HP 48GII User manual

hp 49g+/ hp 48gII graphing calculator
advanced user's reference manual
H
Edition 1
HP part number F2228-90010
Printed Date: 2005/9/17


Notice
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THIS MANUAL OR THE EXAMPLES CONTAINED HEREIN.
© Copyright 1993-1998, 2005 Hewlett-Packard Development Company, L.P.
Reproduction, adaptation, or translation of this manual is prohibited without prior written permission of Hewlett-
Packard Company, except as allowed under the copyright laws.
Hewlett-Packard Company
4995 Murphy Canyon Rd,
Suite 301
San Diego, CA 92123
Acknowledgements
Hewlett-Packard would like to thank the following for their contribution:
Gene Wright, Tony Hutchins, Wlodek Mier-Jedrzejowicz, Jordi Hidalgo, Ted Kerber, Joe Horn, Richard Nelson
and Jake Schwartz.
Printing History
Edition 1 September 2005


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 .............................................................................................................................................1-8
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..............................................................................................................................1-21
Using Loop Counters ................................................................................................................................................1-24
Using Summations Instead of Loops ........................................................................................................................1-25
Using Flags.......................................................................................................................................................................1-25
Types of Flags...........................................................................................................................................................1-26
Setting, Clearing, and Testing Flags ......................................................................................................................... 1-26
Recalling and Storing the Flag States .......................................................................................................................1-27
Using Subroutines ............................................................................................................................................................1-28
Single-Stepping through a Program .................................................................................................................................1-29
Trapping Errors ................................................................................................................................................................1-32
Causing and Analyzing Errors ..................................................................................................................................1-32
Making an Error Trap ...............................................................................................................................................1-33
Input .................................................................................................................................................................................1-35
Data Input Commands...............................................................................................................................................1-35
Using PROMPT … CONT for Input ........................................................................................................................1-35
Using DISP FREEZE HALT … CONT for Input .................................................................................................... 1-37
Using INPUT … ENTER for Input .......................................................................................................................... 1-38
Using INFORM and CHOOSE for Input.................................................................................................................. 1-42
Beeping to Get Attention ..........................................................................................................................................1-45
Stopping a Program for Keystroke Input .........................................................................................................................1-46
Using WAIT for Keystroke Input .............................................................................................................................1-46
Using KEY for Keystroke Input ...............................................................................................................................1-46
Output .......................................................................................................................................................................1-46
Data Output Commands............................................................................................................................................ 1-47
Labeling Output with Tags .......................................................................................................................................1-47
Labeling and Displaying Output as Strings ..............................................................................................................1-48
Pausing to Display Output ........................................................................................................................................ 1-48
Using MSGBOX to Display Output .........................................................................................................................1-49
Using Menus with Programs............................................................................................................................................1-49
Using Menus for Input .............................................................................................................................................. 1-50
Using Menus to Run Programs .................................................................................................................................1-50
Turning Off the hp49g+/hp48gII from a Program ...........................................................................................................1-52
2. RPL Programming Examples ................................................................................................................................................2-1
Fibonacci Numbers ............................................................................................................................................................2-1

Contents - 2
FIB1 (Fibonacci Numbers, Recursive Version).......................................................................................................... 2-1
FIB2 (Fibonacci Numbers, Loop Version) ................................................................................................................. 2-2
FIBT (Comparing Program-Execution Time)............................................................................................................. 2-3
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 ............................................................................................................................ 2-14
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) ........................................................................................................ 2-24
Converting Procedures from Algebraic to RPN .............................................................................................................. 2-27
Bessel Functions .............................................................................................................................................................. 2-29
Animation of Successive Taylor's Polynomials............................................................................................................... 2-30
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.............................................................................................................................................................................. 3-4
ABS ................................................................................................................................................................................... 3-4
ACK ................................................................................................................................................................................... 3-4
ACKALL ............................................................................................................................................................................ 3-4
ACOS ................................................................................................................................................................................ 3-5
ACOS2S ........................................................................................................................................................................... 3-6
ACOSH ............................................................................................................................................................................. 3-6
ADD................................................................................................................................................................................... 3-7
ADDTMOD ....................................................................................................................................................................... 3-8
ADDTOREAL ................................................................................................................................................................... 3-8
ALGB................................................................................................................................................................................. 3-8
ALOG ................................................................................................................................................................................ 3-8
AMORT ............................................................................................................................................................................. 3-8
AND................................................................................................................................................................................... 3-8
ANIMATE.......................................................................................................................................................................... 3-9
ANS ................................................................................................................................................................................. 3-10
APPLY............................................................................................................................................................................. 3-10
ARC................................................................................................................................................................................. 3-10
ARCHIVE........................................................................................................................................................................ 3-11
ARG................................................................................................................................................................................. 3-11
ARIT ................................................................................................................................................................................ 3-12
ARRY→.......................................................................................................................................................................... 3-12
→ARRY .......................................................................................................................................................................... 3-12
ASIN ................................................................................................................................................................................ 3-12
ASIN2C ........................................................................................................................................................................... 3-14
ASIN2T ........................................................................................................................................................................... 3-14

