HP 48gII Graphing Calculator Reference guide

HP 50g / 49g+ / 48gII graphing calculator

advanced user’s reference manual

advanced user’s reference manualadvanced user’s reference manual

advanced user’s reference manual

H

Edition 2

HP part number F2228-90010

Printed Date: 2009/7/14

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Acknowledgements

Hewlett-Packard would like to thank the following for their contribution:

Jordi Hidalgo, Joe Horn, Tony Hutchins, Ted Kerber, Wlodek Mier-Jedrzejowicz, Richard Nelson, Eric Rechlin,

Jake Schwartz and Gene Wright.

Printing History

Edition 1 September 2005

Edition 2 July 2009

Contents - 1

Contents

Contents ............................................................................................................................................................................................... 1

1. RPL Programming.......................................................................................................................................................................1-1

Understanding Programming.................................................................................................................................................1-1

The Contents of a Program.............................................................................................................................................1-1

Calculations in a Program................................................................................................................................................1-2

Entering and Executing Programs ........................................................................................................................................1-3

Viewing and Editing Programs ..............................................................................................................................................1-6

Creating Programs on a Computer........................................................................................................................................1-7

Using Local Variables..............................................................................................................................................................1-7

Creating Local Variables..................................................................................................................................................1-7

Evaluating Local Names..................................................................................................................................................1-9

Defining the Scope of Local Variables..........................................................................................................................1-9

Compiled Local Variables..............................................................................................................................................1-10

Creating User-Defined Functions as Programs.........................................................................................................1-10

Using Tests and Conditional Structures .............................................................................................................................1-11

Testing Conditions..........................................................................................................................................................1-11

Using Conditional Structures and Commands...........................................................................................................1-13

Using Loop Structures...........................................................................................................................................................1-17

Using Definite Loop Structures....................................................................................................................................1-17

Using Indefinite Loop Structures.................................................................................................................................1-22

Using Loop Counters.....................................................................................................................................................1-25

Using Summations Instead of Loops ..........................................................................................................................1-26

Using Flags ..............................................................................................................................................................................1-27

Types of Flags..................................................................................................................................................................1-27

Setting, Clearing, and Testing Flags.............................................................................................................................1-27

Recalling and Storing the Flag States...........................................................................................................................1-28

Using Subroutines ..................................................................................................................................................................1-29

Single-Stepping through a Program.....................................................................................................................................1-31

Trapping Errors......................................................................................................................................................................1-33

Causing and Analyzing Errors......................................................................................................................................1-33

Making an Error Trap....................................................................................................................................................1-35

Input.........................................................................................................................................................................................1-37

Data Input Commands ..................................................................................................................................................1-37

Using PROMPT, CONT for Input.............................................................................................................................1-37

Using DISP FREEZE HALT, CONT for Input......................................................................................................1-39

Using INPUT, ENTER for Input ...............................................................................................................................1-40

Using INFORM and CHOOSE for Input.................................................................................................................1-45

Beeping to Get Attention..............................................................................................................................................1-48

Stopping a Program for Keystroke Input...........................................................................................................................1-48

Using WAIT for Keystroke Input................................................................................................................................1-48

Using KEY for Keystroke Input..................................................................................................................................1-49

Output ..............................................................................................................................................................................1-49

Data Output Commands...............................................................................................................................................1-49

Labeling Output with Tags............................................................................................................................................1-50

Labeling and Displaying Output as Strings ................................................................................................................1-50

Pausing to Display Output............................................................................................................................................1-51

Using MSGBOX to Display Output...........................................................................................................................1-51

Using Menus with Programs ................................................................................................................................................1-52

Using Menus for Input...................................................................................................................................................1-52

Using Menus to Run Programs ....................................................................................................................................1-53

Turning Off the Calculator from a Program .....................................................................................................................1-55

2. RPL Programming Examples....................................................................................................................................................2-1

Contents - 2

Fibonacci Numbers..................................................................................................................................................................2-1

FIB1 (Fibonacci Numbers, Recursive Version)...........................................................................................................2-1

FIB2 (Fibonacci Numbers, Loop Version....................................................................................................................2-2

FIBT (Comparing Program-Execution Time).............................................................................................................2-4

Displaying a Binary Integer.....................................................................................................................................................2-5

PAD (Pad with Leading Spaces).....................................................................................................................................2-5

PRESERVE (Save and Restore Previous Status)........................................................................................................2-6

BDISP (Binary Display)...................................................................................................................................................2-7

Median of Statistics Data ......................................................................................................................................................2-10

%TILE (Percentile of a list)..........................................................................................................................................2-10

MEDIAN (Median of Statistics Data).........................................................................................................................2-11

Expanding and Collecting Completely................................................................................................................................2-13

MULTI (Multiple Execution) .......................................................................................................................................2-14

EXCO (Expand and Collect Completely) ..................................................................................................................2-15

Minimum and Maximum Array Elements..........................................................................................................................2-16

MNX (Minimum or Maximum Element—Version 1).............................................................................................2-16

MNX2 (Minimum or Maximum Element—Version 2)...........................................................................................2-18

Applying a Program to an Array..........................................................................................................................................2-20

Converting Between Number Bases ...................................................................................................................................2-22

Verifying Program Arguments.............................................................................................................................................2-24

NAMES (Check List for Exactly Two Names).........................................................................................................2-25

NAMES...................................................................................................................................................................................2-26

Converting Procedures from Algebraic to RPN...............................................................................................................2-27

Bessel Functions.....................................................................................................................................................................2-29

Animation of Successive Taylor’s Polynomials.................................................................................................................2-31

SINTP (Converting a Plot to a Graphics Object).....................................................................................................2-31

Techniques used in SINTP ...........................................................................................................................................2-31

SETTS (Superimposing Taylor’s polynomials)..........................................................................................................2-32

TSA (Animating Taylor’s Polynomials).......................................................................................................................2-33

Programmatic Use of Statistics and Plotting......................................................................................................................2-34

Trace Mode .............................................................................................................................................................................2-37

Inverse-Function Solver........................................................................................................................................................2-38

