Struct Integer 

pub struct Integer {
    pub val: Integer,
}

Fields

val: Integer

Trait Implementations

impl<'a> Add<&'a Integer> for Integer

type Output = Integer

The resulting type after applying the + operator.

fn add(self, rhs: &Self) -> Self::Output

Performs the + operation.

impl<'a, B> Add<B> for &'a Integer

where Integer: Add<B, Output = Integer>,

type Output = Integer

The resulting type after applying the + operator.

fn add(self, rhs: B) -> Self::Output

Performs the + operation.

impl<B> Add<B> for Integer

where Integer: Add<B, Output = Integer>,

type Output = Integer

The resulting type after applying the + operator.

fn add(self, rhs: B) -> Self::Output

Performs the + operation.

impl<'a> Add<Integer> for &'a Integer

type Output = Integer

The resulting type after applying the + operator.

fn add(self, rhs: Integer) -> Self::Output

Performs the + operation.

impl<'a> Add for &'a Integer

type Output = Integer

The resulting type after applying the + operator.

fn add(self, rhs: &'a Integer) -> Self::Output

Performs the + operation.

impl Add for Integer

type Output = Integer

The resulting type after applying the + operator.

fn add(self, rhs: Integer) -> Self::Output

Performs the + operation.

impl<'a> AddAssign<&'a Integer> for Integer

fn add_assign(&mut self, rhs: &Self)

Performs the += operation.

impl<B> AddAssign<B> for Integer

where Integer: AddAssign<B>,

fn add_assign(&mut self, rhs: B)

Performs the += operation.

impl AddAssign for Integer

fn add_assign(&mut self, rhs: Self)

Performs the += operation.

impl ArchimedeanDiv for Integer

fn embed_nat<N: Natural>(n: N) -> Self

Maps a natural number into this structure preserving addition and using the relevant canonical representation

fn div_arch(self, rhs: Self) -> Self

the unique integer n such that n*rhs <= self and (n+1)*rhs > self

fn rem_arch(self, rhs: Self) -> Self

the remaining difference after dividing by rhs (ie. self - self.div_arch(rhs)*rhs)

fn div_alg_arch(self, rhs: Self) -> (Self, Self)

Divides self by rhs with remainder using the archimdean property

impl Bezout for Integer

fn bezout_with_gcd(self, rhs: Self) -> (Self, Self, Self)

Computes the GCD and the bezout coefficients in one function call

fn bezout_coefficients(self, rhs: Self) -> (Self, Self)

Bezout coefficients of a pair of elements

impl CheckedAdd for Integer

fn checked_add(&self, v: &Self) -> Option<Self>

Adds two numbers, checking for overflow. If overflow happens, None is returned.

impl CheckedDiv for Integer

fn checked_div(&self, v: &Self) -> Option<Self>

Divides two numbers, checking for underflow, overflow and division by zero. If any of that happens, None is returned.

impl CheckedMul for Integer

fn checked_mul(&self, v: &Self) -> Option<Self>

Multiplies two numbers, checking for underflow or overflow. If underflow or overflow happens, None is returned.

impl CheckedNeg for Integer

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

Negates a number, returning None for results that can’t be represented, like signed MIN values that can’t be positive, or non-zero unsigned values that can’t be negative.

impl CheckedRem for Integer

fn checked_rem(&self, v: &Self) -> Option<Self>

Finds the remainder of dividing two numbers, checking for underflow, overflow and division by zero. If any of that happens, None is returned.

impl CheckedShl for Integer

fn checked_shl(&self, v: u32) -> Option<Self>

Checked shift left. Computes self << rhs, returning None if rhs is larger than or equal to the number of bits in self.

impl CheckedShr for Integer

fn checked_shr(&self, v: u32) -> Option<Self>

Checked shift right. Computes self >> rhs, returning None if rhs is larger than or equal to the number of bits in self.

impl CheckedSub for Integer

fn checked_sub(&self, v: &Self) -> Option<Self>

Subtracts two numbers, checking for underflow. If underflow happens, None is returned.