Contents - 3
ASINH..............................................................................................................................................................................3-14
ASN .................................................................................................................................................................................3-14
ASR .................................................................................................................................................................................3-15
ASSUME.........................................................................................................................................................................3-16
ATAN ...............................................................................................................................................................................3-16
ATAN2S ..........................................................................................................................................................................3-17
ATANH ............................................................................................................................................................................3-17
ATICK..............................................................................................................................................................................3-18
ATTACH..........................................................................................................................................................................3-18
AUGMENT......................................................................................................................................................................3-19
AUTO...............................................................................................................................................................................3-19
AXES ...............................................................................................................................................................................3-20
AXL ..................................................................................................................................................................................3-20
AXM .................................................................................................................................................................................3-20
AXQ .................................................................................................................................................................................3-20
BAR .................................................................................................................................................................................3-20
BARPLOT .......................................................................................................................................................................3-21
BASIS ..............................................................................................................................................................................3-22
BAUD...............................................................................................................................................................................3-22
BEEP ...............................................................................................................................................................................3-22
BESTFIT .........................................................................................................................................................................3-22
BIN ...................................................................................................................................................................................3-22
BINS ................................................................................................................................................................................3-23
BLANK.............................................................................................................................................................................3-23
BOX .................................................................................................................................................................................3-23
BUFLEN ..........................................................................................................................................................................3-24
BYTES.............................................................................................................................................................................3-24
B→R................................................................................................................................................................................3-24
C2P..................................................................................................................................................................................3-24
CASCFG .........................................................................................................................................................................3-25
CASCMD ........................................................................................................................................................................3-25
CASE...............................................................................................................................................................................3-25
CEIL.................................................................................................................................................................................3-25
CENTR............................................................................................................................................................................3-26
CF ....................................................................................................................................................................................3-26
%CH ................................................................................................................................................................................3-26
CHINREM .......................................................................................................................................................................3-27
CHOLESKY ....................................................................................................................................................................3-27
CHOOSE ........................................................................................................................................................................3-27
CHR .................................................................................................................................................................................3-27
CIRC................................................................................................................................................................................3-28
CKSM ..............................................................................................................................................................................3-28
CLEAR ............................................................................................................................................................................3-28
CLKADJ ..........................................................................................................................................................................3-28
CLLCD.............................................................................................................................................................................3-29
CLOSEIO ........................................................................................................................................................................3-29
CLΣ..................................................................................................................................................................................3-29
CLVAR ............................................................................................................................................................................3-29
CMPLX............................................................................................................................................................................3-29
CNRM..............................................................................................................................................................................3-30
→COL..............................................................................................................................................................................3-30
COL→..............................................................................................................................................................................3-30
COL– ...............................................................................................................................................................................3-30
COL+ ...............................................................................................................................................................................3-31
COLCT ............................................................................................................................................................................3-31
COLLECT .......................................................................................................................................................................3-31
COLΣ...............................................................................................................................................................................3-31
COMB..............................................................................................................................................................................3-32

Contents - 4
CON................................................................................................................................................................................. 3-32
COND.............................................................................................................................................................................. 3-33
CONIC............................................................................................................................................................................. 3-33
CONJ............................................................................................................................................................................... 3-34
CONLIB........................................................................................................................................................................... 3-34
CONST ........................................................................................................................................................................... 3-35
CONSTANTS................................................................................................................................................................. 3-35
CONT .............................................................................................................................................................................. 3-35
CONVERT...................................................................................................................................................................... 3-35
CORR.............................................................................................................................................................................. 3-35
COS................................................................................................................................................................................. 3-36
COSH.............................................................................................................................................................................. 3-36
COV................................................................................................................................................................................. 3-37
CR.................................................................................................................................................................................... 3-37
CRDIR............................................................................................................................................................................. 3-37
CROSS ........................................................................................................................................................................... 3-37
CSWP ............................................................................................................................................................................. 3-38
CURL............................................................................................................................................................................... 3-38
CYCLOTOMIC............................................................................................................................................................... 3-38
CYLIN.............................................................................................................................................................................. 3-38
C→PX ............................................................................................................................................................................. 3-38
C→R................................................................................................................................................................................ 3-39
DARCY ........................................................................................................................................................................... 3-39
DATE............................................................................................................................................................................... 3-39
→DATE........................................................................................................................................................................... 3-39
DATE+ ............................................................................................................................................................................ 3-40
DBUG.............................................................................................................................................................................. 3-40
DDAYS............................................................................................................................................................................ 3-40
DEC................................................................................................................................................................................. 3-41
DECR .............................................................................................................................................................................. 3-41
DEDICACE..................................................................................................................................................................... 3-41
DEF ................................................................................................................................................................................. 3-41
DEFINE........................................................................................................................................................................... 3-41
DEG................................................................................................................................................................................. 3-42
DEGREE......................................................................................................................................................................... 3-42
DELALARM.................................................................................................................................................................... 3-42
DELAY ............................................................................................................................................................................ 3-42
DELKEYS ....................................................................................................................................................................... 3-42
DEPND ........................................................................................................................................................................... 3-43
DEPTH............................................................................................................................................................................ 3-44
DERIV ............................................................................................................................................................................. 3-44
DERVX............................................................................................................................................................................ 3-44
DESOLVE....................................................................................................................................................................... 3-44
DET ................................................................................................................................................................................. 3-44
DETACH ......................................................................................................................................................................... 3-44
DIAG→............................................................................................................................................................................ 3-45
→DIAG............................................................................................................................................................................ 3-45
DIAGMAP ....................................................................................................................................................................... 3-45
DIFF................................................................................................................................................................................. 3-45
DIFFEQ........................................................................................................................................................................... 3-46
DIR................................................................................................................................................................................... 3-47
DISP ................................................................................................................................................................................ 3-47
DISPXY........................................................................................................................................................................... 3-47
DISTRIB.......................................................................................................................................................................... 3-48
DIV................................................................................................................................................................................... 3-48
DIV2................................................................................................................................................................................. 3-48
DIV2MOD ....................................................................................................................................................................... 3-48
DIVIS ............................................................................................................................................................................... 3-48