Animating a Graphical Image...............................................................................................................................................2-39

3. Full Command and Function Reference..................................................................................................................................3-1

ABCUV......................................................................................................................................................................................3-5

ABS.............................................................................................................................................................................................3-5

ACK............................................................................................................................................................................................3-5

ACKALL ...................................................................................................................................................................................3-6

ACOS .........................................................................................................................................................................................3-6

ACOS2S.....................................................................................................................................................................................3-7

ACOSH......................................................................................................................................................................................3-8

ADD...........................................................................................................................................................................................3-9

ADDTMOD.............................................................................................................................................................................3-9

ADDTOREAL.......................................................................................................................................................................3-10

ALGB.......................................................................................................................................................................................3-10

ALOG......................................................................................................................................................................................3-10

AMORT...................................................................................................................................................................................3-11

AND.........................................................................................................................................................................................3-11

ANIMATE..............................................................................................................................................................................3-12

ANS..........................................................................................................................................................................................3-12

APPLY.....................................................................................................................................................................................3-13

ARC..........................................................................................................................................................................................3-13

ARCHIVE...............................................................................................................................................................................3-14

ARG..........................................................................................................................................................................................3-14

ARIT.........................................................................................................................................................................................3-15

ARRY→...................................................................................................................................................................................3-15

Contents - 3

→ARRY...................................................................................................................................................................................3-15

ASIN.........................................................................................................................................................................................3-15

ASIN2C....................................................................................................................................................................................3-17

ASIN2T....................................................................................................................................................................................3-17

ASINH.....................................................................................................................................................................................3-17

ASN..........................................................................................................................................................................................3-18

ASR...........................................................................................................................................................................................3-19

ASSUME .................................................................................................................................................................................3-19

ATAN ......................................................................................................................................................................................3-20

ATAN2S..................................................................................................................................................................................3-21

ATANH...................................................................................................................................................................................3-22

ATICK.....................................................................................................................................................................................3-22

ATTACH.................................................................................................................................................................................3-23

AUGMENT............................................................................................................................................................................3-23

AUTO ......................................................................................................................................................................................3-24

AXES........................................................................................................................................................................................3-24

AXL..........................................................................................................................................................................................3-25

AXM.........................................................................................................................................................................................3-25

AXQ.........................................................................................................................................................................................3-26

BAR ..........................................................................................................................................................................................3-26

BARPLOT...............................................................................................................................................................................3-27

BASIS.......................................................................................................................................................................................3-27

BAUD ......................................................................................................................................................................................3-27

BEEP........................................................................................................................................................................................3-28

BESTFIT.................................................................................................................................................................................3-28

BIN...........................................................................................................................................................................................3-28

BINS.........................................................................................................................................................................................3-29

BLANK....................................................................................................................................................................................3-29

BOX .........................................................................................................................................................................................3-29

BUFLEN.................................................................................................................................................................................3-30

BYTES.....................................................................................................................................................................................3-30

B→R.........................................................................................................................................................................................3-30

C$..............................................................................................................................................................................................3-31

C2P ...........................................................................................................................................................................................3-31

CASCFG..................................................................................................................................................................................3-31

CASCMD.................................................................................................................................................................................3-32

CASE........................................................................................................................................................................................3-32

CEIL.........................................................................................................................................................................................3-33

CENTR....................................................................................................................................................................................3-33

CF..............................................................................................................................................................................................3-33

%CH.........................................................................................................................................................................................3-33

CHINREM..............................................................................................................................................................................3-34

CHOLESKY...........................................................................................................................................................................3-34

CHOOSE ................................................................................................................................................................................3-35

CHR..........................................................................................................................................................................................3-35

CIRC.........................................................................................................................................................................................3-36

CKSM.......................................................................................................................................................................................3-36

CLEAR.....................................................................................................................................................................................3-37

CLKADJ..................................................................................................................................................................................3-37

CLLCD ....................................................................................................................................................................................3-37

CLOSEIO ...............................................................................................................................................................................3-37

CLΣ...........................................................................................................................................................................................3-38

CLUSR.....................................................................................................................................................................................3-38

CLVAR ....................................................................................................................................................................................3-38

CMPLX....................................................................................................................................................................................3-38

CNRM......................................................................................................................................................................................3-38

Contents - 4

→COL .....................................................................................................................................................................................3-39

COL→ .....................................................................................................................................................................................3-39

COL–........................................................................................................................................................................................3-39

COL+.......................................................................................................................................................................................3-40

COLCT....................................................................................................................................................................................3-40

COLLECT...............................................................................................................................................................................3-40

COLΣ.......................................................................................................................................................................................3-41

COMB......................................................................................................................................................................................3-41

CON.........................................................................................................................................................................................3-41

COND .....................................................................................................................................................................................3-42

CONIC ....................................................................................................................................................................................3-43

CONJ .......................................................................................................................................................................................3-43

CONLIB..................................................................................................................................................................................3-44

CONST....................................................................................................................................................................................3-44

CONSTANTS ........................................................................................................................................................................3-44

CONT......................................................................................................................................................................................3-45

CONVERT.............................................................................................................................................................................3-45

CORR.......................................................................................................................................................................................3-45

COS ..........................................................................................................................................................................................3-46

COSH.......................................................................................................................................................................................3-46

COV .........................................................................................................................................................................................3-46

CR .............................................................................................................................................................................................3-47

CRDIR .....................................................................................................................................................................................3-47

CROSS .....................................................................................................................................................................................3-47

CSWP .......................................................................................................................................................................................3-47

CURL .......................................................................................................................................................................................3-48

CYCLOTOMIC.....................................................................................................................................................................3-48

CYLIN .....................................................................................................................................................................................3-48

C→PX......................................................................................................................................................................................3-49

C→R.........................................................................................................................................................................................3-49

DARCY....................................................................................................................................................................................3-49

DATE.......................................................................................................................................................................................3-49

→DATE..................................................................................................................................................................................3-50

DATE+....................................................................................................................................................................................3-50

DBUG......................................................................................................................................................................................3-50

DDAYS....................................................................................................................................................................................3-51

DEC..........................................................................................................................................................................................3-51