impl Clone for Integer

fn clone(&self) -> Integer

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl ComplexSubset for Integer

type Real = Float

type Natural = Integer

type Integer = Integer

fn as_real(self) -> Self::Real

Converts self to a real number, discarding any imaginary component, if complex.

fn as_natural(self) -> Self::Natural

Converts self to a natural number, truncating when necessary.

fn as_integer(self) -> Self::Integer

Converts self to an integer, truncating when necessary.

fn floor(self) -> Self

Rounds the real and imaginary components of self to the closest integer downward

fn ceil(self) -> Self

Rounds the real and imaginary components of self to the closest integer upward

fn round(self) -> Self

Rounds the real and imaginary components of self to the closest integer

fn trunc(self) -> Self

Rounds the real and imaginary components of self by removing the factional parts

fn fract(self) -> Self

Removes the integral parts of the real and imaginary components of self

fn im(self) -> Self

Sets the real component of self to 0

fn re(self) -> Self

Sets the imaginary component of self to 0

fn conj(self) -> Self

The complex conjugate of self

fn modulus_sqrd(self) -> Self

The square of the complex absolute value of self

fn modulus(self) -> Self::Real

The complex absolute value of self

impl Debug for Integer

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

Formats the value using the given formatter.

impl Display for Integer

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

Formats the value using the given formatter.

impl<'a> Div<&'a Integer> for Integer

type Output = Integer

The resulting type after applying the / operator.

fn div(self, rhs: &Self) -> Self::Output

Performs the / operation.

impl<'a, B> Div<B> for &'a Integer

where Integer: Div<B, Output = Integer>,

type Output = Integer

The resulting type after applying the / operator.

fn div(self, rhs: B) -> Self::Output

Performs the / operation.

impl<B> Div<B> for Integer

where Integer: Div<B, Output = Integer>,

type Output = Integer

The resulting type after applying the / operator.

fn div(self, rhs: B) -> Self::Output

Performs the / operation.

impl<'a> Div<Integer> for &'a Integer

type Output = Integer

The resulting type after applying the / operator.

fn div(self, rhs: Integer) -> Self::Output

Performs the / operation.

impl<'a> Div for &'a Integer

type Output = Integer

The resulting type after applying the / operator.

fn div(self, rhs: &'a Integer) -> Self::Output

Performs the / operation.

impl Div for Integer

type Output = Integer

The resulting type after applying the / operator.

fn div(self, rhs: Integer) -> Self::Output

Performs the / operation.

impl<'a> DivAssign<&'a Integer> for Integer

fn div_assign(&mut self, rhs: &Self)

Performs the /= operation.

impl<B> DivAssign<B> for Integer

where Integer: DivAssign<B>,

fn div_assign(&mut self, rhs: B)

Performs the /= operation.

impl DivAssign for Integer

fn div_assign(&mut self, rhs: Self)

Performs the /= operation.

impl Divisibility for Integer

fn divides(self, rhs: Self) -> bool

Determines if there exists an element x such that self*x = rhs

fn divide(self, rhs: Self) -> Option<Self>

Finds an element x such that self*x = rhs if such an element exists

fn unit(&self) -> bool

Determines if this element has a multiplicative inverse

fn inverse(self) -> Option<Self>

Finds this element’s multiplicative inverse if it exists

impl EuclideanDiv for Integer

type Naturals = Integer

The specific type used for the Euclidean Norm

fn euclid_norm(&self) -> Self::Naturals

A measure of the “degree” of a given element.

fn div_euc(self, rhs: Self) -> Self

The quotient from Euclidean division

fn rem_euc(self, rhs: Self) -> Self

The remainder from the Euclidean division

fn div_alg(self, rhs: Self) -> (Self, Self)

Divides a pair of elements with remainder

impl<T> From<T> for Integer

where Integer: From<T>,

fn from(src: T) -> Self

Converts to this type from the input type.

impl FromPrimitive for Integer

fn from_i64(n: i64) -> Option<Self>

Converts an i64 to return an optional value of this type. If the value cannot be represented by this type, then None is returned.

fn from_u64(n: u64) -> Option<Self>

Converts an u64 to return an optional value of this type. If the value cannot be represented by this type, then None is returned.

fn from_isize(n: isize) -> Option<Self>

Converts an isize to return an optional value of this type. If the value cannot be represented by this type, then None is returned.

