1
2# Polynomial Library
3
4A polynomial is a list of coefficients taken from a ring or a field.
5
6## Theory
7* __polynomial__, definition and basic properties.
8* __polyWeak__, raw polynomials: not normalised, may have leading zero.
9* __polyRing__, polynomials with coefficients from a ring.
10* __polyField__, polynomials with coefficients from a field.
11* __polyDivision__, polynomial Division with quotient and remainder.
12* __polyModuloRing__, polynomial quotient ring by a modulus.
13* __polyMonic__, monic Polynomials, those with leading coefficient equals one.
14* __polyFieldDivision__, division of field polynomials, any nonzero polynomial can be a divisor.
15* __polyRoot__, polynomial factors and roots.
16* __polyEval__, polynomial evaluation, acting as a function.
17* __polyDerivative__,formal derivative for polynomials, symbolic term by term.
18
19## Application
20* __polyBinomial__, polynomial binomial expansion formula.
21* __polyDivides__, polynomial divisibility, relation to vanishing of remainder.
22* __polyRingModulo__, ring polynomial remainder congruences.
23* __polyProduct__, product of polynomials, properties, evaluation, and divisibility.
24* __polyIrreducible__, irreducible polynomials, those without proper factors.
25* __polyCyclic__, properties of cyclic polynomial: quotient of (x^n - 1) by (x - 1).
26* __polyFieldModulo__, field polynomial remainder congruences.
27* __polyGCD__, greatest common divisor of polynomials.
28* __polyMultiplicity__, multiplicity of polynomial factors and roots.
29* __polyMap__, maps between polynomials, under homomorphism or isomorphism of their coefficient rings or fields.
30