DECR.......................................................................................................................................................................................3-51

DEDICACE ...........................................................................................................................................................................3-52

DEF..........................................................................................................................................................................................3-52

DEFINE..................................................................................................................................................................................3-52

DEG.........................................................................................................................................................................................3-53

DEGREE................................................................................................................................................................................3-53

DELALARM ..........................................................................................................................................................................3-53

DELAY....................................................................................................................................................................................3-54

DELKEYS ..............................................................................................................................................................................3-54

DEPND...................................................................................................................................................................................3-55

DEPTH....................................................................................................................................................................................3-55

DERIV.....................................................................................................................................................................................3-56

DERVX ...................................................................................................................................................................................3-56

DESOLVE..............................................................................................................................................................................3-56

DET..........................................................................................................................................................................................3-57

DETACH................................................................................................................................................................................3-57

DIAG→...................................................................................................................................................................................3-58

→DIAG...................................................................................................................................................................................3-58

DIAGMAP..............................................................................................................................................................................3-58

Contents - 5

DIFF.........................................................................................................................................................................................3-59

DIFFEQ..................................................................................................................................................................................3-59

DIR...........................................................................................................................................................................................3-60

DISP.........................................................................................................................................................................................3-60

DISPXY...................................................................................................................................................................................3-61

DISTRIB..................................................................................................................................................................................3-61

DIV...........................................................................................................................................................................................3-62

DIV2.........................................................................................................................................................................................3-62

DIV2MOD..............................................................................................................................................................................3-62

DIVIS.......................................................................................................................................................................................3-63

DIVMOD................................................................................................................................................................................3-63

DIVPC .....................................................................................................................................................................................3-63

dn ..............................................................................................................................................................................................3-64

DO............................................................................................................................................................................................3-64

DOERR...................................................................................................................................................................................3-65

DOLIST...................................................................................................................................................................................3-65

DOMAIN................................................................................................................................................................................3-66

DOSUBS .................................................................................................................................................................................3-66

DOT.........................................................................................................................................................................................3-67

DRAW .....................................................................................................................................................................................3-68

DRAW3DMATRIX ..............................................................................................................................................................3-68

DRAX ......................................................................................................................................................................................3-68

DROITE..................................................................................................................................................................................3-69

DROP ......................................................................................................................................................................................3-69

DROP2 ....................................................................................................................................................................................3-69

DROPN...................................................................................................................................................................................3-70

DTAG......................................................................................................................................................................................3-70

DUP..........................................................................................................................................................................................3-70

DUP2........................................................................................................................................................................................3-70

DUPDUP ................................................................................................................................................................................3-71

DUPN......................................................................................................................................................................................3-71

D→R........................................................................................................................................................................................3-71

e.................................................................................................................................................................................................3-71

EDIT........................................................................................................................................................................................3-72

EDITB .....................................................................................................................................................................................3-72

EGCD......................................................................................................................................................................................3-72

EGV .........................................................................................................................................................................................3-73

EGVL.......................................................................................................................................................................................3-73

ELSE........................................................................................................................................................................................3-73

END.........................................................................................................................................................................................3-73

ENDSUB.................................................................................................................................................................................3-74

ENG.........................................................................................................................................................................................3-74

EPSX0......................................................................................................................................................................................3-74

EQNLIB..................................................................................................................................................................................3-75

EQW ........................................................................................................................................................................................3-75

EQ→........................................................................................................................................................................................3-75

ERASE.....................................................................................................................................................................................3-75

ERR0........................................................................................................................................................................................3-76

ERRM ......................................................................................................................................................................................3-76

ERRN.......................................................................................................................................................................................3-76

EULER ....................................................................................................................................................................................3-76

EVAL.......................................................................................................................................................................................3-77

EXLR .......................................................................................................................................................................................3-77

EXP&LN.................................................................................................................................................................................3-78

EXP ..........................................................................................................................................................................................3-78

EXP2HYP...............................................................................................................................................................................3-79

Contents - 6

EXP2POW..............................................................................................................................................................................3-79

EXPAN....................................................................................................................................................................................3-79

EXPAND................................................................................................................................................................................3-80

EXPANDMOD.....................................................................................................................................................................3-80

EXPFIT...................................................................................................................................................................................3-81

EXPLN....................................................................................................................................................................................3-81

EXPM ......................................................................................................................................................................................3-81

EYEPT.....................................................................................................................................................................................3-81

F0λ ............................................................................................................................................................................................3-82

FACT........................................................................................................................................................................................3-82

FACTOR.................................................................................................................................................................................3-82

FACTORMOD......................................................................................................................................................................3-83

FACTORS...............................................................................................................................................................................3-83

FANNING..............................................................................................................................................................................3-84

FAST3D...................................................................................................................................................................................3-84

FCOEF ....................................................................................................................................................................................3-85

FC?............................................................................................................................................................................................3-85

FC?C.........................................................................................................................................................................................3-85

FDISTRIB...............................................................................................................................................................................3-86

FFT...........................................................................................................................................................................................3-86

FILER ......................................................................................................................................................................................3-87

FINDALARM........................................................................................................................................................................3-87

FINISH....................................................................................................................................................................................3-87

FIX............................................................................................................................................................................................3-87

FLASHEVAL.........................................................................................................................................................................3-88

FLOOR....................................................................................................................................................................................3-88

FONT6 ....................................................................................................................................................................................3-88

FONT7 ....................................................................................................................................................................................3-89

FONT8 ....................................................................................................................................................................................3-89

FONT→..................................................................................................................................................................................3-89

→FONT..................................................................................................................................................................................3-89

FOR..........................................................................................................................................................................................3-90

FOURIER ...............................................................................................................................................................................3-91

FP..............................................................................................................................................................................................3-91

FREE........................................................................................................................................................................................3-91

FREEZE..................................................................................................................................................................................3-91

FROOTS .................................................................................................................................................................................3-92

FS?.............................................................................................................................................................................................3-92

FS?C..........................................................................................................................................................................................3-93

FUNCTION...........................................................................................................................................................................3-93

FXND......................................................................................................................................................................................3-94

