Enum SymbolicExpression

pub enum SymbolicExpression<F> {
    Variable(SymbolicVariable<F>),
    IsFirstRow,
    IsLastRow,
    IsTransition,
    Constant(F),
    Add {
        x: Rc<Self>,
        y: Rc<Self>,
        degree_multiple: usize,
    },
    Sub {
        x: Rc<Self>,
        y: Rc<Self>,
        degree_multiple: usize,
    },
    Neg {
        x: Rc<Self>,
        degree_multiple: usize,
    },
    Mul {
        x: Rc<Self>,
        y: Rc<Self>,
        degree_multiple: usize,
    },
}

An expression over SymbolicVariables.

Variants

Variable(SymbolicVariable<F>)

IsFirstRow

IsLastRow

IsTransition

Constant(F)

Add

Fields

x: Rc<Self>

y: Rc<Self>

degree_multiple: usize

Sub

Fields

x: Rc<Self>

y: Rc<Self>

degree_multiple: usize

Neg

Fields

x: Rc<Self>

degree_multiple: usize

Mul

Fields

x: Rc<Self>

y: Rc<Self>

degree_multiple: usize

Implementations

impl<F> SymbolicExpression<F>

pub const fn degree_multiple(&self) -> usize

Returns the multiple of n (the trace length) in this expression’s degree.

Trait Implementations

impl<F: Field, T> Add<T> for SymbolicExpression<F>

where T: Into<Self>,

type Output = SymbolicExpression<F>

The resulting type after applying the + operator.

fn add(self, rhs: T) -> Self

Performs the + operation.

impl<F: Field, T> AddAssign<T> for SymbolicExpression<F>

where T: Into<Self>,

fn add_assign(&mut self, rhs: T)

Performs the += operation.

impl<F: Clone> Clone for SymbolicExpression<F>

fn clone(&self) -> SymbolicExpression<F>

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl<F: Debug> Debug for SymbolicExpression<F>

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

Formats the value using the given formatter.

impl<F: Field> Default for SymbolicExpression<F>

fn default() -> Self

Returns the “default value” for a type.

impl<F: Field> From<F> for SymbolicExpression<F>

fn from(value: F) -> Self

Converts to this type from the input type.

impl<F: Field> From<SymbolicVariable<F>> for SymbolicExpression<F>

fn from(value: SymbolicVariable<F>) -> Self

Converts to this type from the input type.

impl<F: Field + InjectiveMonomial<N>, const N: u64> InjectiveMonomial<N> for SymbolicExpression<F>

fn injective_exp_n(&self) -> Self

Compute x -> x^n for a given n > 1 such that this map is injective.

impl<F: Field, T: Into<Self>> Mul<T> for SymbolicExpression<F>

type Output = SymbolicExpression<F>

The resulting type after applying the * operator.

fn mul(self, rhs: T) -> Self

Performs the * operation.

impl<F: Field, T> MulAssign<T> for SymbolicExpression<F>

where T: Into<Self>,

fn mul_assign(&mut self, rhs: T)

Performs the *= operation.

impl<F: Field> Neg for SymbolicExpression<F>

type Output = SymbolicExpression<F>

The resulting type after applying the - operator.

fn neg(self) -> Self

Performs the unary - operation.

impl<F: Field> PrimeCharacteristicRing for SymbolicExpression<F>

const ZERO: Self

The additive identity of the ring.

const ONE: Self

The multiplicative identity of the ring.

const TWO: Self

The element in the ring given by ONE + ONE.

const NEG_ONE: Self

The element in the ring given by -ONE.

type PrimeSubfield = <F as PrimeCharacteristicRing>::PrimeSubfield

The field ℤ/p where the characteristic of this ring is p.

fn from_prime_subfield(f: Self::PrimeSubfield) -> Self

Embed an element of the prime field ℤ/p into the ring R.

fn from_bool(b: bool) -> Self

Return Self::ONE if b is true and Self::ZERO if b is false.

