Struct alga::general::Additive

pub struct Additive;

The addition operator, commonly symbolized by +.

Trait Implementations

impl AbstractMagma<Additive> for u8

fn operate(&self, lhs: &Self) -> Self

Performs an operation.

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

Performs specific operation.

impl AbstractMagma<Additive> for u16

fn operate(&self, lhs: &Self) -> Self

Performs an operation.

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

Performs specific operation.

impl AbstractMagma<Additive> for u32

fn operate(&self, lhs: &Self) -> Self

Performs an operation.

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

Performs specific operation.

impl AbstractMagma<Additive> for u64

fn operate(&self, lhs: &Self) -> Self

Performs an operation.

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

Performs specific operation.

impl AbstractMagma<Additive> for usize

fn operate(&self, lhs: &Self) -> Self

Performs an operation.

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

Performs specific operation.

impl AbstractMagma<Additive> for i8

fn operate(&self, lhs: &Self) -> Self

Performs an operation.

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

Performs specific operation.

impl AbstractMagma<Additive> for i16

fn operate(&self, lhs: &Self) -> Self

Performs an operation.

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

Performs specific operation.

impl AbstractMagma<Additive> for i32

fn operate(&self, lhs: &Self) -> Self

Performs an operation.

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

Performs specific operation.

impl AbstractMagma<Additive> for i64

fn operate(&self, lhs: &Self) -> Self

Performs an operation.

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

Performs specific operation.

impl AbstractMagma<Additive> for isize

fn operate(&self, lhs: &Self) -> Self

Performs an operation.

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

Performs specific operation.

impl AbstractMagma<Additive> for f32

fn operate(&self, lhs: &Self) -> Self

Performs an operation.

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

Performs specific operation.

impl AbstractMagma<Additive> for f64

fn operate(&self, lhs: &Self) -> Self

Performs an operation.

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

Performs specific operation.

impl AbstractSemigroup<Additive> for u8

fn prop_is_associative_approx(args: (Self, Self, Self)) -> bool where
    Self: ApproxEq, 

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

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

Returns true if associativity holds for the given arguments.

impl AbstractSemigroup<Additive> for u16

fn prop_is_associative_approx(args: (Self, Self, Self)) -> bool where
    Self: ApproxEq, 

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

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

Returns true if associativity holds for the given arguments.

impl AbstractSemigroup<Additive> for u32

fn prop_is_associative_approx(args: (Self, Self, Self)) -> bool where
    Self: ApproxEq, 

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

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

Returns true if associativity holds for the given arguments.

impl AbstractSemigroup<Additive> for u64

fn prop_is_associative_approx(args: (Self, Self, Self)) -> bool where
    Self: ApproxEq, 

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

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

Returns true if associativity holds for the given arguments.

impl AbstractSemigroup<Additive> for usize

fn prop_is_associative_approx(args: (Self, Self, Self)) -> bool where
    Self: ApproxEq, 

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

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

Returns true if associativity holds for the given arguments.

impl AbstractMonoid<Additive> for u8

fn prop_operating_identity_element_is_noop_approx(args: (Self,)) -> bool where
    Self: ApproxEq, 

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

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 AbstractMonoid<Additive> for u16

fn prop_operating_identity_element_is_noop_approx(args: (Self,)) -> bool where
    Self: ApproxEq, 

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

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 AbstractMonoid<Additive> for u32

fn prop_operating_identity_element_is_noop_approx(args: (Self,)) -> bool where
    Self: ApproxEq, 

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

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 AbstractMonoid<Additive> for u64

fn prop_operating_identity_element_is_noop_approx(args: (Self,)) -> bool where
    Self: ApproxEq, 

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

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 AbstractMonoid<Additive> for usize

fn prop_operating_identity_element_is_noop_approx(args: (Self,)) -> bool where
    Self: ApproxEq, 

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

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: AbstractMagma<Additive>> AbstractMagma<Additive> for Complex<N>

fn operate(&self, lhs: &Self) -> Self

Performs an operation.

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

Performs specific operation.

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

fn prop_is_associative_approx(args: (Self, Self, Self)) -> bool where
    Self: ApproxEq, 

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

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

Returns true if associativity holds for the given arguments.

