diff options
| -rw-r--r-- | man/ChangeLog | 8 | ||||
| -rw-r--r-- | man/calc.texi | 210 |
2 files changed, 108 insertions, 110 deletions
diff --git a/man/ChangeLog b/man/ChangeLog index 1c6d1dbf16b..6b8d53ef246 100644 --- a/man/ChangeLog +++ b/man/ChangeLog | |||
| @@ -1,8 +1,10 @@ | |||
| 1 | 2007-06-20 Jay Belanger <jay.p.belanger@gmail.com> | 1 | 2007-06-20 Jay Belanger <jay.p.belanger@gmail.com> |
| 2 | 2 | ||
| 3 | * calc.texi (Basic Arithmetic, Customizing Calc): | 3 | * calc.texi:Change ifinfo to ifnottex (as appropriate) throughout. |
| 4 | Make description of the variable `calc-multiplication-has-precedence' | 4 | (About This Manual): Remove redundant information. |
| 5 | match its new effect. | 5 | (Getting Started): Mention author. |
| 6 | (Basic Arithmetic, Customizing Calc): Make description of the | ||
| 7 | variable `calc-multiplication-has-precedence' match its new effect. | ||
| 6 | 8 | ||
| 7 | 2007-06-19 Jay Belanger <jay.p.belanger@gmail.com> | 9 | 2007-06-19 Jay Belanger <jay.p.belanger@gmail.com> |
| 8 | 10 | ||
diff --git a/man/calc.texi b/man/calc.texi index 3151d9b7b92..9436e79ef0f 100644 --- a/man/calc.texi +++ b/man/calc.texi | |||
| @@ -124,28 +124,32 @@ Copyright @copyright{} 1990, 1991, 2001, 2002, 2003, 2004, | |||
| 124 | @end titlepage | 124 | @end titlepage |
| 125 | 125 | ||
| 126 | @c [begin] | 126 | @c [begin] |
| 127 | @ifinfo | 127 | @ifnottex |
| 128 | @node Top, Getting Started, (dir), (dir) | 128 | @node Top, Getting Started, (dir), (dir) |
| 129 | @chapter The GNU Emacs Calculator | 129 | @chapter The GNU Emacs Calculator |
| 130 | 130 | ||
| 131 | @noindent | 131 | @noindent |
| 132 | @dfn{Calc} is an advanced desk calculator and mathematical tool | 132 | @dfn{Calc} is an advanced desk calculator and mathematical tool |
| 133 | that runs as part of the GNU Emacs environment. | 133 | written by Dave Gillespie that runs as part of the GNU Emacs environment. |
| 134 | 134 | ||
| 135 | This manual is divided into three major parts: ``Getting Started,'' | 135 | This manual, also written (mostly) by Dave Gillespie, is divided into |
| 136 | the ``Calc Tutorial,'' and the ``Calc Reference.'' The Tutorial | 136 | three major parts: ``Getting Started,'' the ``Calc Tutorial,'' and the |
| 137 | introduces all the major aspects of Calculator use in an easy, | 137 | ``Calc Reference.'' The Tutorial introduces all the major aspects of |
| 138 | hands-on way. The remainder of the manual is a complete reference to | 138 | Calculator use in an easy, hands-on way. The remainder of the manual is |
| 139 | the features of the Calculator. | 139 | a complete reference to the features of the Calculator. |
| 140 | @end ifnottex | ||
| 140 | 141 | ||
| 142 | @ifinfo | ||
| 141 | For help in the Emacs Info system (which you are using to read this | 143 | For help in the Emacs Info system (which you are using to read this |
| 142 | file), type @kbd{?}. (You can also type @kbd{h} to run through a | 144 | file), type @kbd{?}. (You can also type @kbd{h} to run through a |
| 143 | longer Info tutorial.) | 145 | longer Info tutorial.) |
| 144 | |||
| 145 | @end ifinfo | 146 | @end ifinfo |
| 147 | |||
| 146 | @menu | 148 | @menu |
| 147 | * Getting Started:: General description and overview. | 149 | * Getting Started:: General description and overview. |
| 150 | @ifinfo | ||
| 148 | * Interactive Tutorial:: | 151 | * Interactive Tutorial:: |
| 152 | @end ifinfo | ||
| 149 | * Tutorial:: A step-by-step introduction for beginners. | 153 | * Tutorial:: A step-by-step introduction for beginners. |
| 150 | 154 | ||
| 151 | * Introduction:: Introduction to the Calc reference manual. | 155 | * Introduction:: Introduction to the Calc reference manual. |
| @@ -179,7 +183,12 @@ longer Info tutorial.) | |||
| 179 | * Lisp Function Index:: Internal Lisp math functions. | 183 | * Lisp Function Index:: Internal Lisp math functions. |
| 180 | @end menu | 184 | @end menu |
| 181 | 185 | ||
| 186 | @ifinfo | ||
| 182 | @node Getting Started, Interactive Tutorial, Top, Top | 187 | @node Getting Started, Interactive Tutorial, Top, Top |
| 188 | @end ifinfo | ||
| 189 | @ifnotinfo | ||
| 190 | @node Getting Started, Tutorial, Top, Top | ||
| 191 | @end ifnotinfo | ||
| 183 | @chapter Getting Started | 192 | @chapter Getting Started |
| 184 | @noindent | 193 | @noindent |
| 185 | This chapter provides a general overview of Calc, the GNU Emacs | 194 | This chapter provides a general overview of Calc, the GNU Emacs |
| @@ -267,12 +276,6 @@ experience with GNU Emacs in order to get the most out of Calc, | |||
| 267 | this manual ought to be readable even if you don't know or use Emacs | 276 | this manual ought to be readable even if you don't know or use Emacs |
| 268 | regularly. | 277 | regularly. |
| 269 | 278 | ||
| 270 | @ifinfo | ||
| 271 | The manual is divided into three major parts:@: the ``Getting | ||
| 272 | Started'' chapter you are reading now, the Calc tutorial (chapter 2), | ||
| 273 | and the Calc reference manual (the remaining chapters and appendices). | ||
| 274 | @end ifinfo | ||
| 275 | @iftex | ||
| 276 | The manual is divided into three major parts:@: the ``Getting | 279 | The manual is divided into three major parts:@: the ``Getting |
| 277 | Started'' chapter you are reading now, the Calc tutorial (chapter 2), | 280 | Started'' chapter you are reading now, the Calc tutorial (chapter 2), |
| 278 | and the Calc reference manual (the remaining chapters and appendices). | 281 | and the Calc reference manual (the remaining chapters and appendices). |
| @@ -280,7 +283,6 @@ and the Calc reference manual (the remaining chapters and appendices). | |||
| 280 | @c This manual has been printed in two volumes, the @dfn{Tutorial} and the | 283 | @c This manual has been printed in two volumes, the @dfn{Tutorial} and the |
| 281 | @c @dfn{Reference}. Both volumes include a copy of the ``Getting Started'' | 284 | @c @dfn{Reference}. Both volumes include a copy of the ``Getting Started'' |
