4-20 Computer Algebra Commands
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
roots of 1 are {1, i, -1, -i}, but 1 is the 1
st
root of 1 and –1 is a 2
nd
root of 1, so only i
and -i are left, giving the polynomial (x-i)(x+i) = x
2
+1.
Access: Arithmetic, !Þ
POLYNOMIAL
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.
Access: Catalog, …µ
Example: In algebraic mode, the message can be extended. Try: DEDICACE(Salutations)
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.
Access: Catalog, …µ
Input: Level 1/Argument 1: An expression of the form
name=expression or
name(name
1
, … name
n
)=expression(name
1
,… name
n
)
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
1
to name
n
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)
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