Struct alga::general::Multiplicative

pub struct Multiplicative;

The multiplication operator, commonly symbolized by ×.

Trait Implementations

impl AbstractField<Additive, Multiplicative> for f32

impl AbstractField<Additive, Multiplicative> for f64

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

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

impl AbstractGroup<Multiplicative> for f32

impl AbstractGroup<Multiplicative> for f64

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

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

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<Multiplicative> for f32

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

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<Multiplicative> for f64

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

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<N> AbstractLoop<Multiplicative> for Complex<N> where
    N: Num + Clone + ClosedNeg, 

impl AbstractLoop<Multiplicative> for f32

impl AbstractLoop<Multiplicative> for f64

impl AbstractMagma<Multiplicative> for u8

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

Performs an operation.

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

Performs specific operation.

impl AbstractMagma<Multiplicative> for u16

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

Performs an operation.

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

Performs specific operation.

impl AbstractMagma<Multiplicative> for i128

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

Performs an operation.

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

Performs specific operation.

impl AbstractMagma<Multiplicative> for isize

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

Performs an operation.

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

Performs specific operation.

impl AbstractMagma<Multiplicative> for f32

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

Performs an operation.

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

Performs specific operation.

impl AbstractMagma<Multiplicative> for f64

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

Performs an operation.

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

Performs specific operation.

impl<N: Num + Clone> AbstractMagma<Multiplicative> for Complex<N>

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

Performs an operation.

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

Performs specific operation.

impl AbstractMagma<Multiplicative> for u32

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

Performs an operation.

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

Performs specific operation.

impl AbstractMagma<Multiplicative> for u64

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

Performs an operation.

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

Performs specific operation.

impl AbstractMagma<Multiplicative> for u128

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

Performs an operation.

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

Performs specific operation.

impl AbstractMagma<Multiplicative> for usize

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

Performs an operation.

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

Performs specific operation.

impl AbstractMagma<Multiplicative> for i8

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

Performs an operation.

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

Performs specific operation.

impl AbstractMagma<Multiplicative> for i16

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

Performs an operation.

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

Performs specific operation.

impl AbstractMagma<Multiplicative> for i32

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

Performs an operation.

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

Performs specific operation.

impl AbstractMagma<Multiplicative> for i64

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

Performs an operation.

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

Performs specific operation.

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

type AbstractRing = N

The underlying scalar field.

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

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

impl AbstractModule<Additive, Additive, Multiplicative> for i8

type AbstractRing = i8

The underlying scalar field.

fn multiply_by(&self, r: i8) -> Self

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

impl AbstractModule<Additive, Additive, Multiplicative> for i16

type AbstractRing = i16

The underlying scalar field.

fn multiply_by(&self, r: i16) -> Self

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

impl AbstractModule<Additive, Additive, Multiplicative> for i32

type AbstractRing = i32

The underlying scalar field.

fn multiply_by(&self, r: i32) -> Self

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

impl AbstractModule<Additive, Additive, Multiplicative> for i64

type AbstractRing = i64

The underlying scalar field.

fn multiply_by(&self, r: i64) -> Self

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

impl AbstractModule<Additive, Additive, Multiplicative> for isize

type AbstractRing = isize

The underlying scalar field.

fn multiply_by(&self, r: isize) -> Self

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

impl AbstractModule<Additive, Additive, Multiplicative> for f32

type AbstractRing = f32

The underlying scalar field.

fn multiply_by(&self, r: f32) -> Self

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

impl AbstractModule<Additive, Additive, Multiplicative> for f64

type AbstractRing = f64

The underlying scalar field.

fn multiply_by(&self, r: f64) -> Self

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

impl AbstractMonoid<Multiplicative> for u8

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

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<Multiplicative> for u16

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

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<Multiplicative> for i64

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

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<Multiplicative> for i128

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

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<Multiplicative> for isize

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

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<Multiplicative> for f32

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

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<Multiplicative> for f64

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

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<Multiplicative> for u32

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

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<Multiplicative> for u64

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

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<Multiplicative> for u128

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

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<Multiplicative> for usize

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

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> AbstractMonoid<Multiplicative> for Complex<N> where
    N: Num + Clone + ClosedNeg, 

