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2.3.2. 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    ZMOD   POLY   RATFUN  VECTOR IDEAL MODULE MAT LIST
INT    +-*/^  +-*/   *      +-*/   +-*/     *     *     *      *   *
RAT    +-*/^  +-*/          +-*/   +-*/     *     *     *      *   *
ZMOD   *^            +-*/   +-*/   +-*/     *     *     *      *   *
POLY   +-*/^  +-*/   +-*/   +-*/   +-*/     *     *     *      *   *
RATFUN +-*/^  +-*/   +-*/   +-*/   +-*/                        *   *
VECTOR *      *      *      *               +-
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. The division of an ideal I by a polynomial f is the
    division of I by the ideal generated by f.