Modulo

algebraeon_rings::finite_fields::modulo

Struct Modulo

pub struct Modulo<const N: usize> { /* private fields */ }

Implementations§

impl<const N: usize> Modulo<N>

pub const fn new(x: usize) -> Self

impl<const N: usize> Modulo<N>

pub fn lift_nat(&self) -> Natural

pub fn lift_int(&self) -> Integer

Trait Implementations§

impl<const N: usize> Clone for Modulo<N>

fn clone(&self) -> Modulo<N>

Returns a duplicate of the value. Read more

1.0.0 · Source§

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

Performs copy-assignment from source. Read more

impl<const N: usize> Debug for Modulo<N>

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

Formats the value using the given formatter. Read more

impl<const N: usize> Display for Modulo<N>

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

Formats the value using the given formatter. Read more

impl<const N: usize> From<&Integer> for Modulo<N>

fn from(value: &Integer) -> Self

Converts to this type from the input type.

impl<const N: usize> From<Integer> for Modulo<N>

fn from(value: Integer) -> Self

Converts to this type from the input type.

impl<const N: usize> From<Modulo<N>> for usize

fn from(value: Modulo<N>) -> Self

Converts to this type from the input type.

impl<const N: usize> From<i32> for Modulo<N>

fn from(value: i32) -> Self

Converts to this type from the input type.

impl<const N: usize> From<isize> for Modulo<N>

fn from(value: isize) -> Self

Converts to this type from the input type.

impl<const N: usize> From<usize> for Modulo<N>

fn from(value: usize) -> Self

Converts to this type from the input type.

impl<const N: usize> Hash for Modulo<N>

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

Feeds this value into the given Hasher. Read more

1.3.0 · Source§

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

Feeds a slice of this type into the given Hasher. Read more

impl<const N: usize> MetaType for Modulo<N>

type Signature = ModuloCanonicalStructure<N>

fn structure() -> Self::Signature

impl<const N: usize> PartialEq for Modulo<N>

fn eq(&self, other: &Self) -> bool

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

1.0.0 · Source§

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<const N: usize> Eq for Modulo<N>

Auto Trait Implementations§

impl<const N: usize> Freeze for Modulo<N>

impl<const N: usize> RefUnwindSafe for Modulo<N>

impl<const N: usize> Send for Modulo<N>

impl<const N: usize> Sync for Modulo<N>

impl<const N: usize> Unpin for Modulo<N>

impl<const N: usize> UnwindSafe for Modulo<N>

Blanket Implementations§

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

fn type_id(&self) -> TypeId

Gets the TypeId of self. Read more

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

fn borrow(&self) -> &T

Immutably borrows from an owned value. Read more

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

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

Mutably borrows from an owned value. Read more

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

unsafe fn clone_to_uninit(&self, dest: *mut u8)

🔬This is a nightly-only experimental API. (clone_to_uninit)

Performs copy-assignment from self to dest. Read more

impl<Q, K> Equivalent<K> for Q
where Q: Eq + ?Sized, K: Borrow<Q> + ?Sized,

fn equivalent(&self, key: &K) -> bool

Checks if this value is equivalent to the given key. Read more

impl<Q, K> Equivalent<K> for Q
where Q: Eq + ?Sized, K: Borrow<Q> + ?Sized,

fn equivalent(&self, key: &K) -> bool

Compare self to key and return true if they are equal.

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

fn exact_from(value: T) -> U

impl<T, U> ExactInto<U> for T
where U: ExactFrom<T>,

fn exact_into(self) -> U

impl<T> From<T> for T

fn from(t: T) -> T

Returns the argument unchanged.

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

fn into(self) -> U

Calls U::from(self).