Contents - 5
DIVMOD..........................................................................................................................................................................3-48
DIVPC..............................................................................................................................................................................3-48
dn .....................................................................................................................................................................................3-48
DO....................................................................................................................................................................................3-48
DOERR ...........................................................................................................................................................................3-49
DOLIST ...........................................................................................................................................................................3-49
DOMAIN..........................................................................................................................................................................3-50
DOSUBS.........................................................................................................................................................................3-50
DOT .................................................................................................................................................................................3-50
DRAW .............................................................................................................................................................................3-51
DRAW3DMATRIX .........................................................................................................................................................3-51
DRAX...............................................................................................................................................................................3-51
DROITE...........................................................................................................................................................................3-52
DROP ..............................................................................................................................................................................3-52
DROP2............................................................................................................................................................................3-52
DROPN ...........................................................................................................................................................................3-52
DTAG...............................................................................................................................................................................3-52
DUP .................................................................................................................................................................................3-53
DUP2 ...............................................................................................................................................................................3-53
DUPDUP.........................................................................................................................................................................3-53
DUPN ..............................................................................................................................................................................3-53
D→R................................................................................................................................................................................3-54
e.......................................................................................................................................................................................3-54
EDIT.................................................................................................................................................................................3-54
EDITB..............................................................................................................................................................................3-55
EGCD ..............................................................................................................................................................................3-55
EGV .................................................................................................................................................................................3-55
EGVL ...............................................................................................................................................................................3-55
ELSE................................................................................................................................................................................3-55
END .................................................................................................................................................................................3-56
ENDSUB .........................................................................................................................................................................3-56
ENG .................................................................................................................................................................................3-56
EPSX0.............................................................................................................................................................................3-56
EQNLIB ...........................................................................................................................................................................3-56
EQW ................................................................................................................................................................................3-57
EQ→................................................................................................................................................................................3-57
ERASE ............................................................................................................................................................................3-57
ERR0 ...............................................................................................................................................................................3-57
ERRM..............................................................................................................................................................................3-57
ERRN ..............................................................................................................................................................................3-58
EULER ............................................................................................................................................................................3-58
EVAL................................................................................................................................................................................3-58
EXLR ...............................................................................................................................................................................3-59
EX&LN.............................................................................................................................................................................3-59
EXP..................................................................................................................................................................................3-59
EXP2HYP .......................................................................................................................................................................3-60
EXP2POW ......................................................................................................................................................................3-60
EXPAN ............................................................................................................................................................................3-60
EXPAND .........................................................................................................................................................................3-60
EXPANDMOD ................................................................................................................................................................3-60
EXPFIT............................................................................................................................................................................3-60
EXPLN.............................................................................................................................................................................3-60
EXPM ..............................................................................................................................................................................3-60
EYEPT.............................................................................................................................................................................3-61
F0λ...................................................................................................................................................................................3-61
FACT ...............................................................................................................................................................................3-61
FACTOR .........................................................................................................................................................................3-62
FACTORMOD ................................................................................................................................................................3-62

Contents - 6
FACTORS ...................................................................................................................................................................... 3-62
FANNING ....................................................................................................................................................................... 3-62
FAST3D .......................................................................................................................................................................... 3-62
FCOEF............................................................................................................................................................................ 3-63
FC?.................................................................................................................................................................................. 3-63
FC?C............................................................................................................................................................................... 3-63
FDISTRIB ....................................................................................................................................................................... 3-64
FFT .................................................................................................................................................................................. 3-64
FILER .............................................................................................................................................................................. 3-64
FINDALARM .................................................................................................................................................................. 3-64
FINISH ............................................................................................................................................................................ 3-65
FIX ................................................................................................................................................................................... 3-65
FLASHEVAL .................................................................................................................................................................. 3-65
FLOOR............................................................................................................................................................................ 3-66
FONT6 ............................................................................................................................................................................ 3-66
FONT7 ............................................................................................................................................................................ 3-66
FONT8 ............................................................................................................................................................................ 3-66
FONT→........................................................................................................................................................................... 3-67
→FONT........................................................................................................................................................................... 3-67
FOR................................................................................................................................................................................. 3-67
FOURIER ....................................................................................................................................................................... 3-68
FP .................................................................................................................................................................................... 3-68
FREE............................................................................................................................................................................... 3-68
FREEZE.......................................................................................................................................................................... 3-68
FROOTS......................................................................................................................................................................... 3-69
FS? .................................................................................................................................................................................. 3-69
FS?C ............................................................................................................................................................................... 3-69
FUNCTION..................................................................................................................................................................... 3-70
FXND............................................................................................................................................................................... 3-71
GAMMA .......................................................................................................................................................................... 3-71
GAUSS ........................................................................................................................................................................... 3-71
GBASIS........................................................................................................................................................................... 3-71
GCD................................................................................................................................................................................. 3-71
GCDMOD ....................................................................................................................................................................... 3-71
GET ................................................................................................................................................................................. 3-71
GETI ................................................................................................................................................................................ 3-72
GOR ................................................................................................................................................................................ 3-73
GRAD.............................................................................................................................................................................. 3-73
GRAMSCHMIDT ........................................................................................................................................................... 3-73
GREDUCE ..................................................................................................................................................................... 3-73
GRIDMAP....................................................................................................................................................................... 3-73
→GROB.......................................................................................................................................................................... 3-74
GROB.............................................................................................................................................................................. 3-74
GROBADD ..................................................................................................................................................................... 3-74
GXOR.............................................................................................................................................................................. 3-75
HADAMARD................................................................................................................................................................... 3-75
HALFTAN ....................................................................................................................................................................... 3-75
HALT ............................................................................................................................................................................... 3-75
HEAD .............................................................................................................................................................................. 3-75
HEADER→..................................................................................................................................................................... 3-76
→HEADER..................................................................................................................................................................... 3-76
HELP............................................................................................................................................................................... 3-76
HERMITE ....................................................................................................................................................................... 3-76
HESS............................................................................................................................................................................... 3-76
HEX ................................................................................................................................................................................. 3-76
HILBERT......................................................................................................................................................................... 3-77
HISTOGRAM ................................................................................................................................................................. 3-77
HISTPLOT...................................................................................................................................................................... 3-77