| 282 | @c chapter. | 285 | @c chapter. |
| 283 | @end iftex | ||
| 284 | 286 | ||
| 285 | If you are in a hurry to use Calc, there is a brief ``demonstration'' | 287 | If you are in a hurry to use Calc, there is a brief ``demonstration'' |
| 286 | below which illustrates the major features of Calc in just a couple of | 288 | below which illustrates the major features of Calc in just a couple of |
| @@ -321,6 +323,7 @@ you can also go to the part of the manual describing any Calc key, | |||
| 321 | function, or variable using @w{@kbd{h k}}, @kbd{h f}, or @kbd{h v}, | 323 | function, or variable using @w{@kbd{h k}}, @kbd{h f}, or @kbd{h v}, |
| 322 | respectively. @xref{Help Commands}. | 324 | respectively. @xref{Help Commands}. |
| 323 | 325 | ||
| 326 | @ifnottex | ||
| 324 | The Calc manual can be printed, but because the manual is so large, you | 327 | The Calc manual can be printed, but because the manual is so large, you |
| 325 | should only make a printed copy if you really need it. To print the | 328 | should only make a printed copy if you really need it. To print the |
| 326 | manual, you will need the @TeX{} typesetting program (this is a free | 329 | manual, you will need the @TeX{} typesetting program (this is a free |
| @@ -347,7 +350,7 @@ or | |||
| 347 | @example | 350 | @example |
| 348 | dvips calc.dvi | 351 | dvips calc.dvi |
| 349 | @end example | 352 | @end example |
| 350 | 353 | @end ifnottex | |
| 351 | @c Printed copies of this manual are also available from the Free Software | 354 | @c Printed copies of this manual are also available from the Free Software |
| 352 | @c Foundation. | 355 | @c Foundation. |
| 353 | 356 | ||
| @@ -543,13 +546,13 @@ system. Type @kbd{d N} to return to normal notation. | |||
| 543 | Type @kbd{7.5}, then @kbd{s l a @key{RET}} to let @expr{a = 7.5} in these formulas. | 546 | Type @kbd{7.5}, then @kbd{s l a @key{RET}} to let @expr{a = 7.5} in these formulas. |
| 544 | (That's a letter @kbd{l}, not a numeral @kbd{1}.) | 547 | (That's a letter @kbd{l}, not a numeral @kbd{1}.) |
| 545 | 548 | ||
| 546 | @iftex | 549 | @ifnotinfo |
| 547 | @strong{Help functions.} You can read about any command in the on-line | 550 | @strong{Help functions.} You can read about any command in the on-line |
| 548 | manual. Type @kbd{C-x * c} to return to Calc after each of these | 551 | manual. Type @kbd{C-x * c} to return to Calc after each of these |
| 549 | commands: @kbd{h k t N} to read about the @kbd{t N} command, | 552 | commands: @kbd{h k t N} to read about the @kbd{t N} command, |
| 550 | @kbd{h f sqrt @key{RET}} to read about the @code{sqrt} function, and | 553 | @kbd{h f sqrt @key{RET}} to read about the @code{sqrt} function, and |
| 551 | @kbd{h s} to read the Calc summary. | 554 | @kbd{h s} to read the Calc summary. |
| 552 | @end iftex | 555 | @end ifnotinfo |
| 553 | @ifinfo | 556 | @ifinfo |
| 554 | @strong{Help functions.} You can read about any command in the on-line | 557 | @strong{Help functions.} You can read about any command in the on-line |
| 555 | manual. Remember to type the letter @kbd{l}, then @kbd{C-x * c}, to | 558 | manual. Remember to type the letter @kbd{l}, then @kbd{C-x * c}, to |
| @@ -1251,9 +1254,12 @@ Press @kbd{1} now to enter the first section of the Tutorial. | |||
| 1251 | @menu | 1254 | @menu |
| 1252 | * Tutorial:: | 1255 | * Tutorial:: |
| 1253 | @end menu | 1256 | @end menu |
| 1254 | @end ifinfo | ||
| 1255 | 1257 | ||
| 1256 | @node Tutorial, Introduction, Interactive Tutorial, Top | 1258 | @node Tutorial, Introduction, Interactive Tutorial, Top |
| 1259 | @end ifinfo | ||
| 1260 | @ifnotinfo | ||
| 1261 | @node Tutorial, Introduction, Getting Started, Top | ||
| 1262 | @end ifnotinfo | ||
| 1257 | @chapter Tutorial | 1263 | @chapter Tutorial |
| 1258 | 1264 | ||
| 1259 | @noindent | 1265 | @noindent |
| @@ -1272,32 +1278,22 @@ The Quick mode and Keypad mode interfaces are fairly | |||
| 1272 | self-explanatory. @xref{Embedded Mode}, for a description of | 1278 | self-explanatory. @xref{Embedded Mode}, for a description of |
| 1273 | the Embedded mode interface. | 1279 | the Embedded mode interface. |
| 1274 | 1280 | ||
| 1275 | @ifinfo | ||
| 1276 | The easiest way to read this tutorial on-line is to have two windows on | ||
| 1277 | your Emacs screen, one with Calc and one with the Info system. (If you | ||
| 1278 | have a printed copy of the manual you can use that instead.) Press | ||
| 1279 | @kbd{C-x * c} to turn Calc on or to switch into the Calc window, and | ||
| 1280 | press @kbd{C-x * i} to start the Info system or to switch into its window. | ||
| 1281 | Or, you may prefer to use the tutorial in printed form. | ||
| 1282 | @end ifinfo | ||
| 1283 | @iftex | ||
| 1284 | The easiest way to read this tutorial on-line is to have two windows on | 1281 | The easiest way to read this tutorial on-line is to have two windows on |
| 1285 | your Emacs screen, one with Calc and one with the Info system. (If you | 1282 | your Emacs screen, one with Calc and one with the Info system. (If you |
| 1286 | have a printed copy of the manual you can use that instead.) Press | 1283 | have a printed copy of the manual you can use that instead.) Press |
| 1287 | @kbd{C-x * c} to turn Calc on or to switch into the Calc window, and | 1284 | @kbd{C-x * c} to turn Calc on or to switch into the Calc window, and |
| 1288 | press @kbd{C-x * i} to start the Info system or to switch into its window. | 1285 | press @kbd{C-x * i} to start the Info system or to switch into its window. |
| 1289 | @end iftex | ||
| 1290 | 1286 | ||
| 1291 | This tutorial is designed to be done in sequence. But the rest of this | 1287 | This tutorial is designed to be done in sequence. But the rest of this |
| 1292 | manual does not assume you have gone through the tutorial. The tutorial | 1288 | manual does not assume you have gone through the tutorial. The tutorial |
