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| author | Jay Belanger | 2010-05-13 17:33:11 -0500 |
|---|---|---|
| committer | Jay Belanger | 2010-05-13 17:33:11 -0500 |
| commit | 14914c431498a802e271ad42cdd6f06175ae4b4a (patch) | |
| tree | 95bee6775e02daa38277a26ac56e96d83e0241d3 /doc | |
| parent | 2ef3c1449c876f7c9fb327e90c59b6f4df4e4df0 (diff) | |
| download | emacs-14914c431498a802e271ad42cdd6f06175ae4b4a.tar.gz emacs-14914c431498a802e271ad42cdd6f06175ae4b4a.zip | |
calc.texi: Remove "\turnoffactive" commands throughout.
Diffstat (limited to 'doc')
| -rw-r--r-- | doc/misc/ChangeLog | 4 | ||||
| -rw-r--r-- | doc/misc/calc.texi | 43 |
2 files changed, 4 insertions, 43 deletions
diff --git a/doc/misc/ChangeLog b/doc/misc/ChangeLog index 85bf897f41f..c6d3c1be498 100644 --- a/doc/misc/ChangeLog +++ b/doc/misc/ChangeLog | |||
| @@ -1,3 +1,7 @@ | |||
| 1 | 2010-05-13 Jay Belanger <jay.p.belanger@gmail.com> | ||
| 2 | |||
| 3 | * calc.texi: Remove "\turnoffactive" commands througout. | ||
| 4 | |||
| 1 | 2010-05-08 Štěpán Němec <stepnem@gmail.com> (tiny change) | 5 | 2010-05-08 Štěpán Němec <stepnem@gmail.com> (tiny change) |
| 2 | 6 | ||
| 3 | * url.texi (HTTP language/coding, Customization): | 7 | * url.texi (HTTP language/coding, Customization): |
diff --git a/doc/misc/calc.texi b/doc/misc/calc.texi index 96075b6710d..c578e919612 100644 --- a/doc/misc/calc.texi +++ b/doc/misc/calc.texi | |||
| @@ -76,7 +76,6 @@ | |||
| 76 | @newcount@calcpageno | 76 | @newcount@calcpageno |
| 77 | @newtoks@calcoldeverypar @calcoldeverypar=@everypar | 77 | @newtoks@calcoldeverypar @calcoldeverypar=@everypar |
| 78 | @everypar={@calceverypar@the@calcoldeverypar} | 78 | @everypar={@calceverypar@the@calcoldeverypar} |
| 79 | @ifx@turnoffactive@undefinedzzz@def@turnoffactive{}@fi | ||
| 80 | @ifx@ninett@undefinedzzz@font@ninett=cmtt9@fi | 79 | @ifx@ninett@undefinedzzz@font@ninett=cmtt9@fi |
| 81 | @catcode`@\=0 \catcode`\@=11 | 80 | @catcode`@\=0 \catcode`\@=11 |
| 82 | \r@ggedbottomtrue | 81 | \r@ggedbottomtrue |
| @@ -1804,7 +1803,6 @@ or, in large mathematical notation, | |||
| 1804 | @end example | 1803 | @end example |
| 1805 | @end ifnottex | 1804 | @end ifnottex |
| 1806 | @tex | 1805 | @tex |
| 1807 | \turnoffactive | ||
| 1808 | \beforedisplay | 1806 | \beforedisplay |
| 1809 | $$ 2 + { 3 \times 4 \times 5 \over 6 \times 7^8 } - 9 $$ | 1807 | $$ 2 + { 3 \times 4 \times 5 \over 6 \times 7^8 } - 9 $$ |
| 1810 | \afterdisplay | 1808 | \afterdisplay |
| @@ -3358,7 +3356,6 @@ Suppose we had the following set of equations: | |||
| 3358 | @end group | 3356 | @end group |
| 3359 | @end ifnottex | 3357 | @end ifnottex |
| 3360 | @tex | 3358 | @tex |
| 3361 | \turnoffactive | ||
| 3362 | \beforedisplayh | 3359 | \beforedisplayh |