Contents - 7
HMS–...............................................................................................................................................................................3-78
HMS+ ..............................................................................................................................................................................3-78
HMS→.............................................................................................................................................................................3-79
→HMS.............................................................................................................................................................................3-79
HOME..............................................................................................................................................................................3-79
HORNER ........................................................................................................................................................................3-79
i.........................................................................................................................................................................................3-80
IABCUV...........................................................................................................................................................................3-80
IBASIS.............................................................................................................................................................................3-80
IBERNOULLI ..................................................................................................................................................................3-80
IBP ...................................................................................................................................................................................3-80
ICHINREM ......................................................................................................................................................................3-80
IDN...................................................................................................................................................................................3-80
IDIV2................................................................................................................................................................................3-81
IEGCD .............................................................................................................................................................................3-81
IF ......................................................................................................................................................................................3-81
IFERR..............................................................................................................................................................................3-81
IFFT .................................................................................................................................................................................3-82
IFT....................................................................................................................................................................................3-83
IFTE .................................................................................................................................................................................3-83
ILAP .................................................................................................................................................................................3-83
IM .....................................................................................................................................................................................3-83
IMAGE.............................................................................................................................................................................3-84
INCR................................................................................................................................................................................3-84
INDEP..............................................................................................................................................................................3-84
INFORM..........................................................................................................................................................................3-85
INPUT..............................................................................................................................................................................3-86
INT ...................................................................................................................................................................................3-86
INTEGER ........................................................................................................................................................................3-87
INTVX..............................................................................................................................................................................3-87
INV ...................................................................................................................................................................................3-87
INVMOD..........................................................................................................................................................................3-87
IP......................................................................................................................................................................................3-87
IQUOT .............................................................................................................................................................................3-87
IREMAINDER.................................................................................................................................................................3-87
ISOL.................................................................................................................................................................................3-87
ISOM................................................................................................................................................................................3-88
ISPRIME? .......................................................................................................................................................................3-88
I→R..................................................................................................................................................................................3-88
JORDAN .........................................................................................................................................................................3-88
KER .................................................................................................................................................................................3-88
KERRM ...........................................................................................................................................................................3-88
KEY..................................................................................................................................................................................3-89
KEYEVAL........................................................................................................................................................................3-89
→KEYTIME ....................................................................................................................................................................3-89
KEYTIME→....................................................................................................................................................................3-89
KGET...............................................................................................................................................................................3-90
KILL .................................................................................................................................................................................3-90
LABEL .............................................................................................................................................................................3-90
LAGRANGE....................................................................................................................................................................3-90
LANGUAGE→................................................................................................................................................................3-91
→LANGUAGE................................................................................................................................................................3-91
LAP ..................................................................................................................................................................................3-91
LAPL................................................................................................................................................................................3-91
LAST................................................................................................................................................................................3-91
LASTARG .......................................................................................................................................................................3-91
LCD→..............................................................................................................................................................................3-92
→LCD..............................................................................................................................................................................3-92

Contents - 8
LCM................................................................................................................................................................................. 3-92
LCXM .............................................................................................................................................................................. 3-92
LDEC............................................................................................................................................................................... 3-92
LEGENDRE ................................................................................................................................................................... 3-92
LGCD .............................................................................................................................................................................. 3-92
LIBEVAL ......................................................................................................................................................................... 3-92
LIBS................................................................................................................................................................................. 3-93
lim .................................................................................................................................................................................... 3-93
LIMIT ............................................................................................................................................................................... 3-93
LIN ................................................................................................................................................................................... 3-93
LINE................................................................................................................................................................................. 3-93
ΣLINE .............................................................................................................................................................................. 3-93
LINFIT ............................................................................................................................................................................. 3-94
LININ ............................................................................................................................................................................... 3-94
LINSOLVE...................................................................................................................................................................... 3-94
LIST→............................................................................................................................................................................. 3-94
→LIST ............................................................................................................................................................................. 3-94
∆LIST............................................................................................................................................................................... 3-95
ΠLIST.............................................................................................................................................................................. 3-95
ΣLIST............................................................................................................................................................................... 3-95
LN .................................................................................................................................................................................... 3-95
LNAME............................................................................................................................................................................ 3-96
LNCOLLECT.................................................................................................................................................................. 3-97
LNP1 ............................................................................................................................................................................... 3-97
LOCAL ............................................................................................................................................................................ 3-97
LOG................................................................................................................................................................................. 3-97
LOGFIT ........................................................................................................................................................................... 3-98
LQ .................................................................................................................................................................................... 3-98
LR .................................................................................................................................................................................... 3-98
LSQ ................................................................................................................................................................................. 3-99
LU .................................................................................................................................................................................... 3-99
LVAR ............................................................................................................................................................................. 3-100
MAD............................................................................................................................................................................... 3-100
MAIN ............................................................................................................................................................................. 3-100
MANT ............................................................................................................................................................................ 3-100
MAP............................................................................................................................................................................... 3-100
↓MATCH....................................................................................................................................................................... 3-100
↑MATCH....................................................................................................................................................................... 3-101
MATHS ......................................................................................................................................................................... 3-101
MATR ............................................................................................................................................................................ 3-101
MAX............................................................................................................................................................................... 3-101
MAXR............................................................................................................................................................................ 3-102
MAXΣ............................................................................................................................................................................ 3-102
MCALC ......................................................................................................................................................................... 3-102
MEAN............................................................................................................................................................................ 3-103
MEM .............................................................................................................................................................................. 3-103
MENU............................................................................................................................................................................ 3-103
MENUXY ...................................................................................................................................................................... 3-104
MERGE......................................................................................................................................................................... 3-104
MIN ................................................................................................................................................................................ 3-104
MINEHUNT .................................................................................................................................................................. 3-104
MINIFONT→................................................................................................................................................................ 3-105
→MINIFONT ................................................................................................................................................................ 3-105
MINIT............................................................................................................................................................................. 3-105
MINR ............................................................................................................................................................................. 3-106
MINΣ.............................................................................................................................................................................. 3-106
MITM ............................................................................................................................................................................. 3-106
MKISOM ....................................................................................................................................................................... 3-106

