AlgebraicNumber and NumberField (#21)

* AlgebraicNumber initial

* squarefree ineffective impl

* fixed sff for galois fields - new construction and representation of galois elements

* algebraic numbers

* Newton elementary symmetric functions

* newton elementary symmetric tests

* companion matrix generalized

* algebraic number fields

* AlgebraicNumber and NumberField tests

* roots of one algebraic numbers

* tests

* bugfixes - maintain testablilty

* bug evaluation zero polynomial with Matrix

* evaluate polynomial with matrix argument

* remove dependancy on Polynomials.roots

Author: KlausC

src/CommutativeRings.jl

@@ -8,7 +8,7 @@ using Random
 export category_trait, isfield
 export Ring, RingInt, FractionRing, QuotientRing, Polynomial
 export ZZ, QQ, ZZmod, Frac, Quotient, UnivariatePolynomial, MultivariatePolynomial
-export GaloisField, FSeries
+export GaloisField, GF, FSeries, AlgebraicNumber, NumberField, NF
 
 export SpecialPowerSeries, PowerSeries, O, precision, absprecision
 export Conway
@@ -20,26 +20,27 @@ export LC, LM, LT, CC, lcunit, multideg, modulus, value
 export isdiv, pdivrem, divremv, pgcd, pgcdx
 export resultant, discriminant, signed_subresultant_polynomials, sylvester_matrix
 export basetype, basetypes, depth, iszerodiv
-export monom, ismonom, ismonic, issimpler, iscoprime
+export base, approx
+export monom, ismonom, ismonic, issimpler, iscoprime, issquarefree, sff
 export evaluate, derive, pade, pade_normal!
 export mapping, domain, codomain
 export isirreducible, irreducible, irreducibles
 export num_irreducibles, isreducible, reducible, reducibles
 export characteristic, dimension, order
 export ofindex
-export generator
-export GF, homomorphism
+export generator, generators
+export homomorphism
 export num_primitives, isprimitive
+export elementary_symmetric, newton_symmetric
 
 export VectorSpace, complement, sum, intersect, isequal, issubset
 export groebnerbase, SPOL, lextend
-export generators, varnames, varname, factors
+export varnames, varname, factors
 
-export characteristic_polynomial, adjugate, companion
+export characteristic_polynomial, minimal_polynomial, field_polynomial, adjugate, companion
 
 export compose_inv, Li, Ein, lin1p, lin1pe, ver
 
-export minimal_polynomial
 export rational_normal_form, matrix, transformation, polynomials
 export weierstrass_normal_form, smith_normal_form
 export mfactor, killmemo!, memoize
@@ -85,6 +86,8 @@ include("lll.jl")
 include("ll.jl")
 include("fourier.jl")
 include("fastmultiply.jl")
+include("algebraic.jl")
+include("numberfield.jl")
 
 using .SpecialPowerSeries
 using .Conway