| 3363 | $$ \openup1\jot \tabskip=0pt plus1fil | 3360 | $$ \openup1\jot \tabskip=0pt plus1fil |
| 3364 | \halign to\displaywidth{\tabskip=0pt | 3361 | \halign to\displaywidth{\tabskip=0pt |
| @@ -3385,7 +3382,6 @@ This can be cast into the matrix equation, | |||
| 3385 | @end group | 3382 | @end group |
| 3386 | @end ifnottex | 3383 | @end ifnottex |
| 3387 | @tex | 3384 | @tex |
| 3388 | \turnoffactive | ||
| 3389 | \beforedisplay | 3385 | \beforedisplay |
| 3390 | $$ \pmatrix{ 1 & 2 & 3 \cr 4 & 5 & 6 \cr 7 & 6 & 0 } | 3386 | $$ \pmatrix{ 1 & 2 & 3 \cr 4 & 5 & 6 \cr 7 & 6 & 0 } |
| 3391 | \times | 3387 | \times |
| @@ -3457,7 +3453,6 @@ in terms of @expr{a} and @expr{b}. | |||
| 3457 | @end group | 3453 | @end group |
| 3458 | @end ifnottex | 3454 | @end ifnottex |
| 3459 | @tex | 3455 | @tex |
| 3460 | \turnoffactive | ||
| 3461 | \beforedisplay | 3456 | \beforedisplay |
| 3462 | $$ \eqalign{ x &+ a y = 6 \cr | 3457 | $$ \eqalign{ x &+ a y = 6 \cr |
| 3463 | x &+ b y = 10} | 3458 | x &+ b y = 10} |
| @@ -3483,7 +3478,6 @@ on the left by the transpose of @expr{A}: | |||
| 3483 | @samp{trn(A)*A*X = trn(A)*B}. | 3478 | @samp{trn(A)*A*X = trn(A)*B}. |
| 3484 | @end ifnottex | 3479 | @end ifnottex |
| 3485 | @tex | 3480 | @tex |
| 3486 | \turnoffactive | ||
| 3487 | $A^T A \, X = A^T B$, where $A^T$ is the transpose \samp{trn(A)}. | 3481 | $A^T A \, X = A^T B$, where $A^T$ is the transpose \samp{trn(A)}. |
| 3488 | @end tex | 3482 | @end tex |
| 3489 | Now | 3483 | Now |
| @@ -3506,7 +3500,6 @@ system: | |||
| 3506 | @end group | 3500 | @end group |
| 3507 | @end ifnottex | 3501 | @end ifnottex |
| 3508 | @tex | 3502 | @tex |
| 3509 | \turnoffactive | ||
| 3510 | \beforedisplayh | 3503 | \beforedisplayh |
| 3511 | $$ \openup1\jot \tabskip=0pt plus1fil | 3504 | $$ \openup1\jot \tabskip=0pt plus1fil |
| 3512 | \halign to\displaywidth{\tabskip=0pt | 3505 | \halign to\displaywidth{\tabskip=0pt |
| @@ -3778,7 +3771,6 @@ m = (N sum(x y) - sum(x) sum(y)) / (N sum(x^2) - sum(x)^2) | |||
| 3778 | @end example | 3771 | @end example |
| 3779 | @end ifnottex | 3772 | @end ifnottex |
| 3780 | @tex | 3773 | @tex |
| 3781 | \turnoffactive | ||
| 3782 | \beforedisplay | 3774 | \beforedisplay |
| 3783 | $$ m = {N \sum x y - \sum x \sum y \over | 3775 | $$ m = {N \sum x y - \sum x \sum y \over |
| 3784 | N \sum x^2 - \left( \sum x \right)^2} $$ | 3776 | N \sum x^2 - \left( \sum x \right)^2} $$ |
| @@ -3820,7 +3812,6 @@ respectively. (We could have used @kbd{*} to compute @samp{sum(x^2)} and | |||
| 3820 | @samp{sum(x y)}.) | 3812 | @samp{sum(x y)}.) |
| 3821 | @end ifnottex | 3813 | @end ifnottex |
| 3822 | @tex | 3814 | @tex |
| 3823 | \turnoffactive | ||
