Math.RootLoci.Algebra

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

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

Theta (ZMod MultiLam)

Defined in Math.RootLoci.Motivic.Abstract

Methods

theta :: ZMod MultiLam -> ZMod MultiLam

Permute (ZMod MultiLam)

Defined in Math.RootLoci.Motivic.Abstract

Methods

permute :: Permutation -> ZMod MultiLam -> ZMod MultiLam

PsiEvenOdd (ZMod MultiLam)

Defined in Math.RootLoci.Motivic.Abstract

Methods

psiEvenOdd :: ZMod MultiLam -> ZMod MultiLam

(Eq c, Num c) => Psi [FreeMod c SingleLam] (FreeMod c SingleLam)

Defined in Math.RootLoci.Motivic.Abstract

Methods

psi :: [FreeMod c SingleLam] -> FreeMod c SingleLam

(Eq base, Eq coeff) => Eq (FreeMod coeff base)

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)

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)

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)

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)

Defined in Math.Algebra.Polynomial.Pretty

Methods

pretty :: FreeMod c b -> String

prettyInParens :: FreeMod c b -> String

Ord b => FreeModule (FreeMod c b)

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)

Defined in Math.RootLoci.Motivic.Abstract

Methods

omega123 :: FreeMod c MultiLam -> FreeMod c MultiLam

(Eq c, Num c) => Omega (FreeMod c MultiLam)

Defined in Math.RootLoci.Motivic.Abstract

Methods

omega :: Int -> FreeMod c MultiLam -> FreeMod c MultiLam

(Eq c, Num c) => Omega (FreeMod c SingleLam)

Defined in Math.RootLoci.Motivic.Abstract

Methods

omega :: Int -> FreeMod c SingleLam -> FreeMod c SingleLam

(Eq c, Num c) => Cross (FreeMod c MultiLam)

Defined in Math.RootLoci.Motivic.Abstract

Methods

cross :: FreeMod c MultiLam -> FreeMod c MultiLam -> FreeMod c MultiLam

crossMany :: [FreeMod c MultiLam] -> FreeMod c MultiLam

crossInterleave :: FreeMod c MultiLam -> FreeMod c MultiLam -> FreeMod c MultiLam

(Eq c, Num c) => SuperNormalize (FreeMod c MultiLam)

Defined in Math.RootLoci.Motivic.Abstract

Methods

superNormalize :: FreeMod c MultiLam -> FreeMod c MultiLam

(Eq c, Num c) => Normalize (FreeMod c MultiLam)

Defined in Math.RootLoci.Motivic.Abstract

Methods

normalize :: FreeMod c MultiLam -> FreeMod c MultiLam

(Eq c, Num c) => Normalize (FreeMod c SingleLam)

Defined in Math.RootLoci.Motivic.Abstract

Methods

normalize :: FreeMod c SingleLam -> FreeMod c SingleLam

(Eq c, Num c) => Psi (FreeMod c MultiLam) (FreeMod c SingleLam)

Defined in Math.RootLoci.Motivic.Abstract

Methods

psi :: FreeMod c MultiLam -> FreeMod c SingleLam

(Eq c, Num c) => SingleToMulti (FreeMod c SingleLam) (FreeMod c MultiLam)

Defined in Math.RootLoci.Motivic.Abstract

Methods

singleToMulti :: FreeMod c SingleLam -> FreeMod c MultiLam

type CoeffF (FreeMod c b)

Defined in Math.Algebra.Polynomial.FreeModule

type CoeffF (FreeMod c b) = c

type BaseF (FreeMod c b)

Defined in Math.Algebra.Polynomial.FreeModule

type BaseF (FreeMod c b) = b

module Math.RootLoci.Algebra.SymmPoly