Struct na::Additive

pub struct Additive;

The addition operator, commonly symbolized by +.

Trait Implementations

impl<N> TwoSidedInverse<Additive> for Quaternion<N> where
    N: RealField, 

fn two_sided_inverse(&self) -> Quaternion<N>

Returns the two_sided_inverse of self, relative to the operator O.

default fn two_sided_inverse_mut(&mut self)

In-place inversion of self, relative to the operator O.

impl<N, R, C> TwoSidedInverse<Additive> for Matrix<N, R, C, <DefaultAllocator as Allocator<N, R, C>>::Buffer> where
    C: DimName,
    N: Scalar + ClosedNeg,
    R: DimName,
    DefaultAllocator: Allocator<N, R, C>, 

fn two_sided_inverse(
    &self
) -> Matrix<N, R, C, <DefaultAllocator as Allocator<N, R, C>>::Buffer>

Returns the two_sided_inverse of self, relative to the operator O.

fn two_sided_inverse_mut(&mut self)

In-place inversion of self, relative to the operator O.

impl<N, R, C> AbstractGroup<Additive> for Matrix<N, R, C, <DefaultAllocator as Allocator<N, R, C>>::Buffer> where
    C: DimName,
    N: Scalar + AbstractGroup<Additive> + Zero + ClosedAdd<N> + ClosedNeg,
    R: DimName,
    DefaultAllocator: Allocator<N, R, C>, 

impl<N> AbstractGroup<Additive> for Quaternion<N> where
    N: RealField, 

impl<N> AbstractSemigroup<Additive> for Quaternion<N> where
    N: RealField, 

default fn prop_is_associative_approx(args: (Self, Self, Self)) -> bool where
    Self: RelativeEq<Self>, 

Returns true if associativity holds for the given arguments. Approximate equality is used for verifications.

default fn prop_is_associative(args: (Self, Self, Self)) -> bool where
    Self: Eq, 

Returns true if associativity holds for the given arguments.

impl<N, R, C> AbstractSemigroup<Additive> for Matrix<N, R, C, <DefaultAllocator as Allocator<N, R, C>>::Buffer> where
    C: DimName,
    N: Scalar + AbstractSemigroup<Additive> + ClosedAdd<N>,
    R: DimName,
    DefaultAllocator: Allocator<N, R, C>, 

default fn prop_is_associative_approx(args: (Self, Self, Self)) -> bool where
    Self: RelativeEq<Self>, 

Returns true if associativity holds for the given arguments. Approximate equality is used for verifications.

default fn prop_is_associative(args: (Self, Self, Self)) -> bool where
    Self: Eq, 

Returns true if associativity holds for the given arguments.

impl<N> Identity<Additive> for Quaternion<N> where
    N: RealField, 

fn identity() -> Quaternion<N>

The identity element.

default fn id(O) -> Self

Specific identity.

impl<N, R, C> Identity<Additive> for Matrix<N, R, C, <DefaultAllocator as Allocator<N, R, C>>::Buffer> where
    C: DimName,
    N: Scalar + Zero,
    R: DimName,
    DefaultAllocator: Allocator<N, R, C>, 

fn identity(
) -> Matrix<N, R, C, <DefaultAllocator as Allocator<N, R, C>>::Buffer>

The identity element.

default fn id(O) -> Self

Specific identity.

impl<N> AbstractModule<Additive, Additive, Multiplicative> for Quaternion<N> where
    N: RealField, 

type AbstractRing = N

The underlying scalar field.

fn multiply_by(&self, n: N) -> Quaternion<N>

Multiplies an element of the ring with an element of the module.

impl<N, R, C> AbstractModule<Additive, Additive, Multiplicative> for Matrix<N, R, C, <DefaultAllocator as Allocator<N, R, C>>::Buffer> where
    C: DimName,
    N: Scalar + RingCommutative,
    R: DimName,
    DefaultAllocator: Allocator<N, R, C>, 

type AbstractRing = N

The underlying scalar field.

