calc.texi 1.42 MB
 Glenn Morris committed Sep 06, 2007 1 2 3 \input texinfo @c -*-texinfo-*- @comment %**start of header (This is for running Texinfo on a region.) @c smallbook  Glenn Morris committed Sep 06, 2007 4 @setfilename ../../info/calc  Glenn Morris committed Sep 06, 2007 5 @c [title]  Jay Belanger committed Aug 14, 2008 6 @settitle GNU Emacs Calc Manual  Glenn Morris committed Sep 06, 2007 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 @setchapternewpage odd @comment %**end of header (This is for running Texinfo on a region.) @c The following macros are used for conditional output for single lines. @c @texline foo @c foo' will appear only in TeX output @c @infoline foo @c foo' will appear only in non-TeX output @c @expr{expr} will typeset an expression; @c $x$ in TeX, @samp{x} otherwise. @iftex @macro texline @end macro @alias infoline=comment @alias expr=math @alias tfn=code @alias mathit=expr  Jay Belanger committed Jul 23, 2008 26 @alias summarykey=key  Glenn Morris committed Sep 06, 2007 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 @macro cpi{} @math{@pi{}} @end macro @macro cpiover{den} @math{@pi/\den\} @end macro @end iftex @ifnottex @alias texline=comment @macro infoline{stuff} \stuff\ @end macro @alias expr=samp @alias tfn=t @alias mathit=i  Jay Belanger committed Jul 23, 2008 43 44 45 @macro summarykey{ky} \ky\ @end macro  Glenn Morris committed Sep 06, 2007 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 @macro cpi{} @expr{pi} @end macro @macro cpiover{den} @expr{pi/\den\} @end macro @end ifnottex @tex % Suggested by Karl Berry \gdef\!{\mskip-\thinmuskip} @end tex @c Fix some other things specifically for this manual. @iftex @finalout @mathcode@:=@: @c Make Calc fractions come out right in math mode @tex \gdef\coloneq{\mathrel{\mathord:\mathord=}} \gdef\beforedisplay{\vskip-10pt} \gdef\afterdisplay{\vskip-5pt} \gdef\beforedisplayh{\vskip-25pt} \gdef\afterdisplayh{\vskip-10pt} @end tex @newdimen@kyvpos @kyvpos=0pt @newdimen@kyhpos @kyhpos=0pt @newcount@calcclubpenalty @calcclubpenalty=1000 @ignore @newcount@calcpageno @newtoks@calcoldeverypar @calcoldeverypar=@everypar @everypar={@calceverypar@the@calcoldeverypar} @ifx@turnoffactive@undefinedzzz@def@turnoffactive{}@fi @ifx@ninett@undefinedzzz@font@ninett=cmtt9@fi @catcode@\=0 \catcode\@=11 \r@ggedbottomtrue \catcode\@=0 @catcode@\=@active @end ignore @end iftex @copying  Jay Belanger committed Aug 14, 2008 88 @ifinfo  Glenn Morris committed Sep 06, 2007 89 This file documents Calc, the GNU Emacs calculator.  Jay Belanger committed Aug 14, 2008 90 91 92 93 @end ifinfo @ifnotinfo This file documents Calc, the GNU Emacs calculator, included with GNU Emacs 23.1. @end ifnotinfo  Glenn Morris committed Sep 06, 2007 94 95  Copyright @copyright{} 1990, 1991, 2001, 2002, 2003, 2004,  Glenn Morris committed Jan 13, 2010 96 2005, 2006, 2007, 2008, 2009, 2010 Free Software Foundation, Inc.  Glenn Morris committed Sep 06, 2007 97 98 99  @quotation Permission is granted to copy, distribute and/or modify this document  Glenn Morris committed Nov 19, 2008 100 under the terms of the GNU Free Documentation License, Version 1.3 or  Glenn Morris committed Sep 06, 2007 101 102 103 104 105 106 any later version published by the Free Software Foundation; with the Invariant Sections being just GNU GENERAL PUBLIC LICENSE'', with the Front-Cover texts being A GNU Manual,'' and with the Back-Cover Texts as in (a) below. A copy of the license is included in the section entitled GNU Free Documentation License.''  Glenn Morris committed Jun 13, 2008 107 108 109 (a) The FSF's Back-Cover Text is: You have the freedom to copy and modify this GNU manual. Buying copies from the FSF supports it in developing GNU and promoting software freedom.''  Glenn Morris committed Sep 06, 2007 110 111 112 113 114 115 116 117 118 119 120 121 @end quotation @end copying @dircategory Emacs @direntry * Calc: (calc). Advanced desk calculator and mathematical tool. @end direntry @titlepage @sp 6 @center @titlefont{Calc Manual} @sp 4  Jay Belanger committed Aug 14, 2008 122 @center GNU Emacs Calc  Glenn Morris committed Sep 06, 2007 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 @c [volume] @sp 5 @center Dave Gillespie @center daveg@@synaptics.com @page @vskip 0pt plus 1filll @insertcopying @end titlepage @summarycontents @c [end] @contents @c [begin] @ifnottex @node Top, Getting Started, (dir), (dir) @chapter The GNU Emacs Calculator @noindent @dfn{Calc} is an advanced desk calculator and mathematical tool written by Dave Gillespie that runs as part of the GNU Emacs environment. This manual, also written (mostly) by Dave Gillespie, is divided into three major parts: Getting Started,'' the Calc Tutorial,'' and the Calc Reference.'' The Tutorial introduces all the major aspects of Calculator use in an easy, hands-on way. The remainder of the manual is a complete reference to the features of the Calculator. @end ifnottex @ifinfo For help in the Emacs Info system (which you are using to read this file), type @kbd{?}. (You can also type @kbd{h} to run through a longer Info tutorial.) @end ifinfo  Karl Berry committed Feb 16, 2009 162 163 @insertcopying  Glenn Morris committed Sep 06, 2007 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 @menu * Getting Started:: General description and overview. @ifinfo * Interactive Tutorial:: @end ifinfo * Tutorial:: A step-by-step introduction for beginners. * Introduction:: Introduction to the Calc reference manual. * Data Types:: Types of objects manipulated by Calc. * Stack and Trail:: Manipulating the stack and trail buffers. * Mode Settings:: Adjusting display format and other modes. * Arithmetic:: Basic arithmetic functions. * Scientific Functions:: Transcendentals and other scientific functions. * Matrix Functions:: Operations on vectors and matrices. * Algebra:: Manipulating expressions algebraically. * Units:: Operations on numbers with units. * Store and Recall:: Storing and recalling variables. * Graphics:: Commands for making graphs of data. * Kill and Yank:: Moving data into and out of Calc. * Keypad Mode:: Operating Calc from a keypad. * Embedded Mode:: Working with formulas embedded in a file. * Programming:: Calc as a programmable calculator. * Copying:: How you can copy and share Calc. * GNU Free Documentation License:: The license for this documentation. * Customizing Calc:: Customizing Calc. * Reporting Bugs:: How to report bugs and make suggestions. * Summary:: Summary of Calc commands and functions. * Key Index:: The standard Calc key sequences. * Command Index:: The interactive Calc commands. * Function Index:: Functions (in algebraic formulas). * Concept Index:: General concepts. * Variable Index:: Variables used by Calc (both user and internal). * Lisp Function Index:: Internal Lisp math functions. @end menu @ifinfo @node Getting Started, Interactive Tutorial, Top, Top @end ifinfo @ifnotinfo @node Getting Started, Tutorial, Top, Top @end ifnotinfo @chapter Getting Started @noindent This chapter provides a general overview of Calc, the GNU Emacs Calculator: What it is, how to start it and how to exit from it, and what are the various ways that it can be used. @menu * What is Calc:: * About This Manual:: * Notations Used in This Manual:: * Demonstration of Calc:: * Using Calc:: * History and Acknowledgements:: @end menu @node What is Calc, About This Manual, Getting Started, Getting Started @section What is Calc? @noindent @dfn{Calc} is an advanced calculator and mathematical tool that runs as part of the GNU Emacs environment. Very roughly based on the HP-28/48 series of calculators, its many features include: @itemize @bullet @item Choice of algebraic or RPN (stack-based) entry of calculations. @item Arbitrary precision integers and floating-point numbers. @item Arithmetic on rational numbers, complex numbers (rectangular and polar), error forms with standard deviations, open and closed intervals, vectors and matrices, dates and times, infinities, sets, quantities with units, and algebraic formulas. @item Mathematical operations such as logarithms and trigonometric functions. @item Programmer's features (bitwise operations, non-decimal numbers). @item Financial functions such as future value and internal rate of return. @item Number theoretical features such as prime factorization and arithmetic modulo @var{m} for any @var{m}. @item Algebraic manipulation features, including symbolic calculus. @item Moving data to and from regular editing buffers. @item Embedded mode for manipulating Calc formulas and data directly inside any editing buffer. @item Graphics using GNUPLOT, a versatile (and free) plotting program. @item Easy programming using keyboard macros, algebraic formulas, algebraic rewrite rules, or extended Emacs Lisp. @end itemize Calc tries to include a little something for everyone; as a result it is large and might be intimidating to the first-time user. If you plan to use Calc only as a traditional desk calculator, all you really need to read is the Getting Started'' chapter of this manual and possibly the first few sections of the tutorial. As you become more comfortable with the program you can learn its additional features. Calc does not have the scope and depth of a fully-functional symbolic math package, but Calc has the advantages of convenience, portability, and freedom. @node About This Manual, Notations Used in This Manual, What is Calc, Getting Started @section About This Manual @noindent This document serves as a complete description of the GNU Emacs  Jay Belanger committed Dec 01, 2008 289 Calculator. It works both as an introduction for novices and as  Glenn Morris committed Sep 06, 2007 290 291 292 293 294 a reference for experienced users. While it helps to have some experience with GNU Emacs in order to get the most out of Calc, this manual ought to be readable even if you don't know or use Emacs regularly.  Jay Belanger committed Dec 01, 2008 295 This manual is divided into three major parts:@: the Getting  Chong Yidong committed Jul 20, 2009 296 297 Started'' chapter you are reading now, the Calc tutorial, and the Calc reference manual.  Glenn Morris committed Sep 06, 2007 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 @c [when-split] @c This manual has been printed in two volumes, the @dfn{Tutorial} and the @c @dfn{Reference}. Both volumes include a copy of the Getting Started'' @c chapter. If you are in a hurry to use Calc, there is a brief demonstration'' below which illustrates the major features of Calc in just a couple of pages. If you don't have time to go through the full tutorial, this will show you everything you need to know to begin. @xref{Demonstration of Calc}. The tutorial chapter walks you through the various parts of Calc with lots of hands-on examples and explanations. If you are new to Calc and you have some time, try going through at least the beginning of the tutorial. The tutorial includes about 70 exercises with answers. These exercises give you some guided practice with Calc, as well as pointing out some interesting and unusual ways to use its features. The reference section discusses Calc in complete depth. You can read the reference from start to finish if you want to learn every aspect of Calc. Or, you can look in the table of contents or the Concept Index to find the parts of the manual that discuss the things you need to know.  