Struct abstalg::CheckedInts

pub struct CheckedInts<E> where
    E: PrimInt + Signed + Debug + From<i8> + TryFrom<isize>, { /* private fields */ }

The set of integers whose elements are stored in a primitive signed integer type. This structure is functionally equivalent to the set of all integers, but some operations are going to panic if the mathematical result cannot be represented in the primitive type. The lattice order is the normal total order, which is not bounded.

Trait Implementations

impl<E> AbelianGroup for CheckedInts<E> where
    E: PrimInt + Signed + Debug + From<i8> + TryFrom<isize>, 

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

The additive sum of the given elements

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

The difference of the given elements.

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

Returns an integer multiple of the given element.

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

The element is changed to its additive inverse.

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_assign(&self, elem1: &mut Self::Elem, elem2: &Self::Elem)

The second element is subtracted from the first one.

impl<E: Clone> Clone for CheckedInts<E> where
    E: PrimInt + Signed + Debug + From<i8> + TryFrom<isize>, 

fn clone(&self) -> CheckedInts<E>

Returns a copy of the value.

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

Performs copy-assignment from source.

impl<E: Debug> Debug for CheckedInts<E> where
    E: PrimInt + Signed + Debug + From<i8> + TryFrom<isize>, 

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

Formats the value using the given formatter.

impl<E> Domain for CheckedInts<E> where
    E: PrimInt + Signed + Debug + From<i8> + TryFrom<isize>, 

type Elem = E

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<E> EuclideanDomain for CheckedInts<E> where
    E: PrimInt + Signed + Debug + From<i8> + TryFrom<isize>, 

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

Performs the euclidean division algorithm dividing the first elem with the second one and returning the quotient and the remainder. This method panics if the second element is zero (because there is no unique solution)

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

Returns true if the second element is zero or the first element has zero quotient by the second one. These are the representative elements of the factor ring by the principal ideal generated by the second element.

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

Performs the division just like the quo_rem method would do and returns the quotient. This method panics if the second element is zero.

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

Performs the division just like the quo_rem method would do and returns the remainder. This method panics if the second element is zero.

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

Calculates the greatest common divisor of two elements using the Euclidean algorithm.

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

Calculates the lest common divisor of the two elements.

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

Performs the extended Euclidean algorithm which returns the greatest common divisor, and two elements that multiplied with the inputs gives the greatest common divisor.

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

Checks if the given two elements are relative prime.

impl<E> IntegralDomain for CheckedInts<E> where
    E: PrimInt + Signed + Debug + From<i8> + TryFrom<isize>, 

fn try_div(&self, elem1: &Self::Elem, elem2: &Self::Elem) -> Option<Self::Elem>

Checks if the second element divides the first one and returns the unique quotient if it exists. This method panics if the second element is zero (because there would be no unique solution).

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

We assume, that among all associates of the given elem there is a well defined unique one (non-negative for integers, zero or monic for polynomials). This method returns that representative element.

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

Returns the unique invertible element which is the quotient of the associate representative and the given element. This method panics if the element is zero.

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

Checks if the first element is a multiple of (or divisible by) the second one.

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

Returns true if the two elements are associates (divide each other)

impl<E> Lattice for CheckedInts<E> where
    E: PrimInt + Signed + Debug + From<i8> + TryFrom<isize>, 

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<E> Monoid for CheckedInts<E> where
    E: PrimInt + Signed + Debug + From<i8> + TryFrom<isize>, 

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<E> PartialOrder for CheckedInts<E> where
    E: PrimInt + Signed + Debug + From<i8> + TryFrom<isize>, 

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<E> Semigroup for CheckedInts<E> where
    E: PrimInt + Signed + Debug + From<i8> + TryFrom<isize>, 

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<E> UnitaryRing for CheckedInts<E> where
    E: PrimInt + Signed + Debug + From<i8> + TryFrom<isize>, 

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

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

impl<E> DistributiveLattice for CheckedInts<E> where
    E: PrimInt + Signed + Debug + From<i8> + TryFrom<isize>,