fn from_u8(int: u8) -> Self

Given an integer r, return the sum of r copies of ONE:

fn from_u16(int: u16) -> Self

Given an integer r, return the sum of r copies of ONE:

fn from_u32(int: u32) -> Self

Given an integer r, return the sum of r copies of ONE:

fn from_u64(int: u64) -> Self

Given an integer r, return the sum of r copies of ONE:

fn from_u128(int: u128) -> Self

Given an integer r, return the sum of r copies of ONE:

fn from_usize(int: usize) -> Self

Given an integer r, return the sum of r copies of ONE:

fn from_i8(int: i8) -> Self

Given an integer r, return the sum of r copies of ONE:

fn from_i16(int: i16) -> Self

Given an integer r, return the sum of r copies of ONE:

fn from_i32(int: i32) -> Self

Given an integer r, return the sum of r copies of ONE:

fn from_i64(int: i64) -> Self

Given an integer r, return the sum of r copies of ONE:

fn from_i128(int: i128) -> Self

Given an integer r, return the sum of r copies of ONE:

fn from_isize(int: isize) -> Self

Given an integer r, return the sum of r copies of ONE:

fn double(&self) -> Self

The elementary function double(a) = 2*a.

fn square(&self) -> Self

The elementary function square(a) = a^2.

fn cube(&self) -> Self

The elementary function cube(a) = a^3.

fn xor(&self, y: &Self) -> Self

Computes the arithmetic generalization of boolean xor.

fn xor3(&self, y: &Self, z: &Self) -> Self

Computes the arithmetic generalization of a triple xor.

fn andn(&self, y: &Self) -> Self

Computes the arithmetic generalization of andnot.

fn bool_check(&self) -> Self

The vanishing polynomial for boolean values: x * (1 - x).

fn exp_u64(&self, power: u64) -> Self

Exponentiation by a u64 power.

fn exp_const_u64<const POWER: u64>(&self) -> Self

Exponentiation by a small constant power.

fn exp_power_of_2(&self, power_log: usize) -> Self

The elementary function exp_power_of_2(a, power_log) = a^{2^power_log}.

fn mul_2exp_u64(&self, exp: u64) -> Self

The elementary function mul_2exp_u64(a, exp) = a * 2^{exp}.

fn powers(&self) -> Powers<Self>

Construct an iterator which returns powers of self: self^0, self^1, self^2, ....

fn shifted_powers(&self, start: Self) -> Powers<Self>

Construct an iterator which returns powers of self shifted by start: start, start*self^1, start*self^2, ....

fn dot_product<const N: usize>(u: &[Self; N], v: &[Self; N]) -> Self

Compute the dot product of two vectors.

fn sum_array<const N: usize>(input: &[Self]) -> Self

Compute the sum of a slice of elements whose length is a compile time constant.

fn zero_vec(len: usize) -> Vec<Self>

Allocates a vector of zero elements of length len. Many operating systems zero pages before assigning them to a userspace process. In that case, our process should not need to write zeros, which would be redundant. However, the compiler may not always recognize this.

impl<F: Field, T: Into<Self>> Product<T> for SymbolicExpression<F>

fn product<I: Iterator<Item = T>>(iter: I) -> Self

Takes an iterator and generates Self from the elements by multiplying the items.

impl<F: Field, T: Into<Self>> Sub<T> for SymbolicExpression<F>

type Output = SymbolicExpression<F>

The resulting type after applying the - operator.

fn sub(self, rhs: T) -> Self

Performs the - operation.

impl<F: Field, T> SubAssign<T> for SymbolicExpression<F>

where T: Into<Self>,

fn sub_assign(&mut self, rhs: T)

Performs the -= operation.

impl<F: Field, T> Sum<T> for SymbolicExpression<F>

where T: Into<Self>,

fn sum<I: Iterator<Item = T>>(iter: I) -> Self

Takes an iterator and generates Self from the elements by “summing up” the items.

impl<F: Field> Algebra<F> for SymbolicExpression<F>

impl<F: Field> Algebra<SymbolicVariable<F>> for SymbolicExpression<F>