Jay Belanger committed Nov 14, 2008 323 @c @cindex Marginal notes  Glenn Morris committed Sep 06, 2007 324 325 326 Every Calc keyboard command is listed in the Calc Summary, and also in the Key Index. Algebraic functions, @kbd{M-x} commands, and variables also have their own indices.  Jay Belanger committed Nov 14, 2008 327 328 329 330 @c @texline Each @c @infoline In the printed manual, each @c paragraph that is referenced in the Key or Function Index is marked @c in the margin with its index entry.  Glenn Morris committed Sep 06, 2007 331 332  @c [fix-ref Help Commands]  Jay Belanger committed Dec 01, 2008 333 334 335 336 337 338 339 340 341 You can access this manual on-line at any time within Calc by pressing the @kbd{h i} key sequence. Outside of the Calc window, you can press @kbd{C-x * i} to read the manual on-line. From within Calc the command @kbd{h t} will jump directly to the Tutorial; from outside of Calc the command @kbd{C-x * t} will jump to the Tutorial and start Calc if necessary. Pressing @kbd{h s} or @kbd{C-x * s} will take you directly to the Calc Summary. Within Calc, you can also go to the part of the manual describing any Calc key, function, or variable using @w{@kbd{h k}}, @kbd{h f}, or @kbd{h v}, respectively. @xref{Help Commands}.  Glenn Morris committed Sep 06, 2007 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441 442 443 444 445 446 447 448 449 450 451 452 453 454 455 456 457 458 459 460 461 462 463 464 465 466 467 468 469 470 471 472 473 474 475 476 477 478 479 480 481 482 483 484 485 486 487 488 489 490 491 492 493 494 495 496 497 498 499 500 501 502 503 504 505 506 507 508 509 510 511 512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528 529 530 531 532 533 534 535 536 537 538 539 540 541 542 543 544 545 546 547 548 549 550 551  @ifnottex The Calc manual can be printed, but because the manual is so large, you should only make a printed copy if you really need it. To print the manual, you will need the @TeX{} typesetting program (this is a free program by Donald Knuth at Stanford University) as well as the @file{texindex} program and @file{texinfo.tex} file, both of which can be obtained from the FSF as part of the @code{texinfo} package. To print the Calc manual in one huge tome, you will need the source code to this manual, @file{calc.texi}, available as part of the Emacs source. Once you have this file, type @kbd{texi2dvi calc.texi}. Alternatively, change to the @file{man} subdirectory of the Emacs source distribution, and type @kbd{make calc.dvi}. (Don't worry if you get some overfull box'' warnings while @TeX{} runs.) The result will be a device-independent output file called @file{calc.dvi}, which you must print in whatever way is right for your system. On many systems, the command is @example lpr -d calc.dvi @end example @noindent or @example dvips calc.dvi @end example @end ifnottex @c Printed copies of this manual are also available from the Free Software @c Foundation. @node Notations Used in This Manual, Demonstration of Calc, About This Manual, Getting Started @section Notations Used in This Manual @noindent This section describes the various notations that are used throughout the Calc manual. In keystroke sequences, uppercase letters mean you must hold down the shift key while typing the letter. Keys pressed with Control held down are shown as @kbd{C-x}. Keys pressed with Meta held down are shown as @kbd{M-x}. Other notations are @key{RET} for the Return key, @key{SPC} for the space bar, @key{TAB} for the Tab key, @key{DEL} for the Delete key, and @key{LFD} for the Line-Feed key. The @key{DEL} key is called Backspace on some keyboards, it is whatever key you would use to correct a simple typing error when regularly using Emacs. (If you don't have the @key{LFD} or @key{TAB} keys on your keyboard, the @kbd{C-j} and @kbd{C-i} keys are equivalent to them, respectively. If you don't have a Meta key, look for Alt or Extend Char. You can also press @key{ESC} or @kbd{C-[} first to get the same effect, so that @kbd{M-x}, @kbd{@key{ESC} x}, and @kbd{C-[ x} are all equivalent.) Sometimes the @key{RET} key is not shown when it is obvious'' that you must press @key{RET} to proceed. For example, the @key{RET} is usually omitted in key sequences like @kbd{M-x calc-keypad @key{RET}}. Commands are generally shown like this: @kbd{p} (@code{calc-precision}) or @kbd{C-x * k} (@code{calc-keypad}). This means that the command is normally used by pressing the @kbd{p} key or @kbd{C-x * k} key sequence, but it also has the full-name equivalent shown, e.g., @kbd{M-x calc-precision}. Commands that correspond to functions in algebraic notation are written: @kbd{C} (@code{calc-cos}) [@code{cos}]. This means the @kbd{C} key is equivalent to @kbd{M-x calc-cos}, and that the corresponding function in an algebraic-style formula would be @samp{cos(@var{x})}. A few commands don't have key equivalents: @code{calc-sincos} [@code{sincos}]. @node Demonstration of Calc, Using Calc, Notations Used in This Manual, Getting Started @section A Demonstration of Calc @noindent @cindex Demonstration of Calc This section will show some typical small problems being solved with Calc. The focus is more on demonstration than explanation, but everything you see here will be covered more thoroughly in the Tutorial. To begin, start Emacs if necessary (usually the command @code{emacs} does this), and type @kbd{C-x * c} to start the Calculator. (You can also use @kbd{M-x calc} if this doesn't work. @xref{Starting Calc}, for various ways of starting the Calculator.) Be sure to type all the sample input exactly, especially noting the difference between lower-case and upper-case letters. Remember, @key{RET}, @key{TAB}, @key{DEL}, and @key{SPC} are the Return, Tab, Delete, and Space keys. @strong{RPN calculation.} In RPN, you type the input number(s) first, then the command to operate on the numbers. @noindent Type @kbd{2 @key{RET} 3 + Q} to compute @texline @math{\sqrt{2+3} = 2.2360679775}. @infoline the square root of 2+3, which is 2.2360679775. @noindent Type @kbd{P 2 ^} to compute @texline @math{\pi^2 = 9.86960440109}. @infoline the value of pi' squared, 9.86960440109. @noindent Type @key{TAB} to exchange the order of these two results. @noindent Type @kbd{- I H S} to subtract these results and compute the Inverse Hyperbolic sine of the difference, 2.72996136574. @noindent Type @key{DEL} to erase this result. @strong{Algebraic calculation.} You can also enter calculations using conventional algebraic'' notation. To enter an algebraic formula, use the apostrophe key. @noindent Type @kbd{' sqrt(2+3) @key{RET}} to compute @texline @math{\sqrt{2+3}}. @infoline the square root of 2+3. @noindent Type @kbd{' pi^2 @key{RET}} to enter @texline @math{\pi^2}. @infoline pi' squared. To evaluate this symbolic formula as a number, type @kbd{=}. @noindent Type @kbd{' arcsinh(- ) @key{RET}} to subtract the second-most-recent result from the most-recent and compute the Inverse Hyperbolic sine. @strong{Keypad mode.} If you are using the X window system, press @w{@kbd{C-x * k}} to get Keypad mode. (If you don't use X, skip to the next section.) @noindent Click on the @key{2}, @key{ENTER}, @key{3}, @key{+}, and @key{SQRT} buttons'' using your left mouse button. @noindent Click on @key{PI}, @key{2}, and @tfn{y^x}. @noindent Click on @key{INV}, then @key{ENTER} to swap the two results. @noindent Click on @key{-}, @key{INV}, @key{HYP}, and @key{SIN}. @noindent Click on @key{<-} to erase the result, then click @key{OFF} to turn the Keypad Calculator off. @strong{Grabbing data.} Type @kbd{C-x * x} if necessary to exit Calc. Now select the following numbers as an Emacs region: Mark'' the front of the list by typing @kbd{C-@key{SPC}} or @kbd{C-@@} there, then move to the other end of the list. (Either get this list from the on-line copy of this manual, accessed by @w{@kbd{C-x * i}}, or just type these numbers into a scratch file.) Now type @kbd{C-x * g} to grab'' these numbers into Calc. @example @group 1.23 1.97 1.6 2 1.19 1.08 @end group @end example @noindent The result @samp{[1.23, 1.97, 1.6, 2, 1.19, 1.08]} is a Calc vector.'' Type @w{@kbd{V R +}} to compute the sum of these numbers. @noindent Type @kbd{U} to Undo this command, then type @kbd{V R *} to compute the product of the numbers. @noindent You can also grab data as a rectangular matrix. Place the cursor on the upper-leftmost @samp{1} and set the mark, then move to just after the lower-right @samp{8} and press @kbd{C-x * r}. @noindent Type @kbd{v t} to transpose this @texline @math{3\times2} @infoline 3x2 matrix into a @texline @math{2\times3} @infoline 2x3 matrix. Type @w{@kbd{v u}} to unpack the rows into two separate vectors. Now type @w{@kbd{V R + @key{TAB} V R +}} to compute the sums of the two original columns. (There is also a special grab-and-sum-columns command, @kbd{C-x * :}.) @strong{Units conversion.} Units are entered algebraically. Type @w{@kbd{' 43 mi/hr @key{RET}}} to enter the quantity 43 miles-per-hour. Type @w{@kbd{u c km/hr @key{RET}}}. Type @w{@kbd{u c m/s @key{RET}}}. @strong{Date arithmetic.} Type @kbd{t N} to get the current date and time. Type @kbd{90 +} to find the date 90 days from now. Type @kbd{' <25 dec 87> @key{RET}} to enter a date, then @kbd{- 7 /} to see how many weeks have passed since then. @strong{Algebra.} Algebraic entries can also include formulas or equations involving variables. Type @kbd{@w{' [x + y} = a, x y = 1] @key{RET}} to enter a pair of equations involving three variables. (Note the leading apostrophe in this example; also, note that the space  Jay Belanger committed Dec 01, 2008 552 in @samp{x y} is required.) Type @w{@kbd{a S x,y @key{RET}}} to solve  Glenn Morris committed Sep 06, 2007 553 554 555 556 557 558 559 560 561 562 563 these equations for the variables @expr{x} and @expr{y}. @noindent Type @kbd{d B} to view the solutions in more readable notation. Type @w{@kbd{d C}} to view them in C language notation, @kbd{d T} to view them in the notation for the @TeX{} typesetting system, and @kbd{d L} to view them in the notation for the La@TeX{} typesetting system. Type @kbd{d N} to return to normal notation. @noindent Type @kbd{7.5}, then @kbd{s l a @key{RET}} to let @expr{a = 7.5} in these formulas.  Jay Belanger committed Dec 01, 2008 564 (That's the letter @kbd{l}, not the numeral @kbd{1}.)  Glenn Morris committed Sep 06, 2007 565 566 567 568 569 570 571 572 573 574 575 576 577 578 579 580 581 582 583 584 585 586 587 588 589 590 591 592 593 594 595 596 597 598 599 600 601 602 603 604 605 606 607 608 609 610 611 612 613 614 615 616 617 618 619 620 621 622 623 624 625 626 627 628 629 630 631 632 633 634 635 636 637 638 639 640 641 642 643 644 645 646 647 648 649 650 651 652 653 654 655  @ifnotinfo @strong{Help functions.} You can read about any command in the on-line manual. Type @kbd{C-x * c} to return to Calc after each of these commands: @kbd{h k t N} to read about the @kbd{t N} command, @kbd{h f sqrt @key{RET}} to read about the @code{sqrt} function, and @kbd{h s} to read the Calc summary. @end ifnotinfo @ifinfo @strong{Help functions.