| 1293 | does not cover everything in the Calculator, but it touches on most | 1289 | does not cover everything in the Calculator, but it touches on most |
| 1294 | general areas. | 1290 | general areas. |
| 1295 | 1291 | ||
| 1296 | @ifinfo | 1292 | @ifnottex |
| 1297 | You may wish to print out a copy of the Calc Summary and keep notes on | 1293 | You may wish to print out a copy of the Calc Summary and keep notes on |
| 1298 | it as you learn Calc. @xref{About This Manual}, to see how to make a | 1294 | it as you learn Calc. @xref{About This Manual}, to see how to make a |
| 1299 | printed summary. @xref{Summary}. | 1295 | printed summary. @xref{Summary}. |
| 1300 | @end ifinfo | 1296 | @end ifnottex |
| 1301 | @iftex | 1297 | @iftex |
| 1302 | The Calc Summary at the end of the reference manual includes some blank | 1298 | The Calc Summary at the end of the reference manual includes some blank |
| 1303 | space for your own use. You may wish to keep notes there as you learn | 1299 | space for your own use. You may wish to keep notes there as you learn |
| @@ -1334,13 +1330,13 @@ to control various modes of the Calculator. | |||
| 1334 | @subsection RPN Calculations and the Stack | 1330 | @subsection RPN Calculations and the Stack |
| 1335 | 1331 | ||
| 1336 | @cindex RPN notation | 1332 | @cindex RPN notation |
| 1337 | @ifinfo | 1333 | @ifnottex |
| 1338 | @noindent | 1334 | @noindent |
| 1339 | Calc normally uses RPN notation. You may be familiar with the RPN | 1335 | Calc normally uses RPN notation. You may be familiar with the RPN |
| 1340 | system from Hewlett-Packard calculators, FORTH, or PostScript. | 1336 | system from Hewlett-Packard calculators, FORTH, or PostScript. |
| 1341 | (Reverse Polish Notation, RPN, is named after the Polish mathematician | 1337 | (Reverse Polish Notation, RPN, is named after the Polish mathematician |
| 1342 | Jan Lukasiewicz.) | 1338 | Jan Lukasiewicz.) |
| 1343 | @end ifinfo | 1339 | @end ifnottex |
| 1344 | @tex | 1340 | @tex |
| 1345 | \noindent | 1341 | \noindent |
| 1346 | Calc normally uses RPN notation. You may be familiar with the RPN | 1342 | Calc normally uses RPN notation. You may be familiar with the RPN |
| @@ -1769,7 +1765,7 @@ is equivalent to | |||
| 1769 | @noindent | 1765 | @noindent |
| 1770 | or, in large mathematical notation, | 1766 | or, in large mathematical notation, |
| 1771 | 1767 | ||
| 1772 | @ifinfo | 1768 | @ifnottex |
| 1773 | @example | 1769 | @example |
| 1774 | @group | 1770 | @group |
| 1775 | 3 * 4 * 5 | 1771 | 3 * 4 * 5 |
| @@ -1778,7 +1774,7 @@ or, in large mathematical notation, | |||
| 1778 | 6 * 7 | 1774 | 6 * 7 |
| 1779 | @end group | 1775 | @end group |
| 1780 | @end example | 1776 | @end example |
| 1781 | @end ifinfo | 1777 | @end ifnottex |
| 1782 | @tex | 1778 | @tex |
| 1783 | \turnoffactive | 1779 | \turnoffactive |
| 1784 | \beforedisplay | 1780 | \beforedisplay |
| @@ -3325,7 +3321,7 @@ We can multiply these two matrices in either order to get an identity. | |||
| 3325 | Matrix inverses are related to systems of linear equations in algebra. | 3321 | Matrix inverses are related to systems of linear equations in algebra. |
| 3326 | Suppose we had the following set of equations: | 3322 | Suppose we had the following set of equations: |
| 3327 | 3323 | ||
| 3328 | @ifinfo | 3324 | @ifnottex |
| 3329 | @group | 3325 | @group |
| 3330 | @example | 3326 | @example |
| 3331 | a + 2b + 3c = 6 | 3327 | a + 2b + 3c = 6 |
| @@ -3333,7 +3329,7 @@ Suppose we had the following set of equations: | |||
| 3333 | 7a + 6b = 3 | 3329 | 7a + 6b = 3 |
| 3334 | @end example | 3330 | @end example |
| 3335 | @end group | 3331 | @end group |
| 3336 | @end ifinfo | 3332 | @end ifnottex |
| 3337 | @tex | 3333 | @tex |
| 3338 | \turnoffactive | 3334 | \turnoffactive |
| 3339 | \beforedisplayh | 3335 | \beforedisplayh |
| @@ -3352,7 +3348,7 @@ $$ | |||
| 3352 | @noindent | 3348 | @noindent |
| 3353 | This can be cast into the matrix equation, | 3349 | This can be cast into the matrix equation, |
| 3354 | 3350 | ||
| 3355 | @ifinfo | 3351 | @ifnottex |
| 3356 | @group | 3352 | @group |
| 3357 | @example | 3353 | @example |
| 3358 | [ [ 1, 2, 3 ] [ [ a ] [ [ 6 ] | 3354 | [ [ 1, 2, 3 ] [ [ a ] [ [ 6 ] |
| @@ -3360,7 +3356,7 @@ This can be cast into the matrix equation, | |||
| 3360 | [ 7, 6, 0 ] ] [ c ] ] [ 3 ] ] | 3356 | [ 7, 6, 0 ] ] [ c ] ] [ 3 ] ] |
| 3361 | @end example | 3357 | @end example |
| 3362 | @end group | 3358 | @end group |
| 3363 | @end ifinfo | 3359 | @end ifnottex |
| 3364 | @tex | 3360 | @tex |
| 3365 | \turnoffactive | 3361 | \turnoffactive |
| 3366 | \beforedisplay | 3362 | \beforedisplay |
| @@ -3425,14 +3421,14 @@ vectors and matrices that include variables. Solve the following | |||
| 3425 | system of equations to get expressions for @expr{x} and @expr{y} | 3421 | system of equations to get expressions for @expr{x} and @expr{y} |
| 3426 | in terms of @expr{a} and @expr{b}. | 3422 | in terms of @expr{a} and @expr{b}. |
| 3427 | 3423 | ||
| 3428 | @ifinfo | 3424 | @ifnottex |
| 3429 | @group | 3425 | @group |
| 3430 | @example | 3426 | @example |
| 3431 | x + a y = 6 | 3427 | x + a y = 6 |
| 3432 | x + b y = 10 | 3428 | x + b y = 10 |
| 3433 | @end example | 3429 | @end example |
| 3434 | @end group | 3430 | @end group |
| 3435 | @end ifinfo | 3431 | @end ifnottex |
| 3436 | @tex | 3432 | @tex |
| 3437 | \turnoffactive | 3433 | \turnoffactive |
| 3438 | \beforedisplay | 3434 | \beforedisplay |
| @@ -3456,9 +3452,9 @@ you can't solve @expr{A X = B} directly because the matrix @expr{A} | |||
| 3456 | is not square for an over-determined system. Matrix inversion works | 3452 | is not square for an over-determined system. Matrix inversion works |
| 3457 | only for square matrices. One common trick is to multiply both sides | 3453 | only for square matrices. One common trick is to multiply both sides |
| 3458 | on the left by the transpose of @expr{A}: | 3454 | on the left by the transpose of @expr{A}: |
