PA16: Complex coefficients: all roots by the method of Madsen and Reid

To find all the real and complex roots of a polynomial with complex coefficients, i.e. calculate the zeros of \[a _0 + a _1 x + a _2 x ^2 + ... + a _n x ^n = 0\] The user can supply error bounds on the coefficients of the polynomial and the routine returns bounds on the moduli of the errors in the roots. The roots are found by the method of Madsen and error bounds by the application of Rouche’s theorem.

Precision: At least 8-byte arithmetic is recommended.