fn from_i8(n: i8) -> Option<Self>

Converts an i8 to return an optional value of this type. If the value cannot be represented by this type, then None is returned.

fn from_i16(n: i16) -> Option<Self>

Converts an i16 to return an optional value of this type. If the value cannot be represented by this type, then None is returned.

fn from_i32(n: i32) -> Option<Self>

Converts an i32 to return an optional value of this type. If the value cannot be represented by this type, then None is returned.

fn from_i128(n: i128) -> Option<Self>

Converts an i128 to return an optional value of this type. If the value cannot be represented by this type, then None is returned.

fn from_usize(n: usize) -> Option<Self>

Converts a usize to return an optional value of this type. If the value cannot be represented by this type, then None is returned.

fn from_u8(n: u8) -> Option<Self>

Converts an u8 to return an optional value of this type. If the value cannot be represented by this type, then None is returned.

fn from_u16(n: u16) -> Option<Self>

Converts an u16 to return an optional value of this type. If the value cannot be represented by this type, then None is returned.

fn from_u32(n: u32) -> Option<Self>

Converts an u32 to return an optional value of this type. If the value cannot be represented by this type, then None is returned.

fn from_u128(n: u128) -> Option<Self>

Converts an u128 to return an optional value of this type. If the value cannot be represented by this type, then None is returned.

fn from_f32(n: f32) -> Option<Self>

Converts a f32 to return an optional value of this type. If the value cannot be represented by this type, then None is returned.

fn from_f64(n: f64) -> Option<Self>

Converts a f64 to return an optional value of this type. If the value cannot be represented by this type, then None is returned.

impl GCD for Integer

fn gcd(self, rhs: Self) -> Self

Finds the greatest common divisor of two elements

fn lcm(self, rhs: Self) -> Self

Finds the least common multiple of two elements

impl IntegerSubset for Integer

type Signed = Integer

This type’s corresponding signed Integer representation

type Unsigned = Integer

This type’s corresponding unsigned Integer representation

fn as_signed(self) -> Self::Signed

Converts self to a signed integer representation

fn as_unsigned(self) -> Self::Unsigned

Converts self into an unsigned integer representation

fn abs_unsigned(self) -> Self::Unsigned

Takes the absolute value and converts into an unsigned integer representation

fn two() -> Self

A shorthand for 1+1

fn mul_two(self) -> Self

Multiplies by two

fn div_two(self) -> Self

Divides by two

fn even(&self) -> bool

Determines if a number is divisible by two

fn odd(&self) -> bool

Determines if a number is not divisible by two

impl<'a> Mul<&'a Integer> for Integer

type Output = Integer

The resulting type after applying the * operator.

fn mul(self, rhs: &Self) -> Self::Output

Performs the * operation.

impl<'a, B> Mul<B> for &'a Integer

where Integer: Mul<B, Output = Integer>,

type Output = Integer

The resulting type after applying the * operator.

fn mul(self, rhs: B) -> Self::Output

Performs the * operation.

impl<B> Mul<B> for Integer

where Integer: Mul<B, Output = Integer>,

type Output = Integer

The resulting type after applying the * operator.

fn mul(self, rhs: B) -> Self::Output

Performs the * operation.

impl<'a> Mul<Integer> for &'a Integer

type Output = Integer

The resulting type after applying the * operator.

fn mul(self, rhs: Integer) -> Self::Output

Performs the * operation.

impl<'a> Mul for &'a Integer

type Output = Integer

The resulting type after applying the * operator.

fn mul(self, rhs: &'a Integer) -> Self::Output

Performs the * operation.

impl Mul for Integer

type Output = Integer

The resulting type after applying the * operator.

fn mul(self, rhs: Integer) -> Self::Output

Performs the * operation.

impl<'a> MulAssign<&'a Integer> for Integer

fn mul_assign(&mut self, rhs: &Self)

Performs the *= operation.

impl<B> MulAssign<B> for Integer

where Integer: MulAssign<B>,

fn mul_assign(&mut self, rhs: B)

Performs the *= operation.

impl MulAssign for Integer

fn mul_assign(&mut self, rhs: Self)