| 3459 | @ifinfo | 3455 | @ifnottex |
| 3460 | @samp{trn(A)*A*X = trn(A)*B}. | 3456 | @samp{trn(A)*A*X = trn(A)*B}. |
| 3461 | @end ifinfo | 3457 | @end ifnottex |
| 3462 | @tex | 3458 | @tex |
| 3463 | \turnoffactive | 3459 | \turnoffactive |
| 3464 | $A^T A \, X = A^T B$, where $A^T$ is the transpose \samp{trn(A)}. | 3460 | $A^T A \, X = A^T B$, where $A^T$ is the transpose \samp{trn(A)}. |
| @@ -3472,7 +3468,7 @@ solution, which can be regarded as the ``closest'' solution to the set | |||
| 3472 | of equations. Use Calc to solve the following over-determined | 3468 | of equations. Use Calc to solve the following over-determined |
| 3473 | system: | 3469 | system: |
| 3474 | 3470 | ||
| 3475 | @ifinfo | 3471 | @ifnottex |
| 3476 | @group | 3472 | @group |
| 3477 | @example | 3473 | @example |
| 3478 | a + 2b + 3c = 6 | 3474 | a + 2b + 3c = 6 |
| @@ -3481,7 +3477,7 @@ system: | |||
| 3481 | 2a + 4b + 6c = 11 | 3477 | 2a + 4b + 6c = 11 |
| 3482 | @end example | 3478 | @end example |
| 3483 | @end group | 3479 | @end group |
| 3484 | @end ifinfo | 3480 | @end ifnottex |
| 3485 | @tex | 3481 | @tex |
| 3486 | \turnoffactive | 3482 | \turnoffactive |
| 3487 | \beforedisplayh | 3483 | \beforedisplayh |
| @@ -3749,11 +3745,11 @@ stored value from the stack.) | |||
| 3749 | 3745 | ||
| 3750 | In a least squares fit, the slope @expr{m} is given by the formula | 3746 | In a least squares fit, the slope @expr{m} is given by the formula |
| 3751 | 3747 | ||
| 3752 | @ifinfo | 3748 | @ifnottex |
| 3753 | @example | 3749 | @example |
| 3754 | m = (N sum(x y) - sum(x) sum(y)) / (N sum(x^2) - sum(x)^2) | 3750 | m = (N sum(x y) - sum(x) sum(y)) / (N sum(x^2) - sum(x)^2) |
| 3755 | @end example | 3751 | @end example |
| 3756 | @end ifinfo | 3752 | @end ifnottex |
| 3757 | @tex | 3753 | @tex |
| 3758 | \turnoffactive | 3754 | \turnoffactive |
| 3759 | \beforedisplay | 3755 | \beforedisplay |
| @@ -3790,12 +3786,12 @@ this formula uses. | |||
| 3790 | @end group | 3786 | @end group |
| 3791 | @end smallexample | 3787 | @end smallexample |
| 3792 | 3788 | ||
| 3793 | @ifinfo | 3789 | @ifnottex |
| 3794 | @noindent | 3790 | @noindent |
| 3795 | These are @samp{sum(x)}, @samp{sum(x^2)}, @samp{sum(y)}, and @samp{sum(x y)}, | 3791 | These are @samp{sum(x)}, @samp{sum(x^2)}, @samp{sum(y)}, and @samp{sum(x y)}, |
| 3796 | respectively. (We could have used @kbd{*} to compute @samp{sum(x^2)} and | 3792 | respectively. (We could have used @kbd{*} to compute @samp{sum(x^2)} and |
| 3797 | @samp{sum(x y)}.) | 3793 | @samp{sum(x y)}.) |
| 3798 | @end ifinfo | 3794 | @end ifnottex |
| 3799 | @tex | 3795 | @tex |
| 3800 | \turnoffactive | 3796 | \turnoffactive |
| 3801 | These are $\sum x$, $\sum x^2$, $\sum y$, and $\sum x y$, | 3797 | These are $\sum x$, $\sum x^2$, $\sum y$, and $\sum x y$, |
| @@ -3845,11 +3841,11 @@ Now we grind through the formula: | |||
| 3845 | That gives us the slope @expr{m}. The y-intercept @expr{b} can now | 3841 | That gives us the slope @expr{m}. The y-intercept @expr{b} can now |
| 3846 | be found with the simple formula, | 3842 | be found with the simple formula, |
| 3847 | 3843 | ||
| 3848 | @ifinfo | 3844 | @ifnottex |
| 3849 | @example | 3845 | @example |
| 3850 | b = (sum(y) - m sum(x)) / N | 3846 | b = (sum(y) - m sum(x)) / N |
| 3851 | @end example | 3847 | @end example |
| 3852 | @end ifinfo | 3848 | @end ifnottex |
| 3853 | @tex | 3849 | @tex |
| 3854 | \turnoffactive | 3850 | \turnoffactive |
| 3855 | \beforedisplay | 3851 | \beforedisplay |
| @@ -3987,14 +3983,14 @@ The @kbd{C-x * g} command accepts numbers separated by spaces or commas, | |||
| 3987 | with or without surrounding vector brackets. | 3983 | with or without surrounding vector brackets. |
| 3988 | @xref{List Answer 3, 3}. (@bullet{}) | 3984 | @xref{List Answer 3, 3}. (@bullet{}) |
| 3989 | 3985 | ||
| 3990 | @ifinfo | 3986 | @ifnottex |
| 3991 | As another example, a theorem about binomial coefficients tells | 3987 | As another example, a theorem about binomial coefficients tells |
| 3992 | us that the alternating sum of binomial coefficients | 3988 | us that the alternating sum of binomial coefficients |
| 3993 | @var{n}-choose-0 minus @var{n}-choose-1 plus @var{n}-choose-2, and so | 3989 | @var{n}-choose-0 minus @var{n}-choose-1 plus @var{n}-choose-2, and so |
| 3994 | on up to @var{n}-choose-@var{n}, | 3990 | on up to @var{n}-choose-@var{n}, |
| 3995 | always comes out to zero. Let's verify this | 3991 | always comes out to zero. Let's verify this |
| 3996 | for @expr{n=6}. | 3992 | for @expr{n=6}. |
| 3997 | @end ifinfo | 3993 | @end ifnottex |
| 3998 | @tex | 3994 | @tex |
| 3999 | As another example, a theorem about binomial coefficients tells | 3995 | As another example, a theorem about binomial coefficients tells |
| 4000 | us that the alternating sum of binomial coefficients | 3996 | us that the alternating sum of binomial coefficients |
| @@ -5193,12 +5189,12 @@ to be a better approximation than stairsteps. A third method is | |||
| 5193 | that the steps are not required to be flat. Simpson's rule boils | 5189 | that the steps are not required to be flat. Simpson's rule boils |
| 5194 | down to the formula, | 5190 | down to the formula, |
| 5195 | 5191 | ||
| 5196 | @ifinfo | 5192 | @ifnottex |
| 5197 | @example | 5193 | @example |
| 5198 | (h/3) * (f(a) + 4 f(a+h) + 2 f(a+2h) + 4 f(a+3h) + ... | 5194 | (h/3) * (f(a) + 4 f(a+h) + 2 f(a+2h) + 4 f(a+3h) + ... |
| 5199 | + 2 f(a+(n-2)*h) + 4 f(a+(n-1)*h) + f(a+n*h)) | 5195 | + 2 f(a+(n-2)*h) + 4 f(a+(n-1)*h) + f(a+n*h)) |
| 5200 | @end example | 5196 | @end example |
| 5201 | @end ifinfo | 5197 | @end ifnottex |
| 5202 | @tex | 5198 | @tex |
| 5203 | \turnoffactive | 5199 | \turnoffactive |
| 5204 | \beforedisplay | 5200 | \beforedisplay |
| @@ -5215,12 +5211,12 @@ is the width of each slice. These are 10 and 0.1 in our example. | |||
