Math.Algebra.Polynomial.Univariate.Pochhammer

Rising and falling factorials

See https://en.wikipedia.org/wiki/Falling_and_rising_factorials

Rising and Falling factorials

risingFactorial :: Int -> Univariate Integer "x"

fallingFactorial :: Int -> Univariate Integer "x"

Polynomials using rising or falling factorials as bases

newtype RisingPoly coeff

Univariate polynomials using rising factorials as a basis function

Constructors

RisingPoly

Fields

• fromRisingPoly :: FreeMod coeff RisingF

Instances

Eq coeff => Eq (RisingPoly coeff)

Defined in Math.Algebra.Polynomial.Univariate.Pochhammer

Methods

(==) :: RisingPoly coeff -> RisingPoly coeff -> Bool

(/=) :: RisingPoly coeff -> RisingPoly coeff -> Bool

Show coeff => Show (RisingPoly coeff)

Defined in Math.Algebra.Polynomial.Univariate.Pochhammer

Methods

showsPrec :: Int -> RisingPoly coeff -> ShowS

show :: RisingPoly coeff -> String

showList :: [RisingPoly coeff] -> ShowS

newtype FallingPoly coeff

Univariate polynomials using falling factorials as a basis function

Constructors

FallingPoly

Fields

• fromFallingPoly :: FreeMod coeff FallingF

Instances

Eq coeff => Eq (FallingPoly coeff)

Defined in Math.Algebra.Polynomial.Univariate.Pochhammer

Methods

(==) :: FallingPoly coeff -> FallingPoly coeff -> Bool

(/=) :: FallingPoly coeff -> FallingPoly coeff -> Bool

Show coeff => Show (FallingPoly coeff)

Defined in Math.Algebra.Polynomial.Univariate.Pochhammer

Methods

showsPrec :: Int -> FallingPoly coeff -> ShowS

show :: FallingPoly coeff -> String

showList :: [FallingPoly coeff] -> ShowS

expandRisingPoly :: (KnownSymbol var, Typeable c, Eq c, Num c) => FreeMod c RisingF -> Univariate c var

expandFallingPoly :: (KnownSymbol var, Typeable c, Eq c, Num c) => FreeMod c FallingF -> Univariate c var

Rising and falling factorial types

newtype RisingF

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

Constructors

RF Int

Instances

Eq RisingF

Defined in Math.Algebra.Polynomial.Univariate.Pochhammer

Methods

(==) :: RisingF -> RisingF -> Bool

(/=) :: RisingF -> RisingF -> Bool

Ord RisingF

Defined in Math.Algebra.Polynomial.Univariate.Pochhammer

Methods

compare :: RisingF -> RisingF -> Ordering

(<) :: RisingF -> RisingF -> Bool

(<=) :: RisingF -> RisingF -> Bool

(>) :: RisingF -> RisingF -> Bool

(>=) :: RisingF -> RisingF -> Bool

max :: RisingF -> RisingF -> RisingF

min :: RisingF -> RisingF -> RisingF

Show RisingF

Defined in Math.Algebra.Polynomial.Univariate.Pochhammer

Methods

showsPrec :: Int -> RisingF -> ShowS

show :: RisingF -> String

showList :: [RisingF] -> ShowS

Pretty RisingF

Defined in Math.Algebra.Polynomial.Univariate.Pochhammer

Methods

pretty :: RisingF -> String

prettyInParens :: RisingF -> String

newtype FallingF

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

Constructors

FF Int

Instances

Eq FallingF

Defined in Math.Algebra.Polynomial.Univariate.Pochhammer

Methods

(==) :: FallingF -> FallingF -> Bool

(/=) :: FallingF -> FallingF -> Bool

Ord FallingF

Defined in Math.Algebra.Polynomial.Univariate.Pochhammer

Methods

compare :: FallingF -> FallingF -> Ordering

(<) :: FallingF -> FallingF -> Bool

(<=) :: FallingF -> FallingF -> Bool

(>) :: FallingF -> FallingF -> Bool

(>=) :: FallingF -> FallingF -> Bool

max :: FallingF -> FallingF -> FallingF

min :: FallingF -> FallingF -> FallingF

Show FallingF

Defined in Math.Algebra.Polynomial.Univariate.Pochhammer

Methods

showsPrec :: Int -> FallingF -> ShowS

show :: FallingF -> String

showList :: [FallingF] -> ShowS

Pretty FallingF

Defined in Math.Algebra.Polynomial.Univariate.Pochhammer

Methods

pretty :: FallingF -> String

prettyInParens :: FallingF -> String

expandRisingFactorial :: (KnownSymbol var, Typeable c, Eq c, Num c) => RisingF -> Univariate c var

expandFallingFactorial :: (KnownSymbol var, Typeable c, Eq c, Num c) => FallingF -> Univariate c var

expandRisingFactorialZ :: RisingF -> Univariate Integer var

expandFallingFactorialZ :: FallingF -> Univariate Integer var