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MultivariateRing

primitives::algebra::multivariate_ring

Struct MultivariateRing 

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pub struct MultivariateRing<F: FieldExtension, M: Positive, Form> { /* private fields */ }
Expand description

An element P(X_0, ..., X_{N-1}) of the multivariate polynomial ring with N variables.

The polynomial can be either in coefficient or in evaluation form, given by Form parameter. The number of coefficients/evaluations is M = 2 ^ N.

In coefficient representation data are the coefficients of the polynomial: \sum_{i=0..2^N-1} c_i * \Prod_{j=0..N-1} X_j ^ bin(i)_j bin(i) is the binary-decomposition of i (LSB first). For example for N=2 the 2-variate polynomial is c_0 + c_1 . X_0 + c_2 . X_1 + c_3 . X_0 . X_1 and data = [c_0, c_1, c_2, c_3].

In evaluation representation data are the evaluations: e_i = P(bin_signed(i)) bin_signed(i) is the signed binary-decomposition of i (LSB first). For example for N=2 the evaluations are: - e_0 = P(-1, -1) - e_1 = P(-1, 1) - e_2 = P( 1, -1) - e_3 = P( 1, 1) and data = [e_0, e_1, e_2, e_3]

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impl<F: FieldExtension, M: Positive + PowerOfTwo, Form> MultivariateRing<F, M, Form>

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pub fn new(data: SubfieldElements<F, M>) -> Self

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pub fn random(rng: impl CryptoRngCore) -> Self

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pub fn data(&self) -> &SubfieldElements<F, M>

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pub fn into_data(self) -> SubfieldElements<F, M>

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impl<F: FieldExtension, M: Positive + PowerOfTwo> MultivariateRing<F, M, Coefficient>

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pub fn to_eval_repr(self) -> MultivariateRing<F, M, Evaluation>

Transform polynomial from coefficient representation to evaluation representation using the Walsh-Hadamard transform.

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pub fn nb_coefs(&self) -> usize

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impl<F: FieldExtension, M: Positive + PowerOfTwo> MultivariateRing<F, M, Evaluation>

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pub fn new_from_sparse_coef( coefs: impl IntoIterator<Item = (usize, SubfieldElement<F>)>, ) -> Self

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pub fn from_coeffs(coefs: SubfieldElements<F, M>) -> Self

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pub fn square(&self) -> Self

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pub fn nb_evals(&self) -> usize

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impl<F: FieldExtension, M: Positive + PowerOfTwo> Add for MultivariateRing<F, M, Evaluation>

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type Output = MultivariateRing<F, M, Evaluation>

The resulting type after applying the + operator.
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fn add(self, rhs: Self) -> Self::Output

Performs the + operation. Read more
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impl<F: FieldExtension, M: Positive> AddAssign for MultivariateRing<F, M, Evaluation>

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fn add_assign(&mut self, rhs: Self)

Performs the += operation. Read more
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impl<F: Clone + FieldExtension, M: Clone + Positive, Form: Clone> Clone for MultivariateRing<F, M, Form>

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fn clone(&self) -> MultivariateRing<F, M, Form>

Returns a duplicate of the value. Read more
1.0.0 (const: unstable) · Source§

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

Performs copy-assignment from source. Read more
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impl<F: Debug + FieldExtension, M: Debug + Positive, Form: Debug> Debug for MultivariateRing<F, M, Form>

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

Formats the value using the given formatter. Read more
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impl<F: Default + FieldExtension, M: Default + Positive, Form: Default> Default for MultivariateRing<F, M, Form>

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fn default() -> MultivariateRing<F, M, Form>

Returns the “default value” for a type. Read more
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impl<F: FieldExtension, M: Positive + PowerOfTwo> Mul for MultivariateRing<F, M, Evaluation>

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type Output = MultivariateRing<F, M, Evaluation>

The resulting type after applying the * operator.
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fn mul(self, rhs: MultivariateRing<F, M, Evaluation>) -> Self::Output

Performs the * operation. Read more
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impl<F: FieldExtension, M: Positive + PowerOfTwo> Mul<&MultivariateRing<F, M, Evaluation>> for MultivariateRing<F, M, Evaluation>

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type Output = MultivariateRing<F, M, Evaluation>

The resulting type after applying the * operator.
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fn mul(self, rhs: &MultivariateRing<F, M, Evaluation>) -> Self::Output

Performs the * operation. Read more
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impl<F: FieldExtension, M: Positive + PowerOfTwo> Mul<&MultivariateRing<F, M, Evaluation>> for &MultivariateRing<F, M, Evaluation>
where MultivariateRing<F, M, Evaluation>: Clone,

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type Output = MultivariateRing<F, M, Evaluation>

The resulting type after applying the * operator.
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fn mul(self, rhs: &MultivariateRing<F, M, Evaluation>) -> Self::Output

Performs the * operation. Read more
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impl<F: FieldExtension, M: Positive + PowerOfTwo> Mul<MultivariateRing<F, M, Evaluation>> for &MultivariateRing<F, M, Evaluation>
where MultivariateRing<F, M, Evaluation>: Clone,

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type Output = MultivariateRing<F, M, Evaluation>

The resulting type after applying the * operator.
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fn mul(self, rhs: MultivariateRing<F, M, Evaluation>) -> Self::Output

Performs the * operation. Read more
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impl<F: PartialEq + FieldExtension, M: PartialEq + Positive, Form: PartialEq> PartialEq for MultivariateRing<F, M, Form>

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fn eq(&self, other: &MultivariateRing<F, M, Form>) -> bool

Tests for self and other values to be equal, and is used by ==.
1.0.0 (const: unstable) · Source§

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

Tests for !=. The default implementation is almost always sufficient, and should not be overridden without very good reason.
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impl<F: FieldExtension, M: Positive, Form> StructuralPartialEq for MultivariateRing<F, M, Form>

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impl<F: FieldExtension, M: Positive + PowerOfTwo> Sum for MultivariateRing<F, M, Evaluation>

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

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

Auto Trait Implementations§

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impl<F, M, Form> Freeze for MultivariateRing<F, M, Form>

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impl<F, M, Form> RefUnwindSafe for MultivariateRing<F, M, Form>
where Form: RefUnwindSafe, <F as FieldExtension>::Subfield: RefUnwindSafe,

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impl<F, M, Form> Send for MultivariateRing<F, M, Form>
where Form: Send,

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impl<F, M, Form> Sync for MultivariateRing<F, M, Form>
where Form: Sync,

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impl<F, M, Form> Unpin for MultivariateRing<F, M, Form>
where Form: Unpin,

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impl<F, M, Form> UnsafeUnpin for MultivariateRing<F, M, Form>

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impl<F, M, Form> UnwindSafe for MultivariateRing<F, M, Form>
where Form: UnwindSafe, <F as FieldExtension>::Subfield: UnwindSafe,

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where T: 'static + ?Sized,

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