Struct twenty_first::shared_math::mpolynomial::MPolynomial

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pub struct MPolynomial<T: PrimeField> {
    pub variable_count: usize,
    pub coefficients: HashMap<Vec<u64>, T>,
}

Fields

variable_count: usizecoefficients: HashMap<Vec<u64>, T>

Implementations

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pub fn from_constant(element: PFElem, variable_count: usize) -> Self

Returns an MPolynomial instance over variable_count variables that evaluates to element everywhere. I.e. P(x,y..,z) = element

Note that in this encoding P(x,y) == P(x,w) but P(x,y) != P(x,y,z).

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pub fn variables(variable_count: usize, one: PFElem) -> Vec<Self>

Returns a vector of multivariate polynomials that each represent a function of one indeterminate variable to the first power. For example, let p = variables(3, 1.into()) represents the functions

p[0] = $f(x,y,z) = x$
p[1] =$f(x,y,z) = y$
p[2] =$f(x,y,z) = z$

and let p = variables(5, 1.into()) represents the functions

p[0] = $p(a,b,c,d,e) = a$
p[1] = $p(a,b,c,d,e) = b$
p[2] = $p(a,b,c,d,e) = c$
p[3] = $p(a,b,c,d,e) = d$
p[4] = $p(a,b,c,d,e) = e$

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pub fn precalculate_symbolic_exponents(
 mpols: &[Self],
 point: &[Polynomial<PFElem>],
 exponents_memoization: &mut HashMap<Vec<u64>, Polynomial<PFElem>>
) -> Result<(), Box<dyn Error>>

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pub fn evaluate(&self, point: &[PFElem]) -> PFElem

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pub fn extract_exponents_list(
mpols: &[Self]
) -> Result<Vec<Vec<u64>>, Box<dyn Error>>

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pub fn precalculate_scalar_mod_pows(
limit: u64,
point: &[PFElem]
) -> HashMap<(usize, u64), PFElem>

Get a hash map with precalculated values for point[i]^j Only exponents 2 and above are stored.

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pub fn precalculate_scalar_exponents(
 point: &[PFElem],
 precalculated_mod_pows: &HashMap<(usize, u64), PFElem>,
 exponents_list: &[Vec<u64>]
) -> Result<HashMap<Vec<u64>, PFElem>, Box<dyn Error>>

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pub fn evaluate_with_precalculation(
 &self,
 point: &[PFElem],
 intermediate_results: &HashMap<Vec<u64>, PFElem>
) -> PFElem

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pub fn evaluate_symbolic_with_memoization_precalculated(
 &self,
 point: &[Polynomial<PFElem>],
 exponents_memoization: &mut HashMap<Vec<u64>, Polynomial<PFElem>>
) -> Polynomial<PFElem>

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pub fn evaluate_symbolic_with_memoization(
 &self,
 point: &[Polynomial<PFElem>],
 mod_pow_memoization: &mut HashMap<(usize, u64), Polynomial<PFElem>>,
 mul_memoization: &mut HashMap<(Polynomial<PFElem>, (usize, u64)), Polynomial<PFElem>>,
 exponents_memoization: &mut HashMap<Vec<u64>, Polynomial<PFElem>>
) -> Polynomial<PFElem>

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pub fn evaluate_symbolic(
&self,
point: &[Polynomial<PFElem>]
) -> Polynomial<PFElem>

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pub fn lift(
 univariate_polynomial: Polynomial<PFElem>,
 variable_index: usize,
 variable_count: usize
) -> Self

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pub fn scalar_mul(&self, factor: PFElem) -> Self

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pub fn scalar_mul_mut(&mut self, factor: PFElem)

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pub fn mod_pow(&self, pow: BigInt, one: PFElem) -> Self

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pub fn square(&self) -> Self

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pub fn max_exponent(&self) -> u64

Return the highest number present in the list of list of exponents For P(x,y) = x^4*y^3, 4 would be returned.

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pub fn degree(&self) -> Degree

Calculate the “total degree” of a multivariate polynomial.

The total degree is defined as the highest combined degree of any term where the combined degree is the sum of all the term’s variable exponents.

As a convention, the polynomial f(x) = 0 has degree -1.

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pub fn normalize(&mut self)

Removes exponents whose coefficients are 0.

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pub fn symbolic_degree_bound(&self, max_degrees: &[i64]) -> Degree

During symbolic evaluation, i.e., when substituting a univariate polynomial for one of the variables, the total degree of the resulting polynomial can be upper bounded. This bound is the total_degree_bound, and can be calculated across all terms. Only the constant zero polynomial P(x,..) = 0 has a negative degree and it is always -1. All other constant polynomials have degree 0.

max_degrees: the max degrees for each of the univariate polynomials.
total_degree_bound: the max resulting degree from the substitution.