ToySolver.Data.AlgebraicNumber.Root

Manipulating polynomials for corresponding operations for algebraic numbers.

Reference:

• http://www.dpmms.cam.ac.uk/~wtg10/galois.html

Documentation

type Var = Int

normalizePoly :: (Fractional k, Eq k) => UPolynomial k -> UPolynomial k

rootAdd :: (Fractional k, Ord k) => UPolynomial k -> UPolynomial k -> UPolynomial k

rootMul :: (Fractional k, Ord k) => UPolynomial k -> UPolynomial k -> UPolynomial k

rootShift :: (Fractional k, Eq k) => k -> UPolynomial k -> UPolynomial k

rootScale :: (Fractional k, Eq k) => k -> UPolynomial k -> UPolynomial k

rootRecip :: (Fractional k, Eq k) => UPolynomial k -> UPolynomial k

rootSimpPoly :: forall k l. (Fractional k, Ord k) => (l -> UPolynomial k) -> UPolynomial l -> UPolynomial k

Given a polynomial P = Σ_i a_i x^i over L/K where each a_i is a root of polynomial f a_i over K, rootSimpPoly f P computes a polynomial Q over K such that roots of P is a subset of roots of Q.

rootNthRoot :: (Fractional k, Ord k) => Integer -> UPolynomial k -> UPolynomial k

lift2 :: forall k. (Fractional k, Ord k) => (forall a. Num a => a -> a -> a) -> UPolynomial k -> UPolynomial k -> UPolynomial k

findPoly :: forall k. (Fractional k, Ord k) => Polynomial k Var -> [Polynomial k Var] -> UPolynomial k

Given a polynomial P and polynomials {P1,…,Pn} over K, findPoly P [P1..Pn] computes a non-zero polynomial Q such that Q[P] = 0 modulo {P1,…,Pn}.