} You can read about any command in the on-line manual. Remember to type the letter @kbd{l}, then @kbd{C-x * c}, to return here after each of these commands: @w{@kbd{h k t N}} to read about the @w{@kbd{t N}} command, @kbd{h f sqrt @key{RET}} to read about the @code{sqrt} function, and @kbd{h s} to read the Calc summary. @end ifinfo Press @key{DEL} repeatedly to remove any leftover results from the stack. To exit from Calc, press @kbd{q} or @kbd{C-x * c} again. @node Using Calc, History and Acknowledgements, Demonstration of Calc, Getting Started @section Using Calc @noindent Calc has several user interfaces that are specialized for different kinds of tasks. As well as Calc's standard interface, there are Quick mode, Keypad mode, and Embedded mode. @menu * Starting Calc:: * The Standard Interface:: * Quick Mode Overview:: * Keypad Mode Overview:: * Standalone Operation:: * Embedded Mode Overview:: * Other C-x * Commands:: @end menu @node Starting Calc, The Standard Interface, Using Calc, Using Calc @subsection Starting Calc @noindent On most systems, you can type @kbd{C-x *} to start the Calculator. The key sequence @kbd{C-x *} is bound to the command @code{calc-dispatch}, which can be rebound if convenient (@pxref{Customizing Calc}). When you press @kbd{C-x *}, Emacs waits for you to press a second key to complete the command. In this case, you will follow @kbd{C-x *} with a letter (upper- or lower-case, it doesn't matter for @kbd{C-x *}) that says which Calc interface you want to use. To get Calc's standard interface, type @kbd{C-x * c}. To get Keypad mode, type @kbd{C-x * k}. Type @kbd{C-x * ?} to get a brief list of the available options, and type a second @kbd{?} to get a complete list. To ease typing, @kbd{C-x * *} also works to start Calc. It starts the same interface (either @kbd{C-x * c} or @w{@kbd{C-x * k}}) that you last used, selecting the @kbd{C-x * c} interface by default. If @kbd{C-x *} doesn't work for you, you can always type explicit commands like @kbd{M-x calc} (for the standard user interface) or @w{@kbd{M-x calc-keypad}} (for Keypad mode). First type @kbd{M-x} (that's Meta with the letter @kbd{x}), then, at the prompt, type the full command (like @kbd{calc-keypad}) and press Return. The same commands (like @kbd{C-x * c} or @kbd{C-x * *}) that start the Calculator also turn it off if it is already on. @node The Standard Interface, Quick Mode Overview, Starting Calc, Using Calc @subsection The Standard Calc Interface @noindent @cindex Standard user interface Calc's standard interface acts like a traditional RPN calculator, operated by the normal Emacs keyboard. When you type @kbd{C-x * c} to start the Calculator, the Emacs screen splits into two windows with the file you were editing on top and Calc on the bottom. @smallexample @group ... --**-Emacs: myfile (Fundamental)----All---------------------- --- Emacs Calculator Mode --- |Emacs Calculator Trail 2: 17.3 | 17.3 1: -5 | 3 . | 2 | 4 | * 8 | ->-5 |  Jay Belanger committed Jun 29, 2008 656 --%*-Calc: 12 Deg (Calculator)----All----- --%*- *Calc Trail*  Glenn Morris committed Sep 06, 2007 657 658 659 660 661 662 663 664 665 666 667 668 669 670 671 672 673 674 675 676 677 678 679 680 681 682 683 684 685 686 687 688 689 690 691 692 693 694 695 696 697 698 699 700 701 702 703 704 705 706 707 708 709 710 711 712 713 714 715 716 717 718 719 720 @end group @end smallexample In this figure, the mode-line for @file{myfile} has moved up and the Calculator'' window has appeared below it. As you can see, Calc actually makes two windows side-by-side. The lefthand one is called the @dfn{stack window} and the righthand one is called the @dfn{trail window.} The stack holds the numbers involved in the calculation you are currently performing. The trail holds a complete record of all calculations you have done. In a desk calculator with a printer, the trail corresponds to the paper tape that records what you do. In this case, the trail shows that four numbers (17.3, 3, 2, and 4) were first entered into the Calculator, then the 2 and 4 were multiplied to get 8, then the 3 and 8 were subtracted to get @mathit{-5}. (The @samp{>} symbol shows that this was the most recent calculation.) The net result is the two numbers 17.3 and @mathit{-5} sitting on the stack. Most Calculator commands deal explicitly with the stack only, but there is a set of commands that allow you to search back through the trail and retrieve any previous result. Calc commands use the digits, letters, and punctuation keys. Shifted (i.e., upper-case) letters are different from lowercase letters. Some letters are @dfn{prefix} keys that begin two-letter commands. For example, @kbd{e} means enter exponent'' and shifted @kbd{E} means @expr{e^x}. With the @kbd{d} (display modes'') prefix the letter e'' takes on very different meanings: @kbd{d e} means engineering notation'' and @kbd{d E} means @dfn{eqn} language mode.'' There is nothing stopping you from switching out of the Calc window and back into your editing window, say by using the Emacs @w{@kbd{C-x o}} (@code{other-window}) command. When the cursor is inside a regular window, Emacs acts just like normal. When the cursor is in the Calc stack or trail windows, keys are interpreted as Calc commands. When you quit by pressing @kbd{C-x * c} a second time, the Calculator windows go away but the actual Stack and Trail are not gone, just hidden. When you press @kbd{C-x * c} once again you will get the same stack and trail contents you had when you last used the Calculator. The Calculator does not remember its state between Emacs sessions. Thus if you quit Emacs and start it again, @kbd{C-x * c} will give you a fresh stack and trail. There is a command (@kbd{m m}) that lets you save your favorite mode settings between sessions, though. One of the things it saves is which user interface (standard or Keypad) you last used; otherwise, a freshly started Emacs will always treat @kbd{C-x * *} the same as @kbd{C-x * c}. The @kbd{q} key is another equivalent way to turn the Calculator off. If you type @kbd{C-x * b} first and then @kbd{C-x * c}, you get a full-screen version of Calc (@code{full-calc}) in which the stack and trail windows are still side-by-side but are now as tall as the whole Emacs screen. When you press @kbd{q} or @kbd{C-x * c} again to quit, the file you were editing before reappears. The @kbd{C-x * b} key switches back and forth between big'' full-screen mode and the normal partial-screen mode. Finally, @kbd{C-x * o} (@code{calc-other-window}) is like @kbd{C-x * c} except that the Calc window is not selected. The buffer you were  Jay Belanger committed Dec 01, 2008 721 722 723 724 725 editing before remains selected instead. If you are in a Calc window, then @kbd{C-x * o} will switch you out of it, being careful not to switch you to the Calc Trail window. So @kbd{C-x * o} is a handy way to switch out of Calc momentarily to edit your file; you can then type @kbd{C-x * c} to switch back into Calc when you are done.  Glenn Morris committed Sep 06, 2007 726 727 728 729 730 731 732 733 734 735 736 737 738 739 740 741 742 743 744 745 746 747 748 749 750 751 752 753 754 755 756 757 758 759 760 761 762 763 764 765 766 767 768 769 770 771 772 773 774 775  @node Quick Mode Overview, Keypad Mode Overview, The Standard Interface, Using Calc @subsection Quick Mode (Overview) @noindent @dfn{Quick mode} is a quick way to use Calc when you don't need the full complexity of the stack and trail. To use it, type @kbd{C-x * q} (@code{quick-calc}) in any regular editing buffer. Quick mode is very simple: It prompts you to type any formula in standard algebraic notation (like @samp{4 - 2/3}) and then displays the result at the bottom of the Emacs screen (@mathit{3.33333333333} in this case). You are then back in the same editing buffer you were in before, ready to continue editing or to type @kbd{C-x * q} again to do another quick calculation. The result of the calculation will also be in the Emacs kill ring'' so that a @kbd{C-y} command at this point will yank the result into your editing buffer. Calc mode settings affect Quick mode, too, though you will have to go into regular Calc (with @kbd{C-x * c}) to change the mode settings. @c [fix-ref Quick Calculator mode] @xref{Quick Calculator}, for further information. @node Keypad Mode Overview, Standalone Operation, Quick Mode Overview, Using Calc @subsection Keypad Mode (Overview) @noindent @dfn{Keypad mode} is a mouse-based interface to the Calculator. It is designed for use with terminals that support a mouse. If you don't have a mouse, you will have to operate Keypad mode with your arrow keys (which is probably more trouble than it's worth). Type @kbd{C-x * k} to turn Keypad mode on or off. Once again you get two new windows, this time on the righthand side of the screen instead of at the bottom. The upper window is the familiar Calc Stack; the lower window is a picture of a typical calculator keypad. @tex \dimen0=\pagetotal% \advance \dimen0 by 24\baselineskip% \ifdim \dimen0>\pagegoal \vfill\eject \fi% \medskip @end tex @smallexample @group |--- Emacs Calculator Mode --- |2: 17.3 |1: -5 | .  Jay Belanger committed Jun 29, 2008 776 |--%*-Calc: 12 Deg (Calcul  Jay Belanger committed Aug 14, 2008 777 |----+----+--Calc---+----+----1  Glenn Morris committed Sep 06, 2007 778 779 780 781 782 783 784 785 786 787 788 789 790 791 792 793 794 795 796 797 798 799 800 801 802 803 804 805 806 807 808 809 810 811 812 813 814 815 816 817 818 819 820 821 822 823 824 825 826 827 828 829 830 831 832 833 834 835 836 837 838 839 840 841 842 843 844 845 846 847 848 849 850 851 852 853 854 855 856 857 858 859 860 861 862 863 864 865 866 867 868 869 870 871 872 873 874 875 876 |FLR |CEIL|RND |TRNC|CLN2|FLT | |----+----+----+----+----+----| | LN |EXP | |ABS |IDIV|MOD | |----+----+----+----+----+----| |SIN |COS |TAN |SQRT|y^x |1/x | |----+----+----+----+----+----| | ENTER |+/- |EEX |UNDO| <- | |-----+---+-+--+--+-+---++----| | INV | 7 | 8 | 9 | / | |-----+-----+-----+-----+-----| | HYP | 4 | 5 | 6 | * | |-----+-----+-----+-----+-----| |EXEC | 1 | 2 | 3 | - | |-----+-----+-----+-----+-----| | OFF | 0 | . | PI | + | |-----+-----+-----+-----+-----+ @end group @end smallexample Keypad mode is much easier for beginners to learn, because there is no need to memorize lots of obscure key sequences. But not all commands in regular Calc are available on the Keypad. You can always switch the cursor into the Calc stack window to use standard Calc commands if you need. Serious Calc users, though, often find they prefer the standard interface over Keypad mode. To operate the Calculator, just click on the buttons'' of the keypad using your left mouse button. To enter the two numbers shown here you would click @w{@kbd{1 7 .