Struct abstalg::TwoElementAlgebra

pub struct TwoElementAlgebra();

Trait Implementations

impl AbelianGroup for TwoElementAlgebra

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

The additive identity element of the ring.

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

Checks if the given element is the additive identity of the ring.

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

The additive inverse of the given element.

fn neg_assign(&self, _elem: &mut Self::Elem)

The element is changed to its additive inverse.

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

The additive sum of the given elements

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

The second element is added to the first one.

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

Doubles the given element in place.

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

The difference of the given elements.

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

The second element is subtracted from the first one.

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

Returns an integer multiple of the given element.

impl BooleanAlgebra for TwoElementAlgebra

fn not(&self, elem: &Self::Elem) -> Self::Elem

Returns the complement (logical negation) of the given element.

impl BoundedOrder for TwoElementAlgebra

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

Returns the largest element of the lattice.

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

Returns the smallest element of the lattice.

impl Clone for TwoElementAlgebra

fn clone(&self) -> TwoElementAlgebra

Returns a copy of the value.

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

Performs copy-assignment from source.

impl Debug for TwoElementAlgebra

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

Formats the value using the given formatter.

impl Domain for TwoElementAlgebra

type Elem = bool

The type of the elements of this domain.

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

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

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

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

impl Field for TwoElementAlgebra

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

Returns the multiplicative inverse of the given non-zero element. This method panics for the zero element.

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

Returns the quotient of the two elements in the field. This method panics if the second element is zero.

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

Returns an integer power of the given element.

impl Lattice for TwoElementAlgebra

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

Returns the largest element that is less than or equal to both given elements.

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

Returns the smallest element that is greater than or equal to both given elements.

impl Monoid for TwoElementAlgebra

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 PartialOrder for TwoElementAlgebra

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

Returns true if the first element is less than or equal to the second one in the partial order.

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

Returns true if the first element is strictly less than the second one.

fn comparable(&self, _elem1: &Self::Elem, _elem2: &Self::Elem) -> bool

Returns true if one of the elements is less than or equal to the other.

impl Semigroup for TwoElementAlgebra

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.

impl UnitaryRing for TwoElementAlgebra

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

Returns the integer multiple of the one element in the ring.

impl DistributiveLattice for TwoElementAlgebra