Sollya User's Manual

Name:

mod Computes the euclidian division of polynomials or numbers and returns the rest

Library name:

sollya_obj_t sollya_lib_euclidian_mod(sollya_obj_t, sollya_obj_t)

Usage:

mod(a, b) : (function, function) -> function

Parameters:

a is a constant or a polynomial.
b is a constant or a polynomial.

Description:

mod(a,b) computes a - (b * div(a,b)). In other words, it returns the remainder of the Euclidian division of a by b.
See div for subtle cases involving polynomials whose degree can not easily be computed by the tool as their leading coefficient is given as a constant expression that is mathematically zero but for which the tool is unable to detect this fact.

Example 1:

   > mod(1001, 231);
   77
   > mod(13, 17);
   13
   > mod(-14, 15);
   1
   > mod(-213, -5);
   -3
   > print(mod(23/13, 11/17));
   105 / 221
   > print(mod(exp(13),-sin(17)));
   exp(13) + 460177 * sin(17)

Example 2:

   > mod(24 + 68 * x + 74 * x^2 + 39 * x^3 + 10 * x^4 + x^5, 4 + 4 * x + x^2);
   0
   > mod(24 + 68 * x + 74 * x^2 + 39 * x^3 + 10 * x^4 + x^5, 2 * x^3);
   24 + x * (68 + x * 74)
   > mod(x^2, x^3);
   x^2

Example 3:

   > mod(exp(x), x^2);
   exp(x)
   > mod(x^3, sin(x));
   x^3