@: 3 ENTER 5 +/- ENTER}}; to add them together you would then click @kbd{+} (to get 12.3 on the stack). If you click the right mouse button, the top three rows of the keypad change to show other sets of commands, such as advanced math functions, vector operations, and operations on binary numbers. Because Keypad mode doesn't use the regular keyboard, Calc leaves the cursor in your original editing buffer. You can type in this buffer in the usual way while also clicking on the Calculator keypad. One advantage of Keypad mode is that you don't need an explicit command to switch between editing and calculating. If you press @kbd{C-x * b} first, you get a full-screen Keypad mode (@code{full-calc-keypad}) with three windows: The keypad in the lower left, the stack in the lower right, and the trail on top. @c [fix-ref Keypad Mode] @xref{Keypad Mode}, for further information. @node Standalone Operation, Embedded Mode Overview, Keypad Mode Overview, Using Calc @subsection Standalone Operation @noindent @cindex Standalone Operation If you are not in Emacs at the moment but you wish to use Calc, you must start Emacs first. If all you want is to run Calc, you can give the commands: @example emacs -f full-calc @end example @noindent or @example emacs -f full-calc-keypad @end example @noindent which run a full-screen Calculator (as if by @kbd{C-x * b C-x * c}) or a full-screen X-based Calculator (as if by @kbd{C-x * b C-x * k}). In standalone operation, quitting the Calculator (by pressing @kbd{q} or clicking on the keypad @key{EXIT} button) quits Emacs itself. @node Embedded Mode Overview, Other C-x * Commands, Standalone Operation, Using Calc @subsection Embedded Mode (Overview) @noindent @dfn{Embedded mode} is a way to use Calc directly from inside an editing buffer. Suppose you have a formula written as part of a document like this: @smallexample @group The derivative of ln(ln(x)) is @end group @end smallexample @noindent and you wish to have Calc compute and format the derivative for you and store this derivative in the buffer automatically. To do this with Embedded mode, first copy the formula down to where  Jay Belanger committed Dec 01, 2008 877 878 you want the result to be, leaving a blank line before and after the formula:  Glenn Morris committed Sep 06, 2007 879 880 881 882 883 884 885 886 887 888 889 890 891 892  @smallexample @group The derivative of ln(ln(x)) is ln(ln(x)) @end group @end smallexample Now, move the cursor onto this new formula and press @kbd{C-x * e}.  Jay Belanger committed Dec 01, 2008 893 894 895 896 897 898 899 900 901 902 Calc will read the formula (using the surrounding blank lines to tell how much text to read), then push this formula (invisibly) onto the Calc stack. The cursor will stay on the formula in the editing buffer, but the line with the formula will now appear as it would on the Calc stack (in this case, it will be left-aligned) and the buffer's mode line will change to look like the Calc mode line (with mode indicators like @samp{12 Deg} and so on). Even though you are still in your editing buffer, the keyboard now acts like the Calc keyboard, and any new result you get is copied from the stack back into the buffer. To take the derivative, you would type @kbd{a d x @key{RET}}.  Glenn Morris committed Sep 06, 2007 903 904 905 906 907 908 909 910 911 912 913 914 915  @smallexample @group The derivative of ln(ln(x)) is 1 / ln(x) x @end group @end smallexample  Jay Belanger committed Jan 27, 2009 916 917 (Note that by default, Calc gives division lower precedence than multiplication, so that @samp{1 / ln(x) x} is equivalent to @samp{1 / (ln(x) x)}.)  Jay Belanger committed Dec 01, 2008 918   Glenn Morris committed Sep 06, 2007 919 920 921 922 923 924 925 926 927 928 929 930 931 932 933 934 935 936 937 938 939 940 941 942 943 944 945 946 947 948 949 950 951 952 953 954 955 956 957 958 959 960 961 962 963 To make this look nicer, you might want to press @kbd{d =} to center the formula, and even @kbd{d B} to use Big display mode. @smallexample @group The derivative of ln(ln(x)) is % [calc-mode: justify: center] % [calc-mode: language: big] 1 ------- ln(x) x @end group @end smallexample Calc has added annotations to the file to help it remember the modes that were used for this formula. They are formatted like comments in the @TeX{} typesetting language, just in case you are using @TeX{} or La@TeX{}. (In this example @TeX{} is not being used, so you might want to move these comments up to the top of the file or otherwise put them out of the way.) As an extra flourish, we can add an equation number using a righthand label: Type @kbd{d @} (1) @key{RET}}. @smallexample @group % [calc-mode: justify: center] % [calc-mode: language: big] % [calc-mode: right-label: " (1)"] 1 ------- (1) ln(x) x @end group @end smallexample To leave Embedded mode, type @kbd{C-x * e} again. The mode line and keyboard will revert to the way they were before. The related command @kbd{C-x * w} operates on a single word, which  Jay Belanger committed Oct 10, 2008 964 965 966 generally means a single number, inside text. It searches for an expression which looks'' like a number containing the point. Here's an example of its use:  Glenn Morris committed Sep 06, 2007 967 968 969 970 971 972 973 974 975 976 977 978 979 980 981 982 983 984 985 986 987 988 989 990 991 992 993 994 995 996 997 998 999 1000 1001 1002 1003 1004 1005 1006 1007 1008 1009 1010 1011 1012 1013 1014 1015 1016 1017 1018 1019 1020 1021 1022 1023 1024 1025 1026 1027 1028 1029 1030 1031 1032 1033 1034 1035 1036 1037 1038 1039 1040 1041 1042 1043 1044 1045 1046 1047 1048 1049 1050 1051 1052 1053 1054 1055 1056 1057 1058 1059 1060 1061 1062 1063 1064 1065 1066 1067 1068 1069 1070 1071 1072 1073 1074 1075 1076 1077 1078 1079 1080 1081 1082 1083 1084 1085 1086 1087 1088 1089 1090 1091 1092 1093 1094 1095 1096 1097 1098 1099 1100 1101 1102 1103 1104 1105 1106 1107 1108 1109 1110 1111 1112 1113 1114 1115 1116 1117 1118 1119 1120 1121 1122 1123 1124 1125 1126 1127 1128 1129 1130 1131 1132 1133 1134 1135 1136 1137 1138 1139 1140 1141 1142 1143 1144 1145 1146 1147 1148 1149 1150 1151 1152 1153 1154 1155 1156 1157 1158 1159 1160 1161 1162 1163 1164 1165 1166 1167 1168 1169 1170 1171 1172 1173 1174 1175  @smallexample A slope of one-third corresponds to an angle of 1 degrees. @end smallexample Place the cursor on the @samp{1}, then type @kbd{C-x * w} to enable Embedded mode on that number. Now type @kbd{3 /} (to get one-third), and @kbd{I T} (the Inverse Tangent converts a slope into an angle), then @w{@kbd{C-x * w}} again to exit Embedded mode. @smallexample A slope of one-third corresponds to an angle of 18.4349488229 degrees. @end smallexample @c [fix-ref Embedded Mode] @xref{Embedded Mode}, for full details. @node Other C-x * Commands, , Embedded Mode Overview, Using Calc @subsection Other @kbd{C-x *} Commands @noindent Two more Calc-related commands are @kbd{C-x * g} and @kbd{C-x * r}, which grab'' data from a selected region of a buffer into the Calculator. The region is defined in the usual Emacs way, by a mark'' placed at one end of the region, and the Emacs cursor or point'' placed at the other. The @kbd{C-x * g} command reads the region in the usual left-to-right, top-to-bottom order. The result is packaged into a Calc vector of numbers and placed on the stack. Calc (in its standard user interface) is then started. Type @kbd{v u} if you want to unpack this vector into separate numbers on the stack. Also, @kbd{C-u C-x * g} interprets the region as a single number or formula. The @kbd{C-x * r} command reads a rectangle, with the point and mark defining opposite corners of the rectangle. The result is a matrix of numbers on the Calculator stack. Complementary to these is @kbd{C-x * y}, which yanks'' the value at the top of the Calc stack back into an editing buffer. If you type @w{@kbd{C-x * y}} while in such a buffer, the value is yanked at the current position. If you type @kbd{C-x * y} while in the Calc buffer, Calc makes an educated guess as to which editing buffer you want to use. The Calc window does not have to be visible in order to use this command, as long as there is something on the Calc stack. Here, for reference, is the complete list of @kbd{C-x *} commands. The shift, control, and meta keys are ignored for the keystroke following @kbd{C-x *}. @noindent Commands for turning Calc on and off: @table @kbd @item * Turn Calc on or off, employing the same user interface as last time. @item =, +, -, /, \, &, # Alternatives for @kbd{*}. @item C Turn Calc on or off using its standard bottom-of-the-screen interface. If Calc is already turned on but the cursor is not in the Calc window, move the cursor into the window. @item O Same as @kbd{C}, but don't select the new Calc window. If Calc is already turned on and the cursor is in the Calc window, move it out of that window. @item B Control whether @kbd{C-x * c} and @kbd{C-x * k} use the full screen. @item Q Use Quick mode for a single short calculation. @item K Turn Calc Keypad mode on or off. @item E Turn Calc Embedded mode on or off at the current formula. @item J Turn Calc Embedded mode on or off, select the interesting part. @item W Turn Calc Embedded mode on or off at the current word (number). @item Z Turn Calc on in a user-defined way, as defined by a @kbd{Z I} command. @item X Quit Calc; turn off standard, Keypad, or Embedded mode if on. (This is like @kbd{q} or @key{OFF} inside of Calc.) @end table @iftex @sp 2 @end iftex @noindent Commands for moving data into and out of the Calculator: @table @kbd @item G Grab the region into the Calculator as a vector. @item R Grab the rectangular region into the Calculator as a matrix. @item : Grab the rectangular region and compute the sums of its columns. @item _ Grab the rectangular region and compute the sums of its rows. @item Y Yank a value from the Calculator into the current editing buffer. @end table @iftex @sp 2 @end iftex @noindent Commands for use with Embedded mode: @table @kbd @item A Activate'' the current buffer. Locate all formulas that contain @samp{:=} or @samp{=>} symbols and record their locations so that they can be updated automatically as variables are changed. @item D Duplicate the current formula immediately below and select the duplicate. @item F Insert a new formula at the current point. @item N Move the cursor to the next active formula in the buffer. @item P Move the cursor to the previous active formula in the buffer. @item U Update (i.e., as if by the @kbd{=} key) the formula at the current point. @item  Edit (as if by @code{calc-edit}) the formula at the current point. @end table @iftex @sp 2 @end iftex @noindent Miscellaneous commands: @table @kbd @item I Run the Emacs Info system to read the Calc manual. (This is the same as @kbd{h i} inside of Calc.) @item T Run the Emacs Info system to read the Calc Tutorial. @item S Run the Emacs Info system to read the Calc Summary. @item L Load Calc entirely into memory. (Normally the various parts are loaded only as they are needed.) @item M Read a region of written keystroke names (like @kbd{C-n a b c @key{RET}}) and record them as the current keyboard macro. @item 0 (This is the zero'' digit key.) Reset the Calculator to its initial state: Empty stack, and initial mode settings. @end table @node History and Acknowledgements, , Using Calc, Getting Started @section History and Acknowledgements @noindent Calc was originally started as a two-week project to occupy a lull in the author's schedule. Basically, a friend asked if I remembered the value of @texline @math{2^{32}}. @infoline @expr{2^32}. I didn't offhand, but I said, that's easy, just call up an @code{xcalc}.'' @code{Xcalc} duly reported that the answer to our question was @samp{4.294967e+09}---with no way to see the full ten digits even though we knew they were there in the program's memory! I was so annoyed, I vowed to write a calculator of my own, once and for all. I chose Emacs Lisp, a) because I had always been curious about it and b) because, being only a text editor extension language after all, Emacs Lisp would surely reach its limits long before the project got too far out of hand. To make a long story short, Emacs Lisp turned out to be a distressingly solid implementation of Lisp, and the humble task of calculating turned out to be more open-ended than one might have expected. Emacs Lisp didn't have built-in floating point math (now it does), so  Jay Belanger committed Oct 20, 2007 1176 1177 1178 1179 1180 1181 1182 1183 1184 1185 this had to be simulated in software. In fact, Emacs integers would only comfortably fit six decimal digits or so---not enough for a decent calculator. So I had to write my own high-precision integer code as well, and once I had this I figured that arbitrary-size integers were just as easy as large integers. Arbitrary floating-point precision was the logical next step. Also, since the large integer arithmetic was there anyway it seemed only fair to give the user direct access to it, which in turn made it practical to support fractions as well as floats. All these features inspired me to look around for other data types that might be worth having.  