| 3824 | These are $\sum x$, $\sum x^2$, $\sum y$, and $\sum x y$, | 3815 | These are $\sum x$, $\sum x^2$, $\sum y$, and $\sum x y$, |
| 3825 | respectively. (We could have used \kbd{*} to compute $\sum x^2$ and | 3816 | respectively. (We could have used \kbd{*} to compute $\sum x^2$ and |
| 3826 | $\sum x y$.) | 3817 | $\sum x y$.) |
| @@ -3874,7 +3865,6 @@ b = (sum(y) - m sum(x)) / N | |||
| 3874 | @end example | 3865 | @end example |
| 3875 | @end ifnottex | 3866 | @end ifnottex |
| 3876 | @tex | 3867 | @tex |
| 3877 | \turnoffactive | ||
| 3878 | \beforedisplay | 3868 | \beforedisplay |
| 3879 | $$ b = {\sum y - m \sum x \over N} $$ | 3869 | $$ b = {\sum y - m \sum x \over N} $$ |
| 3880 | \afterdisplay | 3870 | \afterdisplay |
| @@ -5223,7 +5213,6 @@ down to the formula, | |||
| 5223 | @end example | 5213 | @end example |
| 5224 | @end ifnottex | 5214 | @end ifnottex |
| 5225 | @tex | 5215 | @tex |
| 5226 | \turnoffactive | ||
| 5227 | \beforedisplay | 5216 | \beforedisplay |
| 5228 | $$ \displaylines{ | 5217 | $$ \displaylines{ |
| 5229 | \qquad {h \over 3} (f(a) + 4 f(a+h) + 2 f(a+2h) + 4 f(a+3h) + \cdots | 5218 | \qquad {h \over 3} (f(a) + 4 f(a+h) + 2 f(a+2h) + 4 f(a+3h) + \cdots |
| @@ -5245,7 +5234,6 @@ h * (f(a) + f(a+h) + f(a+2h) + f(a+3h) + ... | |||
| 5245 | @end example | 5234 | @end example |
| 5246 | @end ifnottex | 5235 | @end ifnottex |
| 5247 | @tex | 5236 | @tex |
| 5248 | \turnoffactive | ||
| 5249 | \beforedisplay | 5237 | \beforedisplay |
| 5250 | $$ h (f(a) + f(a+h) + f(a+2h) + f(a+3h) + \cdots | 5238 | $$ h (f(a) + f(a+h) + f(a+2h) + f(a+3h) + \cdots |
| 5251 | + f(a+(n-2)h) + f(a+(n-1)h)) $$ | 5239 | + f(a+(n-2)h) + f(a+(n-1)h)) $$ |
| @@ -5686,7 +5674,6 @@ cos(x) = 1 - x^2 / 2! + x^4 / 4! - x^6 / 6! + ... | |||
| 5686 | @end example | 5674 | @end example |
| 5687 | @end ifnottex | 5675 | @end ifnottex |
| 5688 | @tex | 5676 | @tex |
| 5689 | \turnoffactive | ||
| 5690 | \beforedisplay | 5677 | \beforedisplay |
| 5691 | $$ \cos x = 1 - {x^2 \over 2!} + {x^4 \over 4!} - {x^6 \over 6!} + \cdots $$ | 5678 | $$ \cos x = 1 - {x^2 \over 2!} + {x^4 \over 4!} - {x^6 \over 6!} + \cdots $$ |
| 5692 | \afterdisplay | 5679 | \afterdisplay |
| @@ -5704,7 +5691,6 @@ cos(x) = 1 - x^2 / 2! + O(x^3) | |||
| 5704 | @end example | 5691 | @end example |
| 5705 | @end ifnottex | 5692 | @end ifnottex |
| 5706 | @tex | 5693 | @tex |
| 5707 | \turnoffactive | ||
| 5708 | \beforedisplay | 5694 | \beforedisplay |
| 5709 | $$ \cos x = 1 - {x^2 \over 2!} + O(x^3) $$ | 5695 | $$ \cos x = 1 - {x^2 \over 2!} + O(x^3) $$ |
| 5710 | \afterdisplay | 5696 | \afterdisplay |
| @@ -6336,7 +6322,6 @@ s(n+1,m) = s(n,m-1) - n s(n,m) for n >= m >= 1. | |||
| 6336 | @end example | 6322 | @end example |
| 6337 | @end ifnottex | 6323 | @end ifnottex |
| 6338 | @tex | 6324 | @tex |