fn multiply_by(
    &self,
    n: N
) -> Matrix<N, R, C, <DefaultAllocator as Allocator<N, R, C>>::Buffer>

Multiplies an element of the ring with an element of the module.

impl<N> AbstractLoop<Additive> for Quaternion<N> where
    N: RealField, 

impl<N, R, C> AbstractLoop<Additive> for Matrix<N, R, C, <DefaultAllocator as Allocator<N, R, C>>::Buffer> where
    C: DimName,
    N: Scalar + AbstractLoop<Additive> + Zero + ClosedAdd<N> + ClosedNeg,
    R: DimName,
    DefaultAllocator: Allocator<N, R, C>, 

impl<N, R, C> AbstractGroupAbelian<Additive> for Matrix<N, R, C, <DefaultAllocator as Allocator<N, R, C>>::Buffer> where
    C: DimName,
    N: Scalar + AbstractGroupAbelian<Additive> + Zero + ClosedAdd<N> + ClosedNeg,
    R: DimName,
    DefaultAllocator: Allocator<N, R, C>, 

default fn prop_is_commutative_approx(args: (Self, Self)) -> bool where
    Self: RelativeEq<Self>, 

Returns true if the operator is commutative for the given argument tuple. Approximate equality is used for verifications.

default fn prop_is_commutative(args: (Self, Self)) -> bool where
    Self: Eq, 

Returns true if the operator is commutative for the given argument tuple.

impl<N> AbstractGroupAbelian<Additive> for Quaternion<N> where
    N: RealField, 

default fn prop_is_commutative_approx(args: (Self, Self)) -> bool where
    Self: RelativeEq<Self>, 

Returns true if the operator is commutative for the given argument tuple. Approximate equality is used for verifications.

default fn prop_is_commutative(args: (Self, Self)) -> bool where
    Self: Eq, 

Returns true if the operator is commutative for the given argument tuple.

impl<N> AbstractMagma<Additive> for Quaternion<N> where
    N: RealField, 

fn operate(&self, rhs: &Quaternion<N>) -> Quaternion<N>

Performs an operation.

default fn op(&self, O, lhs: &Self) -> Self

Performs specific operation.

impl<N, R, C> AbstractMagma<Additive> for Matrix<N, R, C, <DefaultAllocator as Allocator<N, R, C>>::Buffer> where
    C: DimName,
    N: Scalar + ClosedAdd<N>,
    R: DimName,
    DefaultAllocator: Allocator<N, R, C>, 

fn operate(
    &self,
    other: &Matrix<N, R, C, <DefaultAllocator as Allocator<N, R, C>>::Buffer>
) -> Matrix<N, R, C, <DefaultAllocator as Allocator<N, R, C>>::Buffer>

Performs an operation.

default fn op(&self, O, lhs: &Self) -> Self

Performs specific operation.

impl<N, R, C> AbstractMonoid<Additive> for Matrix<N, R, C, <DefaultAllocator as Allocator<N, R, C>>::Buffer> where
    C: DimName,
    N: Scalar + AbstractMonoid<Additive> + Zero + ClosedAdd<N>,
    R: DimName,
    DefaultAllocator: Allocator<N, R, C>, 

default fn prop_operating_identity_element_is_noop_approx(args: (Self,)) -> bool where
    Self: RelativeEq<Self>, 

Checks whether operating with the identity element is a no-op for the given argument. Approximate equality is used for verifications.

default fn prop_operating_identity_element_is_noop(args: (Self,)) -> bool where
    Self: Eq, 

Checks whether operating with the identity element is a no-op for the given argument.

impl<N> AbstractMonoid<Additive> for Quaternion<N> where
    N: RealField, 

default fn prop_operating_identity_element_is_noop_approx(args: (Self,)) -> bool where
    Self: RelativeEq<Self>, 

Checks whether operating with the identity element is a no-op for the given argument. Approximate equality is used for verifications.