Glenn Morris committed Sep 06, 2007 1186 1187 1188 1189 1190 1191 1192 1193 1194 1195 1196 1197 1198 1199 1200 1201 1202 1203 1204 1205 1206 1207 1208 1209 1210 1211 1212 1213 1214 1215 1216 1217 1218 1219 1220 1221 1222 1223  Around this time, my friend Rick Koshi showed me his nifty new HP-28 calculator. It allowed the user to manipulate formulas as well as numerical quantities, and it could also operate on matrices. I decided that these would be good for Calc to have, too. And once things had gone this far, I figured I might as well take a look at serious algebra systems for further ideas. Since these systems did far more than I could ever hope to implement, I decided to focus on rewrite rules and other programming features so that users could implement what they needed for themselves. Rick complained that matrices were hard to read, so I put in code to format them in a 2D style. Once these routines were in place, Big mode was obligatory. Gee, what other language modes would be useful? Scott Hemphill and Allen Knutson, two friends with a strong mathematical bent, contributed ideas and algorithms for a number of Calc features including modulo forms, primality testing, and float-to-fraction conversion. Units were added at the eager insistence of Mass Sivilotti. Later, Ulrich Mueller at CERN and Przemek Klosowski at NIST provided invaluable expert assistance with the units table. As far as I can remember, the idea of using algebraic formulas and variables to represent units dates back to an ancient article in Byte magazine about muMath, an early algebra system for microcomputers. Many people have contributed to Calc by reporting bugs and suggesting features, large and small. A few deserve special mention: Tim Peters, who helped develop the ideas that led to the selection commands, rewrite rules, and many other algebra features; @texline Fran\c{c}ois @infoline Francois Pinard, who contributed an early prototype of the Calc Summary appendix as well as providing valuable suggestions in many other areas of Calc; Carl Witty, whose eagle eyes discovered many typographical and factual errors in the Calc manual; Tim Kay, who drove the development of Embedded mode; Ove Ewerlid, who made many suggestions relating to the algebra commands and contributed some code for polynomial operations;  Jay Belanger committed Sep 07, 2007 1224 Randal Schwartz, who suggested the @code{calc-eval} function; Juha  Glenn Morris committed Sep 06, 2007 1225 Sarlin, who first worked out how to split Calc into quickly-loading  Jay Belanger committed Sep 07, 2007 1226 1227 1228 parts; Bob Weiner, who helped immensely with the Lucid Emacs port; and Robert J. Chassell, who suggested the Calc Tutorial and exercises as well as many other things.  Glenn Morris committed Sep 06, 2007 1229 1230 1231 1232 1233 1234 1235 1236 1237 1238 1239 1240 1241 1242 1243 1244 1245 1246 1247 1248 1249 1250 1251 1252 1253 1254 1255 1256 1257 1258 1259 1260 1261 1262 1263 1264 1265 1266 1267 1268 1269 1270 1271 1272 1273 1274 1275 1276  @cindex Bibliography @cindex Knuth, Art of Computer Programming @cindex Numerical Recipes @c Should these be expanded into more complete references? Among the books used in the development of Calc were Knuth's @emph{Art of Computer Programming} (especially volume II, @emph{Seminumerical Algorithms}); @emph{Numerical Recipes} by Press, Flannery, Teukolsky, and Vetterling; Bevington's @emph{Data Reduction and Error Analysis for the Physical Sciences}; @emph{Concrete Mathematics} by Graham, Knuth, and Patashnik; Steele's @emph{Common Lisp, the Language}; the @emph{CRC Standard Math Tables} (William H. Beyer, ed.); and Abramowitz and Stegun's venerable @emph{Handbook of Mathematical Functions}. Also, of course, Calc could not have been written without the excellent @emph{GNU Emacs Lisp Reference Manual}, by Bil Lewis and Dan LaLiberte. Final thanks go to Richard Stallman, without whose fine implementations of the Emacs editor, language, and environment, Calc would have been finished in two weeks. @c [tutorial] @ifinfo @c This node is accessed by the C-x * t' command. @node Interactive Tutorial, Tutorial, Getting Started, Top @chapter Tutorial @noindent Some brief instructions on using the Emacs Info system for this tutorial: Press the space bar and Delete keys to go forward and backward in a section by screenfuls (or use the regular Emacs scrolling commands for this). Press @kbd{n} or @kbd{p} to go to the Next or Previous section. If the section has a @dfn{menu}, press a digit key like @kbd{1} or @kbd{2} to go to a sub-section from the menu. Press @kbd{u} to go back up from a sub-section to the menu it is part of. Exercises in the tutorial all have cross-references to the appropriate page of the answers'' section. Press @kbd{f}, then the exercise number, to see the answer to an exercise. After you have followed a cross-reference, you can press the letter @kbd{l} to return to where you were before. You can press @kbd{?} at any time for a brief summary of Info commands.  Jay Belanger committed Nov 17, 2008 1277 Press the number @kbd{1} now to enter the first section of the Tutorial.  Glenn Morris committed Sep 06, 2007 1278 1279 1280 1281 1282 1283 1284 1285 1286 1287 1288 1289 1290 1291 1292 1293 1294 1295 1296 1297 1298 1299 1300 1301 1302 1303 1304 1305 1306  @menu * Tutorial:: @end menu @node Tutorial, Introduction, Interactive Tutorial, Top @end ifinfo @ifnotinfo @node Tutorial, Introduction, Getting Started, Top @end ifnotinfo @chapter Tutorial @noindent This chapter explains how to use Calc and its many features, in a step-by-step, tutorial way. You are encouraged to run Calc and work along with the examples as you read (@pxref{Starting Calc}). If you are already familiar with advanced calculators, you may wish @c [not-split] to skip on to the rest of this manual. @c [when-split] @c to skip on to volume II of this manual, the @dfn{Calc Reference}. @c [fix-ref Embedded Mode] This tutorial describes the standard user interface of Calc only. The Quick mode and Keypad mode interfaces are fairly self-explanatory. @xref{Embedded Mode}, for a description of the Embedded mode interface. The easiest way to read this tutorial on-line is to have two windows on  Jay Belanger committed Nov 17, 2008 1307 1308 1309 1310 1311 1312 1313 your Emacs screen, one with Calc and one with the Info system. Press @kbd{C-x * t} to set this up; the on-line tutorial will be opened in the current window and Calc will be started in another window. From the Info window, the command @kbd{C-x * c} can be used to switch to the Calc window and @kbd{C-x * o} can be used to switch back to the Info window. (If you have a printed copy of the manual you can use that instead; in that case you only need to press @kbd{C-x * c} to start Calc.)  Glenn Morris committed Sep 06, 2007 1314 1315 1316 1317 1318 1319 1320 1321 1322 1323 1324 1325 1326 1327 1328 1329 1330 1331 1332 1333 1334 1335 1336 1337 1338 1339 1340 1341 1342 1343 1344 1345 1346 1347 1348 1349 1350 1351 1352 1353 1354 1355 1356 1357 1358 1359 1360 1361 1362 1363 1364 1365 1366 1367 1368 1369 1370 1371 1372 1373 1374 1375 1376 1377 1378 1379 1380 1381 1382 1383 1384 1385 1386 1387 1388 1389 1390 1391 1392 1393 1394 1395 1396 1397 1398 1399 1400 1401 1402 1403 1404 1405 1406 1407 1408 1409 1410 1411 1412 1413 1414 1415 1416 1417 1418 1419 1420 1421 1422 1423 1424 1425 1426 1427 1428 1429 1430 1431 1432 1433 1434 1435 1436 1437 1438 1439 1440 1441 1442 1443 1444 1445 1446 1447 1448 1449 1450 1451 1452 1453 1454 1455 1456 1457 1458 1459 1460 1461 1462 1463 1464 1465 1466 1467 1468 1469 1470 1471 1472 1473 1474 1475 1476 1477 1478 1479 1480 1481 1482 1483 1484 1485 1486 1487 1488 1489 1490 1491 1492 1493 1494 1495 1496 1497 1498 1499 1500 1501 1502 1503 1504 1505 1506 1507 1508 1509 1510 1511 1512 1513 1514 1515 1516 1517 1518 1519 1520 1521 1522 1523 1524 1525 1526 1527 1528 1529 1530 1531 1532 1533 1534 1535 1536 1537 1538 1539 1540 1541 1542 1543 1544 1545 1546 1547 1548 1549 1550 1551 1552 1553 1554 1555 1556 1557 1558 1559 1560 1561 1562 1563 1564 1565 1566 1567 1568 1569 1570 1571 1572 1573 1574 1575 1576 1577 1578 1579 1580 1581 1582 1583 1584 1585 1586 1587 1588 1589 1590 1591 1592 1593 1594 1595 1596 1597 1598 1599 1600 1601 1602 1603 1604 1605 1606 1607 1608 1609 1610 1611 1612 1613 1614 1615 1616 1617 1618 1619 1620 1621 1622 1623 1624 1625 1626 1627 1628 1629 1630 1631 1632 1633 1634 1635 1636 1637 1638 1639 1640 1641 1642 1643 1644 1645 1646 1647 1648 1649 1650 1651 1652 1653 1654 1655 1656 1657 1658 1659 1660 1661 1662 1663 1664 1665 1666 1667 1668 1669 1670 1671 1672 1673 1674 1675 1676 1677 1678 1679 1680 1681 1682 1683 1684 1685 1686 1687 1688 1689 1690 1691 1692 1693 1694 1695 1696 1697 1698 1699 1700 1701 1702 1703 1704 1705 1706 1707 1708 1709 1710 1711 1712 1713 1714 1715 1716 1717 1718 1719 1720 1721 1722 1723 1724 1725 1726 1727 1728 1729 1730 1731 1732 1733 1734 1735 1736 1737 1738 1739 1740 1741 1742 1743 1744 1745 1746 1747 1748 1749 1750 1751 1752 1753 1754 1755 1756 1757 1758 1759 1760  This tutorial is designed to be done in sequence. But the rest of this manual does not assume you have gone through the tutorial. The tutorial does not cover everything in the Calculator, but it touches on most general areas. @ifnottex You may wish to print out a copy of the Calc Summary and keep notes on it as you learn Calc. @xref{About This Manual}, to see how to make a printed summary. @xref{Summary}. @end ifnottex @iftex The Calc Summary at the end of the reference manual includes some blank space for your own use. You may wish to keep notes there as you learn Calc. @end iftex @menu * Basic Tutorial:: * Arithmetic Tutorial:: * Vector/Matrix Tutorial:: * Types Tutorial:: * Algebra Tutorial:: * Programming Tutorial:: * Answers to Exercises:: @end