Struct FF 

pub struct FF<const p: i32>(/* private fields */);

An element of 𝔽_p, stored as a representative in 0 .. p.

Implementations

impl<const p: i32> FF<p>

pub fn new(a: i32) -> Self

pub fn rep(&self) -> &i32

Trait Implementations

impl<const p: i32> Add for FF<p>

type Output = FF<p>

The resulting type after applying the + operator.

fn add(self, rhs: FF<p>) -> Self::Output

Performs the + operation.

impl<const p: i32> Add<&FF<p>> for &FF<p>

type Output = FF<p>

The resulting type after applying the + operator.

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

Performs the + operation.

impl<const p: i32> Add<&FF<p>> for FF<p>

type Output = FF<p>

The resulting type after applying the + operator.

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

Performs the + operation.

impl<const p: i32> Add<FF<p>> for &FF<p>

type Output = FF<p>

The resulting type after applying the + operator.

fn add(self, rhs: FF<p>) -> Self::Output

Performs the + operation.

impl<const p: i32> AddAssign for FF<p>

fn add_assign(&mut self, rhs: FF<p>)

Performs the += operation.

impl<const p: i32> AddAssign<&FF<p>> for FF<p>

fn add_assign(&mut self, rhs: &FF<p>)

Performs the += operation.

impl<const p: i32> AddGrp for FF<p>

impl<const p: i32> AddGrpOps for FF<p>

impl<const p: i32> AddGrpOps<FF<p>> for &FF<p>

impl<const p: i32> AddMon for FF<p>

fn sum<A, I>(itr: I) -> Self

where Self: AddAssign<A>, I: IntoIterator<Item = A>,

Sum an iterator into Self, folding with +=.

impl<const p: i32> AddMonOps for FF<p>

impl<const p: i32> AddMonOps<FF<p>> for &FF<p>

impl<const p: i32> Clone for FF<p>

fn clone(&self) -> FF<p>

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl<const p: i32> Copy for FF<p>

impl<const p: i32> Debug for FF<p>

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

Formats the value using the given formatter.

impl<const p: i32> Default for FF<p>

fn default() -> FF<p>

Returns the “default value” for a type.

impl<const p: i32> Display for FF<p>

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

Formats the value using the given formatter.

impl<const p: i32> Div for FF<p>

type Output = FF<p>

The resulting type after applying the / operator.

fn div(self, rhs: FF<p>) -> Self::Output

Performs the / operation.

impl<const p: i32> Div<&FF<p>> for &FF<p>

type Output = FF<p>

The resulting type after applying the / operator.

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

Performs the / operation.

impl<const p: i32> Div<&FF<p>> for FF<p>

type Output = FF<p>

The resulting type after applying the / operator.

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

Performs the / operation.

impl<const p: i32> Div<FF<p>> for &FF<p>

type Output = FF<p>

The resulting type after applying the / operator.

fn div(self, rhs: FF<p>) -> Self::Output

Performs the / operation.

impl<const p: i32> DivAssign for FF<p>

fn div_assign(&mut self, rhs: FF<p>)

Performs the /= operation.

impl<const p: i32> DivAssign<&FF<p>> for FF<p>

fn div_assign(&mut self, rhs: &FF<p>)

Performs the /= operation.

impl<const p: i32> Eq for FF<p>

impl<const p: i32> EucRing for FF<p>

fn divides(&self, y: &Self) -> bool

true iff self divides y (and self ≠ 0).

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

Greatest common divisor, returned in normalized form.

fn gcdx(x: &Self, y: &Self) -> (Self, Self, Self)

Extended gcd: returns (d, s, t) such that d = gcd(x, y) = s·x + t·y, with d normalized.

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

Least common multiple, returned in normalized form.

impl<const p: i32> EucRingOps for FF<p>

impl<const p: i32> EucRingOps<FF<p>> for &FF<p>

impl<const p: i32> Field for FF<p>

impl<const p: i32> FieldOps for FF<p>

impl<const p: i32> FieldOps<FF<p>> for &FF<p>

impl<const p: i32> From<i32> for FF<p>

fn from(a: i32) -> Self

Converts to this type from the input type.

impl<const p: i32> FromStr for FF<p>

type Err = ParseErr

The associated error which can be returned from parsing.

fn from_str(s: &str) -> Result<Self, Self::Err>

Parses a string s to return a value of this type.

impl<const p: i32> MathType for FF<p>

fn math_symbol() -> String

impl<const p: i32> Mon for FF<p>

fn product<A, I>(itr: I) -> Self

where Self: MulAssign<A>, I: IntoIterator<Item = A>,

Multiply an iterator of factors into Self, folding with *=.

impl<const p: i32> MonOps for FF<p>

impl<const p: i32> MonOps<FF<p>> for &FF<p>

impl<const p: i32> Mul for FF<p>

type Output = FF<p>

The resulting type after applying the * operator.

fn mul(self, rhs: FF<p>) -> Self::Output

Performs the * operation.

impl<const p: i32> Mul<&FF<p>> for &FF<p>

type Output = FF<p>

The resulting type after applying the * operator.

