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The following code generates two polynomials $q_1$ and $q_2$ in complex variables p and c: pp[n_] := If[n > 0, pp[n - 1]^2 + c, p]; q1 = PolynomialQuotient[pp[4] - p, pp[2] - p, p]; q2 = PolynomialRemainder …

When I divide polynomials, I would like Mathematica to NOT create negative powers of variables. …

Follow-up from OP: Based on the very helpful Answers and comments above from @bbgodfrey and @Daniel Lichtblau, I ran the following test, comparing the three methods on speed and precision: z[n_, c_] …

p[3] p[4] p[5]+p[1] p[3] p[4] p[5]+p[2] p[3] p[4] p[5]$$ Into a much more convenient form like this: $$q = 1 - 3c+c^2+(1-2c)e[1] + e[2] + e[3] + e[4]$$ Where the e[]'s are the Elementary Symmetric Polynomials …

Does Solve[] find ALL the exact roots of rational polynomials? I've done a bunch of tests where I created an expression with some analytic roots, and Solve[] always found them all. …

How should I restructure this code? I generate a high-order polynomial poly with integer coefficients, then find roots and divide them out of poly one at a time. I want FindRoot[] to use a very high …

I need to find the roots of a rational polynomial that are near i. In the following code, I try that two different ways. First, I use a constraint to only find roots in the right region. Second, I f …

I need to find all the rational roots of a bunch of high-order polynomials with rational complex coefficients. Is there an efficient way to do this? …

There are polynomials with roots not expressible with radicals but expressible as trigonometric or other functions, for which Solve[] only returns Root[]-form punt results. …

The following code creates two polynomials $q_1$ and $q_2$ in variables $c$ and $p$, then uses NSolve to find roots. But the polynomials don't evaluate to zero at those roots. …