GAMMA..................................................................................................................................................................................3-95

GAUSS.....................................................................................................................................................................................3-95

GBASIS....................................................................................................................................................................................3-95

GCD.........................................................................................................................................................................................3-96

GCDMOD..............................................................................................................................................................................3-96

GET..........................................................................................................................................................................................3-96

GETI........................................................................................................................................................................................3-97

GOR.........................................................................................................................................................................................3-98

GRAD......................................................................................................................................................................................3-98

GRAMSCHMIDT .................................................................................................................................................................3-99

GRAPH ...................................................................................................................................................................................3-99

GREDUCE.............................................................................................................................................................................3-99

GRIDMAP............................................................................................................................................................................3-100

→GROB................................................................................................................................................................................3-100

GROB ....................................................................................................................................................................................3-101

Contents - 7

GROBADD..........................................................................................................................................................................3-101

GXOR....................................................................................................................................................................................3-101

*H............................................................................................................................................................................................3-102

HADAMARD ......................................................................................................................................................................3-102

HALFTAN............................................................................................................................................................................3-102

HALT.....................................................................................................................................................................................3-102

HEAD....................................................................................................................................................................................3-103

HEADER→ .........................................................................................................................................................................3-103

→HEADER .........................................................................................................................................................................3-103

HELP .....................................................................................................................................................................................3-103

HERMITE ............................................................................................................................................................................3-104

HESS......................................................................................................................................................................................3-104

HEX .......................................................................................................................................................................................3-104

HILBERT..............................................................................................................................................................................3-105

HISTOGRAM......................................................................................................................................................................3-105

HISTPLOT ...........................................................................................................................................................................3-106

HMS– .....................................................................................................................................................................................3-106

HMS+ ....................................................................................................................................................................................3-106

HMS→...................................................................................................................................................................................3-107

→HMS...................................................................................................................................................................................3-107

HOME...................................................................................................................................................................................3-108

HORNER..............................................................................................................................................................................3-108

i................................................................................................................................................................................................3-108

IABCUV................................................................................................................................................................................3-108

IBASIS ...................................................................................................................................................................................3-109

IBERNOULLI .....................................................................................................................................................................3-109

IBP..........................................................................................................................................................................................3-109

ICHINREM..........................................................................................................................................................................3-110

IDN ........................................................................................................................................................................................3-110

IDIV2.....................................................................................................................................................................................3-111

IEGCD ..................................................................................................................................................................................3-111

IF.............................................................................................................................................................................................3-112

IFERR....................................................................................................................................................................................3-112

IFFT .......................................................................................................................................................................................3-113

IFT..........................................................................................................................................................................................3-114

IFTE.......................................................................................................................................................................................3-114

ILAP.......................................................................................................................................................................................3-114

IM............................................................................................................................................................................................3-115

IMAGE..................................................................................................................................................................................3-115

INCR......................................................................................................................................................................................3-116

INDEP...................................................................................................................................................................................3-116

INFORM...............................................................................................................................................................................3-116

INPUT ...................................................................................................................................................................................3-117

INT.........................................................................................................................................................................................3-118

INTEGER.............................................................................................................................................................................3-119

INTVX...................................................................................................................................................................................3-119

INV.........................................................................................................................................................................................3-119

INVMOD..............................................................................................................................................................................3-120

IP.............................................................................................................................................................................................3-120

IQUOT..................................................................................................................................................................................3-120

IREMAINDER....................................................................................................................................................................3-121

ISOL.......................................................................................................................................................................................3-121

ISOM......................................................................................................................................................................................3-121

ISPRIME?..............................................................................................................................................................................3-122

I→R........................................................................................................................................................................................3-122

JORDAN...............................................................................................................................................................................3-122

Contents - 8

KER........................................................................................................................................................................................3-123

KERRM.................................................................................................................................................................................3-123

KEY........................................................................................................................................................................................3-123

KEYEVAL............................................................................................................................................................................3-124

→KEYTIME........................................................................................................................................................................3-124

KEYTIME→........................................................................................................................................................................3-125

KGET ....................................................................................................................................................................................3-125

KILL.......................................................................................................................................................................................3-125

LABEL...................................................................................................................................................................................3-125

LAGRANGE........................................................................................................................................................................3-126

LANGUAGE→...................................................................................................................................................................3-126

→LANGUAGE...................................................................................................................................................................3-126

LAP.........................................................................................................................................................................................3-127

LAPL......................................................................................................................................................................................3-127

LAST ......................................................................................................................................................................................3-127

LASTARG.............................................................................................................................................................................3-128

LCD→ ...................................................................................................................................................................................3-128

→LCD ...................................................................................................................................................................................3-128

LCM........................................................................................................................................................................................3-128

LCXM ....................................................................................................................................................................................3-129

LDEC.....................................................................................................................................................................................3-129

LEGENDRE........................................................................................................................................................................3-130

LGCD ....................................................................................................................................................................................3-130

LIBEVAL..............................................................................................................................................................................3-130

LIBS........................................................................................................................................................................................3-130

lim ...........................................................................................................................................................................................3-131

LIMIT.....................................................................................................................................................................................3-131

LIN .........................................................................................................................................................................................3-131

LINE ......................................................................................................................................................................................3-132

ΣLINE....................................................................................................................................................................................3-132

LINFIT ..................................................................................................................................................................................3-132

LININ....................................................................................................................................................................................3-133

LINSOLVE...........................................................................................................................................................................3-133

LIST→...................................................................................................................................................................................3-133

→LIST...................................................................................................................................................................................3-133

∆LIST.....................................................................................................................................................................................3-134

ΠLIST ....................................................................................................................................................................................3-134

ΣLIST.....................................................................................................................................................................................3-134

LN...........................................................................................................................................................................................3-134

LNAME.................................................................................................................................................................................3-136

LNCOLLECT ......................................................................................................................................................................3-136

LNP1......................................................................................................................................................................................3-136

LOCAL..................................................................................................................................................................................3-137

LOG .......................................................................................................................................................................................3-137

LOGFIT ................................................................................................................................................................................3-138

LQ...........................................................................................................................................................................................3-138