Contents - 9
MOD ..............................................................................................................................................................................3-106
MODSTO ......................................................................................................................................................................3-107
MODULAR....................................................................................................................................................................3-107
MROOT.........................................................................................................................................................................3-107
MSGBOX ......................................................................................................................................................................3-107
MSLV.............................................................................................................................................................................3-107
MSOLVR.......................................................................................................................................................................3-107
MULTMOD....................................................................................................................................................................3-108
MUSER .........................................................................................................................................................................3-108
→NDISP........................................................................................................................................................................3-108
NDIST............................................................................................................................................................................3-108
NDUPN .........................................................................................................................................................................3-109
NEG ...............................................................................................................................................................................3-109
NEWOB.........................................................................................................................................................................3-109
NEXT .............................................................................................................................................................................3-110
NEXTPRIME ................................................................................................................................................................3-110
NIP .................................................................................................................................................................................3-110
NOT ...............................................................................................................................................................................3-110
NOVAL ..........................................................................................................................................................................3-111
NΣ..................................................................................................................................................................................3-111
NSUB.............................................................................................................................................................................3-111
→NUM...........................................................................................................................................................................3-111
NUM...............................................................................................................................................................................3-112
NUMX............................................................................................................................................................................3-112
NUMY............................................................................................................................................................................3-112
OBJ→............................................................................................................................................................................3-113
OCT ...............................................................................................................................................................................3-113
OFF................................................................................................................................................................................3-113
OLDPRT........................................................................................................................................................................3-114
OPENIO ........................................................................................................................................................................3-114
OR..................................................................................................................................................................................3-114
ORDER .........................................................................................................................................................................3-115
OVER ............................................................................................................................................................................3-115
P2C................................................................................................................................................................................3-115
PA2B2 ...........................................................................................................................................................................3-115
PARAMETRIC..............................................................................................................................................................3-116
PARITY .........................................................................................................................................................................3-116
PARSURFACE ............................................................................................................................................................3-117
PARTFRAC ..................................................................................................................................................................3-118
PATH .............................................................................................................................................................................3-118
PCAR.............................................................................................................................................................................3-118
PCOEF..........................................................................................................................................................................3-118
PCONTOUR.................................................................................................................................................................3-118
PCOV ............................................................................................................................................................................3-119
PDIM..............................................................................................................................................................................3-119
PERM ............................................................................................................................................................................3-120
PEVAL...........................................................................................................................................................................3-120
PGDIR ...........................................................................................................................................................................3-120
PICK ..............................................................................................................................................................................3-121
PICK3 ............................................................................................................................................................................3-121
PICT...............................................................................................................................................................................3-121
PICTURE ......................................................................................................................................................................3-121
PINIT..............................................................................................................................................................................3-122
PIX? ...............................................................................................................................................................................3-122
PIXOFF .........................................................................................................................................................................3-122
PIXON ...........................................................................................................................................................................3-122
PKT................................................................................................................................................................................3-122
PLOT .............................................................................................................................................................................3-123

Contents - 10
PLOTADD..................................................................................................................................................................... 3-123
PMAX ............................................................................................................................................................................ 3-123
PMIN ............................................................................................................................................................................. 3-123
PMINI ............................................................................................................................................................................ 3-124
POLAR.......................................................................................................................................................................... 3-124
POLYNOMIAL.............................................................................................................................................................. 3-125
POP ............................................................................................................................................................................... 3-125
POS ............................................................................................................................................................................... 3-125
POTENTIAL ................................................................................................................................................................. 3-125
POWEXPAND.............................................................................................................................................................. 3-125
POWMOD..................................................................................................................................................................... 3-125
PR1................................................................................................................................................................................ 3-125
PREDV.......................................................................................................................................................................... 3-126
PREDX.......................................................................................................................................................................... 3-126
PREDY.......................................................................................................................................................................... 3-127
PREVAL........................................................................................................................................................................ 3-127
PREVPRIME ................................................................................................................................................................ 3-127
PRLCD.......................................................................................................................................................................... 3-128
PROMPT ...................................................................................................................................................................... 3-128
PROMPTSTO .............................................................................................................................................................. 3-128
PROOT ......................................................................................................................................................................... 3-128
PROPFRAC ................................................................................................................................................................. 3-129
PRST............................................................................................................................................................................. 3-129
PRSTC.......................................................................................................................................................................... 3-129
PRVAR.......................................................................................................................................................................... 3-129
PSDEV.......................................................................................................................................................................... 3-130
PSI ................................................................................................................................................................................. 3-130
Psi.................................................................................................................................................................................. 3-130
PTAYL........................................................................................................................................................................... 3-130
PURGE ......................................................................................................................................................................... 3-131
PUSH ............................................................................................................................................................................ 3-131
PUT ............................................................................................................................................................................... 3-131
PUTI .............................................................................................................................................................................. 3-132
PVAR............................................................................................................................................................................. 3-133
PVARS.......................................................................................................................................................................... 3-133
PVIEW........................................................................................................................................................................... 3-134
PWRFIT ........................................................................................................................................................................ 3-134
PX→C........................................................................................................................................................................... 3-134
→Q................................................................................................................................................................................ 3-135
→Qπ.............................................................................................................................................................................. 3-135
qr.................................................................................................................................................................................... 3-135
QR ................................................................................................................................................................................. 3-136
QUAD............................................................................................................................................................................ 3-136
QUOT............................................................................................................................................................................ 3-136
QUOTE ......................................................................................................................................................................... 3-136
QXA ............................................................................................................................................................................... 3-137
RAD............................................................................................................................................................................... 3-137
RAND ............................................................................................................................................................................ 3-137
RANK ............................................................................................................................................................................ 3-137
RANM............................................................................................................................................................................ 3-138
RATIO ........................................................................................................................................................................... 3-138
RCEQ............................................................................................................................................................................ 3-139
RCI................................................................................................................................................................................. 3-139
RCIJ............................................................................................................................................................................... 3-139
RCL ............................................................................................................................................................................... 3-139
RCLALARM.................................................................................................................................................................. 3-140
RCLF............................................................................................................................................................................. 3-140
RCLKEYS..................................................................................................................................................................... 3-141