| 6339 | \turnoffactive | ||
| 6340 | \beforedisplay | 6325 | \beforedisplay |
| 6341 | $$ \eqalign{ s(n,n) &= 1 \qquad \hbox{for } n \ge 0, \cr | 6326 | $$ \eqalign{ s(n,n) &= 1 \qquad \hbox{for } n \ge 0, \cr |
| 6342 | s(n,0) &= 0 \qquad \hbox{for } n > 0, \cr | 6327 | s(n,0) &= 0 \qquad \hbox{for } n > 0, \cr |
| @@ -6875,7 +6860,6 @@ get the row sum. Similarly, use @kbd{[1 1] r 4 *} to get the column sum. | |||
| 6875 | @end example | 6860 | @end example |
| 6876 | @end ifnottex | 6861 | @end ifnottex |
| 6877 | @tex | 6862 | @tex |
| 6878 | \turnoffactive | ||
| 6879 | \beforedisplay | 6863 | \beforedisplay |
| 6880 | $$ \eqalign{ x &+ a y = 6 \cr | 6864 | $$ \eqalign{ x &+ a y = 6 \cr |
| 6881 | x &+ b y = 10} | 6865 | x &+ b y = 10} |
| @@ -6939,7 +6923,6 @@ which we can solve using Calc's @samp{/} command. | |||
| 6939 | @end example | 6923 | @end example |
| 6940 | @end ifnottex | 6924 | @end ifnottex |
| 6941 | @tex | 6925 | @tex |
| 6942 | \turnoffactive | ||
| 6943 | \beforedisplayh | 6926 | \beforedisplayh |
| 6944 | $$ \openup1\jot \tabskip=0pt plus1fil | 6927 | $$ \openup1\jot \tabskip=0pt plus1fil |
| 6945 | \halign to\displaywidth{\tabskip=0pt | 6928 | \halign to\displaywidth{\tabskip=0pt |
| @@ -7074,7 +7057,6 @@ the first job is to form the matrix that describes the problem. | |||
| 7074 | @end example | 7057 | @end example |
| 7075 | @end ifnottex | 7058 | @end ifnottex |
| 7076 | @tex | 7059 | @tex |
| 7077 | \turnoffactive | ||
| 7078 | \beforedisplay | 7060 | \beforedisplay |
| 7079 | $$ m \times x + b \times 1 = y $$ | 7061 | $$ m \times x + b \times 1 = y $$ |
| 7080 | \afterdisplay | 7062 | \afterdisplay |
| @@ -7865,7 +7847,6 @@ So the result when we take the modulo after every step is, | |||
| 7865 | @end example | 7847 | @end example |
| 7866 | @end ifnottex | 7848 | @end ifnottex |
| 7867 | @tex | 7849 | @tex |
| 7868 | \turnoffactive | ||
| 7869 | \beforedisplay | 7850 | \beforedisplay |
| 7870 | $$ 3 (3 a + b - 511 m) + c - 511 n $$ | 7851 | $$ 3 (3 a + b - 511 m) + c - 511 n $$ |
| 7871 | \afterdisplay | 7852 | \afterdisplay |
| @@ -7881,7 +7862,6 @@ the distributive law yields | |||
| 7881 | @end example | 7862 | @end example |
| 7882 | @end ifnottex | 7863 | @end ifnottex |
| 7883 | @tex | 7864 | @tex |
| 7884 | \turnoffactive | ||
| 7885 | \beforedisplay | 7865 | \beforedisplay |
| 7886 | $$ 9 a + 3 b + c - 511\times3 m - 511 n $$ | 7866 | $$ 9 a + 3 b + c - 511\times3 m - 511 n $$ |
| 7887 | \afterdisplay | 7867 | \afterdisplay |
| @@ -7899,7 +7879,6 @@ term. So we can take it out to get an equivalent formula with | |||
| 7899 | @end example | 7879 | @end example |
| 7900 | @end ifnottex | 7880 | @end ifnottex |
| 7901 | @tex | 7881 | @tex |
| 7902 | \turnoffactive | ||
