Struct Gf 

pub struct Gf<const P: u64>(/* private fields */);

An element of GF(P) for a prime P fixed at compile time.

Implementations

impl<const P: u64> Gf<P>

pub const fn new(v: u64) -> Gf<P>

pub const fn from_i64(x: i64) -> Gf<P>

pub const fn value(self) -> u64

pub const fn modulus(self) -> u64

Trait Implementations

impl<const P: u64> Add for Gf<P>

type Output = Gf<P>

The resulting type after applying the + operator.

fn add(self, o: Gf<P>) -> Gf<P>

Performs the + operation.

impl<const P: u64> Clone for Gf<P>

fn clone(&self) -> Gf<P>

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl<const P: u64> Copy for Gf<P>

impl<const P: u64> Debug for Gf<P>

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

Formats the value using the given formatter.

impl<const P: u64> Default for Gf<P>

fn default() -> Gf<P>

Returns the “default value” for a type.

impl<const P: u64> Display for Gf<P>

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

Formats the value using the given formatter.

impl<const P: u64> Div for Gf<P>

type Output = Gf<P>

The resulting type after applying the / operator.

fn div(self, o: Gf<P>) -> Gf<P>

Performs the / operation.

impl<const P: u64> Eq for Gf<P>

impl<const P: u64> F4Field for PrimeField<P>

fn echelonize_traced( pivots: &Reducers<Self>, rows: &[SparseRow<Self>], ncols: usize, ) -> (Vec<SparseRow<Self>>, Vec<usize>)

Echelon form and indices of independent input rows, used when learning a trace.

fn echelonize( pivots: &Reducers<Self>, rows: &[SparseRow<Self>], ncols: usize, ) -> Vec<SparseRow<Self>>

Reduce rows modulo the monic pivots (distinct leading columns), then echelonize and interreduce the remainders, returning the nonzero monic rows.

fn reduce_rows( pivots: &Reducers<Self>, rows: &[SparseRow<Self>], ncols: usize, ) -> Vec<SparseRow<Self>>

Fully reduce each row modulo the monic pivots (distinct leading columns).

fn modular( _polynomials: &[Polynomial<Self>], _canonicalize: bool, ) -> Option<Result<Vec<Polynomial<Self>>, GroebnerError>>

Optional multi-modular backend. Return None to use direct F4.

impl<const P: u64> From<i32> for Gf<P>

fn from(x: i32) -> Gf<P>

Converts to this type from the input type.

impl<const P: u64> From<u32> for Gf<P>

fn from(v: u32) -> Gf<P>

Converts to this type from the input type.

impl<const P: u64> From<u64> for Gf<P>

fn from(v: u64) -> Gf<P>

Converts to this type from the input type.

impl<const P: u64> FromStr for Gf<P>

Reduces as it reads, so any number of digits is accepted.

type Err = ParseFpError

The associated error which can be returned from parsing.

fn from_str(s: &str) -> Result<Gf<P>, ParseFpError>

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

impl<const P: u64> Hash for Gf<P>

fn hash<__H>(&self, state: &mut __H)

where __H: Hasher,

Feeds this value into the given Hasher.

fn hash_slice<H>(data: &[Self], state: &mut H)

where H: Hasher, Self: Sized,

Feeds a slice of this type into the given Hasher.

impl<const P: u64> Modular for Gf<P>

fn modulus(&self) -> u64

The prime, or 0 for a constant not yet bound to one.

fn residue(&self) -> u64

The stored residue; a signed integer in two’s complement while unbound.

fn from_residue(v: u64, _: u64) -> Gf<P>

fn residue_mod(&self, p: u64) -> u64

The residue in [0, p), binding an unbound constant to p.

impl<const P: u64> Mul for Gf<P>

type Output = Gf<P>

The resulting type after applying the * operator.

fn mul(self, o: Gf<P>) -> Gf<P>

Performs the * operation.

impl<const P: u64> Neg for Gf<P>

type Output = Gf<P>

The resulting type after applying the - operator.

fn neg(self) -> Gf<P>

Performs the unary - operation.

impl<const P: u64> One for Gf<P>

fn one() -> Gf<P>

Returns the multiplicative identity element of Self, 1.

fn set_one(&mut self)

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

fn is_one(&self) -> bool

where Self: PartialEq,

Returns true if self is equal to the multiplicative identity.

impl<const P: u64> Ord for Gf<P>

fn cmp(&self, other: &Gf<P>) -> 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.

fn clamp_to<R>(self, range: R) -> Self

where Self: Sized, R: ClampBounds<Self>,

🔬This is a nightly-only experimental API. (clamp_to)

Restrict a value to a certain range.

impl<const P: u64> ParseCoefficient for PrimeField<P>

fn parse_coefficient( numerator: &str, denominator: Option<&str>, _modulus: Option<u64>, ) -> Result<Self, ParsePolynomialError>

fn parameter_power(_exponent: u32) -> Option<Self>

The ring parameter raised to exponent, for fields with a parameter.

fn parameter(index: usize, count: usize) -> Option<Self>

Parameter index of count, for fields with parameters. The default is Self::parameter_power for a single parameter.

fn format_coefficient_in(&self, parameters: &[String]) -> String

Text for this coefficient as a factor of a term, with the parameters named parameters.

fn format_coefficient_latex_in(&self, parameters: &[String]) -> String

LaTeX for this coefficient, with the parameters already in LaTeX.

fn format_coefficient(&self, _parameter: &str) -> String

Text for this coefficient as a factor of a term, with the parameter named parameter.

fn format_coefficient_latex(&self, parameter: &str) -> String

fn minus_one() -> Self

fn bind_modulus(self, _modulus: Option<u64>) -> Self

impl<const P: u64> PartialEq for Gf<P>

fn eq(&self, other: &Gf<P>) -> bool

Equality operator ==.

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

Inequality operator !=.

impl<const P: u64> PartialOrd for Gf<P>

fn partial_cmp(&self, other: &Gf<P>) -> 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<const P: u64> StructuralPartialEq for Gf<P>

impl<const P: u64> Sub for Gf<P>

type Output = Gf<P>

The resulting type after applying the - operator.

fn sub(self, o: Gf<P>) -> Gf<P>

Performs the - operation.

impl<const P: u64> Zero for Gf<P>

fn zero() -> Gf<P>

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.