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

impl<T> IntoEither for T

fn into_either(self, into_left: bool) -> Either<Self, Self>

Converts self into a Left variant of Either<Self, Self> if into_left is true. Converts self into a Right variant of Either<Self, Self> otherwise. Read more

fn into_either_with<F>(self, into_left: F) -> Either<Self, Self>
where F: FnOnce(&Self) -> bool,

Converts self into a Left variant of Either<Self, Self> if into_left(&self) returns true. Converts self into a Right variant of Either<Self, Self> otherwise. Read more

impl<T> IntoErgonomic for T
where T: MetaType,

fn into_ergonomic(self) -> StructuredElement<Self::Signature>

impl<T> MetaAreAssociateMultiplicationSignature for T
where T: MetaType, <T as MetaType>::Signature: AreAssociateMultiplicationSignature,

fn are_associate(&self, b: &Self) -> bool

impl<T> MetaBezoutDomainSignature for T
where T: MetaType, <T as MetaType>::Signature: BezoutDomainSignature,

fn xgcd(&self, b: &Self) -> (Self, Self, Self)

fn xgcd_list(elems: Vec<&Self>) -> (Self, Vec<Self>)

impl<T> MetaEuclideanDivisionSignature for T
where T: MetaType, <T as MetaType>::Signature: EuclideanDivisionSignature,

fn norm(&self) -> Option<Natural>

None for 0 and Some(norm) for everything else

fn quorem(&self, b: &Self) -> Option<(Self, Self)>

None if b is 0 and Some((q, r)) such that a=bq+r and r=0 or norm(r) < norm(b)

fn quo(&self, b: &Self) -> Option<Self>

fn rem(&self, b: &Self) -> Self

fn euclidean_gcd(self, y: Self) -> Self
where Self::Signature: FavoriteAssociateSignature,

fn euclidean_xgcd(self, y: Self) -> (Self, Self, Self)
where Self::Signature: FavoriteAssociateSignature + IntegralDomainSignature,

impl<R> MetaFactoringMonoid for R
where R: MetaType, <R as MetaType>::Signature: FactoringMonoidSignature,

fn is_irreducible(&self) -> bool

fn factor_unchecked( &self, ) -> Factored<Self, <<Self::Signature as UniqueFactorizationMonoidSignature>::FactoredExponent as SetSignature>::Set>

fn factor( &self, ) -> Factored<Self, <<Self::Signature as UniqueFactorizationMonoidSignature>::FactoredExponent as SetSignature>::Set>

impl<R> MetaFactoringMonoidNaturalExponent for R
where R: MetaType, <R as MetaType>::Signature: FactoringMonoidNaturalExponentSignature,

fn gcd_by_factor(a: &Self, b: &Self) -> Self

fn lcm_by_factor(a: &Self, b: &Self) -> Option<Self>

fn is_squarefree(&self) -> bool

impl<T> MetaFavoriteAssociateSignature for T
where T: MetaType, <T as MetaType>::Signature: FavoriteAssociateSignature,

fn factor_fav_assoc(&self) -> (Self, Self)

fn fav_assoc(&self) -> Self

fn is_fav_assoc(&self) -> bool

impl<T> MetaFiniteUnitsSignature for T
where T: MetaType, <T as MetaType>::Signature: FiniteUnitsSignature,

fn all_units() -> Vec<Self>

fn all_units_and_zero() -> Vec<Self>

impl<T> MetaGreatestCommonDivisorSignature for T
where T: MetaType, <T as MetaType>::Signature: GreatestCommonDivisorSignature,

fn gcd(&self, y: &Self) -> Self

fn gcd_list(elems: Vec<impl Borrow<Self>>) -> Self

fn lcm(&self, y: &Self) -> Self

fn lcm_list(elems: Vec<impl Borrow<Self>>) -> Self

impl<T> MetaLeftCancellativeMultiplicationSignature for T
where T: MetaType, <T as MetaType>::Signature: LeftCancellativeMultiplicationSignature,

fn try_left_divide(&self, b: &Self) -> Option<Self>

Try to find x such that a = b * x.

impl<T> MetaMultiplicativeMonoidTryInverseSignature for T
where T: MetaType, <T as MetaType>::Signature: MultiplicativeMonoidTryInverseSignature,

fn try_int_pow(&self, n: &Integer) -> Option<Self>

impl<T> MetaRightCancellativeMultiplicationSignature for T
where T: MetaType, <T as MetaType>::Signature: RightCancellativeMultiplicationSignature,

fn try_right_divide(&self, b: &Self) -> Option<Self>

Try to find x such that a = x * b.