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

fn prop_operating_identity_element_is_noop_approx(args: (Self,)) -> bool where
    Self: ApproxEq, 

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

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

fn prop_inv_is_latin_square_approx(args: (Self, Self)) -> bool where
    Self: ApproxEq, 

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

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

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

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

fn prop_is_commutative_approx(args: (Self, Self)) -> bool where
    Self: ApproxEq, 

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

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

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

impl AbstractSemigroup<Additive> for i8

fn prop_is_associative_approx(args: (Self, Self, Self)) -> bool where
    Self: ApproxEq, 

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

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

Returns true if associativity holds for the given arguments.

impl AbstractSemigroup<Additive> for i16

fn prop_is_associative_approx(args: (Self, Self, Self)) -> bool where
    Self: ApproxEq, 

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

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

Returns true if associativity holds for the given arguments.

impl AbstractSemigroup<Additive> for i32

fn prop_is_associative_approx(args: (Self, Self, Self)) -> bool where
    Self: ApproxEq, 

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

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

Returns true if associativity holds for the given arguments.

impl AbstractSemigroup<Additive> for i64

fn prop_is_associative_approx(args: (Self, Self, Self)) -> bool where
    Self: ApproxEq, 

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

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

Returns true if associativity holds for the given arguments.

impl AbstractSemigroup<Additive> for isize

fn prop_is_associative_approx(args: (Self, Self, Self)) -> bool where
    Self: ApproxEq, 

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

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

Returns true if associativity holds for the given arguments.

impl AbstractMonoid<Additive> for i8

fn prop_operating_identity_element_is_noop_approx(args: (Self,)) -> bool where
    Self: ApproxEq, 

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

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 AbstractMonoid<Additive> for i16

fn prop_operating_identity_element_is_noop_approx(args: (Self,)) -> bool where
    Self: ApproxEq, 

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

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 AbstractMonoid<Additive> for i32

fn prop_operating_identity_element_is_noop_approx(args: (Self,)) -> bool where
    Self: ApproxEq, 

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

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 AbstractMonoid<Additive> for i64

fn prop_operating_identity_element_is_noop_approx(args: (Self,)) -> bool where
    Self: ApproxEq, 

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

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 AbstractMonoid<Additive> for isize

fn prop_operating_identity_element_is_noop_approx(args: (Self,)) -> bool where
    Self: ApproxEq, 

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

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 AbstractQuasigroup<Additive> for i8

fn prop_inv_is_latin_square_approx(args: (Self, Self)) -> bool where
    Self: ApproxEq, 

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

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

Returns true if latin squareness holds for the given arguments.

impl AbstractQuasigroup<Additive> for i16

fn prop_inv_is_latin_square_approx(args: (Self, Self)) -> bool where
    Self: ApproxEq, 

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

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

Returns true if latin squareness holds for the given arguments.

impl AbstractQuasigroup<Additive> for i32

fn prop_inv_is_latin_square_approx(args: (Self, Self)) -> bool where
    Self: ApproxEq, 

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

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

Returns true if latin squareness holds for the given arguments.

impl AbstractQuasigroup<Additive> for i64

fn prop_inv_is_latin_square_approx(args: (Self, Self)) -> bool where
    Self: ApproxEq, 

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

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

Returns true if latin squareness holds for the given arguments.

impl AbstractQuasigroup<Additive> for isize

fn prop_inv_is_latin_square_approx(args: (Self, Self)) -> bool where
    Self: ApproxEq, 

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

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

Returns true if latin squareness holds for the given arguments.

impl AbstractLoop<Additive> for i8

impl AbstractLoop<Additive> for i16

impl AbstractLoop<Additive> for i32

impl AbstractLoop<Additive> for i64

impl AbstractLoop<Additive> for isize

impl AbstractGroup<Additive> for i8

impl AbstractGroup<Additive> for i16

impl AbstractGroup<Additive> for i32

impl AbstractGroup<Additive> for i64

impl AbstractGroup<Additive> for isize

impl AbstractGroupAbelian<Additive> for i8

fn prop_is_commutative_approx(args: (Self, Self)) -> bool where
    Self: ApproxEq, 

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

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

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

impl AbstractGroupAbelian<Additive> for i16

fn prop_is_commutative_approx(args: (Self, Self)) -> bool where
    Self: ApproxEq, 

