e-1*lambda[1]+.999787562382425*I*lambda[1]-.393639535350173*lambda[2]-.919264878154985*I*lambda[2]

(5) -.265696199740034*lambda[1]-.964056808203595*I*lambda[1]+.682144814381376*lambda[2]-.731217103337031*I*lambda[2]-1

See Also

phc , phc[solve] , phc[refine]

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