Struct alga::general::Additive

source · 
pub struct Additive;
Expand description

The addition operator, commonly symbolized by +.

Trait Implementations§

source§

impl AbstractGroupAbelian<Additive> for f32

source§

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.
source§

impl AbstractGroupAbelian<Additive> for f64

source§

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.
source§

impl AbstractGroupAbelian<Additive> for i128

source§

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

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

impl AbstractGroupAbelian<Additive> for i16

source§

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

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

impl AbstractGroupAbelian<Additive> for i32

source§

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

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

impl AbstractGroupAbelian<Additive> for i64

source§

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

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

impl AbstractGroupAbelian<Additive> for i8

source§

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

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

impl AbstractGroupAbelian<Additive> for isize

source§

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

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

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

source§

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

Performs an operation.
source§

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

Performs specific operation.
source§

impl AbstractMagma<Additive> for f32

source§

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

Performs an operation.
source§

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

Performs specific operation.
source§

impl AbstractMagma<Additive> for f64

source§

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

Performs an operation.
source§

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

Performs specific operation.
source§

impl AbstractMagma<Additive> for i128

source§

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

Performs an operation.
source§

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

Performs specific operation.
source§

impl AbstractMagma<Additive> for i16

source§

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

Performs an operation.
source§

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

Performs specific operation.
source§

impl AbstractMagma<Additive> for i32

source§

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

Performs an operation.
source§

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

Performs specific operation.
source§

impl AbstractMagma<Additive> for i64

source§

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

Performs an operation.
source§

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

Performs specific operation.
source§

impl AbstractMagma<Additive> for i8

source§

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

Performs an operation.
source§

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

Performs specific operation.
source§

impl AbstractMagma<Additive> for isize

source§

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

Performs an operation.
source§

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

Performs specific operation.
source§

impl AbstractMagma<Additive> for u128

source§

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

Performs an operation.
source§

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

Performs specific operation.
source§

impl AbstractMagma<Additive> for u16

source§

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

Performs an operation.
source§

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

Performs specific operation.
source§

impl AbstractMagma<Additive> for u32

source§

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

Performs an operation.
source§

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

Performs specific operation.
source§

impl AbstractMagma<Additive> for u64

source§

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

Performs an operation.
source§

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

Performs specific operation.
source§

impl AbstractMagma<Additive> for u8

source§

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

Performs an operation.
source§

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

Performs specific operation.
source§

impl AbstractMagma<Additive> for usize

source§

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

Performs an operation.
source§

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

Performs specific operation.
source§

impl AbstractMonoid<Additive> for f32

source§

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.
source§

impl AbstractMonoid<Additive> for f64

source§

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.
source§

impl AbstractMonoid<Additive> for i128

source§

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.
source§

impl AbstractMonoid<Additive> for i16

source§

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.
source§

impl AbstractMonoid<Additive> for i32

source§

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.
source§

impl AbstractMonoid<Additive> for i64

source§

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.
source§

impl AbstractMonoid<Additive> for i8

source§

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.
source§

impl AbstractMonoid<Additive> for isize

source§

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.
source§

impl AbstractMonoid<Additive> for u128

source§

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.
source§

impl AbstractMonoid<Additive> for u16

source§

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.
source§

impl AbstractMonoid<Additive> for u32

source§

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.
source§

impl AbstractMonoid<Additive> for u64

source§

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.
source§

impl AbstractMonoid<Additive> for u8

source§

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.
source§

impl AbstractMonoid<Additive> for usize

source§

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.
source§

impl AbstractQuasigroup<Additive> for f32

source§

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. Read more
source§

impl AbstractQuasigroup<Additive> for f64

source§

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. Read more
source§

impl AbstractQuasigroup<Additive> for i128

source§

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

Returns true if latin squareness holds for the given arguments. Read more
source§

impl AbstractQuasigroup<Additive> for i16

source§

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

Returns true if latin squareness holds for the given arguments. Read more
source§

impl AbstractQuasigroup<Additive> for i32

source§

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

Returns true if latin squareness holds for the given arguments. Read more
source§

impl AbstractQuasigroup<Additive> for i64

source§

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

Returns true if latin squareness holds for the given arguments. Read more
source§

impl AbstractQuasigroup<Additive> for i8

source§

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

Returns true if latin squareness holds for the given arguments. Read more
source§

impl AbstractQuasigroup<Additive> for isize

source§

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

Returns true if latin squareness holds for the given arguments. Read more
source§