Performs the *= operation.

impl Neg for Integer

type Output = Integer

The resulting type after applying the - operator.

fn neg(self) -> Self::Output

Performs the unary - operation.

impl One for Integer

fn one() -> Self

Returns the multiplicative identity element of Self, 1.

fn is_one(&self) -> bool

Returns true if self is equal to the multiplicative identity.

fn set_one(&mut self)

Sets self to the multiplicative identity element of Self, 1.

impl Ord for Integer

fn cmp(&self, other: &Integer) -> 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 PartialEq for Integer

fn eq(&self, other: &Integer) -> 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 PartialOrd for Integer

fn partial_cmp(&self, other: &Integer) -> 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 Primality for Integer

fn prime(&self) -> bool

Trial division algorithm

fn irreducible(&self) -> bool

Determines if this element cannot be produced from the product of two other non-invertible elements

impl<'a> Rem<&'a Integer> for Integer

type Output = Integer

The resulting type after applying the % operator.

fn rem(self, rhs: &Self) -> Self::Output

Performs the % operation.

impl<'a, B> Rem<B> for &'a Integer

where Integer: Rem<B, Output = Integer>,

type Output = Integer

The resulting type after applying the % operator.

fn rem(self, rhs: B) -> Self::Output

Performs the % operation.

impl<B> Rem<B> for Integer

where Integer: Rem<B, Output = Integer>,

type Output = Integer

The resulting type after applying the % operator.

fn rem(self, rhs: B) -> Self::Output

Performs the % operation.

impl<'a> Rem<Integer> for &'a Integer

type Output = Integer

The resulting type after applying the % operator.

fn rem(self, rhs: Integer) -> Self::Output

Performs the % operation.

impl<'a> Rem for &'a Integer

type Output = Integer

The resulting type after applying the % operator.

fn rem(self, rhs: &'a Integer) -> Self::Output

Performs the % operation.

impl Rem for Integer

type Output = Integer

The resulting type after applying the % operator.

fn rem(self, rhs: Integer) -> Self::Output

Performs the % operation.

impl<'a> RemAssign<&'a Integer> for Integer

fn rem_assign(&mut self, rhs: &Self)

Performs the %= operation.

impl<B> RemAssign<B> for Integer

where Integer: RemAssign<B>,

fn rem_assign(&mut self, rhs: B)

Performs the %= operation.

impl RemAssign for Integer

fn rem_assign(&mut self, rhs: Self)

Performs the %= operation.

impl<'a, B> Shl<B> for &'a Integer

where Integer: Shl<B, Output = Integer>,

type Output = Integer

The resulting type after applying the << operator.

fn shl(self, rhs: B) -> Self::Output

Performs the << operation.

impl<B> Shl<B> for Integer

where Integer: Shl<B, Output = Integer>,

type Output = Integer

The resulting type after applying the << operator.

fn shl(self, rhs: B) -> Self::Output

Performs the << operation.

impl<B> ShlAssign<B> for Integer

where Integer: ShlAssign<B>,

fn shl_assign(&mut self, rhs: B)

Performs the <<= operation.

impl<'a, B> Shr<B> for &'a Integer

where Integer: Shr<B, Output = Integer>,

type Output = Integer

The resulting type after applying the >> operator.

fn shr(self, rhs: B) -> Self::Output

Performs the >> operation.

impl<B> Shr<B> for Integer

where Integer: Shr<B, Output = Integer>,

type Output = Integer

The resulting type after applying the >> operator.

fn shr(self, rhs: B) -> Self::Output

Performs the >> operation.

impl<B> ShrAssign<B> for Integer

where Integer: ShrAssign<B>,

fn shr_assign(&mut self, rhs: B)

Performs the >>= operation.

impl Sign for Integer

fn signum(self) -> Self

Returns 1 if positive, -1 if negative, or itself (ie. 0 or NaN) if neither

fn abs(self) -> Self

Returns this element’s negative if less than 0 or itself otherwise

impl<'a> Sub<&'a Integer> for Integer

type Output = Integer

The resulting type after applying the - operator.

fn sub(self, rhs: &Self) -> Self::Output

Performs the - operation.