default fn prop_operating_identity_element_is_noop(args: (Self,)) -> bool where
    Self: Eq, 

Checks whether operating with the identity element is a no-op for the given argument.

impl<N, R, C> AbstractQuasigroup<Additive> for Matrix<N, R, C, <DefaultAllocator as Allocator<N, R, C>>::Buffer> where
    C: DimName,
    N: Scalar + AbstractQuasigroup<Additive> + ClosedAdd<N> + ClosedNeg,
    R: DimName,
    DefaultAllocator: Allocator<N, R, C>, 

default fn prop_inv_is_latin_square_approx(args: (Self, Self)) -> bool where
    Self: RelativeEq<Self>, 

Returns true if latin squareness holds for the given arguments. Approximate equality is used for verifications.

default fn prop_inv_is_latin_square(args: (Self, Self)) -> bool where
    Self: Eq, 

Returns true if latin squareness holds for the given arguments.

impl<N> AbstractQuasigroup<Additive> for Quaternion<N> where
    N: RealField, 

default fn prop_inv_is_latin_square_approx(args: (Self, Self)) -> bool where
    Self: RelativeEq<Self>, 

Returns true if latin squareness holds for the given arguments. Approximate equality is used for verifications.

default fn prop_inv_is_latin_square(args: (Self, Self)) -> bool where
    Self: Eq, 

Returns true if latin squareness holds for the given arguments.

impl<N> AbstractRingCommutative<Additive, Multiplicative> for Complex<N> where
    N: AbstractRingCommutative<Additive, Multiplicative> + ClosedNeg + Clone + Num, 

default fn prop_mul_is_commutative_approx(args: (Self, Self)) -> bool where
    Self: RelativeEq<Self>, 

Returns true if the multiplication operator is commutative for the given argument tuple. Approximate equality is used for verifications.

default fn prop_mul_is_commutative(args: (Self, Self)) -> bool where
    Self: Eq, 

Returns true if the multiplication operator is commutative for the given argument tuple.

impl Copy for Additive

impl Clone for Additive

fn clone(&self) -> Additive

Returns a copy of the value.

default fn clone_from(&mut self, source: &Self)

Performs copy-assignment from source.

impl<N> AbstractGroup<Additive> for Complex<N> where
    N: AbstractGroupAbelian<Additive>, 

impl<N> AbstractLoop<Additive> for Complex<N> where
    N: AbstractGroupAbelian<Additive>, 

impl<N> TwoSidedInverse<Additive> for Complex<N> where
    N: TwoSidedInverse<Additive>, 

fn two_sided_inverse(&self) -> Complex<N>

Returns the two_sided_inverse of self, relative to the operator O.

default fn two_sided_inverse_mut(&mut self)

In-place inversion of self, relative to the operator O.

impl<N> AbstractModule<Additive, Additive, Multiplicative> for Complex<N> where
    N: AbstractRingCommutative<Additive, Multiplicative> + ClosedNeg + Num, 

type AbstractRing = N

The underlying scalar field.

fn multiply_by(&self, r: N) -> Complex<N>

Multiplies an element of the ring with an element of the module.

impl<N> AbstractField<Additive, Multiplicative> for Complex<N> where
    N: AbstractField<Additive, Multiplicative> + ClosedNeg + Clone + Num, 

impl<N> AbstractQuasigroup<Additive> for Complex<N> where
    N: AbstractGroupAbelian<Additive>, 

default fn prop_inv_is_latin_square_approx(args: (Self, Self)) -> bool where
    Self: RelativeEq<Self>, 

Returns true if latin squareness holds for the given arguments. Approximate equality is used for verifications.

default fn prop_inv_is_latin_square(args: (Self, Self)) -> bool where
    Self: Eq, 

Returns true if latin squareness holds for the given arguments.

impl<N> AbstractMagma<Additive> for Complex<N> where
    N: AbstractMagma<Additive>, 

fn operate(&self, lhs: &Complex<N>) -> Complex<N>

Performs an operation.