Contents - 11
RCLMENU....................................................................................................................................................................3-141
RCLVX ..........................................................................................................................................................................3-141
RCLΣ.............................................................................................................................................................................3-141
RCWS ...........................................................................................................................................................................3-142
RDM...............................................................................................................................................................................3-142
RDZ ...............................................................................................................................................................................3-142
RE ..................................................................................................................................................................................3-143
RECN ............................................................................................................................................................................3-143
RECT.............................................................................................................................................................................3-143
RECV.............................................................................................................................................................................3-144
REF................................................................................................................................................................................3-144
REMAINDER................................................................................................................................................................3-144
RENAME.......................................................................................................................................................................3-144
REORDER....................................................................................................................................................................3-144
REPEAT........................................................................................................................................................................3-144
REPL .............................................................................................................................................................................3-144
RES ...............................................................................................................................................................................3-145
RESTORE ....................................................................................................................................................................3-146
RESULTANT ................................................................................................................................................................3-146
REVLIST .......................................................................................................................................................................3-146
REWRITE .....................................................................................................................................................................3-147
RISCH ...........................................................................................................................................................................3-147
RKF................................................................................................................................................................................3-147
RKFERR .......................................................................................................................................................................3-147
RKFSTEP .....................................................................................................................................................................3-148
RL...................................................................................................................................................................................3-148
RLB................................................................................................................................................................................3-148
RND ...............................................................................................................................................................................3-149
RNRM............................................................................................................................................................................3-149
ROLL .............................................................................................................................................................................3-150
ROLLD ..........................................................................................................................................................................3-150
ROMUPLOAD ..............................................................................................................................................................3-150
ROOT ............................................................................................................................................................................3-150
ROT ...............................................................................................................................................................................3-151
ROW–............................................................................................................................................................................3-151
ROW+............................................................................................................................................................................3-151
ROW→..........................................................................................................................................................................3-151
→ROW ..........................................................................................................................................................................3-152
RPL>..............................................................................................................................................................................3-152
RR..................................................................................................................................................................................3-152
RRB ...............................................................................................................................................................................3-153
rref..................................................................................................................................................................................3-153
RREF.............................................................................................................................................................................3-153
RREFMOD....................................................................................................................................................................3-153
RRK ...............................................................................................................................................................................3-153
RRKSTEP.....................................................................................................................................................................3-154
RSBERR .......................................................................................................................................................................3-155
RSD ...............................................................................................................................................................................3-155
RSWP............................................................................................................................................................................3-156
RULES ..........................................................................................................................................................................3-156
R→B..............................................................................................................................................................................3-156
R→C..............................................................................................................................................................................3-156
R→D..............................................................................................................................................................................3-157
R→I................................................................................................................................................................................3-157
SAME ............................................................................................................................................................................3-157
SBRK.............................................................................................................................................................................3-157
SCALE...........................................................................................................................................................................3-158
SCALEH........................................................................................................................................................................3-158

Contents - 12
SCALEW....................................................................................................................................................................... 3-158
SCATRPLOT................................................................................................................................................................ 3-158
SCATTER..................................................................................................................................................................... 3-159
SCHUR ......................................................................................................................................................................... 3-159
SCI................................................................................................................................................................................. 3-160
SCLΣ............................................................................................................................................................................. 3-160
SCONJ.......................................................................................................................................................................... 3-160
SCROLL ....................................................................................................................................................................... 3-160
SDEV............................................................................................................................................................................. 3-161
SEND ............................................................................................................................................................................ 3-161
SEQ ............................................................................................................................................................................... 3-161
SERIES......................................................................................................................................................................... 3-162
SERVER ....................................................................................................................................................................... 3-162
SEVAL........................................................................................................................................................................... 3-162
SF .................................................................................................................................................................................. 3-162
SHOW ........................................................................................................................................................................... 3-162
SIDENS......................................................................................................................................................................... 3-163
SIGMA........................................................................................................................................................................... 3-163
SIGMAVX ..................................................................................................................................................................... 3-163
SIGN.............................................................................................................................................................................. 3-163
SIGNTAB...................................................................................................................................................................... 3-164
SIMP2 ........................................................................................................................................................................... 3-164
SIMPLIFY ..................................................................................................................................................................... 3-164
SIN................................................................................................................................................................................. 3-164
SINCOS ........................................................................................................................................................................ 3-164
SINH.............................................................................................................................................................................. 3-164
SINV .............................................................................................................................................................................. 3-165
SIZE............................................................................................................................................................................... 3-165
SL................................................................................................................................................................................... 3-165
SLB................................................................................................................................................................................ 3-166
SLOPEFIELD............................................................................................................................................................... 3-166
SNEG ............................................................................................................................................................................ 3-167
SNRM............................................................................................................................................................................ 3-167
SOLVE .......................................................................................................................................................................... 3-167
SOLVEQN .................................................................................................................................................................... 3-167
SOLVER ....................................................................................................................................................................... 3-168
SOLVEVX..................................................................................................................................................................... 3-168
SORT ............................................................................................................................................................................ 3-168
SPHERE ....................................................................................................................................................................... 3-168
SQ.................................................................................................................................................................................. 3-168
SR.................................................................................................................................................................................. 3-169
SRAD ............................................................................................................................................................................ 3-169
SRB ............................................................................................................................................................................... 3-169
SRECV.......................................................................................................................................................................... 3-169
SREPL .......................................................................................................................................................................... 3-170
START .......................................................................................................................................................................... 3-170
STD ............................................................................................................................................................................... 3-171
STEP ............................................................................................................................................................................. 3-172
STEQ............................................................................................................................................................................. 3-172
STIME ........................................................................................................................................................................... 3-172
STO ............................................................................................................................................................................... 3-172
STOALARM.................................................................................................................................................................. 3-173
STOF............................................................................................................................................................................. 3-173
STOKEYS..................................................................................................................................................................... 3-174
STORE.......................................................................................................................................................................... 3-174
STOVX.......................................................................................................................................................................... 3-174
STO+............................................................................................................................................................................. 3-174
STO– ............................................................................................................................................................................. 3-174
STO*.............................................................................................................................................................................. 3-175