| 5215 | For reference, here is the corresponding formula for the stairstep | 5211 | For reference, here is the corresponding formula for the stairstep |
| 5216 | method: | 5212 | method: |
| 5217 | 5213 | ||
| 5218 | @ifinfo | 5214 | @ifnottex |
| 5219 | @example | 5215 | @example |
| 5220 | h * (f(a) + f(a+h) + f(a+2h) + f(a+3h) + ... | 5216 | h * (f(a) + f(a+h) + f(a+2h) + f(a+3h) + ... |
| 5221 | + f(a+(n-2)*h) + f(a+(n-1)*h)) | 5217 | + f(a+(n-2)*h) + f(a+(n-1)*h)) |
| 5222 | @end example | 5218 | @end example |
| 5223 | @end ifinfo | 5219 | @end ifnottex |
| 5224 | @tex | 5220 | @tex |
| 5225 | \turnoffactive | 5221 | \turnoffactive |
| 5226 | \beforedisplay | 5222 | \beforedisplay |
| @@ -5657,11 +5653,11 @@ so that @expr{2 - 3 (x + y) + x y} is a sum of three terms.) | |||
| 5657 | infinite series that exactly equals the value of that function at | 5653 | infinite series that exactly equals the value of that function at |
| 5658 | values of @expr{x} near zero. | 5654 | values of @expr{x} near zero. |
| 5659 | 5655 | ||
| 5660 | @ifinfo | 5656 | @ifnottex |
| 5661 | @example | 5657 | @example |
| 5662 | cos(x) = 1 - x^2 / 2! + x^4 / 4! - x^6 / 6! + ... | 5658 | cos(x) = 1 - x^2 / 2! + x^4 / 4! - x^6 / 6! + ... |
| 5663 | @end example | 5659 | @end example |
| 5664 | @end ifinfo | 5660 | @end ifnottex |
| 5665 | @tex | 5661 | @tex |
| 5666 | \turnoffactive | 5662 | \turnoffactive |
| 5667 | \beforedisplay | 5663 | \beforedisplay |
| @@ -5675,11 +5671,11 @@ Calc represents the truncated Taylor series as a polynomial in @expr{x}. | |||
| 5675 | Mathematicians often write a truncated series using a ``big-O'' notation | 5671 | Mathematicians often write a truncated series using a ``big-O'' notation |
| 5676 | that records what was the lowest term that was truncated. | 5672 | that records what was the lowest term that was truncated. |
| 5677 | 5673 | ||
| 5678 | @ifinfo | 5674 | @ifnottex |
| 5679 | @example | 5675 | @example |
| 5680 | cos(x) = 1 - x^2 / 2! + O(x^3) | 5676 | cos(x) = 1 - x^2 / 2! + O(x^3) |
| 5681 | @end example | 5677 | @end example |
| 5682 | @end ifinfo | 5678 | @end ifnottex |
| 5683 | @tex | 5679 | @tex |
| 5684 | \turnoffactive | 5680 | \turnoffactive |
| 5685 | \beforedisplay | 5681 | \beforedisplay |
| @@ -6204,11 +6200,11 @@ equations numerically is @dfn{Newton's Method}. Given the equation | |||
| 6204 | @expr{x_0} which is reasonably close to the desired solution, apply | 6200 | @expr{x_0} which is reasonably close to the desired solution, apply |
| 6205 | this formula over and over: | 6201 | this formula over and over: |
| 6206 | 6202 | ||
| 6207 | @ifinfo | 6203 | @ifnottex |
| 6208 | @example | 6204 | @example |
| 6209 | new_x = x - f(x)/f'(x) | 6205 | new_x = x - f(x)/f'(x) |
| 6210 | @end example | 6206 | @end example |
| 6211 | @end ifinfo | 6207 | @end ifnottex |
| 6212 | @tex | 6208 | @tex |
| 6213 | \beforedisplay | 6209 | \beforedisplay |
| 6214 | $$ x_{\rm new} = x - {f(x) \over f'(x)} $$ | 6210 | $$ x_{\rm new} = x - {f(x) \over f'(x)} $$ |
| @@ -6242,11 +6238,11 @@ is defined as the derivative of | |||
| 6242 | @infoline @expr{ln(gamma(z))}. | 6238 | @infoline @expr{ln(gamma(z))}. |
| 6243 | For large values of @expr{z}, it can be approximated by the infinite sum | 6239 | For large values of @expr{z}, it can be approximated by the infinite sum |
| 6244 | 6240 | ||
| 6245 | @ifinfo | 6241 | @ifnottex |
| 6246 | @example | 6242 | @example |
| 6247 | psi(z) ~= ln(z) - 1/2z - sum(bern(2 n) / 2 n z^(2 n), n, 1, inf) | 6243 | psi(z) ~= ln(z) - 1/2z - sum(bern(2 n) / 2 n z^(2 n), n, 1, inf) |
| 6248 | @end example | 6244 | @end example |
| 6249 | @end ifinfo | 6245 | @end ifnottex |
| 6250 | @tex | 6246 | @tex |
| 6251 | \beforedisplay | 6247 | \beforedisplay |
| 6252 | $$ \psi(z) \approx \ln z - {1\over2z} - | 6248 | $$ \psi(z) \approx \ln z - {1\over2z} - |
| @@ -6305,13 +6301,13 @@ a way to convert from this form back to the standard algebraic form. | |||
| 6305 | (@bullet{}) @strong{Exercise 11.} The @dfn{Stirling numbers of the | 6301 | (@bullet{}) @strong{Exercise 11.} The @dfn{Stirling numbers of the |
| 6306 | first kind} are defined by the recurrences, | 6302 | first kind} are defined by the recurrences, |
| 6307 | 6303 | ||
| 6308 | @ifinfo | 6304 | @ifnottex |
| 6309 | @example | 6305 | @example |
| 6310 | s(n,n) = 1 for n >= 0, | 6306 | s(n,n) = 1 for n >= 0, |
| 6311 | s(n,0) = 0 for n > 0, | 6307 | s(n,0) = 0 for n > 0, |
| 6312 | s(n+1,m) = s(n,m-1) - n s(n,m) for n >= m >= 1. | 6308 | s(n+1,m) = s(n,m-1) - n s(n,m) for n >= m >= 1. |
| 6313 | @end example | 6309 | @end example |
| 6314 | @end ifinfo | 6310 | @end ifnottex |
| 6315 | @tex | 6311 | @tex |
| 6316 | \turnoffactive | 6312 | \turnoffactive |
| 6317 | \beforedisplay | 6313 | \beforedisplay |
| @@ -6843,14 +6839,14 @@ get the row sum. Similarly, use @kbd{[1 1] r 4 *} to get the column sum. | |||
| 6843 | @node Matrix Answer 2, Matrix Answer 3, Matrix Answer 1, Answers to Exercises | 6839 | @node Matrix Answer 2, Matrix Answer 3, Matrix Answer 1, Answers to Exercises |
| 6844 | @subsection Matrix Tutorial Exercise 2 | 6840 | @subsection Matrix Tutorial Exercise 2 |
| 6845 | 6841 | ||
| 6846 | @ifinfo | 6842 | @ifnottex |
| 6847 | @example | 6843 | @example |
| 6848 | @group | 6844 | @group |
| 6849 | x + a y = 6 | 6845 | x + a y = 6 |
| 6850 | x + b y = 10 | 6846 | x + b y = 10 |
| 6851 | @end group | 6847 | @end group |
| 6852 | @end example | 6848 | @end example |
| 6853 | @end ifinfo | 6849 | @end ifnottex |
| 6854 | @tex | 6850 | @tex |
| 6855 | \turnoffactive | 6851 | \turnoffactive |
| 6856 | \beforedisplay | 6852 | \beforedisplay |
| @@ -6905,7 +6901,7 @@ now, we have a system | |||
| 6905 | @infoline @expr{A2 * X = B2} | 6901 | @infoline @expr{A2 * X = B2} |
| 6906 | which we can solve using Calc's @samp{/} command. | 6902 | which we can solve using Calc's @samp{/} command. |
| 6907 | 6903 | ||
| 6908 | @ifinfo | 6904 | @ifnottex |
| 6909 | @example | 6905 | @example |
