competitive::algebra

Struct AdditiveOperation

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pub struct AdditiveOperation<T>
where
    T: Clone + Zero + Add<Output = T>,
{ /* private fields */ }
Expand description

$+$

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impl<T> Invertible for AdditiveOperation<T>
where T: Clone + Zero + Add<Output = T> + Sub<Output = T> + Neg<Output = T>,

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fn inverse(x: &Self::T) -> Self::T

$a$ where $a \circ x = e$
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fn rinv_operate(x: &Self::T, y: &Self::T) -> Self::T

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fn rinv_operate_assign(x: &mut Self::T, y: &Self::T)

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impl<T> Magma for AdditiveOperation<T>
where T: Clone + Zero + Add<Output = T>,

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type T = T

type of operands: $T$
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fn operate(x: &Self::T, y: &Self::T) -> Self::T

binary operaion: $\circ$
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fn reverse_operate(x: &Self::T, y: &Self::T) -> Self::T

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fn operate_assign(x: &mut Self::T, y: &Self::T)

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impl<T> Unital for AdditiveOperation<T>
where T: Clone + Zero + Add<Output = T>,

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fn unit() -> Self::T

identity element: $e$
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fn is_unit(x: &Self::T) -> bool
where <Self as Magma>::T: PartialEq,

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fn set_unit(x: &mut Self::T)

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impl<T> Associative for AdditiveOperation<T>
where T: Clone + Zero + Add<Output = T>,

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impl<T> Commutative for AdditiveOperation<T>
where T: Clone + Zero + Add<Output = T>,

Auto Trait Implementations§

Blanket Implementations§

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

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fn type_id(&self) -> TypeId

Gets the TypeId of self. Read more
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impl<T> Borrow<T> for T
where T: ?Sized,

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fn borrow(&self) -> &T

Immutably borrows from an owned value. Read more
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impl<T> BorrowMut<T> for T
where T: ?Sized,

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

Mutably borrows from an owned value. Read more
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impl<T> From<T> for T

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fn from(t: T) -> T

Returns the argument unchanged.

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impl<G> Group for G
where G: Monoid + Invertible,

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fn signed_pow<E>(x: Self::T, exp: E) -> Self::T
where E: SignedExpBits,

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

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fn into(self) -> U

Calls U::from(self).

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

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impl<M> Monoid for M
where M: SemiGroup + Unital,

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fn pow<E>(x: Self::T, exp: E) -> Self::T
where E: ExpBits,

binary exponentiation: $x^n = x\circ\ddots\circ x$
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fn fold<I>(iter: I) -> Self::T
where I: IntoIterator<Item = Self::T>,

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

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type Error = Infallible

The type returned in the event of a conversion error.
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fn try_from(value: U) -> Result<T, <T as TryFrom<U>>::Error>

Performs the conversion.
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impl<T, U> TryInto<U> for T
where U: TryFrom<T>,

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

The type returned in the event of a conversion error.
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fn try_into(self) -> Result<U, <U as TryFrom<T>>::Error>

Performs the conversion.
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impl<G> AbelianGroup for G
where G: Group + Commutative,

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impl<M> AbelianMonoid for M
where M: Monoid + Commutative,

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impl<S> SemiGroup for S
where S: Magma + Associative,