| 7903 | \beforedisplay | 7882 | \beforedisplay |
| 7904 | $$ 9 a + 3 b + c - 511 n^{\prime} $$ | 7883 | $$ 9 a + 3 b + c - 511 n^{\prime} $$ |
| 7905 | \afterdisplay | 7884 | \afterdisplay |
| @@ -14408,7 +14387,6 @@ $$ \sin\left( a^2 \over b_i \right) $$ | |||
| 14408 | @end group | 14387 | @end group |
| 14409 | @end example | 14388 | @end example |
| 14410 | @tex | 14389 | @tex |
| 14411 | \turnoffactive | ||
| 14412 | $$ [3 + 4i, {3 \over 4}, 3 \pm 4, [ 3 \ldots \infty)] $$ | 14390 | $$ [3 + 4i, {3 \over 4}, 3 \pm 4, [ 3 \ldots \infty)] $$ |
| 14413 | @end tex | 14391 | @end tex |
| 14414 | @sp 1 | 14392 | @sp 1 |
| @@ -14434,7 +14412,6 @@ $$ [|a|, \left| a \over b \right|, | |||
| 14434 | @end group | 14412 | @end group |
| 14435 | @end example | 14413 | @end example |
| 14436 | @tex | 14414 | @tex |
| 14437 | \turnoffactive | ||
| 14438 | $$ [\sin{a}, \sin{2 a}, \sin(2 + a), \sin\left( {a \over b} \right)] $$ | 14415 | $$ [\sin{a}, \sin{2 a}, \sin(2 + a), \sin\left( {a \over b} \right)] $$ |
| 14439 | @end tex | 14416 | @end tex |
| 14440 | @sp 2 | 14417 | @sp 2 |
| @@ -14467,7 +14444,6 @@ First with @samp{\def\evalto@{@}}, then with @samp{\def\evalto#1\to@{@}}: | |||
| 14467 | @end group | 14444 | @end group |
| 14468 | @end example | 14445 | @end example |
| 14469 | @tex | 14446 | @tex |
| 14470 | \turnoffactive | ||
| 14471 | $$ 2 + 3 \to 5 $$ | 14447 | $$ 2 + 3 \to 5 $$ |
| 14472 | $$ 5 $$ | 14448 | $$ 5 $$ |
| 14473 | @end tex | 14449 | @end tex |
| @@ -14482,7 +14458,6 @@ First with standard @code{\to}, then with @samp{\let\to\Rightarrow}: | |||
| 14482 | @end group | 14458 | @end group |
| 14483 | @end example | 14459 | @end example |
| 14484 | @tex | 14460 | @tex |
| 14485 | \turnoffactive | ||
| 14486 | $$ [{2 + 3 \to 5}, {{a \over 2} \to {b + c \over 2}}] $$ | 14461 | $$ [{2 + 3 \to 5}, {{a \over 2} \to {b + c \over 2}}] $$ |
| 14487 | {\let\to\Rightarrow | 14462 | {\let\to\Rightarrow |
| 14488 | $$ [{2 + 3 \to 5}, {{a \over 2} \to {b + c \over 2}}] $$} | 14463 | $$ [{2 + 3 \to 5}, {{a \over 2} \to {b + c \over 2}}] $$} |
| @@ -14499,7 +14474,6 @@ Matrices normally, then changing @code{\matrix} to @code{\pmatrix}: | |||
| 14499 | @end group | 14474 | @end group |
| 14500 | @end example | 14475 | @end example |
| 14501 | @tex | 14476 | @tex |
| 14502 | \turnoffactive | ||
| 14503 | $$ \matrix{ {a \over b} & 0 \cr 0 & 2^{(x + 1)} } $$ | 14477 | $$ \matrix{ {a \over b} & 0 \cr 0 & 2^{(x + 1)} } $$ |
| 14504 | $$ \pmatrix{ {a \over b} & 0 \cr 0 & 2^{(x + 1)} } $$ | 14478 | $$ \pmatrix{ {a \over b} & 0 \cr 0 & 2^{(x + 1)} } $$ |
| 14505 | @end tex | 14479 | @end tex |
| @@ -17935,7 +17909,6 @@ ddb(cost, salv, life, per) = --------, book = cost - depreciation so far | |||
| 17935 | @end example | 17909 | @end example |
