coincident-root-loci-0.2: Equivariant CSM classes of coincident root loci

Math.RootLoci.Algebra.Polynomial

Description

Univariate polynomials

Synopsis

# Polynomials

newtype Poly coeff Source #

Standard univariate polynomials

Constructors

 Poly FieldsfromPoly :: FreeMod coeff X

Instances

 Eq coeff => Eq (Poly coeff) Source # Methods(==) :: Poly coeff -> Poly coeff -> Bool #(/=) :: Poly coeff -> Poly coeff -> Bool # (Num coeff, Eq coeff) => Num (Poly coeff) Source # Methods(+) :: Poly coeff -> Poly coeff -> Poly coeff #(-) :: Poly coeff -> Poly coeff -> Poly coeff #(*) :: Poly coeff -> Poly coeff -> Poly coeff #negate :: Poly coeff -> Poly coeff #abs :: Poly coeff -> Poly coeff #signum :: Poly coeff -> Poly coeff #fromInteger :: Integer -> Poly coeff # Show coeff => Show (Poly coeff) Source # MethodsshowsPrec :: Int -> Poly coeff -> ShowS #show :: Poly coeff -> String #showList :: [Poly coeff] -> ShowS # (Num c, Show c, Eq c, IsSigned c) => Pretty (Poly c) Source # Methodspretty :: Poly c -> String Source #

newtype RisingPoly coeff Source #

Univariate polynomials using rising factorials as a basis function

Constructors

 RisingPoly FieldsfromRisingPoly :: FreeMod coeff RisingF

Instances

 Eq coeff => Eq (RisingPoly coeff) Source # Methods(==) :: RisingPoly coeff -> RisingPoly coeff -> Bool #(/=) :: RisingPoly coeff -> RisingPoly coeff -> Bool # Show coeff => Show (RisingPoly coeff) Source # MethodsshowsPrec :: Int -> RisingPoly coeff -> ShowS #show :: RisingPoly coeff -> String #showList :: [RisingPoly coeff] -> ShowS # (Num c, Show c, Eq c, IsSigned c) => Pretty (RisingPoly c) Source # Methods

newtype FallingPoly coeff Source #

Univariate polynomials using falling factorials as a basis function

Constructors

 FallingPoly FieldsfromFallingPoly :: FreeMod coeff FallingF

Instances

 Eq coeff => Eq (FallingPoly coeff) Source # Methods(==) :: FallingPoly coeff -> FallingPoly coeff -> Bool #(/=) :: FallingPoly coeff -> FallingPoly coeff -> Bool # Show coeff => Show (FallingPoly coeff) Source # MethodsshowsPrec :: Int -> FallingPoly coeff -> ShowS #show :: FallingPoly coeff -> String #showList :: [FallingPoly coeff] -> ShowS # (Num c, Show c, Eq c, IsSigned c) => Pretty (FallingPoly c) Source # Methods

# Monomials

newtype X Source #

A power of x (that is, a monomial of the form x^i)

Constructors

 X Int

Instances

 Source # Methods(==) :: X -> X -> Bool #(/=) :: X -> X -> Bool # Source # Methodscompare :: X -> X -> Ordering #(<) :: X -> X -> Bool #(<=) :: X -> X -> Bool #(>) :: X -> X -> Bool #(>=) :: X -> X -> Bool #max :: X -> X -> X #min :: X -> X -> X # Source # MethodsshowsPrec :: Int -> X -> ShowS #show :: X -> String #showList :: [X] -> ShowS # Source # Methodsmempty :: X #mappend :: X -> X -> X #mconcat :: [X] -> X # Source # Methods

# Rising and falling factorials

newtype RisingF Source #

Rising factorial x^(k) = x(x+1)(x+2)...(x+k-1)

Constructors

 RF Int

Instances

 Source # Methods(==) :: RisingF -> RisingF -> Bool #(/=) :: RisingF -> RisingF -> Bool # Source # Methods(<) :: RisingF -> RisingF -> Bool #(<=) :: RisingF -> RisingF -> Bool #(>) :: RisingF -> RisingF -> Bool #(>=) :: RisingF -> RisingF -> Bool # Source # MethodsshowList :: [RisingF] -> ShowS # Source # Methods

newtype FallingF Source #

Falling factorial x_(k) = x(x-1)(x-2)...(x-k+1)

Constructors

 FF Int

Instances

 Source # Methods Source # Methods(<) :: FallingF -> FallingF -> Bool #(>) :: FallingF -> FallingF -> Bool # Source # MethodsshowList :: [FallingF] -> ShowS # Source # Methods