Computer Algebra Commands 4-25
DIVMOD
Type: Function
Description: Divides two expressions modulo the current modulus.
Access: Arithmetic, !Þ MODULO
Input: Level 2/Argument 1: The dividend.
Level 1/Argument 2: The divisor.
Output: The quotient of the terms modulo the current modulus.
Flags: Exact mode must be set (flag –105 clear).
Numeric mode must not be set (flag –3 clear).
Example: Modulo 3, divide 5x
2
+4x+2 by x
2
+1.
Command:
DIVMOD(5*X^2+4*X+2,X^2+1)
Result: -((X^2-X+1)/X^2+1))
DIVPC
Type: Command
Description: Returns a Taylor polynomial for the quotient of two polynomial expressions.
Access: Calculus, !Ö LIMITS & SERIES
Input: Level 3/Argument 1: The numerator expression.
Level 2/Argument 2: The denominator expression.
Level 1/Argument 3: The degree of the Taylor polynomial.
Output: The Taylor polynomial at x = 0 of the quotient of the two expressions, to the specified
degree.
Flags: Exact mode must be set (flag –105 clear).
Numeric mode must not be set (flag –3 clear). Radians mode must be set (flag –17 set).
Incremental power mode must be set (flag –114 set).
Example: Find the fourth degree Taylor polynomial for the following:
x
3
4x 12++
11x
11
1+
-----------------------------
Command:
DIVPC(X^3+4*X+12,11*X^11+1,4)
Result: 12+4*X+X^3
See also: TAYLOR0, TAYLR, SERIES
DOMAIN
Type: Command
Description: For a function of the current variable, lists the domains of real numbers for which the
function is defined and for which it is undefined. DOMAIN works for functions of more
than one argument, for example DOMAIN (X*X), and for user defined functions, as in the
example below. For functions which it does not recognize, DOMAIN returns the message
“Unknown operator”.
Access: Catalog, …µ
Input: Level 1/Item 1: A function, or an expression, in terms of the current variable.
Output: Level 1/Item 1: A list with regions where the function is undefined marked by
'?' and
regions where the function is defined marked by +. Rational singularities, such as 0 in 1/x,
are not listed.
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