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

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

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

impl AbstractGroupAbelian<Additive> for i32

fn prop_is_commutative_approx(args: (Self, Self)) -> bool where
    Self: ApproxEq, 

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

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

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

impl AbstractGroupAbelian<Additive> for i64

fn prop_is_commutative_approx(args: (Self, Self)) -> bool where
    Self: ApproxEq, 

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

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

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

impl AbstractGroupAbelian<Additive> for isize

fn prop_is_commutative_approx(args: (Self, Self)) -> bool where
    Self: ApproxEq, 

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

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

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

impl AbstractRing<Additive, Multiplicative> for i8

fn prop_mul_and_add_are_distributive_approx(args: (Self, Self, Self)) -> bool where
    Self: ApproxEq, 

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

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 AbstractRing<Additive, Multiplicative> for i16

fn prop_mul_and_add_are_distributive_approx(args: (Self, Self, Self)) -> bool where
    Self: ApproxEq, 

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

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 AbstractRing<Additive, Multiplicative> for i32

fn prop_mul_and_add_are_distributive_approx(args: (Self, Self, Self)) -> bool where
    Self: ApproxEq, 

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

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 AbstractRing<Additive, Multiplicative> for i64

fn prop_mul_and_add_are_distributive_approx(args: (Self, Self, Self)) -> bool where
    Self: ApproxEq, 

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

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 AbstractRing<Additive, Multiplicative> for isize

fn prop_mul_and_add_are_distributive_approx(args: (Self, Self, Self)) -> bool where
    Self: ApproxEq, 

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

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 AbstractRingCommutative<Additive, Multiplicative> for i8

fn prop_mul_is_commutative_approx(args: (Self, Self)) -> bool where
    Self: ApproxEq, 

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

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 AbstractRingCommutative<Additive, Multiplicative> for i16

fn prop_mul_is_commutative_approx(args: (Self, Self)) -> bool where
    Self: ApproxEq, 

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

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 AbstractRingCommutative<Additive, Multiplicative> for i32

fn prop_mul_is_commutative_approx(args: (Self, Self)) -> bool where
    Self: ApproxEq, 

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

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 AbstractRingCommutative<Additive, Multiplicative> for i64

fn prop_mul_is_commutative_approx(args: (Self, Self)) -> bool where
    Self: ApproxEq, 

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

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 AbstractRingCommutative<Additive, Multiplicative> for isize

fn prop_mul_is_commutative_approx(args: (Self, Self)) -> bool where
    Self: ApproxEq, 

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

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 AbstractSemigroup<Additive> for f32

fn prop_is_associative_approx(args: (Self, Self, Self)) -> bool where
    Self: ApproxEq, 

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

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

Returns true if associativity holds for the given arguments.

impl AbstractSemigroup<Additive> for f64

fn prop_is_associative_approx(args: (Self, Self, Self)) -> bool where
    Self: ApproxEq, 

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

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

Returns true if associativity holds for the given arguments.

impl AbstractMonoid<Additive> for f32

fn prop_operating_identity_element_is_noop_approx(args: (Self,)) -> bool where
    Self: ApproxEq, 

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

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 AbstractMonoid<Additive> for f64

fn prop_operating_identity_element_is_noop_approx(args: (Self,)) -> bool where
    Self: ApproxEq, 

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

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 AbstractQuasigroup<Additive> for f32

fn prop_inv_is_latin_square_approx(args: (Self, Self)) -> bool where
    Self: ApproxEq, 

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

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

Returns true if latin squareness holds for the given arguments.

impl AbstractQuasigroup<Additive> for f64

fn prop_inv_is_latin_square_approx(args: (Self, Self)) -> bool where
    Self: ApproxEq, 

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

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

Returns true if latin squareness holds for the given arguments.

impl AbstractLoop<Additive> for f32

impl AbstractLoop<Additive> for f64

impl AbstractGroup<Additive> for f32

impl AbstractGroup<Additive> for f64

impl AbstractGroupAbelian<Additive> for f32

fn prop_is_commutative_approx(args: (Self, Self)) -> bool where
    Self: ApproxEq, 

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

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

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

impl AbstractGroupAbelian<Additive> for f64

fn prop_is_commutative_approx(args: (Self, Self)) -> bool where
    Self: ApproxEq, 