Contents - 13
STO/ ..............................................................................................................................................................................3-175
STOΣ.............................................................................................................................................................................3-176
STR→............................................................................................................................................................................3-176
→STR............................................................................................................................................................................3-176
STREAM .......................................................................................................................................................................3-176
STURM..........................................................................................................................................................................3-177
STURMAB ....................................................................................................................................................................3-177
STWS ............................................................................................................................................................................3-177
SUB ...............................................................................................................................................................................3-177
SUBST ..........................................................................................................................................................................3-178
SUBTMOD....................................................................................................................................................................3-178
SVD ...............................................................................................................................................................................3-178
SVL ................................................................................................................................................................................3-178
SWAP............................................................................................................................................................................3-179
SYSEVAL......................................................................................................................................................................3-179
SYLVESTER ................................................................................................................................................................3-179
SYST2MAT...................................................................................................................................................................3-179
%T..................................................................................................................................................................................3-179
TABVAL ........................................................................................................................................................................3-180
TABVAR........................................................................................................................................................................3-180
→TAG............................................................................................................................................................................3-180
TAIL ...............................................................................................................................................................................3-180
TAN................................................................................................................................................................................3-180
TAN2CS2......................................................................................................................................................................3-181
TAN2SC ........................................................................................................................................................................3-181
TAN2SC2......................................................................................................................................................................3-181
TANH.............................................................................................................................................................................3-181
TAYLOR0......................................................................................................................................................................3-181
TAYLR...........................................................................................................................................................................3-181
TCHEBYCHEFF ..........................................................................................................................................................3-182
TCOLLECT...................................................................................................................................................................3-182
TDELTA ........................................................................................................................................................................3-182
TESTS...........................................................................................................................................................................3-182
TEVAL ...........................................................................................................................................................................3-182
TEXPAND.....................................................................................................................................................................3-183
TEXT..............................................................................................................................................................................3-183
THEN.............................................................................................................................................................................3-183
TICKS............................................................................................................................................................................3-183
TIME ..............................................................................................................................................................................3-183
→TIME ..........................................................................................................................................................................3-183
TINC ..............................................................................................................................................................................3-184
TLIN ...............................................................................................................................................................................3-184
TLINE ............................................................................................................................................................................3-184
TMENU..........................................................................................................................................................................3-184
TOT................................................................................................................................................................................3-185
TRACE ..........................................................................................................................................................................3-185
TRAN.............................................................................................................................................................................3-185
TRANSIO ......................................................................................................................................................................3-185
TRIG ..............................................................................................................................................................................3-186
TRIGCOS......................................................................................................................................................................3-186
TRIGO ...........................................................................................................................................................................3-186
TRIGSIN........................................................................................................................................................................3-186
TRIGTAN ......................................................................................................................................................................3-186
TRN ...............................................................................................................................................................................3-186
TRNC.............................................................................................................................................................................3-186
TRUNC..........................................................................................................................................................................3-187
TRUTH ..........................................................................................................................................................................3-187
TSIMP............................................................................................................................................................................3-188

Contents - 14
TSTR ............................................................................................................................................................................. 3-188
TVARS .......................................................................................................................................................................... 3-188
TVM ............................................................................................................................................................................... 3-188
TVMBEG....................................................................................................................................................................... 3-189
TVMEND....................................................................................................................................................................... 3-189
TVMROOT ................................................................................................................................................................... 3-189
TYPE ............................................................................................................................................................................. 3-189
UBASE.......................................................................................................................................................................... 3-190
UFACT .......................................................................................................................................................................... 3-190
UFL1→MINIF............................................................................................................................................................... 3-191
UNASSIGN................................................................................................................................................................... 3-191
UNASSUME................................................................................................................................................................. 3-191
UNBIND ........................................................................................................................................................................ 3-191
→UNIT .......................................................................................................................................................................... 3-191
UNPICK ........................................................................................................................................................................ 3-191
UNROT ......................................................................................................................................................................... 3-191
UNTIL............................................................................................................................................................................ 3-192
UPDIR ........................................................................................................................................................................... 3-192
UTPC............................................................................................................................................................................. 3-192
UTPF ............................................................................................................................................................................. 3-192
UTPN............................................................................................................................................................................. 3-193
UTPT ............................................................................................................................................................................. 3-193
UVAL ............................................................................................................................................................................. 3-194
V→................................................................................................................................................................................. 3-194
→V2............................................................................................................................................................................... 3-195
→V3............................................................................................................................................................................... 3-195
VANDERMONDE........................................................................................................................................................ 3-195
VAR ............................................................................................................................................................................... 3-196
VARS............................................................................................................................................................................. 3-196
VER ............................................................................................................................................................................... 3-196
VERSION ..................................................................................................................................................................... 3-196
VISIT ............................................................................................................................................................................. 3-196
VISITB........................................................................................................................................................................... 3-197
VPOTENTIAL............................................................................................................................................................... 3-197
VTYPE .......................................................................................................................................................................... 3-197
WAIT ............................................................................................................................................................................. 3-197
WHILE........................................................................................................................................................................... 3-198
WIREFRAME ............................................................................................................................................................... 3-198
WSLOG......................................................................................................................................................................... 3-199
ΣX.................................................................................................................................................................................. 3-200
ΣX2 ................................................................................................................................................................................ 3-200
XCOL............................................................................................................................................................................. 3-201
XGET............................................................................................................................................................................. 3-201
XMIT.............................................................................................................................................................................. 3-201
XNUM............................................................................................................................................................................ 3-202
XOR............................................................................................................................................................................... 3-202
XPON ............................................................................................................................................................................ 3-202
XPUT............................................................................................................................................................................. 3-203
XQ.................................................................................................................................................................................. 3-203
XRECV.......................................................................................................................................................................... 3-203
XRNG............................................................................................................................................................................ 3-203
XROOT ......................................................................................................................................................................... 3-204
XSEND.......................................................................................................................................................................... 3-204
XSERV.......................................................................................................................................................................... 3-205
XVOL............................................................................................................................................................................. 3-205
XXRNG ......................................................................................................................................................................... 3-205
ΣXY................................................................................................................................................................................ 3-205
ΣY.................................................................................................................................................................................. 3-206