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

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<Multiplicative> for i8

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

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<Multiplicative> for i16

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

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<Multiplicative> for i32

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

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

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

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<Multiplicative> for f32

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

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<Multiplicative> for f64

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

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 AbstractRing<Additive, Multiplicative> for i8

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

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: RelativeEq, 

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: RelativeEq, 

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: RelativeEq, 

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 i128

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

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: RelativeEq, 

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 f32

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

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: RelativeEq, 

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

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

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: RelativeEq, 

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: RelativeEq, 

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: RelativeEq, 

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: RelativeEq, 

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 i128

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

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: RelativeEq, 

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 f32

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

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: RelativeEq, 

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

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

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<Multiplicative> for u8

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

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<Multiplicative> for u16

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

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<Multiplicative> for i64

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

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<Multiplicative> for i128

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

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<Multiplicative> for isize

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

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<Multiplicative> for f32

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

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<Multiplicative> for f64

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

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<Multiplicative> for u32

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

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<Multiplicative> for u64

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

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<Multiplicative> for u128

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

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<Multiplicative> for usize

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

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> AbstractSemigroup<Multiplicative> for Complex<N> where
    N: Num + Clone + ClosedNeg, 

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

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<Multiplicative> for i8

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

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<Multiplicative> for i16

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

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<Multiplicative> for i32

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

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 Clone for Multiplicative

fn clone(&self) -> Multiplicative

Returns a copy of the value.

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

Performs copy-assignment from source.

impl Copy for Multiplicative

impl Identity<Multiplicative> for u8

fn identity() -> u8

The identity element.

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

Specific identity.

impl Identity<Multiplicative> for u16

fn identity() -> u16

The identity element.

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

Specific identity.

impl Identity<Multiplicative> for i128

fn identity() -> i128

The identity element.

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

Specific identity.

impl Identity<Multiplicative> for isize

fn identity() -> isize

The identity element.

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

Specific identity.

impl Identity<Multiplicative> for f32

fn identity() -> f32

The identity element.

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

Specific identity.

impl Identity<Multiplicative> for f64

fn identity() -> f64

The identity element.

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

Specific identity.

impl<N: Num + Clone> Identity<Multiplicative> for Complex<N>

fn identity() -> Self

The identity element.

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

Specific identity.

impl Identity<Multiplicative> for u32

fn identity() -> u32

The identity element.

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

Specific identity.

impl Identity<Multiplicative> for u64

fn identity() -> u64

The identity element.

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

Specific identity.

impl Identity<Multiplicative> for u128

fn identity() -> u128

The identity element.

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

Specific identity.

impl Identity<Multiplicative> for usize

fn identity() -> usize

The identity element.

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

Specific identity.

impl Identity<Multiplicative> for i8

fn identity() -> i8

The identity element.

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

Specific identity.

impl Identity<Multiplicative> for i16

fn identity() -> i16

The identity element.

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

Specific identity.

impl Identity<Multiplicative> for i32

fn identity() -> i32

The identity element.

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

Specific identity.

impl Identity<Multiplicative> for i64

fn identity() -> i64

The identity element.

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

Specific identity.

impl Operator for Multiplicative

fn operator_token() -> Self

Returns the structure that identifies the operator.

impl TwoSidedInverse<Multiplicative> for f32

fn two_sided_inverse(&self) -> f32

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 TwoSidedInverse<Multiplicative> for f64

fn two_sided_inverse(&self) -> f64

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: Num + Clone + ClosedNeg> TwoSidedInverse<Multiplicative> for Complex<N>

fn two_sided_inverse(&self) -> Self

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.