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1.4.2 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.