Cyclotomic; Dedicace; Def - HP 48gII Advanced User's Reference Manual

CYCLOTOMIC

Type: Function
Description: Returns the cyclotomic polynomial of order n. This is the polynomial whose roots are all the
nth roots of 1, except those that are also roots of 1 for smaller values of n. For example, if n is
4, the 4
th
and -i are left, giving the polynomial (x-i)(x+i) = x
Arithmetic, !Þ
Access:
Input: A non-negative integer n
Output: The cyclotomic polynomial of order n.
Flags: Exact mode must be set (flag –105 clear).
Numeric mode must not be set (flag –3 clear).
Example: Find the 20th cyclotomic polynomial.
Command:
CYCLOTOMIC(20)
Result:
X^8-X^6+X^4-X^2+1

DEDICACE

Type: Function
Description: Displays a greeting from the CAS team and dedication to all HP calculator users.
Catalog, ...µ
Access:
Example: In algebraic mode, the message can be extended. Try:

DEF

Type: Function
Description: Defines a variable or a function. Works like the DEFINE command, except that it returns a
result and can be included in an algebraic expression. Given an expression as input, DEF
stores the expression, unlike STORE which evaluates the expression and stores the numerical
value.
Catalog, ...µ
Access:
Input: Level 1/Argument 1: An expression of the form
name=expression or
name(name
In the first case, name is the name of a variable, and expression is an expression or a number to
be stored in the variable. If the variable does not exist, it is created in the current directory. In
the second case, name is the name of a variable that will be treated as a function, name
are formal variables used to define inputs the function will take.
Output: Level 1/Item 1: Unlike DEFINE, which returns NOVAL in Algebraic mode, and no result in
RPN mode, DEF returns the expression used as the input.
Flags: Exact mode must be set (flag –105 clear).
Numeric mode must not be set (flag –3 clear).
Example 1: Define a new function that calculates:
(a-b)/(a+b)
Command:
DEF(NEW(A,B)=(A-B)/(A+B))
Result:
NEW(A,B)=(A-B)/(A+B)
Example 2: Check that the newly defined function works:
Command:
NEW(2,1)
4-20 Computer Algebra Commands
roots of 1 are {1, i, -1, -i}, but 1 is the 1
POLYNOMIAL
, ... name )=expression(name
1 n
root of 1 and –1 is a 2
st
+1.
2
DEDICACE(Salutations)
,... name )
1 n
root of 1, so only i
nd
to name
1 n