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

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

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

impl AbstractRing<Additive, Multiplicative> for f32

fn prop_mul_and_add_are_distributive_approx(args: (Self, Self, Self)) -> bool where
    Self: ApproxEq, 

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

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 AbstractRing<Additive, Multiplicative> for f64

fn prop_mul_and_add_are_distributive_approx(args: (Self, Self, Self)) -> bool where
    Self: ApproxEq, 

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

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 AbstractRingCommutative<Additive, Multiplicative> for f32

fn prop_mul_is_commutative_approx(args: (Self, Self)) -> bool where
    Self: ApproxEq, 

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

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 AbstractRingCommutative<Additive, Multiplicative> for f64

fn prop_mul_is_commutative_approx(args: (Self, Self)) -> bool where
    Self: ApproxEq, 

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

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 AbstractField<Additive, Multiplicative> for f32

impl AbstractField<Additive, Multiplicative> for f64

impl Identity<Additive> for u8

fn identity() -> u8

The identity element.

fn id(_: O) -> Self where
    Self: Sized, 

Specific identity.

impl Identity<Additive> for u16

fn identity() -> u16

The identity element.

fn id(_: O) -> Self where
    Self: Sized, 

Specific identity.

impl Identity<Additive> for u32

fn identity() -> u32

The identity element.

fn id(_: O) -> Self where
    Self: Sized, 

Specific identity.

impl Identity<Additive> for u64

fn identity() -> u64

The identity element.

fn id(_: O) -> Self where
    Self: Sized, 

Specific identity.

impl Identity<Additive> for usize

fn identity() -> usize

The identity element.

fn id(_: O) -> Self where
    Self: Sized, 

Specific identity.

impl Identity<Additive> for i8

fn identity() -> i8

The identity element.

fn id(_: O) -> Self where
    Self: Sized, 

Specific identity.

impl Identity<Additive> for i16

fn identity() -> i16

The identity element.

fn id(_: O) -> Self where
    Self: Sized, 

Specific identity.

impl Identity<Additive> for i32

fn identity() -> i32

The identity element.

fn id(_: O) -> Self where
    Self: Sized, 

Specific identity.

impl Identity<Additive> for i64

fn identity() -> i64

The identity element.

fn id(_: O) -> Self where
    Self: Sized, 

Specific identity.

impl Identity<Additive> for isize

fn identity() -> isize

The identity element.

fn id(_: O) -> Self where
    Self: Sized, 

Specific identity.

impl Identity<Additive> for f32

fn identity() -> f32

The identity element.

fn id(_: O) -> Self where
    Self: Sized, 

Specific identity.

impl Identity<Additive> for f64

fn identity() -> f64

The identity element.

fn id(_: O) -> Self where
    Self: Sized, 

Specific identity.

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

fn identity() -> Self

The identity element.

fn id(_: O) -> Self where
    Self: Sized, 

Specific identity.

impl Clone for Additive

fn clone(&self) -> Additive

Returns a copy of the value.

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

Performs copy-assignment from source.

impl Copy for Additive

impl Operator for Additive

fn operator_token() -> Self

Returns the structure that identifies the operator.

impl Inverse<Additive> for i8

fn inverse(&self) -> Self

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

fn inverse_mut(&mut self)

In-place inversin of self.

impl Inverse<Additive> for i16

fn inverse(&self) -> Self

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

fn inverse_mut(&mut self)

In-place inversin of self.

impl Inverse<Additive> for i32

fn inverse(&self) -> Self

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

fn inverse_mut(&mut self)

In-place inversin of self.

impl Inverse<Additive> for i64

fn inverse(&self) -> Self

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

fn inverse_mut(&mut self)

In-place inversin of self.

impl Inverse<Additive> for isize

fn inverse(&self) -> Self

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

fn inverse_mut(&mut self)

In-place inversin of self.

impl Inverse<Additive> for f32

fn inverse(&self) -> Self

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

fn inverse_mut(&mut self)

In-place inversin of self.

impl Inverse<Additive> for f64

fn inverse(&self) -> Self

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

fn inverse_mut(&mut self)

In-place inversin of self.

impl<N: Inverse<Additive>> Inverse<Additive> for Complex<N>

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

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

fn inverse_mut(&mut self)

In-place inversin of self.