Type of coefficients.

Type of polynomials.

of_list [(m_1, a_1);..; (m_n, a_n)] builds the polynomial a_1 m_1 + ... + a_n m_n. Duplicates or zeros coefficients are accepted (for instance 2 x_0 + 0 x_1 + 3 x_0 is a valid input for 5 x_0).

Returns a list sorted in increasing order of Monomial.compare without duplicates nor zeros.

var ?c ?d i returns c xi^d, this is equivalent to of_list [c, Monomial.var ~d i]. c is Coeff.one and d is 1 by default. i and d must be non negative.

const c is equivalent to var ~c ~d:0 0.

monomial m is equivalent to of_list [m, Coeff.one].

power p n computes p^n, n must be non negative.

compose p [q_1;...; q_n] returns the polynomial p' such that p'(x_1,..., x_m) = p(q_1(x_1,..., x_m),..., q_n(x_1,..., x_m)).

• raises Dimension_error

  if p is defined on more than n variables.

derive p i returns the derivative of the polynomial p with respect to variable i (indices starting from 0). i must be non negative.

eval p [x_1;...; x_n] returns p(x_1,..., x_n).

• raises Invalid_argument

  "Polynomial.eval" if n is less than nb_vars p.

nb_vars p returns the largest index (starting from 0) of a variable appearing in p plus one (0 if none). For instance, nb_var p returns 5 if p is the polynomial x_2^2 + x_4 (even if variables x_0, x_1 and x_3 don't actually appear in p)

-1 for the null polynomial.

degree_list p returns a list of length nb_vars p with the maximal degree for each variable in p.

is_var p returns Some (c, d, i) if p is a polynomial of the form c xi^d and None otherwise.

is_const p returns Some c if p is the constant polynomial c and None otherwise.

is_monomial p returns Some m if p is a monmial x_0^i_0 ... x_n^i_n and None otherwise.

var

const

mult_scalar

Unary minus, ~- p is syntactic sugar for sub zero p.

add

sub

mult

p / c is equivaent to mult_scalar (Coeff.div Coeff.one c) p.

c1 /. c2 is equivaent to !c1 / c2.

power

See Monomial.pp for details about names.