default fn op(&self, O, lhs: &Self) -> Self

Performs specific operation.

impl Operator for Additive

fn operator_token() -> Additive

Returns the structure that identifies the operator.

impl Identity<Additive> for i64

fn identity() -> i64

The identity element.

default fn id(O) -> Self

Specific identity.

impl Identity<Additive> for u64

fn identity() -> u64

The identity element.

default fn id(O) -> Self

Specific identity.

impl Identity<Additive> for f64

fn identity() -> f64

The identity element.

default fn id(O) -> Self

Specific identity.

impl Identity<Additive> for u8

fn identity() -> u8

The identity element.

default fn id(O) -> Self

Specific identity.

impl<N> Identity<Additive> for Complex<N> where
    N: Identity<Additive>, 

fn identity() -> Complex<N>

The identity element.

default fn id(O) -> Self

Specific identity.

impl Identity<Additive> for usize

fn identity() -> usize

The identity element.

default fn id(O) -> Self

Specific identity.

impl Identity<Additive> for i16

fn identity() -> i16

The identity element.

default fn id(O) -> Self

Specific identity.

impl Identity<Additive> for u32

fn identity() -> u32

The identity element.

default fn id(O) -> Self

Specific identity.

impl Identity<Additive> for i32

fn identity() -> i32

The identity element.

default fn id(O) -> Self

Specific identity.

impl Identity<Additive> for i8

fn identity() -> i8

The identity element.

default fn id(O) -> Self

Specific identity.

impl Identity<Additive> for u16

fn identity() -> u16

The identity element.

default fn id(O) -> Self

Specific identity.

impl Identity<Additive> for isize

fn identity() -> isize

The identity element.

default fn id(O) -> Self

Specific identity.

impl Identity<Additive> for f32

fn identity() -> f32

The identity element.

default fn id(O) -> Self

Specific identity.

impl<N> AbstractRing<Additive, Multiplicative> for Complex<N> where
    N: AbstractRing<Additive, Multiplicative> + ClosedNeg + Clone + Num, 

default fn prop_mul_and_add_are_distributive_approx(
    args: (Self, Self, Self)
) -> bool where
    Self: RelativeEq<Self>, 

Returns true if the multiplication and addition operators are distributive for the given argument tuple. Approximate equality is used for verifications.

default fn prop_mul_and_add_are_distributive(args: (Self, Self, Self)) -> bool where
    Self: Eq, 

Returns true if the multiplication and addition operators are distributive for the given argument tuple.

impl<N> AbstractGroupAbelian<Additive> for Complex<N> where
    N: AbstractGroupAbelian<Additive>, 

default fn prop_is_commutative_approx(args: (Self, Self)) -> bool where
    Self: RelativeEq<Self>, 

Returns true if the operator is commutative for the given argument tuple. Approximate equality is used for verifications.

default fn prop_is_commutative(args: (Self, Self)) -> bool where
    Self: Eq, 

Returns true if the operator is commutative for the given argument tuple.

impl<N> AbstractMonoid<Additive> for Complex<N> where
    N: AbstractGroupAbelian<Additive>, 

default fn prop_operating_identity_element_is_noop_approx(args: (Self,)) -> bool where
    Self: RelativeEq<Self>, 

Checks whether operating with the identity element is a no-op for the given argument. Approximate equality is used for verifications.

default fn prop_operating_identity_element_is_noop(args: (Self,)) -> bool where
    Self: Eq, 

Checks whether operating with the identity element is a no-op for the given argument.

impl<N> AbstractSemigroup<Additive> for Complex<N> where
    N: AbstractGroupAbelian<Additive>, 

default fn prop_is_associative_approx(args: (Self, Self, Self)) -> bool where
    Self: RelativeEq<Self>, 

Returns true if associativity holds for the given arguments. Approximate equality is used for verifications.

default fn prop_is_associative(args: (Self, Self, Self)) -> bool where
    Self: Eq, 

Returns true if associativity holds for the given arguments.