LR............................................................................................................................................................................................3-138

LSQ.........................................................................................................................................................................................3-139

LU...........................................................................................................................................................................................3-139

LVAR .....................................................................................................................................................................................3-140

MAD.......................................................................................................................................................................................3-140

MAIN.....................................................................................................................................................................................3-141

MANT....................................................................................................................................................................................3-141

MAP........................................................................................................................................................................................3-141

↓MATCH...............................................................................................................................................................................3-141

↑MATCH...............................................................................................................................................................................3-142

Contents - 9

MATHS..................................................................................................................................................................................3-143

MATR ....................................................................................................................................................................................3-143

MAX.......................................................................................................................................................................................3-143

MAXR....................................................................................................................................................................................3-144

MAXΣ....................................................................................................................................................................................3-144

MCALC..................................................................................................................................................................................3-144

MEAN....................................................................................................................................................................................3-145

MEM ......................................................................................................................................................................................3-145

MENU ...................................................................................................................................................................................3-145

MENUXY.............................................................................................................................................................................3-146

MERGE.................................................................................................................................................................................3-147

MIN........................................................................................................................................................................................3-147

MINEHUNT........................................................................................................................................................................3-147

MINIFONT→ .....................................................................................................................................................................3-148

→MINIFONT .....................................................................................................................................................................3-148

MINIT....................................................................................................................................................................................3-148

MINR.....................................................................................................................................................................................3-148

MINΣ.....................................................................................................................................................................................3-149

MITM.....................................................................................................................................................................................3-149

MKISOM...............................................................................................................................................................................3-149

MOD......................................................................................................................................................................................3-150

MODSTO .............................................................................................................................................................................3-150

MODULAR ..........................................................................................................................................................................3-150

MOLWT................................................................................................................................................................................3-151

MROOT ................................................................................................................................................................................3-151

MSGBOX..............................................................................................................................................................................3-151

MSLV .....................................................................................................................................................................................3-152

MSOLVR...............................................................................................................................................................................3-152

MULTMOD..........................................................................................................................................................................3-153

MUSER..................................................................................................................................................................................3-153

→NDISP...............................................................................................................................................................................3-153

NDIST ...................................................................................................................................................................................3-154

NDUPN.................................................................................................................................................................................3-154

NEG.......................................................................................................................................................................................3-154

NEWOB................................................................................................................................................................................3-155

NEXT ....................................................................................................................................................................................3-155

NEXTPRIME.......................................................................................................................................................................3-155

NIP .........................................................................................................................................................................................3-156

NOT.......................................................................................................................................................................................3-156

NOVAL.................................................................................................................................................................................3-156

NΣ...........................................................................................................................................................................................3-157

NSUB .....................................................................................................................................................................................3-157

→NUM..................................................................................................................................................................................3-157

NUM ......................................................................................................................................................................................3-157

NUMX ...................................................................................................................................................................................3-158

NUMY ...................................................................................................................................................................................3-158

OBJ→.....................................................................................................................................................................................3-158

OCT........................................................................................................................................................................................3-159

OFF ........................................................................................................................................................................................3-159

OLDPRT...............................................................................................................................................................................3-159

OPENIO...............................................................................................................................................................................3-160

OR...........................................................................................................................................................................................3-160

ORDER.................................................................................................................................................................................3-161

OVER ....................................................................................................................................................................................3-161

P2C .........................................................................................................................................................................................3-162

Contents - 10

PA2B2 ....................................................................................................................................................................................3-162

PARAMETRIC ....................................................................................................................................................................3-162

PARITY.................................................................................................................................................................................3-163

PARSURFACE.....................................................................................................................................................................3-164

PARTFRAC..........................................................................................................................................................................3-164

PATH.....................................................................................................................................................................................3-165

PCAR......................................................................................................................................................................................3-165

PCOEF ..................................................................................................................................................................................3-165

PCONTOUR........................................................................................................................................................................3-166

PCOV.....................................................................................................................................................................................3-166

PDIM .....................................................................................................................................................................................3-167

PERINFO .............................................................................................................................................................................3-167

PERM.....................................................................................................................................................................................3-167

PERTBL ................................................................................................................................................................................3-168

PEVAL...................................................................................................................................................................................3-168

PGDIR...................................................................................................................................................................................3-168

PICK.......................................................................................................................................................................................3-168

PICK3 ....................................................................................................................................................................................3-168

PICT.......................................................................................................................................................................................3-169

PICTURE..............................................................................................................................................................................3-169

PINIT.....................................................................................................................................................................................3-169

PIX?........................................................................................................................................................................................3-170

PIXOFF.................................................................................................................................................................................3-170

PIXON...................................................................................................................................................................................3-170

PKT ........................................................................................................................................................................................3-170

PLOT .....................................................................................................................................................................................3-171

PLOTADD ...........................................................................................................................................................................3-171

PMAX ....................................................................................................................................................................................3-171

PMIN .....................................................................................................................................................................................3-171

PMINI....................................................................................................................................................................................3-172

POLAR ..................................................................................................................................................................................3-172

POLYNOMIAL...................................................................................................................................................................3-173

POP ........................................................................................................................................................................................3-173

POS.........................................................................................................................................................................................3-174

POTENTIAL .......................................................................................................................................................................3-174

POWEXPAND....................................................................................................................................................................3-174

POWMOD............................................................................................................................................................................3-175

PR1 .........................................................................................................................................................................................3-175

PREDV..................................................................................................................................................................................3-176

PREDX..................................................................................................................................................................................3-176

PREDY..................................................................................................................................................................................3-177

PREVAL................................................................................................................................................................................3-177

PREVPRIME........................................................................................................................................................................3-178

PRLCD...................................................................................................................................................................................3-178

PROMPT...............................................................................................................................................................................3-178

PROMPTSTO......................................................................................................................................................................3-178

PROOT..................................................................................................................................................................................3-179

PROPFRAC..........................................................................................................................................................................3-179

PRST.......................................................................................................................................................................................3-180

PRSTC....................................................................................................................................................................................3-180

PRVAR...................................................................................................................................................................................3-180

