Module complex_algebraic 

Complex algebraic numbers re + im·i with real algebraic parts, and every complex root of a polynomial with rational coefficients.

A non-real root z = a + b·i of an irreducible g has its conjugate as a root too, so 2a = z + z̄ is a real root of S(x) = Res_y(g(y), g(x − y)), whose roots are the sums of two roots of g; and z − z̄ = 2b·i, so −4b² is a negative real root of E, where E(x²) = Res_y(g(y), g(x + y)) / x^deg g has the nonzero differences of roots for roots. A floating-point approximation of each root orders the candidates nearest first, and a candidate pair is accepted only once g(a + b·i) = 0 is checked exactly — the approximation guides the search and never decides it.

Structs

ComplexAlgebraic

re + im·i with real algebraic parts.

Functions

complex_roots

Every complex root of p (nonzero), once each: the real roots ascending, then each conjugate pair by its upper root, upper before lower.