| 6910 | @group | 6906 | @group |
| 6911 | a + 2b + 3c = 6 | 6907 | a + 2b + 3c = 6 |
| @@ -6914,7 +6910,7 @@ which we can solve using Calc's @samp{/} command. | |||
| 6914 | 2a + 4b + 6c = 11 | 6910 | 2a + 4b + 6c = 11 |
| 6915 | @end group | 6911 | @end group |
| 6916 | @end example | 6912 | @end example |
| 6917 | @end ifinfo | 6913 | @end ifnottex |
| 6918 | @tex | 6914 | @tex |
| 6919 | \turnoffactive | 6915 | \turnoffactive |
| 6920 | \beforedisplayh | 6916 | \beforedisplayh |
| @@ -7045,11 +7041,11 @@ vector. | |||
| 7045 | Given @expr{x} and @expr{y} vectors in quick variables 1 and 2 as before, | 7041 | Given @expr{x} and @expr{y} vectors in quick variables 1 and 2 as before, |
| 7046 | the first job is to form the matrix that describes the problem. | 7042 | the first job is to form the matrix that describes the problem. |
| 7047 | 7043 | ||
| 7048 | @ifinfo | 7044 | @ifnottex |
| 7049 | @example | 7045 | @example |
| 7050 | m*x + b*1 = y | 7046 | m*x + b*1 = y |
| 7051 | @end example | 7047 | @end example |
| 7052 | @end ifinfo | 7048 | @end ifnottex |
| 7053 | @tex | 7049 | @tex |
| 7054 | \turnoffactive | 7050 | \turnoffactive |
| 7055 | \beforedisplay | 7051 | \beforedisplay |
| @@ -7836,11 +7832,11 @@ Why does this work? Think about a two-step computation: | |||
| 7836 | subtracting off enough 511's to put the result in the desired range. | 7832 | subtracting off enough 511's to put the result in the desired range. |
| 7837 | So the result when we take the modulo after every step is, | 7833 | So the result when we take the modulo after every step is, |
| 7838 | 7834 | ||
| 7839 | @ifinfo | 7835 | @ifnottex |
| 7840 | @example | 7836 | @example |
| 7841 | 3 (3 a + b - 511 m) + c - 511 n | 7837 | 3 (3 a + b - 511 m) + c - 511 n |
| 7842 | @end example | 7838 | @end example |
| 7843 | @end ifinfo | 7839 | @end ifnottex |
| 7844 | @tex | 7840 | @tex |
| 7845 | \turnoffactive | 7841 | \turnoffactive |
| 7846 | \beforedisplay | 7842 | \beforedisplay |
| @@ -7852,11 +7848,11 @@ $$ 3 (3 a + b - 511 m) + c - 511 n $$ | |||
| 7852 | for some suitable integers @expr{m} and @expr{n}. Expanding out by | 7848 | for some suitable integers @expr{m} and @expr{n}. Expanding out by |
| 7853 | the distributive law yields | 7849 | the distributive law yields |
| 7854 | 7850 | ||
| 7855 | @ifinfo | 7851 | @ifnottex |
| 7856 | @example | 7852 | @example |
| 7857 | 9 a + 3 b + c - 511*3 m - 511 n | 7853 | 9 a + 3 b + c - 511*3 m - 511 n |
| 7858 | @end example | 7854 | @end example |
| 7859 | @end ifinfo | 7855 | @end ifnottex |
| 7860 | @tex | 7856 | @tex |
| 7861 | \turnoffactive | 7857 | \turnoffactive |
| 7862 | \beforedisplay | 7858 | \beforedisplay |
| @@ -7870,11 +7866,11 @@ contribution it makes could just as easily be made by the @expr{n} | |||
| 7870 | term. So we can take it out to get an equivalent formula with | 7866 | term. So we can take it out to get an equivalent formula with |
| 7871 | @expr{n' = 3m + n}, | 7867 | @expr{n' = 3m + n}, |
| 7872 | 7868 | ||
| 7873 | @ifinfo | 7869 | @ifnottex |
| 7874 | @example | 7870 | @example |
| 7875 | 9 a + 3 b + c - 511 n' | 7871 | 9 a + 3 b + c - 511 n' |
| 7876 | @end example | 7872 | @end example |
| 7877 | @end ifinfo | 7873 | @end ifnottex |
| 7878 | @tex | 7874 | @tex |
| 7879 | \turnoffactive | 7875 | \turnoffactive |
| 7880 | \beforedisplay | 7876 | \beforedisplay |
| @@ -11285,7 +11281,7 @@ from 1 to 8. Interval arithmetic is used to get a worst-case estimate | |||
| 11285 | of the possible range of values a computation will produce, given the | 11281 | of the possible range of values a computation will produce, given the |
| 11286 | set of possible values of the input. | 11282 | set of possible values of the input. |
| 11287 | 11283 | ||
| 11288 | @ifinfo | 11284 | @ifnottex |
| 11289 | Calc supports several varieties of intervals, including @dfn{closed} | 11285 | Calc supports several varieties of intervals, including @dfn{closed} |
| 11290 | intervals of the type shown above, @dfn{open} intervals such as | 11286 | intervals of the type shown above, @dfn{open} intervals such as |
| 11291 | @samp{(2 ..@: 4)}, which represents the range of numbers from 2 to 4 | 11287 | @samp{(2 ..@: 4)}, which represents the range of numbers from 2 to 4 |
| @@ -11296,7 +11292,7 @@ terms, | |||
| 11296 | @samp{[2 ..@: 4)} represents @expr{2 <= x < 4}, | 11292 | @samp{[2 ..@: 4)} represents @expr{2 <= x < 4}, |
| 11297 | @samp{(2 ..@: 4]} represents @expr{2 < x <= 4}, and | 11293 | @samp{(2 ..@: 4]} represents @expr{2 < x <= 4}, and |
| 11298 | @samp{(2 ..@: 4)} represents @expr{2 < x < 4}. | 11294 | @samp{(2 ..@: 4)} represents @expr{2 < x < 4}. |
| 11299 | @end ifinfo | 11295 | @end ifnottex |
| 11300 | @tex | 11296 | @tex |
| 11301 | Calc supports several varieties of intervals, including \dfn{closed} | 11297 | Calc supports several varieties of intervals, including \dfn{closed} |
| 11302 | intervals of the type shown above, \dfn{open} intervals such as | 11298 | intervals of the type shown above, \dfn{open} intervals such as |
| @@ -11929,14 +11925,14 @@ commands, @kbd{t h} works only when Calc Trail is the selected window. | |||
| 11929 | @pindex calc-trail-isearch-forward | 11925 | @pindex calc-trail-isearch-forward |
| 11930 | @kindex t r | 11926 | @kindex t r |
| 11931 | @pindex calc-trail-isearch-backward | 11927 | @pindex calc-trail-isearch-backward |
| 11932 | @ifinfo | 11928 | @ifnottex |
| 11933 | The @kbd{t s} (@code{calc-trail-isearch-forward}) and @kbd{t r} | 11929 | The @kbd{t s} (@code{calc-trail-isearch-forward}) and @kbd{t r} |
| 11934 | (@code{calc-trail-isearch-backward}) commands perform an incremental | 11930 | (@code{calc-trail-isearch-backward}) commands perform an incremental |
| 11935 | search forward or backward through the trail. You can press @key{RET} | 11931 | search forward or backward through the trail. You can press @key{RET} |