menu @node Basic Tutorial, Arithmetic Tutorial, Tutorial, Tutorial @section Basic Tutorial @noindent In this section, we learn how RPN and algebraic-style calculations work, how to undo and redo an operation done by mistake, and how to control various modes of the Calculator. @menu * RPN Tutorial:: Basic operations with the stack. * Algebraic Tutorial:: Algebraic entry; variables. * Undo Tutorial:: If you make a mistake: Undo and the trail. * Modes Tutorial:: Common mode-setting commands. @end menu @node RPN Tutorial, Algebraic Tutorial, Basic Tutorial, Basic Tutorial @subsection RPN Calculations and the Stack @cindex RPN notation @ifnottex @noindent Calc normally uses RPN notation. You may be familiar with the RPN system from Hewlett-Packard calculators, FORTH, or PostScript. (Reverse Polish Notation, RPN, is named after the Polish mathematician Jan Lukasiewicz.) @end ifnottex @tex \noindent Calc normally uses RPN notation. You may be familiar with the RPN system from Hewlett-Packard calculators, FORTH, or PostScript. (Reverse Polish Notation, RPN, is named after the Polish mathematician Jan \L ukasiewicz.) @end tex The central component of an RPN calculator is the @dfn{stack}. A calculator stack is like a stack of dishes. New dishes (numbers) are added at the top of the stack, and numbers are normally only removed from the top of the stack. @cindex Operators @cindex Operands In an operation like @expr{2+3}, the 2 and 3 are called the @dfn{operands} and the @expr{+} is the @dfn{operator}. In an RPN calculator you always enter the operands first, then the operator. Each time you type a number, Calc adds or @dfn{pushes} it onto the top of the Stack. When you press an operator key like @kbd{+}, Calc @dfn{pops} the appropriate number of operands from the stack and pushes back the result. Thus we could add the numbers 2 and 3 in an RPN calculator by typing: @kbd{2 @key{RET} 3 @key{RET} +}. (The @key{RET} key, Return, corresponds to the @key{ENTER} key on traditional RPN calculators.) Try this now if you wish; type @kbd{C-x * c} to switch into the Calc window (you can type @kbd{C-x * c} again or @kbd{C-x * o} to switch back to the Tutorial window). The first four keystrokes push'' the numbers 2 and 3 onto the stack. The @kbd{+} key pops'' the top two numbers from the stack, adds them, and pushes the result (5) back onto the stack. Here's how the stack will look at various points throughout the calculation: @smallexample @group . 1: 2 2: 2 1: 5 . . 1: 3 . . C-x * c 2 @key{RET} 3 @key{RET} + @key{DEL} @end group @end smallexample The @samp{.} symbol is a marker that represents the top of the stack. Note that the top'' of the stack is really shown at the bottom of the Stack window. This may seem backwards, but it turns out to be less distracting in regular use. @cindex Stack levels @cindex Levels of stack The numbers @samp{1:} and @samp{2:} on the left are @dfn{stack level numbers}. Old RPN calculators always had four stack levels called @expr{x}, @expr{y}, @expr{z}, and @expr{t}. Calc's stack can grow as large as you like, so it uses numbers instead of letters. Some stack-manipulation commands accept a numeric argument that says which stack level to work on. Normal commands like @kbd{+} always work on the top few levels of the stack. @c [fix-ref Truncating the Stack] The Stack buffer is just an Emacs buffer, and you can move around in it using the regular Emacs motion commands. But no matter where the cursor is, even if you have scrolled the @samp{.} marker out of view, most Calc commands always move the cursor back down to level 1 before doing anything. It is possible to move the @samp{.} marker upwards through the stack, temporarily hiding'' some numbers from commands like @kbd{+}. This is called @dfn{stack truncation} and we will not cover it in this tutorial; @pxref{Truncating the Stack}, if you are interested. You don't really need the second @key{RET} in @kbd{2 @key{RET} 3 @key{RET} +}. That's because if you type any operator name or other non-numeric key when you are entering a number, the Calculator automatically enters that number and then does the requested command. Thus @kbd{2 @key{RET} 3 +} will work just as well. Examples in this tutorial will often omit @key{RET} even when the stack displays shown would only happen if you did press @key{RET}: @smallexample @group 1: 2 2: 2 1: 5 . 1: 3 . . 2 @key{RET} 3 + @end group @end smallexample @noindent Here, after pressing @kbd{3} the stack would really show @samp{1: 2} with @samp{Calc:@: 3} in the minibuffer. In these situations, you can press the optional @key{RET} to see the stack as the figure shows. (@bullet{}) @strong{Exercise 1.} (This tutorial will include exercises at various points. Try them if you wish. Answers to all the exercises are located at the end of the Tutorial chapter. Each exercise will include a cross-reference to its particular answer. If you are reading with the Emacs Info system, press @kbd{f} and the exercise number to go to the answer, then the letter @kbd{l} to return to where you were.) @noindent Here's the first exercise: What will the keystrokes @kbd{1 @key{RET} 2 @key{RET} 3 @key{RET} 4 + * -} compute? (@samp{*} is the symbol for multiplication.) Figure it out by hand, then try it with Calc to see if you're right. @xref{RPN Answer 1, 1}. (@bullet{}) (@bullet{}) @strong{Exercise 2.} Compute @texline @math{(2\times4) + (7\times9.4) + {5\over4}} @infoline @expr{2*4 + 7*9.5 + 5/4} using the stack. @xref{RPN Answer 2, 2}. (@bullet{}) The @key{DEL} key is called Backspace on some keyboards. It is whatever key you would use to correct a simple typing error when regularly using Emacs. The @key{DEL} key pops and throws away the top value on the stack. (You can still get that value back from the Trail if you should need it later on.) There are many places in this tutorial where we assume you have used @key{DEL} to erase the results of the previous example at the beginning of a new example. In the few places where it is really important to use @key{DEL} to clear away old results, the text will remind you to do so. (It won't hurt to let things accumulate on the stack, except that whenever you give a display-mode-changing command Calc will have to spend a long time reformatting such a large stack.) Since the @kbd{-} key is also an operator (it subtracts the top two stack elements), how does one enter a negative number? Calc uses the @kbd{_} (underscore) key to act like the minus sign in a number. So, typing @kbd{-5 @key{RET}} won't work because the @kbd{-} key will try to do a subtraction, but @kbd{_5 @key{RET}} works just fine. You can also press @kbd{n}, which means change sign.'' It changes the number at the top of the stack (or the number being entered) from positive to negative or vice-versa: @kbd{5 n @key{RET}}. @cindex Duplicating a stack entry If you press @key{RET} when you're not entering a number, the effect is to duplicate the top number on the stack. Consider this calculation: @smallexample @group 1: 3 2: 3 1: 9 2: 9 1: 81 . 1: 3 . 1: 9 . . . 3 @key{RET} @key{RET} * @key{RET} * @end group @end smallexample @noindent (Of course, an easier way to do this would be @kbd{3 @key{RET} 4 ^}, to raise 3 to the fourth power.) The space-bar key (denoted @key{SPC} here) performs the same function as @key{RET}; you could replace all three occurrences of @key{RET} in the above example with @key{SPC} and the effect would be the same. @cindex Exchanging stack entries Another stack manipulation key is @key{TAB}. This exchanges the top two stack entries. Suppose you have computed @kbd{2 @key{RET} 3 +} to get 5, and then you realize what you really wanted to compute was @expr{20 / (2+3)}. @smallexample @group 1: 5 2: 5 2: 20 1: 4 . 1: 20 1: 5 . . . 2 @key{RET} 3 + 20 @key{TAB} / @end group @end smallexample @noindent Planning ahead, the calculation would have gone like this: @smallexample @group 1: 20 2: 20 3: 20 2: 20 1: 4 . 1: 2 2: 2 1: 5 . . 1: 3 . . 20 @key{RET} 2 @key{RET} 3 + / @end group @end smallexample A related stack command is @kbd{M-@key{TAB}} (hold @key{META} and type @key{TAB}). It rotates the top three elements of the stack upward, bringing the object in level 3 to the top. @smallexample @group 1: 10 2: 10 3: 10 3: 20 3: 30 . 1: 20 2: 20 2: 30 2: 10 . 1: 30 1: 10 1: 20 . . . 10 @key{RET} 20 @key{RET} 30 @key{RET} M-@key{TAB} M-@key{TAB} @end group @end smallexample (@bullet{}) @strong{Exercise 3.} Suppose the numbers 10, 20, and 30 are on the stack. Figure out how to add one to the number in level 2 without affecting the rest of the stack. Also figure out how to add one to the number in level 3. @xref{RPN Answer 3, 3}. (@bullet{}) Operations like @kbd{+}, @kbd{-}, @kbd{*}, @kbd{/}, and @kbd{^} pop two arguments from the stack and push a result. Operations like @kbd{n} and @kbd{Q} (square root) pop a single number and push the result. You can think of them as simply operating on the top element of the stack. @smallexample @group 1: 3 1: 9 2: 9 1: 25 1: 5 . . 1: 16 . . . 3 @key{RET} @key{RET} * 4 @key{RET} @key{RET} * + Q @end group @end smallexample @noindent (Note that capital @kbd{Q} means to hold down the Shift key while typing @kbd{q}. Remember, plain unshifted @kbd{q} is the Quit command.) @cindex Pythagorean Theorem Here we've used the Pythagorean Theorem to determine the hypotenuse of a right triangle. Calc actually has a built-in command for that called @kbd{f h}, but let's suppose we can't remember the necessary keystrokes. We can still enter it by its full name using @kbd{M-x} notation: @smallexample @group 1: 3 2: 3 1: 5 . 1: 4 . . 3 @key{RET} 4 @key{RET} M-x calc-hypot @end group @end smallexample All Calculator commands begin with the word @samp{calc-}. Since it gets tiring to type this, Calc provides an @kbd{x} key which is just like the regular Emacs @kbd{M-x} key except that it types the @samp{calc-} prefix for you: @smallexample @group 1: 3 2: 3 1: 5 . 1: 4 . . 3 @key{RET} 4 @key{RET} x hypot @end group @end smallexample What happens if you take the square root of a negative number? @smallexample @group 1: 4 1: -4 1: (0, 2) . . . 4 @key{RET} n Q @end group @end smallexample @noindent The notation @expr{(a, b)} represents a complex number. Complex numbers are more traditionally written @expr{a + b i}; Calc can display in this format, too, but for now we'll stick to the @expr{(a, b)} notation. If you don't know how complex numbers work, you can safely ignore this feature. Complex numbers only arise from operations that would be errors in a calculator that didn't have complex numbers. (For example, taking the square root or logarithm of a negative number produces a complex result.) Complex numbers are entered in the notation shown. The @kbd{(} and @kbd{,} and @kbd{)} keys manipulate incomplete complex numbers.'' @smallexample @group 1: ( ... 2: ( ... 1: (2, ... 1: (2, ... 1: (2, 3) . 1: 2 . 3 . . . ( 2 , 3 ) @end group @end smallexample You can perform calculations while entering parts of incomplete objects. However, an incomplete object cannot actually participate in a calculation: @smallexample @group 1: ( ... 2: ( ... 3: ( ... 1: ( ... 1: ( ... . 1: 2 2: 2 5 5 . 