PSDEV...................................................................................................................................................................................3-181

PSI...........................................................................................................................................................................................3-181

Psi............................................................................................................................................................................................3-181

PTAYL...................................................................................................................................................................................3-182

PTPROP................................................................................................................................................................................3-182

Contents - 11

PURGE..................................................................................................................................................................................3-182

PUSH......................................................................................................................................................................................3-183

PUT ........................................................................................................................................................................................3-183

PUTI.......................................................................................................................................................................................3-184

PVAR .....................................................................................................................................................................................3-185

PVARS...................................................................................................................................................................................3-185

PVIEW...................................................................................................................................................................................3-186

PWRFIT.................................................................................................................................................................................3-186

PX→C....................................................................................................................................................................................3-187

→Q.........................................................................................................................................................................................3-187

→Qπ.......................................................................................................................................................................................3-187

qr .............................................................................................................................................................................................3-188

QR...........................................................................................................................................................................................3-188

QUAD....................................................................................................................................................................................3-188

QUOT....................................................................................................................................................................................3-189

QUOTE.................................................................................................................................................................................3-189

QXA.......................................................................................................................................................................................3-190

RAD........................................................................................................................................................................................3-190

RAND....................................................................................................................................................................................3-190

RANK....................................................................................................................................................................................3-190

RANM....................................................................................................................................................................................3-191

RATIO...................................................................................................................................................................................3-191

RCEQ.....................................................................................................................................................................................3-192

RCI..........................................................................................................................................................................................3-192

RCIJ........................................................................................................................................................................................3-192

RCL.........................................................................................................................................................................................3-193

RCLALARM.........................................................................................................................................................................3-193

RCLF......................................................................................................................................................................................3-194

RCLKEYS.............................................................................................................................................................................3-194

RCLMENU...........................................................................................................................................................................3-194

RCLVX ..................................................................................................................................................................................3-195

RCLΣ......................................................................................................................................................................................3-195

RCWS.....................................................................................................................................................................................3-195

RDM.......................................................................................................................................................................................3-195

RDZ........................................................................................................................................................................................3-196

RE...........................................................................................................................................................................................3-196

RECN.....................................................................................................................................................................................3-197

RECT .....................................................................................................................................................................................3-197

RECV.....................................................................................................................................................................................3-197

REF.........................................................................................................................................................................................3-198

REMAINDER......................................................................................................................................................................3-198

RENAME..............................................................................................................................................................................3-198

REORDER ...........................................................................................................................................................................3-199

REPEAT................................................................................................................................................................................3-199

REPL......................................................................................................................................................................................3-199

RES.........................................................................................................................................................................................3-200

RESTORE.............................................................................................................................................................................3-201

RESULTANT.......................................................................................................................................................................3-201

REVLIST...............................................................................................................................................................................3-202

REWRITE.............................................................................................................................................................................3-202

RISCH....................................................................................................................................................................................3-202

RKF........................................................................................................................................................................................3-203

RKFERR ...............................................................................................................................................................................3-203

RKFSTEP..............................................................................................................................................................................3-204

RL............................................................................................................................................................................................3-204

RLB.........................................................................................................................................................................................3-205

Contents - 12

RND.......................................................................................................................................................................................3-205

RNRM....................................................................................................................................................................................3-206

ROLL .....................................................................................................................................................................................3-206

ROLLD..................................................................................................................................................................................3-206

ROMUPLOAD....................................................................................................................................................................3-206

ROOT....................................................................................................................................................................................3-207

ROT........................................................................................................................................................................................3-207

ROW– ....................................................................................................................................................................................3-207

ROW+ ...................................................................................................................................................................................3-208

ROW→..................................................................................................................................................................................3-208

→ROW..................................................................................................................................................................................3-208

RPL>......................................................................................................................................................................................3-209

RR ...........................................................................................................................................................................................3-209

RRB ........................................................................................................................................................................................3-209

rref...........................................................................................................................................................................................3-210

RREF......................................................................................................................................................................................3-210

RREFMOD...........................................................................................................................................................................3-211

RRK........................................................................................................................................................................................3-211

RRKSTEP .............................................................................................................................................................................3-212

RSBERR ................................................................................................................................................................................3-213

RSD ........................................................................................................................................................................................3-213

RSWP .....................................................................................................................................................................................3-214

RULES...................................................................................................................................................................................3-214

R→B.......................................................................................................................................................................................3-214

R→C.......................................................................................................................................................................................3-215

R→D......................................................................................................................................................................................3-215

R→I........................................................................................................................................................................................3-215

SAME.....................................................................................................................................................................................3-215

SBRK......................................................................................................................................................................................3-216

SCALE...................................................................................................................................................................................3-216

SCALEH................................................................................................................................................................................3-216

SCALEW...............................................................................................................................................................................3-216

SCATRPLOT........................................................................................................................................................................3-217

SCATTER .............................................................................................................................................................................3-217

SCHUR ..................................................................................................................................................................................3-218

SCI ..........................................................................................................................................................................................3-218

SCLΣ ......................................................................................................................................................................................3-218

SCONJ ...................................................................................................................................................................................3-219

SCROLL................................................................................................................................................................................3-219

SDEV.....................................................................................................................................................................................3-219

SEND.....................................................................................................................................................................................3-219

SEQ ........................................................................................................................................................................................3-220

SERIES..................................................................................................................................................................................3-220

SERVER................................................................................................................................................................................3-221

SEVAL...................................................................................................................................................................................3-221

SF ............................................................................................................................................................................................3-221

SHOW....................................................................................................................................................................................3-222

SIDENS.................................................................................................................................................................................3-222

SIGMA...................................................................................................................................................................................3-222

SIGMAVX ............................................................................................................................................................................3-223

SIGN......................................................................................................................................................................................3-223

SIGNTAB .............................................................................................................................................................................3-224

SIMP2.....................................................................................................................................................................................3-224

SIMPLIFY.............................................................................................................................................................................3-225

SIN..........................................................................................................................................................................................3-225

SINCOS.................................................................................................................................................................................3-225

Contents - 13

SINH......................................................................................................................................................................................3-226

