package tezos-bls12-381-polynomial

allocate len creates a zero polynomial of size len

erase p overwrites a polynomial p with a zero polynomial of the same size as the polynomial p

generate_biased_random_polynomial n generates a random polynomial of degree strictly lower than n, the distribution is NOT uniform, it is biased towards sparse polynomials and particularly towards the zero polynomial

random n generates a uniformly sampled polynomial among the set of all polynomials of degree strictly lower than n

degree p returns the degree of a polynomial p. Returns -1 for the zero polynomial

get p i returns the i-th element of a given array p, a coefficient of X^i in p

to_string p returns the string representation of a polynomial p

copy p returns a copy of a polynomial p

to_dense_coefficients p returns the dense representation of a polynomial p, i.e., it converts a C array to an OCaml array

of_dense p creates a value of type t from the dense representation of a polynomial p, i.e., it converts an OCaml array to a C array

of_coefficients p creates a value of type t from the sparse representation of a polynomial p, i.e., it converts an OCaml array to a C array

equal a b checks whether a polynomial a is equal to a polynomial b

is_zero p checks whether a polynomial p is the zero polynomial

zero is the zero polynomial, the neutral element for polynomial addition

one is the constant polynomial one, the neutral element for polynomial multiplication

add computes polynomial addition

add_inplace res a b computes polynomial addition of a and b and writes the result in res

Note: res can be equal to either a or b

sub computes polynomial subtraction

sub_inplace res a b computes polynomial subtraction of a and b and writes the result in res

Note: res can be equal to either a or b

mul computes polynomial multiplication

Note: naive quadratic algorithm, result's size is the sum of arguments' size

mul_by_scalar computes multiplication of a polynomial by a blst_fr element

mul_by_scalar_inplace res s p computes multiplication of a polynomial p by a blst_fr element s and stores it in res

linear p s computes ∑ᵢ s.(i)·p.(i)

linear_with_powers p s computes ∑ᵢ sⁱ·p.(i). This function is more efficient than linear + powers

opposite computes polynomial negation

opposite_inplace p computes polynomial negation

Note: The argument p is overwritten

evaluate p x evaluates a polynomial p at x

division_xn p n c returns the quotient and remainder of the division of p by (X^n + c)

mul_xn p n c returns the product of p and (X^n + c)

derivative p returns the formal derivative of p

blind ~nb_blinds n p adds to polynomial p a random multiple of polynomial (X^n - 1), chosen by uniformly sampling a polynomial b of degree strictly lower than nb_blinds and multiplying it by (X^n - 1), b is returned as the second argument

Infix operator for equal

Infix operator for add

Infix operator for sub

Infix operator for mul

constant s creates a value of type t from a blst_fr element s