| 11936 | to terminate the search; the trail pointer moves to the current line. | 11932 | to terminate the search; the trail pointer moves to the current line. |
| 11937 | If you cancel the search with @kbd{C-g}, the trail pointer stays where | 11933 | If you cancel the search with @kbd{C-g}, the trail pointer stays where |
| 11938 | it was when the search began. | 11934 | it was when the search began. |
| 11939 | @end ifinfo | 11935 | @end ifnottex |
| 11940 | @tex | 11936 | @tex |
| 11941 | The @kbd{t s} (@code{calc-trail-isearch-forward}) and @kbd{t r} | 11937 | The @kbd{t s} (@code{calc-trail-isearch-forward}) and @kbd{t r} |
| 11942 | (@code{calc-trail-isearch-backward}) com\-mands perform an incremental | 11938 | (@code{calc-trail-isearch-backward}) com\-mands perform an incremental |
| @@ -14237,10 +14233,10 @@ font information. | |||
| 14237 | Also, the ``discretionary multiplication sign'' @samp{\*} is read | 14233 | Also, the ``discretionary multiplication sign'' @samp{\*} is read |
| 14238 | the same as @samp{*}. | 14234 | the same as @samp{*}. |
| 14239 | 14235 | ||
| 14240 | @ifinfo | 14236 | @ifnottex |
| 14241 | The @TeX{} version of this manual includes some printed examples at the | 14237 | The @TeX{} version of this manual includes some printed examples at the |
| 14242 | end of this section. | 14238 | end of this section. |
| 14243 | @end ifinfo | 14239 | @end ifnottex |
| 14244 | @iftex | 14240 | @iftex |
| 14245 | Here are some examples of how various Calc formulas are formatted in @TeX{}: | 14241 | Here are some examples of how various Calc formulas are formatted in @TeX{}: |
| 14246 | 14242 | ||
| @@ -17656,7 +17652,7 @@ formulas below for symbolic arguments only when you use the @kbd{a "} | |||
| 17656 | (@code{calc-expand-formula}) command, or when taking derivatives or | 17652 | (@code{calc-expand-formula}) command, or when taking derivatives or |
| 17657 | integrals or solving equations involving the functions. | 17653 | integrals or solving equations involving the functions. |
| 17658 | 17654 | ||
| 17659 | @ifinfo | 17655 | @ifnottex |
| 17660 | These formulas are shown using the conventions of Big display | 17656 | These formulas are shown using the conventions of Big display |
| 17661 | mode (@kbd{d B}); for example, the formula for @code{fv} written | 17657 | mode (@kbd{d B}); for example, the formula for @code{fv} written |
| 17662 | linearly is @samp{pmt * ((1 + rate)^n) - 1) / rate}. | 17658 | linearly is @samp{pmt * ((1 + rate)^n) - 1) / rate}. |
| @@ -17736,7 +17732,7 @@ syd(cost, salv, life, per) = -------------------------------- | |||
| 17736 | ddb(cost, salv, life, per) = --------, book = cost - depreciation so far | 17732 | ddb(cost, salv, life, per) = --------, book = cost - depreciation so far |
| 17737 | life | 17733 | life |
| 17738 | @end example | 17734 | @end example |
| 17739 | @end ifinfo | 17735 | @end ifnottex |
| 17740 | @tex | 17736 | @tex |
| 17741 | \turnoffactive | 17737 | \turnoffactive |
| 17742 | $$ \code{fv}(r, n, p) = p { (1 + r)^n - 1 \over r } $$ | 17738 | $$ \code{fv}(r, n, p) = p { (1 + r)^n - 1 \over r } $$ |
| @@ -18385,14 +18381,14 @@ some authors, is computed by the @kbd{I f G} [@code{gammaQ}] command. | |||
| 18385 | You can think of this as taking the other half of the integral, from | 18381 | You can think of this as taking the other half of the integral, from |
| 18386 | @expr{x} to infinity. | 18382 | @expr{x} to infinity. |
| 18387 | 18383 | ||
| 18388 | @ifinfo | 18384 | @ifnottex |
| 18389 | The functions corresponding to the integrals that define @expr{P(a,x)} | 18385 | The functions corresponding to the integrals that define @expr{P(a,x)} |
| 18390 | and @expr{Q(a,x)} but without the normalizing @expr{1/gamma(a)} | 18386 | and @expr{Q(a,x)} but without the normalizing @expr{1/gamma(a)} |
| 18391 | factor are called @expr{g(a,x)} and @expr{G(a,x)}, respectively | 18387 | factor are called @expr{g(a,x)} and @expr{G(a,x)}, respectively |
| 18392 | (where @expr{g} and @expr{G} represent the lower- and upper-case Greek | 18388 | (where @expr{g} and @expr{G} represent the lower- and upper-case Greek |
| 18393 | letter gamma). You can obtain these using the @kbd{H f G} [@code{gammag}] | 18389 | letter gamma). You can obtain these using the @kbd{H f G} [@code{gammag}] |
| 18394 | and @kbd{H I f G} [@code{gammaG}] commands. | 18390 | and @kbd{H I f G} [@code{gammaG}] commands. |
| 18395 | @end ifinfo | 18391 | @end ifnottex |
| 18396 | @tex | 18392 | @tex |
| 18397 | \turnoffactive | 18393 | \turnoffactive |
| 18398 | The functions corresponding to the integrals that define $P(a,x)$ | 18394 | The functions corresponding to the integrals that define $P(a,x)$ |
| @@ -18908,10 +18904,10 @@ real numbers by | |||
| 18908 | @kindex H k c | 18904 | @kindex H k c |
| 18909 | @pindex calc-perm | 18905 | @pindex calc-perm |
| 18910 | @tindex perm | 18906 | @tindex perm |
| 18911 | @ifinfo | 18907 | @ifnottex |
| 18912 | The @kbd{H k c} (@code{calc-perm}) [@code{perm}] command computes the | 18908 | The @kbd{H k c} (@code{calc-perm}) [@code{perm}] command computes the |
| 18913 | number-of-permutations function @expr{N! / (N-M)!}. | 18909 | number-of-permutations function @expr{N! / (N-M)!}. |
| 18914 | @end ifinfo | 18910 | @end ifnottex |
| 18915 | @tex | 18911 | @tex |
| 18916 | The \kbd{H k c} (\code{calc-perm}) [\code{perm}] command computes the | 18912 | The \kbd{H k c} (\code{calc-perm}) [\code{perm}] command computes the |
| 18917 | number-of-perm\-utations function $N! \over (N-M)!\,$. | 18913 | number-of-perm\-utations function $N! \over (N-M)!\,$. |
| @@ -23151,13 +23147,13 @@ integral of the expression on top of the stack. In this case, the | |||
| 23151 | command will again prompt for an integration variable, then prompt for a | 23147 | command will again prompt for an integration variable, then prompt for a |
| 23152 | lower limit and an upper limit. | 23148 | lower limit and an upper limit. |
