Math.Algebra.Polynomial.Monomial.Compact

Multivariate compact monomials where the variable set looks like {x_1, x_2, ... , x_N}.

This is very similar to the "Indexed" version, but should have much more compact in-memory representation (which is useful in case of large or many polynomials, and should be in theory also faster, because of cache friendlyness)

Monomials

newtype Compact (var :: Symbol) (n :: Nat)

Monomials of the variables x1,x2,...,xn. The internal representation is a compact vector of the exponents.

The type is indexed by the name of the variables, and then the number of variables.

Note that we assume here that the internal vector has length n.

Constructors

Compact WordVec

Instances

Eq (Compact var n)

Defined in Math.Algebra.Polynomial.Monomial.Compact

Methods

(==) :: Compact var n -> Compact var n -> Bool

(/=) :: Compact var n -> Compact var n -> Bool

Ord (Compact var n)

Defined in Math.Algebra.Polynomial.Monomial.Compact

Methods

compare :: Compact var n -> Compact var n -> Ordering

(<) :: Compact var n -> Compact var n -> Bool

(<=) :: Compact var n -> Compact var n -> Bool

(>) :: Compact var n -> Compact var n -> Bool

(>=) :: Compact var n -> Compact var n -> Bool

max :: Compact var n -> Compact var n -> Compact var n

min :: Compact var n -> Compact var n -> Compact var n

Show (Compact var n)

Defined in Math.Algebra.Polynomial.Monomial.Compact

Methods

showsPrec :: Int -> Compact var n -> ShowS

show :: Compact var n -> String

showList :: [Compact var n] -> ShowS

KnownNat n => Semigroup (Compact var n)

Defined in Math.Algebra.Polynomial.Monomial.Compact

Methods

(<>) :: Compact var n -> Compact var n -> Compact var n

sconcat :: NonEmpty (Compact var n) -> Compact var n

stimes :: Integral b => b -> Compact var n -> Compact var n

KnownNat n => Monoid (Compact var n)

Defined in Math.Algebra.Polynomial.Monomial.Compact

Methods

mempty :: Compact var n

mappend :: Compact var n -> Compact var n -> Compact var n

mconcat :: [Compact var n] -> Compact var n

KnownSymbol var => Pretty (Compact var n)

Defined in Math.Algebra.Polynomial.Monomial.Compact

Methods

pretty :: Compact var n -> String

prettyInParens :: Compact var n -> String

(KnownNat n, KnownSymbol v) => Monomial (Compact v n)

Defined in Math.Algebra.Polynomial.Monomial.Compact

Associated Types

type VarM (Compact v n)

Methods

normalizeM :: Compact v n -> Compact v n

isNormalM :: Compact v n -> Bool

fromListM :: [(VarM (Compact v n), Int)] -> Compact v n

toListM :: Compact v n -> [(VarM (Compact v n), Int)]

emptyM :: Compact v n

isEmptyM :: Compact v n -> Bool

variableM :: VarM (Compact v n) -> Compact v n

singletonM :: VarM (Compact v n) -> Int -> Compact v n

mulM :: Compact v n -> Compact v n -> Compact v n

productM :: [Compact v n] -> Compact v n

powM :: Compact v n -> Int -> Compact v n

divM :: Compact v n -> Compact v n -> Maybe (Compact v n)

diffM :: Num c => VarM (Compact v n) -> Int -> Compact v n -> Maybe (Compact v n, c)

maxDegM :: Compact v n -> Int

totalDegM :: Compact v n -> Int

evalM :: Num c => (VarM (Compact v n) -> c) -> Compact v n -> c

varSubsM :: (VarM (Compact v n) -> VarM (Compact v n)) -> Compact v n -> Compact v n

termSubsM :: Num c => (VarM (Compact v n) -> Maybe c) -> (Compact v n, c) -> (Compact v n, c)

type VarM (Compact v n)

Defined in Math.Algebra.Polynomial.Monomial.Compact

type VarM (Compact v n) = Index

compactVar :: KnownSymbol var => Compact var n -> String

Name of the variables

nOfCompact :: KnownNat n => Compact var n -> Int

Number of variables

Conversion

compactFromList :: KnownNat n => [(Index, Int)] -> Compact v n

from (variable,exponent) pairs

compactToList :: Compact v n -> [(Index, Int)]

to (variable,exponent) pairs

compactFromWordExpoList :: KnownNat n => [Word] -> Compact var n

from Word exponent list

compactToWordExpoList :: Compact var n -> [Word]

to Word exponent list

compactFromExponents :: KnownNat n => [Int] -> Compact v n

from Int exponent list

compactToExponents :: KnownNat n => Compact v n -> [Int]

to Int exponent list

compactFromXS :: KnownNat n => XS v n -> Compact v n

from XS exponent list

compactToXS :: KnownNat n => Compact v n -> XS v n

to XS exponent list

empty (all zero exponents)

emptyCompact :: KnownNat n => Compact v n

isEmptyCompact :: Compact v n -> Bool

normalization

isNormalCompact :: KnownNat n => Compact v n -> Bool

creation

variableCompact :: KnownNat n => Index -> Compact v n

singletonCompact :: KnownNat n => Index -> Int -> Compact v n

products

mulCompact :: KnownNat n => Compact v n -> Compact v n -> Compact v n

productCompact :: (KnownNat n, Foldable f) => f (Compact v n) -> Compact v n

powCompact :: KnownNat n => Compact v n -> Int -> Compact v n

divCompact :: KnownNat n => Compact v n -> Compact v n -> Maybe (Compact v n)

degree

maxDegCompact :: Compact v n -> Int

totalDegCompact :: Compact v n -> Int

differentiation

diffCompact :: Num c => Index -> Int -> Compact v n -> Maybe (Compact v n, c)