SINV.......................................................................................................................................................................................3-226

SIZE.......................................................................................................................................................................................3-226

SL............................................................................................................................................................................................3-227

SLB .........................................................................................................................................................................................3-227

SLOPEFIELD......................................................................................................................................................................3-227

SNEG.....................................................................................................................................................................................3-228

SNRM.....................................................................................................................................................................................3-228

SOLVE...................................................................................................................................................................................3-229

SOLVEQN ...........................................................................................................................................................................3-229

SOLVER................................................................................................................................................................................3-230

SOLVEVX............................................................................................................................................................................3-230

SORT......................................................................................................................................................................................3-230

SPHERE................................................................................................................................................................................3-231

SQ ...........................................................................................................................................................................................3-231

SR............................................................................................................................................................................................3-231

SRAD .....................................................................................................................................................................................3-231

SRB.........................................................................................................................................................................................3-232

SRECV...................................................................................................................................................................................3-232

SREPL....................................................................................................................................................................................3-233

SST..........................................................................................................................................................................................3-233

SST↓........................................................................................................................................................................................3-233

START ...................................................................................................................................................................................3-234

STD ........................................................................................................................................................................................3-234

STEP ......................................................................................................................................................................................3-235

STEQ .....................................................................................................................................................................................3-235

STIME....................................................................................................................................................................................3-235

STO ........................................................................................................................................................................................3-236

STOALARM.........................................................................................................................................................................3-236

STOF......................................................................................................................................................................................3-237

STOKEYS.............................................................................................................................................................................3-237

STORE...................................................................................................................................................................................3-238

STOVX..................................................................................................................................................................................3-238

STO+ .....................................................................................................................................................................................3-238

STO–......................................................................................................................................................................................3-239

STO* ......................................................................................................................................................................................3-239

STO/......................................................................................................................................................................................3-239

STOΣ......................................................................................................................................................................................3-240

STR→.....................................................................................................................................................................................3-240

→STR.....................................................................................................................................................................................3-240

STREAM...............................................................................................................................................................................3-241

STRM .....................................................................................................................................................................................3-241

STURM..................................................................................................................................................................................3-241

STURMAB............................................................................................................................................................................3-242

STWS......................................................................................................................................................................................3-242

SUB.........................................................................................................................................................................................3-242

SUBST....................................................................................................................................................................................3-243

SUBTMOD...........................................................................................................................................................................3-243

SVD........................................................................................................................................................................................3-244

SVL.........................................................................................................................................................................................3-244

SWAP.....................................................................................................................................................................................3-244

SYSEVAL..............................................................................................................................................................................3-245

SYLVESTER........................................................................................................................................................................3-245

SYST2MAT...........................................................................................................................................................................3-245

%T ..........................................................................................................................................................................................3-246

TABVAL ...............................................................................................................................................................................3-246

Contents - 14

TABVAR...............................................................................................................................................................................3-247

→TAG...................................................................................................................................................................................3-247

TAIL.......................................................................................................................................................................................3-247

TAN........................................................................................................................................................................................3-248

TAN2CS2..............................................................................................................................................................................3-248

TAN2SC ................................................................................................................................................................................3-248

TAN2SC2..............................................................................................................................................................................3-249

TANH....................................................................................................................................................................................3-249

TAYLOR0.............................................................................................................................................................................3-250

TAYLR...................................................................................................................................................................................3-250

TCHEBYCHEFF ................................................................................................................................................................3-250

TCOLLECT..........................................................................................................................................................................3-251

TDELTA...............................................................................................................................................................................3-251

TESTS....................................................................................................................................................................................3-251

TEVAL ..................................................................................................................................................................................3-252

TEXPAND ...........................................................................................................................................................................3-252

TEXT.....................................................................................................................................................................................3-252

THEN....................................................................................................................................................................................3-252

TICKS....................................................................................................................................................................................3-253

TIME......................................................................................................................................................................................3-253

→TIME.................................................................................................................................................................................3-253

TINC......................................................................................................................................................................................3-253

TLIN ......................................................................................................................................................................................3-254

TLINE ...................................................................................................................................................................................3-254

TMENU.................................................................................................................................................................................3-255

TOT........................................................................................................................................................................................3-255

TRACE ..................................................................................................................................................................................3-255

TRAN.....................................................................................................................................................................................3-255

TRANSIO .............................................................................................................................................................................3-256

TRIG......................................................................................................................................................................................3-256

TRIGCOS .............................................................................................................................................................................3-257

TRIGO...................................................................................................................................................................................3-257

TRIGSIN...............................................................................................................................................................................3-257

TRIGTAN.............................................................................................................................................................................3-257

TRN........................................................................................................................................................................................3-258

TRNC.....................................................................................................................................................................................3-258

TRUNC..................................................................................................................................................................................3-259

TRUTH..................................................................................................................................................................................3-259

TSIMP....................................................................................................................................................................................3-260

TSTR ......................................................................................................................................................................................3-260

TVARS...................................................................................................................................................................................3-261

TVM .......................................................................................................................................................................................3-261

TVMBEG..............................................................................................................................................................................3-261

TVMEND.............................................................................................................................................................................3-261

TVMROOT ..........................................................................................................................................................................3-261

TYPE......................................................................................................................................................................................3-262

UBASE...................................................................................................................................................................................3-262

UFACT ..................................................................................................................................................................................3-263

UFL1→MINIF.....................................................................................................................................................................3-263

UNASSIGN..........................................................................................................................................................................3-263

UNASSUME.........................................................................................................................................................................3-263

UNBIND...............................................................................................................................................................................3-264

→UNIT.................................................................................................................................................................................3-264

UNPICK................................................................................................................................................................................3-264

UNROT.................................................................................................................................................................................3-265

UNTIL...................................................................................................................................................................................3-265

Contents - 15

UPDIR...................................................................................................................................................................................3-265

UTPC .....................................................................................................................................................................................3-265

UTPF......................................................................................................................................................................................3-266

UTPN.....................................................................................................................................................................................3-266

UTPT......................................................................................................................................................................................3-267

UVAL.....................................................................................................................................................................................3-267