| 23153 | 23149 | ||
| 23154 | @ifinfo | 23150 | @ifnottex |
| 23155 | If you use the @code{integ} function directly in an algebraic formula, | 23151 | If you use the @code{integ} function directly in an algebraic formula, |
| 23156 | you can also write @samp{integ(f,x,v)} which expresses the resulting | 23152 | you can also write @samp{integ(f,x,v)} which expresses the resulting |
| 23157 | indefinite integral in terms of variable @code{v} instead of @code{x}. | 23153 | indefinite integral in terms of variable @code{v} instead of @code{x}. |
| 23158 | With four arguments, @samp{integ(f(x),x,a,b)} represents a definite | 23154 | With four arguments, @samp{integ(f(x),x,a,b)} represents a definite |
| 23159 | integral from @code{a} to @code{b}. | 23155 | integral from @code{a} to @code{b}. |
| 23160 | @end ifinfo | 23156 | @end ifnottex |
| 23161 | @tex | 23157 | @tex |
| 23162 | If you use the @code{integ} function directly in an algebraic formula, | 23158 | If you use the @code{integ} function directly in an algebraic formula, |
| 23163 | you can also write @samp{integ(f,x,v)} which expresses the resulting | 23159 | you can also write @samp{integ(f,x,v)} which expresses the resulting |
| @@ -24038,14 +24034,14 @@ name only those and let the parameters use default names. | |||
| 24038 | 24034 | ||
| 24039 | For example, suppose the data matrix | 24035 | For example, suppose the data matrix |
| 24040 | 24036 | ||
| 24041 | @ifinfo | 24037 | @ifnottex |
| 24042 | @example | 24038 | @example |
| 24043 | @group | 24039 | @group |
| 24044 | [ [ 1, 2, 3, 4, 5 ] | 24040 | [ [ 1, 2, 3, 4, 5 ] |
| 24045 | [ 5, 7, 9, 11, 13 ] ] | 24041 | [ 5, 7, 9, 11, 13 ] ] |
| 24046 | @end group | 24042 | @end group |
| 24047 | @end example | 24043 | @end example |
| 24048 | @end ifinfo | 24044 | @end ifnottex |
| 24049 | @tex | 24045 | @tex |
| 24050 | \turnoffactive | 24046 | \turnoffactive |
| 24051 | \turnoffactive | 24047 | \turnoffactive |
| @@ -24102,11 +24098,11 @@ Calc has chosen a line that best approximates the data points using | |||
| 24102 | the method of least squares. The idea is to define the @dfn{chi-square} | 24098 | the method of least squares. The idea is to define the @dfn{chi-square} |
| 24103 | error measure | 24099 | error measure |
| 24104 | 24100 | ||
| 24105 | @ifinfo | 24101 | @ifnottex |
| 24106 | @example | 24102 | @example |
| 24107 | chi^2 = sum((y_i - (a + b x_i))^2, i, 1, N) | 24103 | chi^2 = sum((y_i - (a + b x_i))^2, i, 1, N) |
| 24108 | @end example | 24104 | @end example |
| 24109 | @end ifinfo | 24105 | @end ifnottex |
| 24110 | @tex | 24106 | @tex |
| 24111 | \turnoffactive | 24107 | \turnoffactive |
| 24112 | \beforedisplay | 24108 | \beforedisplay |
| @@ -24291,11 +24287,11 @@ then the | |||
| 24291 | @infoline @expr{chi^2} | 24287 | @infoline @expr{chi^2} |
| 24292 | statistic is now, | 24288 | statistic is now, |
| 24293 | 24289 | ||
| 24294 | @ifinfo | 24290 | @ifnottex |
| 24295 | @example | 24291 | @example |
| 24296 | chi^2 = sum(((y_i - (a + b x_i)) / sigma_i)^2, i, 1, N) | 24292 | chi^2 = sum(((y_i - (a + b x_i)) / sigma_i)^2, i, 1, N) |
| 24297 | @end example | 24293 | @end example |
| 24298 | @end ifinfo | 24294 | @end ifnottex |
| 24299 | @tex | 24295 | @tex |
| 24300 | \turnoffactive | 24296 | \turnoffactive |
| 24301 | \beforedisplay | 24297 | \beforedisplay |
| @@ -27613,9 +27609,9 @@ The unit @code{A} stands for Amperes; the name @code{Ang} is used | |||
| 27613 | @tex | 27609 | @tex |
| 27614 | for \AA ngstroms. | 27610 | for \AA ngstroms. |
| 27615 | @end tex | 27611 | @end tex |
| 27616 | @ifinfo | 27612 | @ifnottex |
| 27617 | for Angstroms. | 27613 | for Angstroms. |
| 27618 | @end ifinfo | 27614 | @end ifnottex |
| 27619 | 27615 | ||
| 27620 | The unit @code{pt} stands for pints; the name @code{point} stands for | 27616 | The unit @code{pt} stands for pints; the name @code{point} stands for |
| 27621 | a typographical point, defined by @samp{72 point = 1 in}. This is | 27617 | a typographical point, defined by @samp{72 point = 1 in}. This is |
| @@ -34535,9 +34531,9 @@ modification follow. | |||
| 34535 | @iftex | 34531 | @iftex |
| 34536 | @unnumberedsec TERMS AND CONDITIONS FOR COPYING, DISTRIBUTION AND MODIFICATION | 34532 | @unnumberedsec TERMS AND CONDITIONS FOR COPYING, DISTRIBUTION AND MODIFICATION |
| 34537 | @end iftex | 34533 | @end iftex |
| 34538 | @ifinfo | 34534 | @ifnottex |
| 34539 | @center TERMS AND CONDITIONS FOR COPYING, DISTRIBUTION AND MODIFICATION | 34535 | @center TERMS AND CONDITIONS FOR COPYING, DISTRIBUTION AND MODIFICATION |
| 34540 | @end ifinfo | 34536 | @end ifnottex |
| 34541 | 34537 | ||
| 34542 | @enumerate 0 | 34538 | @enumerate 0 |
| 34543 | @item | 34539 | @item |
| @@ -34760,9 +34756,9 @@ of promoting the sharing and reuse of software generally. | |||
| 34760 | @iftex | 34756 | @iftex |
| 34761 | @heading NO WARRANTY | 34757 | @heading NO WARRANTY |
| 34762 | @end iftex | 34758 | @end iftex |
| 34763 | @ifinfo | 34759 | @ifnottex |
| 34764 | @center NO WARRANTY | 34760 | @center NO WARRANTY |
| 34765 | @end ifinfo | 34761 | @end ifnottex |
| 34766 | 34762 | ||
| 34767 | @item | 34763 | @item |
| 34768 | BECAUSE THE PROGRAM IS LICENSED FREE OF CHARGE, THERE IS NO WARRANTY | 34764 | BECAUSE THE PROGRAM IS LICENSED FREE OF CHARGE, THERE IS NO WARRANTY |
| @@ -34790,9 +34786,9 @@ POSSIBILITY OF SUCH DAMAGES. | |||
| 34790 | @iftex | 34786 | @iftex |
| 34791 | @heading END OF TERMS AND CONDITIONS | 34787 | @heading END OF TERMS AND CONDITIONS |
| 34792 | @end iftex | 34788 | @end iftex |
| 34793 | @ifinfo | 34789 | @ifnottex |
| 34794 | @center END OF TERMS AND CONDITIONS | 34790 | @center END OF TERMS AND CONDITIONS |
| 34795 | @end ifinfo | 34791 | @end ifnottex |
| 34796 | 34792 | ||
| 34797 | @page | 34793 | @page |
| 34798 | @unnumberedsec Appendix: How to Apply These Terms to Your New Programs | 34794 | @unnumberedsec Appendix: How to Apply These Terms to Your New Programs |