                C++ Toolbox for Verified Computing I
                       Basic Numerical Problems

    Copyright (c) 1995 Rolf Hammer, Matthias Hocks, Dietmar Ratz

The function CPolyZero(p,t) computes verified enclosures of the roots of a
complex polynomial p starting from t  by enclosing the zeros in narrow
bounds. The coefficients of the deflated polynomial are also enclosed.

The function returns a vector with entries [y;p;err] where y is a complex
enclosure of the root close to t, p the complex enclosure of the reduced
polynomial and err represents an eventual error messages. The functions
cpzero(p,t) and cpreduce(p,t) just return the enclosure of the root or
of the reduced polynomial.

   >X=poly("X");p=X^4-(5+3*i)*X^3+(6+7*i)*X*X-(54-22*i)*X+120+90*i;
   >CPolyZero(p,1+i)
    [([   1.4142135623,   1.4142135624]+[   2.8284271247, 2.8284271248]*i);
     X^3+([-3.5857864377, -3.5857864376]+[-0.1715728753,-0.1715728752]*i)*X^2
     +([  1.4142135623,  1.4142135624]+[ -3.3847763109,-3.3847763108]*i)*X
     +([-42.4264068712,-42.4264068711]+[ 21.2132034355,21.2132034356]*i);""]
   >cpzero(p,4)
     ([4.9999999999,5.0000000001]+[-2.2569491536E-036,2.2569491536E-036]*i)