V→ .........................................................................................................................................................................................3-267

→V2.......................................................................................................................................................................................3-268

→V3.......................................................................................................................................................................................3-268

VANDERMONDE ............................................................................................................................................................3-269

VAR........................................................................................................................................................................................3-269

VARS......................................................................................................................................................................................3-270

VER........................................................................................................................................................................................3-270

VERSION.............................................................................................................................................................................3-270

VISIT......................................................................................................................................................................................3-271

VISITB...................................................................................................................................................................................3-271

VPOTENTIAL....................................................................................................................................................................3-271

VTYPE...................................................................................................................................................................................3-272

*W...........................................................................................................................................................................................3-272

WAIT .....................................................................................................................................................................................3-272

WHILE ..................................................................................................................................................................................3-273

WIREFRAME......................................................................................................................................................................3-273

WSLOG.................................................................................................................................................................................3-274

ΣX...........................................................................................................................................................................................3-275

ΣX2.........................................................................................................................................................................................3-275

ΣX^2 ......................................................................................................................................................................................3-276

XCOL.....................................................................................................................................................................................3-276

XGET ....................................................................................................................................................................................3-276

XMIT......................................................................................................................................................................................3-276

XNUM ...................................................................................................................................................................................3-277

XOR .......................................................................................................................................................................................3-277

XPON....................................................................................................................................................................................3-278

XPUT.....................................................................................................................................................................................3-278

XQ ..........................................................................................................................................................................................3-278

XRECV..................................................................................................................................................................................3-279

XRNG....................................................................................................................................................................................3-279

XROOT.................................................................................................................................................................................3-279

XSEND..................................................................................................................................................................................3-280

XSERV...................................................................................................................................................................................3-280

XVOL.....................................................................................................................................................................................3-281

XXRNG.................................................................................................................................................................................3-281

ΣXY........................................................................................................................................................................................3-281

ΣX*Y......................................................................................................................................................................................3-281

ΣY...........................................................................................................................................................................................3-282

ΣY2.........................................................................................................................................................................................3-282

ΣY^2.......................................................................................................................................................................................3-282

YCOL.....................................................................................................................................................................................3-282

YRNG....................................................................................................................................................................................3-283

YSLICE..................................................................................................................................................................................3-283

YVOL.....................................................................................................................................................................................3-284

YYRNG.................................................................................................................................................................................3-284

ZEROS ..................................................................................................................................................................................3-284

ZFACTOR............................................................................................................................................................................3-285

ZVOL.....................................................................................................................................................................................3-285

^ (Power) ...........................................................................................................................................................................3-285

| (Where)...........................................................................................................................................................................3-286

Contents - 16

√ (Square Root).................................................................................................................................................................3-286

∫ (Integrate).......................................................................................................................................................................3-288

? (Undefined)....................................................................................................................................................................3-288

∞ (Infinity)........................................................................................................................................................................3-289

Σ (Summation).................................................................................................................................................................3-289

Σ+ (Sigma Plus)..............................................................................................................................................................3-289

Σ– (Sigma Minus)..........................................................................................................................................................3-290

π (Pi)..................................................................................................................................................................................3-290

∂ (Derivative) ....................................................................................................................................................................3-291

! (Factorial) .......................................................................................................................................................................3-291

% (Percent)........................................................................................................................................................................3-292

_ (Unit attachment)..........................................................................................................................................................3-292

« » (Program delimiters)...............................................................................................................................................3-293

< (Less than)......................................................................................................................................................................3-293

≤ (Less than or Equal) .....................................................................................................................................................3-294

> (Greater than)................................................................................................................................................................3-295

≥ (Greater than or Equal)................................................................................................................................................3-295

≠ (Not equal).....................................................................................................................................................................3-296

* (Multiply)........................................................................................................................................................................3-297

+ (Add)...............................................................................................................................................................................3-298

– (Subtract)........................................................................................................................................................................3-299

/ (Divide)...........................................................................................................................................................................3-300

= (Equal) ............................................................................................................................................................................3-301

== (Logical Equality) ....................................................................................................................................................3-302

 (Store)..............................................................................................................................................................................3-303

→ (Create Local)...........................................................................................................................................................3-303

; (Semicolon)....................................................................................................................................................................3-304

4. Computer Algebra System .........................................................................................................................................................4-1

CAS Settings..............................................................................................................................................................................4-1

Selecting CAS Settings .....................................................................................................................................................4-1

The CAS directory, CASDIR..........................................................................................................................................4-1

Points to note when choosing settings..........................................................................................................................4-1

Using the CAS...........................................................................................................................................................................4-3

Examples and Help ..........................................................................................................................................................4-3

Compatibility with Other Calculators............................................................................................................................4-3

Extending the CAS...........................................................................................................................................................4-3

Dealing with unexpected CAS results or messages.....................................................................................................4-3

5. Equation Reference.....................................................................................................................................................................5-1

Columns and Beams (1) ..........................................................................................................................................................5-3

Elastic Buckling (1, 1).......................................................................................................................................................5-4

Eccentric Columns (1, 2).................................................................................................................................................5-4

Simple Deflection (1, 3)...................................................................................................................................................5-5

Simple Slope (1, 4)............................................................................................................................................................5-5

Simple Moment (1, 5).......................................................................................................................................................5-6

Simple Shear (1, 6)............................................................................................................................................................5-6

Cantilever Deflection (1, 7).............................................................................................................................................5-7

Cantilever Slope (1, 8)......................................................................................................................................................5-7

Cantilever Moment (1, 9).................................................................................................................................................5-7

Cantilever Shear (1, 10)....................................................................................................................................................5-8

Electricity (2).............................................................................................................................................................................5-9

Coulomb’s Law (2, 1).....................................................................................................................................................5-10

Ohm’s Law and Power (2, 2)........................................................................................................................................5-10

Voltage Divider (2, 3).....................................................................................................................................................5-11

Current Divider (2, 4).....................................................................................................................................................5-11

Wire Resistance (2, 5).....................................................................................................................................................5-11

Series and Parallel R (2, 6) .............................................................................................................................................5-12

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