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1.3.2 Algebraic Operators

The algebraic operators are:

      +  -  *  /  :  ^

The following table shows which operations the system can perform between two objects of the same or of different types; the first column lists the type of the first operand and the first row lists the type of the second operand. So, for example, the symbol : in the box on the seventh row and fourth column means that it is possible to divide an ideal by a polynomial.

          INT    RAT  RINGELEM  MODULEELEM IDEAL MODULE MAT LIST
INT       +-*/^  +-*/   +-*/      *         *     *      *   *
RAT       +-*/^  +-*/   +-*/      *         *     *      *   *
RINGELEM  +-*/^  +-*/   +-*/      *         *     *      *   *
MODULEELEM *     *      *         +-
IDEAL     *^     *      *                   +*:   *
MODULE    *      *      *                   *     +:
MAT       *^     *      *                                +-*
LIST      *      *      *                                    +-

                           Algebraic operators

Remarks:

* Let F and G be two polynomials. If F is a multiple of G, then F/G is the polynomial obtained from the division of F by G, otherwise F/G is a rational function (common factors are simplified). The functions div and mod can be used to get the quotient and the remainder of a polynomial division.

* Let L_1 and L_2 be two lists of the same length. Then L_1 + L_2 is the list obtained by adding L_1 to L_2 componentwise.

* If I and J are both ideals or both modules, then I : J is the ideal consisting of all polynomials f such that fg is in I for all g in J.