up previous next
3.3.2 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.