Struct AddMulMod

pub struct AddMulMod<T: ZZ>(pub T);

$\mathbb{Z} / m \mathbb{Z}$の環

Tuple Fields

0: T

Trait Implementations

impl<T: Clone + ZZ> Clone for AddMulMod<T>

fn clone(&self) -> AddMulMod<T>

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl<T: Debug + ZZ> Debug for AddMulMod<T>

fn fmt(&self, f: &mut Formatter<'_>) -> Result

Formats the value using the given formatter.

impl<T: Default + ZZ> Default for AddMulMod<T>

fn default() -> AddMulMod<T>

Returns the “default value” for a type.

impl<T: FF> Field for AddMulMod<T>

where T::Element: FFElem,

fn inv(&self, a: Self::Element) -> Self::Element

乗法の逆元 $a^{-1}$

fn div(&self, a: Self::Element, b: Self::Element) -> Self::Element

$a \otimes b^{-1}$

impl<T: Hash + ZZ> Hash for AddMulMod<T>

fn hash<__H: Hasher>(&self, state: &mut __H)

Feeds this value into the given Hasher.

fn hash_slice<H>(data: &[Self], state: &mut H)

where H: Hasher, Self: Sized,

Feeds a slice of this type into the given Hasher.

impl<T: Ord + ZZ> Ord for AddMulMod<T>

fn cmp(&self, other: &AddMulMod<T>) -> Ordering

This method returns an Ordering between self and other.

fn max(self, other: Self) -> Self

where Self: Sized,

Compares and returns the maximum of two values.

fn min(self, other: Self) -> Self

where Self: Sized,

Compares and returns the minimum of two values.

fn clamp(self, min: Self, max: Self) -> Self

where Self: Sized,

Restrict a value to a certain interval.

impl<T: PartialEq + ZZ> PartialEq for AddMulMod<T>

fn eq(&self, other: &AddMulMod<T>) -> bool

Tests for self and other values to be equal, and is used by ==.

fn ne(&self, other: &Rhs) -> bool

Tests for !=. The default implementation is almost always sufficient, and should not be overridden without very good reason.

impl<T: PartialOrd + ZZ> PartialOrd for AddMulMod<T>

fn partial_cmp(&self, other: &AddMulMod<T>) -> Option<Ordering>

This method returns an ordering between self and other values if one exists.

fn lt(&self, other: &Rhs) -> bool

Tests less than (for self and other) and is used by the < operator.

fn le(&self, other: &Rhs) -> bool

Tests less than or equal to (for self and other) and is used by the <= operator.

fn gt(&self, other: &Rhs) -> bool

Tests greater than (for self and other) and is used by the > operator.

fn ge(&self, other: &Rhs) -> bool

Tests greater than or equal to (for self and other) and is used by the >= operator.

impl<T: ZZ> Ring for AddMulMod<T>

fn neg(&self, a: Self::Element) -> Self::Element

加法の逆元 $-a$

fn sub(&self, a: Self::Element, b: Self::Element) -> Self::Element

$a \oplus (-b)$

impl<T: ZZ> Semiring for AddMulMod<T>

type Element = <T as ZZ>::Element

集合の元

fn zero(&self) -> Self::Element

加法の単位元

fn one(&self) -> Self::Element

乗法の単位元

fn add(&self, a: Self::Element, b: Self::Element) -> Self::Element

加法$\oplus$

fn mul(&self, a: Self::Element, b: Self::Element) -> Self::Element

乗法$\otimes$

fn times(&self, a: Self::Element, n: u64) -> Self::Element

$\underbrace{a \oplus a \oplus \dots \oplus a \oplus a}_{n}$を計算する。

impl<T: Copy + ZZ> Copy for AddMulMod<T>

impl<T: Eq + ZZ> Eq for AddMulMod<T>

impl<T: ZZ> StructuralPartialEq for AddMulMod<T>