| 17936 | @end ifnottex | 17910 | @end ifnottex |
| 17937 | @tex | 17911 | @tex |
| 17938 | \turnoffactive | ||
| 17939 | $$ \code{fv}(r, n, p) = p { (1 + r)^n - 1 \over r } $$ | 17912 | $$ \code{fv}(r, n, p) = p { (1 + r)^n - 1 \over r } $$ |
| 17940 | $$ \code{fvb}(r, n, p) = p { ((1 + r)^n - 1) (1 + r) \over r } $$ | 17913 | $$ \code{fvb}(r, n, p) = p { ((1 + r)^n - 1) (1 + r) \over r } $$ |
| 17941 | $$ \code{fvl}(r, n, p) = p (1 + r)^n $$ | 17914 | $$ \code{fvl}(r, n, p) = p (1 + r)^n $$ |
| @@ -18591,7 +18564,6 @@ letter gamma). You can obtain these using the @kbd{H f G} [@code{gammag}] | |||
| 18591 | and @kbd{H I f G} [@code{gammaG}] commands. | 18564 | and @kbd{H I f G} [@code{gammaG}] commands. |
| 18592 | @end ifnottex | 18565 | @end ifnottex |
| 18593 | @tex | 18566 | @tex |
| 18594 | \turnoffactive | ||
| 18595 | The functions corresponding to the integrals that define $P(a,x)$ | 18567 | The functions corresponding to the integrals that define $P(a,x)$ |
| 18596 | and $Q(a,x)$ but without the normalizing $1/\Gamma(a)$ | 18568 | and $Q(a,x)$ but without the normalizing $1/\Gamma(a)$ |
| 18597 | factor are called $\gamma(a,x)$ and $\Gamma(a,x)$, respectively. | 18569 | factor are called $\gamma(a,x)$ and $\Gamma(a,x)$, respectively. |
| @@ -20559,7 +20531,6 @@ this is the weighted mean of the @expr{x} values with weights | |||
| 20559 | @texline @math{1 /\sigma^2}. | 20531 | @texline @math{1 /\sigma^2}. |
| 20560 | @infoline @expr{1 / s^2}. | 20532 | @infoline @expr{1 / s^2}. |
| 20561 | @tex | 20533 | @tex |
| 20562 | \turnoffactive | ||
| 20563 | $$ \mu = { \displaystyle \sum { x_i \over \sigma_i^2 } \over | 20534 | $$ \mu = { \displaystyle \sum { x_i \over \sigma_i^2 } \over |
| 20564 | \displaystyle \sum { 1 \over \sigma_i^2 } } $$ | 20535 | \displaystyle \sum { 1 \over \sigma_i^2 } } $$ |
| 20565 | @end tex | 20536 | @end tex |
| @@ -20593,7 +20564,6 @@ root of the reciprocal of the sum of the reciprocals of the squares | |||
| 20593 | of the input errors. (I.e., the variance is the reciprocal of the | 20564 | of the input errors. (I.e., the variance is the reciprocal of the |
| 20594 | sum of the reciprocals of the variances.) | 20565 | sum of the reciprocals of the variances.) |
| 20595 | @tex | 20566 | @tex |
| 20596 | \turnoffactive | ||
| 20597 | $$ \sigma_\mu^2 = {1 \over \displaystyle \sum {1 \over \sigma_i^2}} $$ | 20567 | $$ \sigma_\mu^2 = {1 \over \displaystyle \sum {1 \over \sigma_i^2}} $$ |
| 20598 | @end tex | 20568 | @end tex |
| 20599 | If the inputs are plain | 20569 | If the inputs are plain |
| @@ -20603,7 +20573,6 @@ out to be equivalent to calculating the standard deviation and | |||