impl AbstractSemigroup<Additive> for f32

source§

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.
source§

impl AbstractSemigroup<Additive> for f64

source§

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.
source§

impl AbstractSemigroup<Additive> for i128

source§

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

Returns true if associativity holds for the given arguments.
source§

impl AbstractSemigroup<Additive> for i16

source§

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

Returns true if associativity holds for the given arguments.
source§

impl AbstractSemigroup<Additive> for i32

source§

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

Returns true if associativity holds for the given arguments.
source§

impl AbstractSemigroup<Additive> for i64

source§

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

Returns true if associativity holds for the given arguments.
source§

impl AbstractSemigroup<Additive> for i8

source§

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

Returns true if associativity holds for the given arguments.
source§

impl AbstractSemigroup<Additive> for isize

source§

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

Returns true if associativity holds for the given arguments.
source§

impl AbstractSemigroup<Additive> for u128

source§

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

Returns true if associativity holds for the given arguments.
source§

impl AbstractSemigroup<Additive> for u16

source§

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

Returns true if associativity holds for the given arguments.
source§

impl AbstractSemigroup<Additive> for u32

source§

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

Returns true if associativity holds for the given arguments.
source§

impl AbstractSemigroup<Additive> for u64

source§

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

Returns true if associativity holds for the given arguments.
source§

impl AbstractSemigroup<Additive> for u8

source§

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

Returns true if associativity holds for the given arguments.
source§

impl AbstractSemigroup<Additive> for usize

source§

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

Returns true if associativity holds for the given arguments.
source§

impl Clone for Additive

source§

fn clone(&self) -> Additive

Returns a copy of the value. Read more
1.0.0 · source§

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

Performs copy-assignment from source. Read more
source§

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

source§

fn identity() -> Self

The identity element.
source§

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

Specific identity.
source§

impl Identity<Additive> for f32

source§

fn identity() -> f32

The identity element.
source§

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

Specific identity.
source§

impl Identity<Additive> for f64

source§

fn identity() -> f64

The identity element.
source§

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

Specific identity.
source§

impl Identity<Additive> for i128

source§

fn identity() -> i128

The identity element.
source§

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

Specific identity.
source§

impl Identity<Additive> for i16

source§

fn identity() -> i16

The identity element.
source§

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

Specific identity.
source§

impl Identity<Additive> for i32

source§

fn identity() -> i32

The identity element.
source§

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

Specific identity.
source§

impl Identity<Additive> for i64

source§

fn identity() -> i64

The identity element.
source§

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

Specific identity.
source§

impl Identity<Additive> for i8

source§

fn identity() -> i8

The identity element.
source§

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

Specific identity.
source§

impl Identity<Additive> for isize

source§

fn identity() -> isize

The identity element.
source§

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

Specific identity.
source§

impl Identity<Additive> for u128

source§

fn identity() -> u128

The identity element.
source§

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

Specific identity.
source§

impl Identity<Additive> for u16

source§

fn identity() -> u16

The identity element.
source§

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

Specific identity.
source§

impl Identity<Additive> for u32

source§

fn identity() -> u32

The identity element.
source§

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

Specific identity.
source§

impl Identity<Additive> for u64

source§

fn identity() -> u64

The identity element.
source§

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

Specific identity.
source§

impl Identity<Additive> for u8

source§

fn identity() -> u8

The identity element.
source§

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

Specific identity.
source§

impl Identity<Additive> for usize

source§

fn identity() -> usize

The identity element.
source§

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

Specific identity.
source§

impl Operator for Additive

source§

fn operator_token() -> Self

Returns the structure that identifies the operator.
source§

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

source§

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

Returns the two_sided_inverse of self, relative to the operator O. Read more
source§

fn two_sided_inverse_mut(&mut self)

In-place inversion of self, relative to the operator O. Read more
source§

impl TwoSidedInverse<Additive> for f32

source§

fn two_sided_inverse(&self) -> Self

Returns the two_sided_inverse of self, relative to the operator O. Read more
source§

fn two_sided_inverse_mut(&mut self)

In-place inversion of self, relative to the operator O. Read more
source§

impl TwoSidedInverse<Additive> for f64

source§

fn two_sided_inverse(&self) -> Self

Returns the two_sided_inverse of self, relative to the operator O. Read more
source§

fn two_sided_inverse_mut(&mut self)

In-place inversion of self, relative to the operator O. Read more
source§

impl TwoSidedInverse<Additive> for i128

source§

fn two_sided_inverse(&self) -> Self

Returns the two_sided_inverse of self, relative to the operator O. Read more
source§

fn two_sided_inverse_mut(&mut self)

In-place inversion of self, relative to the operator O. Read more
source§

impl TwoSidedInverse<Additive> for i16

source§

fn two_sided_inverse(&self) -> Self

Returns the two_sided_inverse of self, relative to the operator O. Read more
source§

fn two_sided_inverse_mut(&mut self)