Contents - 15
ΣY2 ................................................................................................................................................................................3-206
YCOL.............................................................................................................................................................................3-206
YRNG ............................................................................................................................................................................3-206
YSLICE..........................................................................................................................................................................3-207
YVOL .............................................................................................................................................................................3-207
YYRNG..........................................................................................................................................................................3-208
ZEROS..........................................................................................................................................................................3-208
ZFACTOR.....................................................................................................................................................................3-208
ZVOL .............................................................................................................................................................................3-208
^ (Power) ...................................................................................................................................................................3-209
| (Where) ..................................................................................................................................................................3-209
√ (Square Root)......................................................................................................................................................3-210
∫(Integrate) ..............................................................................................................................................................3-211
? (Undefined) ..........................................................................................................................................................3-212
∞(Infinity).............................................................................................................................................................3-212
Σ(Summation) ........................................................................................................................................................3-212
Σ+(Sigma Plus) ....................................................................................................................................................3-212
Σ– (Sigma Minus) .................................................................................................................................................3-213
π(Pi) ..........................................................................................................................................................................3-213
∂(Derivative) ...........................................................................................................................................................3-213
!(Factorial)...............................................................................................................................................................3-214
%(Percent)...............................................................................................................................................................3-214
_(Unit attachment) ................................................................................................................................................3-215
«»(Program delimeters)......................................................................................................................................3-215
<(Less than) ...........................................................................................................................................................3-215
≤(Less than or Equal).............................................................................................................................................3-216
>(Greater than)......................................................................................................................................................3-217
≥(Greater than or Equal)........................................................................................................................................3-218
≠(Not equal).............................................................................................................................................................3-219
*(Multiply) ................................................................................................................................................................3-219
+(Add) .....................................................................................................................................................................3-220
–(Subtract) ...............................................................................................................................................................3-222
/(Divide)...................................................................................................................................................................3-223
=(Equal) ..................................................................................................................................................................3-223
== (Logical Equality) ............................................................................................................................................3-224
!(Store) ....................................................................................................................................................................3-225
→(Create Local)......................................................................................................................................................3-225
4. Computer Algebra Commands ..............................................................................................................................................4-1
Introduction........................................................................................................................................................................4-1
CAS Operations .................................................................................................................................................................4-1
CAS Settings ......................................................................................................................................................................4-2
Selecting CAS Settings ...............................................................................................................................................4-2
The CAS directory, CASDIR...................................................................................................................................... 4-2
Points to note when choosing settings ........................................................................................................................4-3
Using the CAS....................................................................................................................................................................4-4
Examples and Help .....................................................................................................................................................4-4
Compatibility with Other Calculators .........................................................................................................................4-4
Extending the CAS......................................................................................................................................................4-4
Dealing with unexpected CAS results or messages .................................................................................................... 4-4
ABCUV............................................................................................................................................................................4-12
ACOS2S..........................................................................................................................................................................4-12
ADDTMOD......................................................................................................................................................................4-12
ADDTOREAL .................................................................................................................................................................4-13
ALGB ...............................................................................................................................................................................4-13
ARIT.................................................................................................................................................................................4-13
ASIN2C ...........................................................................................................................................................................4-14
ASIN2T............................................................................................................................................................................4-14
ASSUME.........................................................................................................................................................................4-14

Contents - 16
ATAN2S.......................................................................................................................................................................... 4-15
AUGMENT ..................................................................................................................................................................... 4-15
AXL.................................................................................................................................................................................. 4-15
AXM................................................................................................................................................................................. 4-16
AXQ ................................................................................................................................................................................. 4-16
BASIS.............................................................................................................................................................................. 4-16
C2P.................................................................................................................................................................................. 4-17
CASCFG......................................................................................................................................................................... 4-17
CASCMD ........................................................................................................................................................................ 4-17
CHINREM....................................................................................................................................................................... 4-17
CHOLESKY.................................................................................................................................................................... 4-18
CIRC................................................................................................................................................................................ 4-18
COLLECT ....................................................................................................................................................................... 4-19
CONSTANTS................................................................................................................................................................. 4-19
CURL............................................................................................................................................................................... 4-19
CYCLOTOMIC............................................................................................................................................................... 4-20
DEDICACE..................................................................................................................................................................... 4-20
DEF ................................................................................................................................................................................. 4-20
DEGREE......................................................................................................................................................................... 4-21
DERIV ............................................................................................................................................................................. 4-21
DERVX............................................................................................................................................................................ 4-21
DESOLVE....................................................................................................................................................................... 4-22
DIAGMAP ....................................................................................................................................................................... 4-22
DIFF................................................................................................................................................................................. 4-23
DISTRIB.......................................................................................................................................................................... 4-23
DIV................................................................................................................................................................................... 4-23
DIV2................................................................................................................................................................................. 4-23
DIV2MOD ....................................................................................................................................................................... 4-24
DIVIS ............................................................................................................................................................................... 4-24
DIVMOD ......................................................................................................................................................................... 4-25
DIVPC ............................................................................................................................................................................. 4-25
DOMAIN ......................................................................................................................................................................... 4-25
DROITE .......................................................................................................................................................................... 4-26
dn..................................................................................................................................................................................... 4-26
EGCD.............................................................................................................................................................................. 4-27
EPSX0............................................................................................................................................................................. 4-27
EULER ............................................................................................................................................................................ 4-28
EXLR ............................................................................................................................................................................... 4-28
EXP&LN.......................................................................................................................................................................... 4-28
EXP2HYP ....................................................................................................................................................................... 4-28
EXP2POW...................................................................................................................................................................... 4-29
EXPAND ......................................................................................................................................................................... 4-29
EXPANDMOD................................................................................................................................................................ 4-30
EXPLN ............................................................................................................................................................................ 4-30
FACTOR ......................................................................................................................................................................... 4-30
FACTORMOD................................................................................................................................................................ 4-31
FACTORS ...................................................................................................................................................................... 4-31
FCOEF............................................................................................................................................................................ 4-31
FDISTRIB ....................................................................................................................................................................... 4-32
FOURIER ....................................................................................................................................................................... 4-32
FROOTS......................................................................................................................................................................... 4-33
FXND............................................................................................................................................................................... 4-33
GAUSS ........................................................................................................................................................................... 4-33
GBASIS........................................................................................................................................................................... 4-34
GCD................................................................................................................................................................................. 4-34
GCDMOD ....................................................................................................................................................................... 4-35
GRAMSCHMIDT ........................................................................................................................................................... 4-35
GREDUCE ..................................................................................................................................................................... 4-35
HADAMARD................................................................................................................................................................... 4-36
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