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

Performs the * operation.

impl<const p: i32> Mul<&FF<p>> for FF<p>

type Output = FF<p>

The resulting type after applying the * operator.

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

Performs the * operation.

impl<const p: i32> Mul<FF<p>> for &FF<p>

type Output = FF<p>

The resulting type after applying the * operator.

fn mul(self, rhs: FF<p>) -> Self::Output

Performs the * operation.

impl<const p: i32> MulAssign for FF<p>

fn mul_assign(&mut self, rhs: FF<p>)

Performs the *= operation.

impl<const p: i32> MulAssign<&FF<p>> for FF<p>

fn mul_assign(&mut self, rhs: &FF<p>)

Performs the *= operation.

impl<const p: i32> Neg for FF<p>

type Output = FF<p>

The resulting type after applying the - operator.

fn neg(self) -> Self::Output

Performs the unary - operation.

impl<const p: i32> Neg for &FF<p>

type Output = FF<p>

The resulting type after applying the - operator.

fn neg(self) -> Self::Output

Performs the unary - operation.

impl<const p: i32> One for FF<p>

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<const p: i32> PartialEq for FF<p>

fn eq(&self, other: &FF<p>) -> bool

Equality operator ==.

fn ne(&self, other: &Rhs) -> bool

Inequality operator !=.

impl<const p: i32> Rem for FF<p>

type Output = FF<p>

The resulting type after applying the % operator.

fn rem(self, rhs: FF<p>) -> Self::Output

Performs the % operation.

impl<const p: i32> Rem<&FF<p>> for &FF<p>

type Output = FF<p>

The resulting type after applying the % operator.

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

Performs the % operation.

impl<const p: i32> Rem<&FF<p>> for FF<p>

type Output = FF<p>

The resulting type after applying the % operator.

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

Performs the % operation.

impl<const p: i32> Rem<FF<p>> for &FF<p>

type Output = FF<p>

The resulting type after applying the % operator.

fn rem(self, rhs: FF<p>) -> Self::Output

Performs the % operation.

impl<const p: i32> RemAssign for FF<p>

fn rem_assign(&mut self, rhs: FF<p>)

Performs the %= operation.

impl<const p: i32> RemAssign<&FF<p>> for FF<p>

fn rem_assign(&mut self, rhs: &FF<p>)

Performs the %= operation.

impl<const p: i32> Ring for FF<p>

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

Multiplicative inverse, if this element is a unit; otherwise None.

fn is_unit(&self) -> bool

true iff this element is a unit (has a multiplicative inverse).

fn normalizing_unit(&self) -> Self

A unit u such that self * u is the chosen canonical associate of self.

fn from_sign(s: Sign) -> Self

+1 if s is positive, -1 otherwise.

fn normalized(&self) -> Self

The canonical associate of self (i.e. self * self.normalizing_unit()).

fn into_normalized(self) -> Self

Like normalized, but consuming.

fn is_pm_one(&self) -> bool

true iff self is +1 or -1.

fn c_weight(&self) -> f64

Heuristic cost of working with this element, used by chain-reduction pivot selection. Default: 0.0 for zero, 1.0 otherwise.

impl<const p: i32> RingOps for FF<p>

impl<const p: i32> RingOps<FF<p>> for &FF<p>

impl<const p: i32> StructuralPartialEq for FF<p>

impl<const p: i32> Sub for FF<p>

type Output = FF<p>

The resulting type after applying the - operator.

fn sub(self, rhs: FF<p>) -> Self::Output

Performs the - operation.

impl<const p: i32> Sub<&FF<p>> for &FF<p>

type Output = FF<p>

The resulting type after applying the - operator.

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

Performs the - operation.

impl<const p: i32> Sub<&FF<p>> for FF<p>

type Output = FF<p>

The resulting type after applying the - operator.

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

Performs the - operation.

impl<const p: i32> Sub<FF<p>> for &FF<p>

type Output = FF<p>

The resulting type after applying the - operator.

fn sub(self, rhs: FF<p>) -> Self::Output

Performs the - operation.

impl<const p: i32> SubAssign for FF<p>

fn sub_assign(&mut self, rhs: FF<p>)

Performs the -= operation.

impl<const p: i32> SubAssign<&FF<p>> for FF<p>

fn sub_assign(&mut self, rhs: &FF<p>)

Performs the -= operation.

impl<const p: i32> TeX for FF<p>

fn tex_math_symbol() -> String

fn tex_string(&self) -> String

impl<const p: i32> Zero for FF<p>

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.