In-place inversion of self, relative to the operator O. Read more
source§

impl TwoSidedInverse<Additive> for i32

source§

fn two_sided_inverse(&self) -> Self

Returns the two_sided_inverse of self, relative to the operator O. Read more
source§

fn two_sided_inverse_mut(&mut self)

In-place inversion of self, relative to the operator O. Read more
source§

impl TwoSidedInverse<Additive> for i64

source§

fn two_sided_inverse(&self) -> Self

Returns the two_sided_inverse of self, relative to the operator O. Read more
source§

fn two_sided_inverse_mut(&mut self)

In-place inversion of self, relative to the operator O. Read more
source§

impl TwoSidedInverse<Additive> for i8

source§

fn two_sided_inverse(&self) -> Self

Returns the two_sided_inverse of self, relative to the operator O. Read more
source§

fn two_sided_inverse_mut(&mut self)

In-place inversion of self, relative to the operator O. Read more
source§

impl TwoSidedInverse<Additive> for isize

source§

fn two_sided_inverse(&self) -> Self

Returns the two_sided_inverse of self, relative to the operator O. Read more
source§

fn two_sided_inverse_mut(&mut self)

In-place inversion of self, relative to the operator O. Read more
source§

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

source§

impl AbstractGroup<Additive> for f32

source§

impl AbstractGroup<Additive> for f64

source§

impl AbstractGroup<Additive> for i128

source§

impl AbstractGroup<Additive> for i16

source§

impl AbstractGroup<Additive> for i32

source§

impl AbstractGroup<Additive> for i64

source§

impl AbstractGroup<Additive> for i8

source§

impl AbstractGroup<Additive> for isize

source§

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

source§

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

source§

impl AbstractLoop<Additive> for f32

source§

impl AbstractLoop<Additive> for f64

source§

impl AbstractLoop<Additive> for i128

source§

impl AbstractLoop<Additive> for i16

source§

impl AbstractLoop<Additive> for i32

source§

impl AbstractLoop<Additive> for i64

source§

impl AbstractLoop<Additive> for i8

source§

impl AbstractLoop<Additive> for isize

source§

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

source§

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

source§

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

source§

impl Copy for Additive

Auto Trait Implementations§

Blanket Implementations§

source§

impl<T> Any for T
where T: 'static + ?Sized,

source§

fn type_id(&self) -> TypeId

Gets the TypeId of self. Read more
source§

impl<T> Borrow<T> for T
where T: ?Sized,

source§

fn borrow(&self) -> &T

Immutably borrows from an owned value. Read more
source§

impl<T> BorrowMut<T> for T
where T: ?Sized,

source§

fn borrow_mut(&mut self) -> &mut T

Mutably borrows from an owned value. Read more
source§

impl<T> From<T> for T

source§

fn from(t: T) -> T

Returns the argument unchanged.

source§

impl<T, U> Into<U> for T
where U: From<T>,

source§

fn into(self) -> U

Calls U::from(self).

That is, this conversion is whatever the implementation of From<T> for U chooses to do.

source§

impl<SS, SP> SupersetOf<SS> for SP
where SS: SubsetOf<SP>,

source§

fn to_subset(&self) -> Option<SS>

The inverse inclusion map: attempts to construct self from the equivalent element of its superset. Read more
source§

fn is_in_subset(&self) -> bool

Checks if self is actually part of its subset T (and can be converted to it).
source§

unsafe fn to_subset_unchecked(&self) -> SS

Use with care! Same as self.to_subset but without any property checks. Always succeeds.
source§

fn from_subset(element: &SS) -> SP

The inclusion map: converts self to the equivalent element of its superset.
source§

impl<T> ToOwned for T
where T: Clone,

§

type Owned = T

The resulting type after obtaining ownership.
source§

fn to_owned(&self) -> T

Creates owned data from borrowed data, usually by cloning. Read more
source§

fn clone_into(&self, target: &mut T)

Uses borrowed data to replace owned data, usually by cloning. Read more
source§

impl<T, U> TryFrom<U> for T
where U: Into<T>,

§

type Error = Infallible

The type returned in the event of a conversion error.
source§

fn try_from(value: U) -> Result<T, <T as TryFrom<U>>::Error>

Performs the conversion.
source§

impl<T, U> TryInto<U> for T
where U: TryFrom<T>,

§

type Error = <U as TryFrom<T>>::Error

The type returned in the event of a conversion error.
source§

fn try_into(self) -> Result<U, <U as TryFrom<T>>::Error>

Performs the conversion.