1: 3 . . . (error) ( 2 @key{RET} 3 + + @end group @end smallexample @noindent Adding 5 to an incomplete object makes no sense, so the last command produces an error message and leaves the stack the same. Incomplete objects can't participate in arithmetic, but they can be moved around by the regular stack commands. @smallexample @group 2: 2 3: 2 3: 3 1: ( ... 1: (2, 3) 1: 3 2: 3 2: ( ... 2 . . 1: ( ... 1: 2 3 . . . 2 @key{RET} 3 @key{RET} ( M-@key{TAB} M-@key{TAB} ) @end group @end smallexample @noindent Note that the @kbd{,} (comma) key did not have to be used here. When you press @kbd{)} all the stack entries between the incomplete entry and the top are collected, so there's never really a reason to use the comma. It's up to you. (@bullet{}) @strong{Exercise 4.} To enter the complex number @expr{(2, 3)}, your friend Joe typed @kbd{( 2 , @key{SPC} 3 )}. What happened? (Joe thought of a clever way to correct his mistake in only two keystrokes, but it didn't quite work. Try it to find out why.) @xref{RPN Answer 4, 4}. (@bullet{}) Vectors are entered the same way as complex numbers, but with square brackets in place of parentheses. We'll meet vectors again later in the tutorial. Any Emacs command can be given a @dfn{numeric prefix argument} by typing a series of @key{META}-digits beforehand. If @key{META} is awkward for you, you can instead type @kbd{C-u} followed by the necessary digits. Numeric prefix arguments can be negative, as in @kbd{M-- M-3 M-5} or @w{@kbd{C-u - 3 5}}. Calc commands use numeric prefix arguments in a variety of ways. For example, a numeric prefix on the @kbd{+} operator adds any number of stack entries at once: @smallexample @group 1: 10 2: 10 3: 10 3: 10 1: 60 . 1: 20 2: 20 2: 20 . . 1: 30 1: 30 . . 10 @key{RET} 20 @key{RET} 30 @key{RET} C-u 3 + @end group @end smallexample For stack manipulation commands like @key{RET}, a positive numeric prefix argument operates on the top @var{n} stack entries at once. A negative argument operates on the entry in level @var{n} only. An argument of zero operates on the entire stack. In this example, we copy the second-to-top element of the stack: @smallexample @group 1: 10 2: 10 3: 10 3: 10 4: 10 . 1: 20 2: 20 2: 20 3: 20 . 1: 30 1: 30 2: 30 . . 1: 20 . 10 @key{RET} 20 @key{RET} 30 @key{RET} C-u -2 @key{RET} @end group @end smallexample @cindex Clearing the stack @cindex Emptying the stack Another common idiom is @kbd{M-0 @key{DEL}}, which clears the stack. (The @kbd{M-0} numeric prefix tells @key{DEL} to operate on the entire stack.) @node Algebraic Tutorial, Undo Tutorial, RPN Tutorial, Basic Tutorial @subsection Algebraic-Style Calculations @noindent If you are not used to RPN notation, you may prefer to operate the Calculator in Algebraic mode, which is closer to the way non-RPN calculators work. In Algebraic mode, you enter formulas in traditional @expr{2+3} notation.  Jay Belanger committed Jan 27, 2009 1761 1762 1763 @strong{Notice:} Calc gives @samp{/} lower precedence than @samp{*}, so that @samp{a/b*c} is interpreted as @samp{a/(b*c)}; this is not standard across all computer languages. See below for details.  Glenn Morris committed Sep 06, 2007 1764 1765 1766 1767 1768 1769 1770 1771 1772 1773 1774 1775 1776 1777 1778 1779 1780 1781 1782 1783 1784 1785 1786 1787 1788 1789 1790 1791 1792 1793 1794 1795 1796 1797 1798 1799 1800 1801 1802 1803 1804 1805 1806 1807 1808 1809 1810 1811 1812 1813 1814 1815 1816 1817 1818 1819 1820 1821 1822 1823 1824 1825 1826 1827 1828 1829 1830 1831 1832 1833 1834 1835 1836 1837 1838 1839 1840 1841 1842 1843 1844 1845 1846 1847 1848 1849 1850 1851 1852 1853 1854 1855 1856 1857 1858 1859 1860 1861 1862 1863 1864 1865 1866 1867 1868 1869 1870 1871 1872 1873 1874 1875 1876 1877 1878 1879 1880 1881 1882 1883 1884 1885 1886 1887 1888 1889 1890 1891 1892 1893 1894 1895 1896 1897 1898 1899 1900 1901 1902 1903 1904 1905 1906 1907 1908 1909 1910 1911 1912 1913 1914 1915 1916 1917 1918 1919 1920 1921 1922 1923 1924 1925 1926 1927 1928 1929 1930 1931 1932 1933 1934 1935 1936 1937 1938 1939 1940 1941 1942 1943 1944 1945 1946 1947 1948 1949 1950 1951 1952 1953 1954 1955 1956 1957 1958 1959 1960 1961 1962 1963 1964 1965 1966 1967 1968 1969 1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 2018 2019 2020 2021 2022 2023 2024 2025 2026 2027 2028 2029 2030 2031 2032 2033 2034 2035 2036 2037 2038 2039 2040 2041 2042 2043 2044 2045 2046 2047 2048 2049 2050 2051 2052 2053 2054 2055 2056 2057 2058 2059 2060 2061 2062 2063 2064 2065 2066 2067 2068 2069 2070 2071 2072 2073 2074 2075 2076 2077 2078 2079 2080 2081 2082 2083 2084 2085 2086 2087 2088 2089 2090 2091 2092 2093 2094 2095 2096 2097 2098 2099 2100 2101 2102 2103 2104 2105 2106 2107 2108 2109 2110 2111 2112 2113 2114 2115 2116 2117 2118 2119 2120 2121 2122 2123 2124 2125 2126 2127 2128 2129 2130 2131 2132 2133 2134 2135 2136 2137 2138 2139 2140 2141 2142 2143 2144 2145 2146 2147 2148 2149 2150 2151 2152 2153 2154 2155 2156 2157 2158 2159 2160 2161 2162 2163 2164 2165 2166 2167 2168 2169 2170 2171 2172 2173 2174 2175 2176 2177 2178 2179 2180 2181 2182 2183 2184 2185 2186 2187 2188 2189 2190 2191 2192 2193 2194 2195 2196 2197 2198 2199 2200 2201 2202  You don't really need any special mode'' to enter algebraic formulas. You can enter a formula at any time by pressing the apostrophe (@kbd{'}) key. Answer the prompt with the desired formula, then press @key{RET}. The formula is evaluated and the result is pushed onto the RPN stack. If you don't want to think in RPN at all, you can enter your whole computation as a formula, read the result from the stack, then press @key{DEL} to delete it from the stack. Try pressing the apostrophe key, then @kbd{2+3+4}, then @key{RET}. The result should be the number 9. Algebraic formulas use the operators @samp{+}, @samp{-}, @samp{*}, @samp{/}, and @samp{^}. You can use parentheses to make the order of evaluation clear. In the absence of parentheses, @samp{^} is evaluated first, then @samp{*}, then @samp{/}, then finally @samp{+} and @samp{-}. For example, the expression @example 2 + 3*4*5 / 6*7^8 - 9 @end example @noindent is equivalent to @example 2 + ((3*4*5) / (6*(7^8)) - 9 @end example @noindent or, in large mathematical notation, @ifnottex @example @group 3 * 4 * 5 2 + --------- - 9 8 6 * 7 @end group @end example @end ifnottex @tex \turnoffactive \beforedisplay 2 + { 3 \times 4 \times 5 \over 6 \times 7^8 } - 9 $$\afterdisplay @end tex @noindent The result of this expression will be the number @mathit{-6.99999826533}. Calc's order of evaluation is the same as for most computer languages, except that @samp{*} binds more strongly than @samp{/}, as the above example shows. As in normal mathematical notation, the @samp{*} symbol can often be omitted: @samp{2 a} is the same as @samp{2*a}. Operators at the same level are evaluated from left to right, except that @samp{^} is evaluated from right to left. Thus, @samp{2-3-4} is equivalent to @samp{(2-3)-4} or @mathit{-5}, whereas @samp{2^3^4} is equivalent to @samp{2^(3^4)} (a very large integer; try it!). If you tire of typing the apostrophe all the time, there is Algebraic mode, where Calc automatically senses when you are about to type an algebraic expression. To enter this mode, press the two letters @w{@kbd{m a}}. (An @samp{Alg} indicator should appear in the Calc window's mode line.) Press @kbd{m a}, then @kbd{2+3+4} with no apostrophe, then @key{RET}. In Algebraic mode, when you press any key that would normally begin entering a number (such as a digit, a decimal point, or the @kbd{_} key), or if you press @kbd{(} or @kbd{[}, Calc automatically begins an algebraic entry. Functions which do not have operator symbols like @samp{+} and @samp{*} must be entered in formulas using function-call notation. For example, the function name corresponding to the square-root key @kbd{Q} is @code{sqrt}. To compute a square root in a formula, you would use the notation @samp{sqrt(@var{x})}. Press the apostrophe, then type @kbd{sqrt(5*2) - 3}. The result should be @expr{0.16227766017}. Note that if the formula begins with a function name, you need to use the apostrophe even if you are in Algebraic mode. If you type @kbd{arcsin} out of the blue, the @kbd{a r} will be taken as an Algebraic Rewrite command, and the @kbd{csin} will be taken as the name of the rewrite rule to use! Some people prefer to enter complex numbers and vectors in algebraic form because they find RPN entry with incomplete objects to be too distracting, even though they otherwise use Calc as an RPN calculator. Still in Algebraic mode, type: @smallexample @group 1: (2, 3) 2: (2, 3) 1: (8, -1) 2: (8, -1) 1: (9, -1) . 1: (1, -2) . 1: 1 . . . (2,3) @key{RET} (1,-2) @key{RET} * 1 @key{RET} + @end group @end smallexample Algebraic mode allows us to enter complex numbers without pressing an apostrophe first, but it also means we need to press @key{RET} after every entry, even for a simple number like @expr{1}. (You can type @kbd{C-u m a} to enable a special Incomplete Algebraic mode in which the @kbd{(} and @kbd{[} keys use algebraic entry even though regular numeric keys still use RPN numeric entry. There is also Total Algebraic mode, started by typing @kbd{m t}, in which all normal keys begin algebraic entry. You must then use the @key{META} key to type Calc commands: @kbd{M-m t} to get back out of Total Algebraic mode, @kbd{M-q} to quit, etc.) If you're still in Algebraic mode, press @kbd{m a} again to turn it off. Actual non-RPN calculators use a mixture of algebraic and RPN styles. In general, operators of two numbers (like @kbd{+} and @kbd{*}) use algebraic form, but operators of one number (like @kbd{n} and @kbd{Q}) use RPN form. Also, a non-RPN calculator allows you to see the intermediate results of a calculation as you go along. You can accomplish this in Calc by performing your calculation as a series of algebraic entries, using the @kbd{} sign to tie them together. In an algebraic formula, @kbd{} represents the number on the top of the stack. Here, we perform the calculation @texline @math{\sqrt{2\times4+1}}, @infoline @expr{sqrt(2*4+1)}, which on a traditional calculator would be done by pressing @kbd{2 * 4 + 1 =} and then the square-root key. @smallexample @group 1: 8 1: 9 1: 3 . . . ' 2*4 @key{RET} +1 @key{RET} Q @end group @end smallexample @noindent Notice that we didn't need to press an apostrophe for the @kbd{+1}, because the dollar sign always begins an algebraic entry. (@bullet{}) @strong{Exercise 1.} How could you get the same effect as pressing @kbd{Q} but using an algebraic entry instead? How about if the @kbd{Q} key on your keyboard were broken? @xref{Algebraic Answer 1, 1}. (@bullet{}) The notations @kbd{$$}, @kbd{$$}, and so on stand for higher stack entries. For example, @kbd{'$$+ @key{RET}} is just like typing @kbd{+}. Algebraic formulas can include @dfn{variables}. To store in a variable, press @kbd{s s}, then type the variable name, then press @key{RET}. (There are actually two flavors of store command: @kbd{s s} stores a number in a variable but also leaves the number on the stack, while @w{@kbd{s t}} removes a number from the stack and stores it in the variable.) A variable name should consist of one or more letters or digits, beginning with a letter. @smallexample @group 1: 17 . 1: a + a^2 1: 306 . . . 