User manual HP 49G+ HP 48GII GRAPHING CALCULATOR

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 REGISTER YOUR PRODUCT AT: www.register.hp.com THIS MANUAL AND ANY EXAMPLES CONTAINED HEREIN ARE PROVIDED "AS IS" AND ARE SUBJECT TO CHANGE WITHOUT NOTICE. HEWLETT-PACKARD COMPANY MAKES NO WARRANTY OF ANY KIND WITH REGARD TO THIS MANUAL, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY, NON-INFRINGEMENT AND FITNESS FOR A PARTICULAR PURPOSE. HEWLETT-PACKARD CO. SHALL NOT BE LIABLE FOR ANY ERRORS OR FOR INCIDENTAL OR CONSEQUENTIAL DAMAGES IN CONNECTION WITH THE FURNISHING, PERFORMANCE, OR USE OF 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 HewlettPackard 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 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 -1 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 - 2 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 BR ................................................................................................................................................................................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 CL ..................................................................................................................................................................................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 COL ...............................................................................................................................................................................3-31 COMB..............................................................................................................................................................................3-32 Contents - 3 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 CPX ............................................................................................................................................................................. 3-38 CR................................................................................................................................................................................ 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 - 4 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 DR ................................................................................................................................................................................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 F0...................................................................................................................................................................................3-61 FACT ...............................................................................................................................................................................3-61 FACTOR .........................................................................................................................................................................3-62 FACTORMOD ................................................................................................................................................................3-62 Contents - 5 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 - 6 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 IR..................................................................................................................................................................................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 - 7 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 LINE .............................................................................................................................................................................. 3-93 LINFIT ............................................................................................................................................................................. 3-94 LININ ............................................................................................................................................................................... 3-94 LINSOLVE ...................................................................................................................................................................... 3-94 LIST ............................................................................................................................................................................. 3-94 LIST ............................................................................................................................................................................. 3-94 LIST............................................................................................................................................................................... 3-95 LIST .............................................................................................................................................................................. 3-95 LIST............................................................................................................................................................................... 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 MAX ............................................................................................................................................................................ 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 MIN.............................................................................................................................................................................. 3-106 MITM ............................................................................................................................................................................. 3-106 MKISOM ....................................................................................................................................................................... 3-106 Contents - 8 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 N ..................................................................................................................................................................................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 - 9 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 PXC ........................................................................................................................................................................... 3-134 Q ................................................................................................................................................................................ 3-135 Q .............................................................................................................................................................................. 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 - 10 RCLMENU ....................................................................................................................................................................3-141 RCLVX ..........................................................................................................................................................................3-141 RCL .............................................................................................................................................................................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 RB ..............................................................................................................................................................................3-156 RC ..............................................................................................................................................................................3-156 RD ..............................................................................................................................................................................3-157 RI................................................................................................................................................................................3-157 SAME ............................................................................................................................................................................3-157 SBRK.............................................................................................................................................................................3-157 SCALE...........................................................................................................................................................................3-158 SCALEH........................................................................................................................................................................3-158 Contents - 11 SCALEW....................................................................................................................................................................... 3-158 SCATRPLOT................................................................................................................................................................ 3-158 SCATTER..................................................................................................................................................................... 3-159 SCHUR ......................................................................................................................................................................... 3-159 SCI................................................................................................................................................................................. 3-160 SCL ............................................................................................................................................................................. 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 - 12 STO/ ..............................................................................................................................................................................3-175 STO .............................................................................................................................................................................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 - 13 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 UFL1MINIF............................................................................................................................................................... 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 X .................................................................................................................................................................................. 3-200 X2 ................................................................................................................................................................................ 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 XY................................................................................................................................................................................ 3-205 Y .................................................................................................................................................................................. 3-206 Contents - 14 Y2 ................................................................................................................................................................................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 (Summation) ........................................................................................................................................................3-212 + (Sigma Plus) ....................................................................................................................................................3-212 ­ (Sigma Minus) .................................................................................................................................................3-213 (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 - 15 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 Contents - 16