Safe Haskell	None
Language	Haskell2010

Math.RootLoci.Algebra

Description

Re-exporting the Algebra.* modules.

Because of limitations of the import-export mechanism, you still have to do

import Math.RootLoci.Algebra
import qualified Math.Algebra.Polynomial.FreeModule as ZMod

Synopsis

type ZMod base = FreeMod Integer base
type QMod base = FreeMod Rational base
data FreeMod coeff base
module Math.RootLoci.Algebra.SymmPoly

Documentation

type ZMod base = FreeMod Integer base #

Free module with integer coefficients

type QMod base = FreeMod Rational base #

Free module with rational coefficients

data FreeMod coeff base #

Free module over a coefficient ring with the given base. Internally a map storing the coefficients. We maintain the invariant that the coefficients are never zero.

Instances

Instances details

Theta (ZMod MultiLam) Source #
Instance details Defined in Math.RootLoci.Motivic.Abstract Methods theta :: ZMod MultiLam -> ZMod MultiLam Source #
Permute (ZMod MultiLam) Source #
Instance details Defined in Math.RootLoci.Motivic.Abstract Methods permute :: Permutation -> ZMod MultiLam -> ZMod MultiLam Source #
PsiEvenOdd (ZMod MultiLam) Source #
Instance details Defined in Math.RootLoci.Motivic.Abstract Methods psiEvenOdd :: ZMod MultiLam -> ZMod MultiLam Source #
(Eq c, Num c) => Psi [FreeMod c SingleLam] (FreeMod c SingleLam) Source #
Instance details Defined in Math.RootLoci.Motivic.Abstract Methods psi :: [FreeMod c SingleLam] -> FreeMod c SingleLam Source #
(Eq base, Eq coeff) => Eq (FreeMod coeff base)
Instance details Defined in Math.Algebra.Polynomial.FreeModule Methods (==) :: FreeMod coeff base -> FreeMod coeff base -> Bool # (/=) :: FreeMod coeff base -> FreeMod coeff base -> Bool #
(Monoid b, Ord b, Eq c, Num c) => Num (FreeMod c b)
Instance details Defined in Math.Algebra.Polynomial.FreeModule Methods (+) :: FreeMod c b -> FreeMod c b -> FreeMod c b # (-) :: FreeMod c b -> FreeMod c b -> FreeMod c b # (*) :: FreeMod c b -> FreeMod c b -> FreeMod c b # negate :: FreeMod c b -> FreeMod c b # abs :: FreeMod c b -> FreeMod c b # signum :: FreeMod c b -> FreeMod c b # fromInteger :: Integer -> FreeMod c b #
(Ord base, Ord coeff) => Ord (FreeMod coeff base)
Instance details Defined in Math.Algebra.Polynomial.FreeModule Methods compare :: FreeMod coeff base -> FreeMod coeff base -> Ordering # (<) :: FreeMod coeff base -> FreeMod coeff base -> Bool # (<=) :: FreeMod coeff base -> FreeMod coeff base -> Bool # (>) :: FreeMod coeff base -> FreeMod coeff base -> Bool # (>=) :: FreeMod coeff base -> FreeMod coeff base -> Bool # max :: FreeMod coeff base -> FreeMod coeff base -> FreeMod coeff base # min :: FreeMod coeff base -> FreeMod coeff base -> FreeMod coeff base #
(Show base, Show coeff) => Show (FreeMod coeff base)
Instance details Defined in Math.Algebra.Polynomial.FreeModule Methods showsPrec :: Int -> FreeMod coeff base -> ShowS # show :: FreeMod coeff base -> String # showList :: [FreeMod coeff base] -> ShowS #
(Num c, Eq c, Pretty c, IsSigned c, Pretty b) => Pretty (FreeMod c b)
Instance details Defined in Math.Algebra.Polynomial.Pretty Methods pretty :: FreeMod c b -> String # prettyInParens :: FreeMod c b -> String #
Ord b => FreeModule (FreeMod c b)
Instance details Defined in Math.Algebra.Polynomial.FreeModule Associated Types type BaseF (FreeMod c b) # type CoeffF (FreeMod c b) # Methods toFreeModule :: FreeMod c b -> FreeMod (CoeffF (FreeMod c b)) (BaseF (FreeMod c b)) # fromFreeModule :: FreeMod (CoeffF (FreeMod c b)) (BaseF (FreeMod c b)) -> FreeMod c b #
(Eq c, Num c) => Omega123 (FreeMod c MultiLam) Source #
Instance details Defined in Math.RootLoci.Motivic.Abstract Methods omega123 :: FreeMod c MultiLam -> FreeMod c MultiLam Source #
(Eq c, Num c) => Omega (FreeMod c MultiLam) Source #
Instance details Defined in Math.RootLoci.Motivic.Abstract Methods omega :: Int -> FreeMod c MultiLam -> FreeMod c MultiLam Source #
(Eq c, Num c) => Omega (FreeMod c SingleLam) Source #
Instance details Defined in Math.RootLoci.Motivic.Abstract Methods omega :: Int -> FreeMod c SingleLam -> FreeMod c SingleLam Source #
(Eq c, Num c) => Cross (FreeMod c MultiLam) Source #
Instance details Defined in Math.RootLoci.Motivic.Abstract Methods cross :: FreeMod c MultiLam -> FreeMod c MultiLam -> FreeMod c MultiLam Source # crossMany :: [FreeMod c MultiLam] -> FreeMod c MultiLam Source # crossInterleave :: FreeMod c MultiLam -> FreeMod c MultiLam -> FreeMod c MultiLam Source #
(Eq c, Num c) => SuperNormalize (FreeMod c MultiLam) Source #
Instance details Defined in Math.RootLoci.Motivic.Abstract Methods superNormalize :: FreeMod c MultiLam -> FreeMod c MultiLam Source #
(Eq c, Num c) => Normalize (FreeMod c MultiLam) Source #
Instance details Defined in Math.RootLoci.Motivic.Abstract Methods normalize :: FreeMod c MultiLam -> FreeMod c MultiLam Source #
(Eq c, Num c) => Normalize (FreeMod c SingleLam) Source #
Instance details Defined in Math.RootLoci.Motivic.Abstract Methods normalize :: FreeMod c SingleLam -> FreeMod c SingleLam Source #
(Eq c, Num c) => Psi (FreeMod c MultiLam) (FreeMod c SingleLam) Source #
Instance details Defined in Math.RootLoci.Motivic.Abstract Methods psi :: FreeMod c MultiLam -> FreeMod c SingleLam Source #
(Eq c, Num c) => SingleToMulti (FreeMod c SingleLam) (FreeMod c MultiLam) Source #
Instance details Defined in Math.RootLoci.Motivic.Abstract Methods singleToMulti :: FreeMod c SingleLam -> FreeMod c MultiLam Source #
type CoeffF (FreeMod c b)
Instance details Defined in Math.Algebra.Polynomial.FreeModule type CoeffF (FreeMod c b) = c
type BaseF (FreeMod c b)
Instance details Defined in Math.Algebra.Polynomial.FreeModule type BaseF (FreeMod c b) = b

module Math.RootLoci.Algebra.SymmPoly