impl<'a, B> Sub<B> for &'a Integer

where Integer: Sub<B, Output = Integer>,

type Output = Integer

The resulting type after applying the - operator.

fn sub(self, rhs: B) -> Self::Output

Performs the - operation.

impl<B> Sub<B> for Integer

where Integer: Sub<B, Output = Integer>,

type Output = Integer

The resulting type after applying the - operator.

fn sub(self, rhs: B) -> Self::Output

Performs the - operation.

impl<'a> Sub<Integer> for &'a Integer

type Output = Integer

The resulting type after applying the - operator.

fn sub(self, rhs: Integer) -> Self::Output

Performs the - operation.

impl<'a> Sub for &'a Integer

type Output = Integer

The resulting type after applying the - operator.

fn sub(self, rhs: &'a Integer) -> Self::Output

Performs the - operation.

impl Sub for Integer

type Output = Integer

The resulting type after applying the - operator.

fn sub(self, rhs: Integer) -> Self::Output

Performs the - operation.

impl<'a> SubAssign<&'a Integer> for Integer

fn sub_assign(&mut self, rhs: &Self)

Performs the -= operation.

impl<B> SubAssign<B> for Integer

where Integer: SubAssign<B>,

fn sub_assign(&mut self, rhs: B)

Performs the -= operation.

impl SubAssign for Integer

fn sub_assign(&mut self, rhs: Self)

Performs the -= operation.

impl ToPrimitive for Integer

fn to_i64(&self) -> Option<i64>

Converts the value of self to an i64. If the value cannot be represented by an i64, then None is returned.

fn to_u64(&self) -> Option<u64>

Converts the value of self to a u64. If the value cannot be represented by a u64, then None is returned.

fn to_isize(&self) -> Option<isize>

Converts the value of self to an isize. If the value cannot be represented by an isize, then None is returned.

fn to_i8(&self) -> Option<i8>

Converts the value of self to an i8. If the value cannot be represented by an i8, then None is returned.

fn to_i16(&self) -> Option<i16>

Converts the value of self to an i16. If the value cannot be represented by an i16, then None is returned.

fn to_i32(&self) -> Option<i32>

Converts the value of self to an i32. If the value cannot be represented by an i32, then None is returned.

fn to_i128(&self) -> Option<i128>

Converts the value of self to an i128. If the value cannot be represented by an i128 (i64 under the default implementation), then None is returned.

fn to_usize(&self) -> Option<usize>

Converts the value of self to a usize. If the value cannot be represented by a usize, then None is returned.

fn to_u8(&self) -> Option<u8>

Converts the value of self to a u8. If the value cannot be represented by a u8, then None is returned.

fn to_u16(&self) -> Option<u16>

Converts the value of self to a u16. If the value cannot be represented by a u16, then None is returned.

fn to_u32(&self) -> Option<u32>

Converts the value of self to a u32. If the value cannot be represented by a u32, then None is returned.

fn to_u128(&self) -> Option<u128>

Converts the value of self to a u128. If the value cannot be represented by a u128 (u64 under the default implementation), then None is returned.

fn to_f32(&self) -> Option<f32>

Converts the value of self to an f32. Overflows may map to positive or negative inifinity, otherwise None is returned if the value cannot be represented by an f32.

fn to_f64(&self) -> Option<f64>

Converts the value of self to an f64. Overflows may map to positive or negative inifinity, otherwise None is returned if the value cannot be represented by an f64.

impl Zero for Integer

fn zero() -> Self

Returns the additive identity element of Self, 0.

fn is_zero(&self) -> bool

Returns true if self is equal to the additive identity.

fn set_zero(&mut self)

Sets self to the additive identity element of Self, 0.

impl AddAssociative for Integer

impl AddCommutative for Integer

impl AddOrdered for Integer

impl ArchimedeanProperty for Integer

impl Distributive for Integer

impl Eq for Integer

impl Integer for Integer

impl MulAssociative for Integer

impl MulCommutative for Integer

impl MulOrdered for Integer

impl Natural for Integer

impl NoZeroDivisors for Integer

impl StructuralPartialEq for Integer

impl UniquelyFactorizable for Integer