HP 48GII User Manual

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)

HP 48GII Specifications

General

Battery type	CR2032
Type	Scientific
Form factor	Pocket

Weight and Dimensions

Weight	220 g
Dimensions (WxDxH)	184 x 87 x 23.5 mm

Summary

RPL Programming

Understanding Programs

Programs as objects, delimiters, and basic structure.

Entering and Executing Programs

Details on how to create, store, and run programs.

Using Conditional Structures

Covers IF, CASE, IFT, IFTE structures for program decision-making.

Input and Output Commands

Details commands like PROMPT, INPUT, INFORM, CHOOSE for user interaction.

RPL Programming Examples

Fibonacci Numbers

Demonstrates recursive and loop-based Fibonacci calculations.

Minimum and Maximum Array Elements

Details finding min/max elements using MNX and MNX2.

Applying a Program to an Array

Explains the APLY command for transforming array elements.

Full Command and Function Reference

How to Access Commands and Functions

Explains key presses and menu paths to access commands.

ABS (Absolute Value)

Details the absolute value function and its array behavior.

ACOS (Arc Cosine)

Explains the inverse cosine function, domain, and range.

Computer Algebra Commands

CAS Operations

Overview of CAS operations and their categorization by menu.

Algebra commands

Lists and describes commands for algebraic manipulation.

Calculus Commands

Covers derivation, integration, and limit commands.

Equation Reference

Columns and Beams (1)

Provides equations for structural mechanics.

Electricity (2)

Lists equations related to electrical circuits and laws.

Fluids (3)

Covers equations for fluid mechanics.

The Development Library

Introduction

Explains the purpose and usage of the development library.

Tools for Development

Details APEEK, PEEK, POKE, POKEARM commands.

MASD Compiler

Discusses syntax, modes, and directives for MASD.

Error and Status Messages

Messages Listed Alphabetically

Alphabetical list of error messages.

Messages Listed Numerically

Numerical list of error messages by hex code.

System Flags

System Flags (continued)

Description of various system flags.

System Flags (continued)

Continuation of system flags description.

Reserved Variables

Contents of the Reserved Variables

Explanation of key reserved variables.

PPAR

Details plotting parameters.

Technical Reference

Object Sizes

Lists object sizes in bytes.

Symbolic Integration Patterns

Provides a table of symbolic integration patterns.

Parallel Processing With Lists

General rules for parallel processing

Explains conditions for parallel list processing.

Group 4: ADD and +

Describes how ADD and + handle parallel list operations.

Keyboard Shortcuts

Press and Hold key combinations

Lists functions performed by key combinations.

Shifted softkeys

Explains shift key effects on menu labels.

The Menu-Number Table

-- menus 0-117 are semi-compatible with 48G menus --

Menu numbers and paths for built-in menus.

-- New Library 222 commands --

Details commands available in Library 222.