Struct MultiplicativeGroup

pub struct MultiplicativeGroup<A>
where
    A: Monoid,
{ /* private fields */ }

The multiplicative group of a unitary ring or field, or more generally the group of invertible elements of any monoid.

Implementations

impl<A> MultiplicativeGroup<A>

where A: Monoid,

pub fn new(base: A) -> Self

Creates a new multiplicative group from the given base.

pub fn base(&self) -> &A

Returns the base monoid from which this group was created.

Trait Implementations

impl<A> Clone for MultiplicativeGroup<A>

where A: Monoid + Clone,

fn clone(&self) -> MultiplicativeGroup<A>

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl<A> Debug for MultiplicativeGroup<A>

where A: Monoid + Debug,

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

Formats the value using the given formatter.

impl<A> Domain for MultiplicativeGroup<A>

where A: Monoid,

type Elem = <A as Domain>::Elem

The type of the elements of this domain.

fn contains(&self, elem: &Self::Elem) -> bool

Checks if the given object is a member of the domain.

fn equals(&self, elem1: &Self::Elem, elem2: &Self::Elem) -> bool

Checks if the given objects represent the same element of the set.

impl<A> Group for MultiplicativeGroup<A>

where A: Monoid,

fn inv(&self, elem: &Self::Elem) -> Self::Elem

Returns the inverse of the given element element.

fn power(&self, num: isize, elem: &Self::Elem) -> Self::Elem

Returns the power of the given element using the square and multiply method.

impl<A> Monoid for MultiplicativeGroup<A>

where A: Monoid,

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

The multiplicative identity element of the ring.

fn is_one(&self, elem: &Self::Elem) -> bool

Checks if the given element is the multiplicative identity.

fn try_inv(&self, elem: &Self::Elem) -> Option<Self::Elem>

Calculates the multiplicative inverse of the given element if it exists.

fn invertible(&self, _elem: &Self::Elem) -> bool

Returns true if the given element has a multiplicative inverse.

impl<A> Semigroup for MultiplicativeGroup<A>

where A: Monoid,

fn mul(&self, elem1: &Self::Elem, elem2: &Self::Elem) -> Self::Elem

The multiplicative product of the given elements.

fn mul_assign(&self, elem1: &mut Self::Elem, elem2: &Self::Elem)

The first element is multiplied with the second one in place.

fn square(&self, elem: &mut Self::Elem)

Squares the given element in place.