impl<T> MetaTryLeftReciprocalSignature for T
where T: MetaType, <T as MetaType>::Signature: TryLeftReciprocalSignature,

fn try_left_reciprocal(&self) -> Option<Self>

x such that x*a=1 or None if no such x exists.

impl<T> MetaTryRightReciprocalSignature for T
where T: MetaType, <T as MetaType>::Signature: TryRightReciprocalSignature,

fn try_right_reciprocal(&self) -> Option<Self>

x such that a*x=1 or None if no such x exists.

impl<R> MetaUniqueFactorizationMonoidSignature for R
where R: MetaType, <R as MetaType>::Signature: UniqueFactorizationMonoidSignature,

fn try_is_irreducible(&self) -> Option<bool>

impl<T> MetaZeroEqSignature for T
where T: MetaType, <T as MetaType>::Signature: ZeroEqSignature,

fn is_zero(&self) -> bool

impl<T, U> OverflowingInto<U> for T
where U: OverflowingFrom<T>,

fn overflowing_into(self) -> (U, bool)

impl<T> Pointable for T

const ALIGN: usize

The alignment of pointer.

type Init = T

The type for initializers.

unsafe fn init(init: <T as Pointable>::Init) -> usize

Initializes a with the given initializer. Read more

unsafe fn deref<'a>(ptr: usize) -> &'a T

Dereferences the given pointer. Read more

unsafe fn deref_mut<'a>(ptr: usize) -> &'a mut T

Mutably dereferences the given pointer. Read more

unsafe fn drop(ptr: usize)

Drops the object pointed to by the given pointer. Read more

impl<T, U> RoundingInto<U> for T
where U: RoundingFrom<T>,

fn rounding_into(self, rm: RoundingMode) -> (U, Ordering)

impl<T> Same for T

type Output = T

Should always be Self

impl<T, U> SaturatingInto<U> for T
where U: SaturatingFrom<T>,

fn saturating_into(self) -> U

impl<T> ToDebugString for T
where T: Debug,

fn to_debug_string(&self) -> String

Returns the String produced by Ts Debug implementation.

§Examples

use malachite_base::strings::ToDebugString;

assert_eq!([1, 2, 3].to_debug_string(), "[1, 2, 3]");
assert_eq!(
    [vec![2, 3], vec![], vec![4]].to_debug_string(),
    "[[2, 3], [], [4]]"
);
assert_eq!(Some(5).to_debug_string(), "Some(5)");

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

type Owned = T

The resulting type after obtaining ownership.

fn to_owned(&self) -> T

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

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

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

impl<T> ToString for T
where T: Display + ?Sized,

fn to_string(&self) -> String

Converts the given value to a String. Read more

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

type Error = Infallible

The type returned in the event of a conversion error.

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

Performs the conversion.

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.

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

Performs the conversion.

impl<V, T> VZip<V> for T
where V: MultiLane<T>,

fn vzip(self) -> V

impl<T, U> WrappingInto<U> for T
where U: WrappingFrom<T>,

fn wrapping_into(self) -> U

impl<Domain, Range, M, BM> BorrowedMorphism<Domain, Range, M> for BM
where Domain: Signature, Range: Signature, M: Morphism<Domain, Range>, BM: Borrow<M> + Clone + Debug + Send + Sync,

impl<S, BS> BorrowedSet<S> for BS
where BS: Borrow<S> + Clone + Debug + Send + Sync,

impl<S, BS> BorrowedStructure<S> for BS
where S: Signature, BS: Borrow<S> + Clone + Debug + Eq + Send + Sync,

impl<T> MetaEuclideanDomainSignature for T
where T: MetaType, <T as MetaType>::Signature: EuclideanDomainSignature,

impl<T> MetaRingEqSignature for T
where T: MetaType, <T as MetaType>::Signature: RingEqSignature,

impl<T> MetaRingUnitsSignature for T
where T: MetaType, <T as MetaType>::Signature: RingUnitsSignature,

impl<T> MetaSemiRingEqSignature for T
where T: MetaType, <T as MetaType>::Signature: SemiRingEqSignature,