Noether.Algebra.Vector.Unboxed

Documentation

newtype UVector n v

UVector n v ≅ v^n for Unbox types v.

Constructors

UVector (Vector v)

Instances

(Unbox b, KnownNat n, ActsK k lr op a b s) => ActsK k lr op a (UVector n b) (ActsTagged UVectorLift s)

Actions of a on b extend to actions of a on 'UVector n b'.

Methods

actK :: Proxy lr a -> Proxy ActsE s -> Proxy Side op -> UVector n b -> ActsTagged UVectorLift s -> ActsTagged UVectorLift s

(Unbox v, KnownNat n, NeutralK k op v s) => NeutralK k op (UVector n v) (NeutralTagged UVectorLift s)

Neutral elements for addition and multiplication.

Methods

neutralK :: Proxy op (UVector n v) -> Proxy NeutralE s -> NeutralTagged UVectorLift s

(Unbox v, MagmaK k op v s) => MagmaK k op (UVector n v) (MagmaTagged UVectorLift s)

Lifting addition and multiplication coordinatewise (Hadamard?)

Methods

binaryOpK :: Proxy op (UVector n v) -> Proxy MagmaE s -> MagmaTagged UVectorLift s -> MagmaTagged UVectorLift s -> MagmaTagged UVectorLift s

(Unbox v, KnownNat n, CancellativeK k op v s) => CancellativeK k op (UVector n v) (CancellativeTagged UVectorLift s)

Pointwise negation and inversion.

Note that v^n has (a lot of) nontrivial zerodivisors even if v does not. The zerodivisors are all elements with a zero(divisor) in some coordinate, e.g. (1,0) and (0,1) are zerodivisors in R^2.

(This corresponds to the idea that the Spec of a product ring is disconnected!)

Methods

cancelK :: Proxy op (UVector n v) -> Proxy CancellativeE s -> CancellativeTagged UVectorLift s -> CancellativeTagged UVectorLift s

(Unbox v, Show v) => Show (UVector n v)

Methods

showsPrec :: Int -> UVector n v -> ShowS

show :: UVector n v -> String

showList :: [UVector n v] -> ShowS

type ActorLinearS BinaryNumeric BinaryNumeric BinaryNumeric lr Mul Add a Add (UVector n a)

type ActorLinearS BinaryNumeric BinaryNumeric BinaryNumeric lr Mul Add a Add (UVector n a) = DeriveActorLinearActs_Acts_Semigroup_Semigroup BinaryNumeric BinaryNumeric BinaryNumeric lr Mul Add a Add (UVector n a)

type CompatibleS BinaryNumeric BinaryNumeric lr Mul Mul a (UVector n b)

type CompatibleS BinaryNumeric BinaryNumeric lr Mul Mul a (UVector n b) = DeriveCompatible_Acts_Semigroup BinaryNumeric BinaryNumeric lr Mul Mul a (UVector n b)

type ActeeLinearS BinaryNumeric BinaryNumeric lr Mul a Add (UVector n a)

type ActeeLinearS BinaryNumeric BinaryNumeric lr Mul a Add (UVector n a) = DeriveActeeLinearActs_Acts_Semigroup BinaryNumeric BinaryNumeric lr Mul a Add (UVector n a)

type ActsS BinaryNumeric lr Mul a (UVector n b)

type ActsS BinaryNumeric lr Mul a (UVector n b) = DeriveActs_Tagged BinaryNumeric UVectorLift lr Mul a b

type NeutralS BinaryNumeric op (UVector n a)

type NeutralS BinaryNumeric op (UVector n a) = DeriveNeutral_Tagged BinaryNumeric UVectorLift op a

type MagmaS BinaryNumeric op (UVector n a)

type MagmaS BinaryNumeric op (UVector n a) = DeriveMagma_Tagged BinaryNumeric UVectorLift op a

type SemigroupS BinaryNumeric op (UVector n a)

type SemigroupS BinaryNumeric op (UVector n a) = DeriveSemigroup_Magma BinaryNumeric op (UVector n a)

type MonoidS BinaryNumeric op (UVector n a)

type MonoidS BinaryNumeric op (UVector n a) = DeriveMonoid_Semigroup_Neutral BinaryNumeric op (UVector n a)

type CommutativeS BinaryNumeric op (UVector n a)

type CommutativeS BinaryNumeric op (UVector n a) = DeriveCommutative_Tagged BinaryNumeric UVectorLift op a

type CancellativeS BinaryNumeric Add (UVector n a)

type CancellativeS BinaryNumeric Add (UVector n a) = DeriveCancellative_Tagged BinaryNumeric UVectorLift Add a

type GroupS BinaryNumeric Add (UVector n a)

type GroupS BinaryNumeric Add (UVector n a) = DeriveGroup_Monoid_Cancellative BinaryNumeric Add (UVector n a)

type AbelianGroupS BinaryNumeric Add (UVector n a)

type AbelianGroupS BinaryNumeric Add (UVector n a) = DeriveAbelianGroup_Commutative_Group BinaryNumeric Add (UVector n a)

v :: UVector 10 Double

w :: UVector 10 Double

f :: (MagmaK BinaryNumeric Mul a (MagmaS BinaryNumeric Mul a), MagmaK BinaryNumeric Add a (MagmaS BinaryNumeric Add a), CancellativeK BinaryNumeric Add a (CancellativeS BinaryNumeric Add a)) => a -> a

g :: [UVector 10 Double]

This is equal to > UVector [5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0,5.0]