Noether.Algebra.Vector.Boxed

Documentation

newtype BVector n v

BVector n v ≅ v^n.

Constructors

BVector (Vector v)

Instances

ActsK k1 lr op a b s => ActsK k1 lr op a (BVector k n b) (ActsTagged BVectorLift s)

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

Methods

actK :: Proxy lr a -> Proxy ActsE s -> Proxy Side op -> BVector k n b -> ActsTagged BVectorLift s -> ActsTagged BVectorLift s

(KnownNat n, NeutralK k op v s) => NeutralK k op (BVector Nat n v) (NeutralTagged BVectorLift s)

Neutral elements for addition and multiplication.

Methods

neutralK :: Proxy op (BVector Nat n v) -> Proxy NeutralE s -> NeutralTagged BVectorLift s

MagmaK k1 op v s => MagmaK k1 op (BVector k n v) (MagmaTagged BVectorLift s)

Lifting addition and multiplication coordinatewise (Hadamard?)

Methods

binaryOpK :: Proxy op (BVector k n v) -> Proxy MagmaE s -> MagmaTagged BVectorLift s -> MagmaTagged BVectorLift s -> MagmaTagged BVectorLift s

CancellativeK k1 op v s => CancellativeK k1 op (BVector k n v) (CancellativeTagged BVectorLift 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 (BVector k n v) -> Proxy CancellativeE s -> CancellativeTagged BVectorLift s -> CancellativeTagged BVectorLift s

Show v => Show (BVector k n v)

Methods

showsPrec :: Int -> BVector k n v -> ShowS

show :: BVector k n v -> String

showList :: [BVector k n v] -> ShowS

type ActorLinearS BinaryNumeric BinaryNumeric BinaryNumeric lr Mul Add a Add (BVector k n a)

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

type CompatibleS BinaryNumeric BinaryNumeric lr Mul Mul a (BVector k n b)

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

type ActeeLinearS BinaryNumeric BinaryNumeric lr Mul a Add (BVector k n a)

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

type ActsS BinaryNumeric lr Mul a (BVector k n b)

type ActsS BinaryNumeric lr Mul a (BVector k n b) = DeriveActs_Tagged BinaryNumeric BVectorLift lr Mul a b

type NeutralS BinaryNumeric op (BVector k n a)

type NeutralS BinaryNumeric op (BVector k n a) = DeriveNeutral_Tagged BinaryNumeric BVectorLift op a

type MagmaS BinaryNumeric op (BVector k n a)

type MagmaS BinaryNumeric op (BVector k n a) = DeriveMagma_Tagged BinaryNumeric BVectorLift op a

type SemigroupS BinaryNumeric op (BVector k n a)

type SemigroupS BinaryNumeric op (BVector k n a) = DeriveSemigroup_Magma BinaryNumeric op (BVector k n a)

type MonoidS BinaryNumeric op (BVector k n a)

type MonoidS BinaryNumeric op (BVector k n a) = DeriveMonoid_Semigroup_Neutral BinaryNumeric op (BVector k n a)

type CommutativeS BinaryNumeric op (BVector k n a)

type CommutativeS BinaryNumeric op (BVector k n a) = DeriveCommutative_Tagged BinaryNumeric BVectorLift op a

type CancellativeS BinaryNumeric Add (BVector k n a)

type CancellativeS BinaryNumeric Add (BVector k n a) = DeriveCancellative_Tagged BinaryNumeric BVectorLift Add a

type GroupS BinaryNumeric Add (BVector k n a)

type GroupS BinaryNumeric Add (BVector k n a) = DeriveGroup_Monoid_Cancellative BinaryNumeric Add (BVector k n a)

type AbelianGroupS BinaryNumeric Add (BVector k n a)

type AbelianGroupS BinaryNumeric Add (BVector k n a) = DeriveAbelianGroup_Commutative_Group BinaryNumeric Add (BVector k n a)

unsafeFromList :: [a] -> BVector n a

unsafeChangeDimension :: forall k l m n a. BVector m a -> BVector n a