17 s t a @key{RET} ' a+a^2 @key{RET} = @end group @end smallexample @noindent The @kbd{=} key @dfn{evaluates} a formula by replacing all its variables by the values that were stored in them. For RPN calculations, you can recall a variable's value on the stack either by entering its name as a formula and pressing @kbd{=}, or by using the @kbd{s r} command. @smallexample @group 1: 17 2: 17 3: 17 2: 17 1: 306 . 1: 17 2: 17 1: 289 . . 1: 2 . . s r a @key{RET} ' a @key{RET} = 2 ^ + @end group @end smallexample If you press a single digit for a variable name (as in @kbd{s t 3}, you get one of ten @dfn{quick variables} @code{q0} through @code{q9}. They are quick'' simply because you don't have to type the letter @code{q} or the @key{RET} after their names. In fact, you can type simply @kbd{s 3} as a shorthand for @kbd{s s 3}, and likewise for @kbd{t 3} and @w{@kbd{r 3}}. Any variables in an algebraic formula for which you have not stored values are left alone, even when you evaluate the formula. @smallexample @group 1: 2 a + 2 b 1: 34 + 2 b . . ' 2a+2b @key{RET} = @end group @end smallexample Calls to function names which are undefined in Calc are also left alone, as are calls for which the value is undefined. @smallexample @group 1: 2 + log10(0) + log10(x) + log10(5, 6) + foo(3) . ' log10(100) + log10(0) + log10(x) + log10(5,6) + foo(3) @key{RET} @end group @end smallexample @noindent In this example, the first call to @code{log10} works, but the other calls are not evaluated. In the second call, the logarithm is undefined for that value of the argument; in the third, the argument is symbolic, and in the fourth, there are too many arguments. In the fifth case, there is no function called @code{foo}. You will see a Wrong number of arguments'' message referring to @samp{log10(5,6)}. Press the @kbd{w} (why'') key to see any other messages that may have arisen from the last calculation. In this case you will get logarithm of zero,'' then number expected: @code{x}''. Calc automatically displays the first message only if the message is sufficiently important; for example, Calc considers wrong number of arguments'' and logarithm of zero'' to be important enough to report automatically, while a message like number expected: @code{x}'' will only show up if you explicitly press the @kbd{w} key. (@bullet{}) @strong{Exercise 2.} Joe entered the formula @samp{2 x y}, stored 5 in @code{x}, pressed @kbd{=}, and got the expected result, @samp{10 y}. He then tried the same for the formula @samp{2 x (1+y)}, expecting @samp{10 (1+y)}, but it didn't work. Why not? @xref{Algebraic Answer 2, 2}. (@bullet{}) (@bullet{}) @strong{Exercise 3.} What result would you expect @kbd{1 @key{RET} 0 /} to give? What if you then type @kbd{0 *}? @xref{Algebraic Answer 3, 3}. (@bullet{}) One interesting way to work with variables is to use the @dfn{evaluates-to} (@samp{=>}) operator. It works like this: Enter a formula algebraically in the usual way, but follow the formula with an @samp{=>} symbol. (There is also an @kbd{s =} command which builds an @samp{=>} formula using the stack.) On the stack, you will see two copies of the formula with an @samp{=>} between them. The lefthand formula is exactly like you typed it; the righthand formula has been evaluated as if by typing @kbd{=}. @smallexample @group 2: 2 + 3 => 5 2: 2 + 3 => 5 1: 2 a + 2 b => 34 + 2 b 1: 2 a + 2 b => 20 + 2 b . . ' 2+3 => @key{RET} ' 2a+2b @key{RET} s = 10 s t a @key{RET} @end group @end smallexample @noindent Notice that the instant we stored a new value in @code{a}, all @samp{=>} operators already on the stack that referred to @expr{a} were updated to use the new value. With @samp{=>}, you can push a set of formulas on the stack, then change the variables experimentally to see the effects on the formulas' values. You can also unstore'' a variable when you are through with it: @smallexample @group 2: 2 + 5 => 5 1: 2 a + 2 b => 2 a + 2 b . s u a @key{RET} @end group @end smallexample We will encounter formulas involving variables and functions again when we discuss the algebra and calculus features of the Calculator. @node Undo Tutorial, Modes Tutorial, Algebraic Tutorial, Basic Tutorial @subsection Undo and Redo @noindent If you make a mistake, you can usually correct it by pressing shift-@kbd{U}, the undo'' command. First, clear the stack (@kbd{M-0 @key{DEL}}) and exit and restart Calc (@kbd{C-x * * C-x * *}) to make sure things start off with a clean slate. Now: @smallexample @group 1: 2 2: 2 1: 8 2: 2 1: 6 . 1: 3 . 1: 3 . . . 2 @key{RET} 3 ^ U * @end group @end smallexample You can undo any number of times. Calc keeps a complete record of all you have done since you last opened the Calc window. After the above example, you could type: @smallexample @group 1: 6 2: 2 1: 2 . . . 1: 3 . . (error) U U U U @end group @end smallexample You can also type @kbd{D} to redo'' a command that you have undone mistakenly. @smallexample @group . 1: 2 2: 2 1: 6 1: 6 . 1: 3 . . . (error) D D D D @end group @end smallexample @noindent It was not possible to redo past the @expr{6}, since that was placed there by something other than an undo command. @cindex Time travel You can think of undo and redo as a sort of time machine.'' Press @kbd{U} to go backward in time, @kbd{D} to go forward. If you go backward and do something (like @kbd{*}) then, as any science fiction reader knows, you have changed your future and you cannot go forward again. Thus, the inability to redo past the @expr{6} even though there was an earlier undo command. You can always recall an earlier result using the Trail. We've ignored the trail so far, but it has been faithfully recording everything we did since we loaded the Calculator. If the Trail is not displayed, press @kbd{t d} now to turn it on. Let's try grabbing an earlier result. The @expr{8} we computed was undone by a @kbd{U} command, and was lost even to Redo when we pressed @kbd{*}, but it's still there in the trail. There should be a little @samp{>} arrow (the @dfn{trail pointer}) resting on the last trail entry. If there isn't, press @kbd{t ]} to reset the trail pointer. Now, press @w{@kbd{t p}} to move the arrow onto the line containing @expr{8}, and press @w{@kbd{t y}} to yank'' that number back onto the stack. If you press @kbd{t ]} again, you will see that even our Yank command went into the trail. Let's go further back in time. Earlier in the tutorial we computed a huge integer using the formula @samp{2^3^4}. We don't remember what it was, but the first digits were 241''. Press @kbd{t r} (which stands for trail-search-reverse), then type @kbd{241}. The trail cursor will jump back to the next previous occurrence of the string 241'' in the trail. This is just a regular Emacs incremental search; you can now press @kbd{C-s} or @kbd{C-r} to continue the search forwards or backwards as you like. To finish the search, press @key{RET}. This halts the incremental search and leaves the trail pointer at the thing we found. Now we can type @kbd{t y} to yank that number onto the stack. If we hadn't remembered the 241'', we could simply have searched for @kbd{2^3^4}, then pressed @kbd{@key{RET} t n} to halt and then move to the next item. You may have noticed that all the trail-related commands begin with the letter @kbd{t}. (The store-and-recall commands, on the other hand, all began with @kbd{s}.) Calc has so many commands that there aren't enough keys for all of them, so various commands are grouped into two-letter sequences where the first letter is called the @dfn{prefix} key. If you type a prefix key by accident, you can press @kbd{C-g} to cancel it. (In fact, you can press @kbd{C-g} to cancel almost anything in Emacs.) To get help on a prefix key, press that key followed by @kbd{?}. Some prefixes have several lines of help, so you need to press @kbd{?} repeatedly to see them all. You can also type @kbd{h h} to see all the help at once. Try pressing @kbd{t ?} now. You will see a line of the form, @smallexample trail/time: Display; Fwd, Back; Next, Prev, Here, [, ]; Yank: [MORE] t- @end smallexample @noindent The word trail'' indicates that the @kbd{t} prefix key contains trail-related commands. Each entry on the line shows one command, with a single capital letter showing which letter you press to get that command. We have used @kbd{t n}, @kbd{t p}, @kbd{t ]}, and @kbd{t y} so far. The @samp{[MORE]} means you can press @kbd{?} again to see more @kbd{t}-prefix commands. Notice that the commands are roughly divided (by semicolons) into related groups. When you are in the help display for a prefix key, the prefix is still active. If you press another key, like @kbd{y} for example, it will be interpreted as a @kbd{t y} command. If all you wanted was to look at the help messages, press @kbd{C-g} afterwards to cancel the prefix. One more way to correct an error is by editing the stack entries. The actual Stack buffer is marked read-only and must not be edited directly, but you can press @kbd{} (the backquote or accent grave) to edit a stack entry. Try entering @samp{3.141439} now. If this is supposed to represent @cpi{}, it's got several errors. Press @kbd{} to edit this number. Now use the normal Emacs cursor motion and editing keys to change the second 4 to a 5, and to transpose the 3 and the 9. When you press @key{RET}, the number on the stack will be replaced by your new number. This works for formulas, vectors, and all other types of values you can put on the stack. The @kbd{} key also works during entry of a number or algebraic formula. @node Modes Tutorial, , Undo Tutorial, Basic Tutorial @subsection Mode-Setting Commands @noindent Calc has many types of @dfn{modes} that affect the way it interprets your commands or the way it displays data. We have already seen one mode, namely Algebraic mode. There are many others, too; we'll try some of the most common ones here. Perhaps the most fundamental mode in Calc is the current @dfn{precision}. Notice the @samp{12} on the Calc window's mode line: @smallexample  Jay Belanger committed Jun 29, 2008 2203 --%*-Calc: 12 Deg (Calculator)----All------ ` Glenn Morris committed Sep 06, 2007 2204 2205 2206 2207 2208 2209 2210 2211 2212 2213 2214 2215 2216 2217 2218 2219 2220 2221 2222 2223 2224 2225 2226 2227 2228 2229 2230 2231 2232 2233 2234 2235 2236 2237 2238 2239 2240 2241 2242 2243 2244 2245 2246 2247 2248 2249 2250 2251 2252 2253 2254 2255 2256 2257 2258 2259 2260 2261 2262 2263 2264 2265 2266 2267 2268 2269 2270 2271 2272 2273 2274 2275 2276 2277 2278 2279 2280 2281 2282 2283 2284 2285 2286 2287 2288 2289 2290 2291 2292 2293 2294 2295 2296 2297 2298 2299 2300 2301 2302 2303 2304 2305 2306 2307 2308 2309 2310 2311 2312 2313 2314 2315 2316 2317 2318 2319 2320 2321 2322 2323 2324 2325 2326 2327 2328 2329 2330 2331 2332 2333 2334 2335 2336 2337 2338 2339 2340 2341 2342 2343 2344 2345 2346 2347 2348 2349 2350 2351 2352 2353 2354 2355 2356 2357 2358 2359 2360 2361 2362 2363 2364 2365 2366 2367 2368 2369 2370 2371 2372 2373 2374 2375 2376 2377 2378 2379 2380 2381 2382 2383 2384 2385 2386 2387 2388 2389 2390 2391 2392 2393 2394 2395 2396 2397 2398 2399 2400 2401 2402 2403 2404 2405 2406 2407 2408 2409 2410 2411 2412 2413 2414 2415 2416 2417 2418 2419 2420 2421 2422 2423 2424 2425 2426 2427 2428 2429 2430 2431 2432 2433 2434 2435 2436 2437 2438 2439 2440 2441 2442 2443