Exercise 1 - Usual operations over polynomials

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OCaml programs

Exercise 1 - Usual operations over polynomials

Assume an Objective Caml toplevel in which the following modules (download an archive containing them) have been loaded and opened:

•  List_1 : to deal with lists.
•  Rat : provides the type  rat  to deal with rational numbers.
•  Rat_poly : provides the type  rat_poly  to deal with polynomials in one variable and whose coefficients are rational numbers.
•  Ex_rat_poly : provides some  rat_poly  values.

1

Name:  eq_poly . Type:  rat_poly * rat_poly -> bool . Tests two polynomials for equality.

2

Name:  add_poly . Type:  rat_poly * rat_poly -> rat_poly . Adds two polynomials.

3

Name:  x_times . Type:  rat_poly -> rat_poly . Multiply a polynomial by the monomial X.

4

Name:  deriv_poly . Type:  rat_poly -> rat_poly . Computes the derivative of a polynomial.

5

Name:  rat_times_poly . Type:  rat * rat_poly -> rat_poly . Computes the polynomial ap given the pair (a,p) where a is a rational and p is a polynomial.

6

Name:  mult_poly . Type:  rat_poly * rat_poly -> rat_poly . Multiplies two polynomials.

7

Name:  degree . Type:  rat_poly -> int . Computes the degree of a non-zero polynomial. Fails if the polynomial is zero.

8

Name:  leading_coef . Type:  rat_poly -> rat . Computes the leading coefficient of a non-zero polynomial. Fails if the polynomial is zero.

9

Name:  monomial . Type:  rat * int -> rat_poly . Computes the monomial aXd from a pair (a,d) where a is a non-zero rational and d is a non-negative integer. Fails if a=0 or d<0.

10

Name:  euclid_div_poly . Type:  rat_poly * rat_poly -> rat_poly * rat_poly . Computes the pair (q,r) where q is the quotient and r is the remainder in the euclidean division of p1 by p2, given a pair (p1,p2) of polynomials where the divisor p2 is non-zero. Fails if p2 is zero.

11

Name:  quotient_poly . Type:  rat_poly * rat_poly -> rat_poly . Computes the quotient in the euclidean division of p1 by p2, given a pair (p1,p2) of polynomials where the divisor p2 is non-zero. Fails if p2 is zero.

12

Name:  mod_poly . Type:  rat_poly * rat_poly -> rat_poly . Computes the remainder in the euclidean division of p1 by p2, given a pair (p1,p2) of polynomials where the divisor p2 is non-zero. Fails if p2 is zero.

13

Name:  gcd_poly . Type:  rat_poly * rat_poly -> rat_poly . Computes the gcd (greatest common divisor) of a pair of non-zero polynomials. Fails if a component of the pair is zero.

14

Name:  eval_poly . Type:  rat_poly * rat -> rat . Evaluation of a polynomial.

15

Name:  function_of_poly . Type:  rat_poly -> (rat -> rat) . Computes the polynomial function associated with a polynomial.

16

Name:  poly_of_coef_list . Type:  rat list -> rat_poly . Computes the polynomial given a list of its coefficients ordered according to decreasing degrees (it is written a list rather than the list because this list can begin with useless zeros).

Exercise 1 - Usual operations over polynomials

Documentation and user's manual

Table of contents

OCaml programs