| 20603 | then assuming each value's error is equal to this standard | 20573 | then assuming each value's error is equal to this standard |
| 20604 | deviation.) | 20574 | deviation.) |
| 20605 | @tex | 20575 | @tex |
| 20606 | \turnoffactive | ||
| 20607 | $$ \sigma_\mu^2 = {\sigma^2 \over N} $$ | 20576 | $$ \sigma_\mu^2 = {\sigma^2 \over N} $$ |
| 20608 | @end tex | 20577 | @end tex |
| 20609 | 20578 | ||
| @@ -20636,7 +20605,6 @@ command computes the harmonic mean of the data values. This is | |||
| 20636 | defined as the reciprocal of the arithmetic mean of the reciprocals | 20605 | defined as the reciprocal of the arithmetic mean of the reciprocals |
| 20637 | of the values. | 20606 | of the values. |
| 20638 | @tex | 20607 | @tex |
| 20639 | \turnoffactive | ||
| 20640 | $$ { N \over \displaystyle \sum {1 \over x_i} } $$ | 20608 | $$ { N \over \displaystyle \sum {1 \over x_i} } $$ |
| 20641 | @end tex | 20609 | @end tex |
| 20642 | 20610 | ||
| @@ -20650,7 +20618,6 @@ is the @var{n}th root of the product of the values. This is also | |||
| 20650 | equal to the @code{exp} of the arithmetic mean of the logarithms | 20618 | equal to the @code{exp} of the arithmetic mean of the logarithms |
| 20651 | of the data values. | 20619 | of the data values. |
| 20652 | @tex | 20620 | @tex |
| 20653 | \turnoffactive | ||
| 20654 | $$ \exp \left ( \sum { \ln x_i } \right ) = | 20621 | $$ \exp \left ( \sum { \ln x_i } \right ) = |
| 20655 | \left ( \prod { x_i } \right)^{1 / N} $$ | 20622 | \left ( \prod { x_i } \right)^{1 / N} $$ |
| 20656 | @end tex | 20623 | @end tex |
| @@ -20662,7 +20629,6 @@ mean'' of two numbers taken from the stack. This is computed by | |||
| 20662 | replacing the two numbers with their arithmetic mean and geometric | 20629 | replacing the two numbers with their arithmetic mean and geometric |
| 20663 | mean, then repeating until the two values converge. | 20630 | mean, then repeating until the two values converge. |
| 20664 | @tex | 20631 | @tex |
| 20665 | \turnoffactive | ||
| 20666 | $$ a_{i+1} = { a_i + b_i \over 2 } , \qquad b_{i+1} = \sqrt{a_i b_i} $$ | 20632 | $$ a_{i+1} = { a_i + b_i \over 2 } , \qquad b_{i+1} = \sqrt{a_i b_i} $$ |
| 20667 | @end tex | 20633 | @end tex |
| 20668 | 20634 | ||
| @@ -20685,7 +20651,6 @@ deviation, whose value is the square root of the sum of the squares of | |||
| 20685 | the differences between the values and the mean of the @expr{N} values, | 20651 | the differences between the values and the mean of the @expr{N} values, |
| 20686 | divided by @expr{N-1}. | 20652 | divided by @expr{N-1}. |
| 20687 | @tex | 20653 | @tex |
| 20688 | \turnoffactive | ||
| 20689 | $$ \sigma^2 = {1 \over N - 1} \sum (x_i - \mu)^2 $$ | 20654 | $$ \sigma^2 = {1 \over N - 1} \sum (x_i - \mu)^2 $$ |
| 20690 | @end tex | 20655 | @end tex |
| 20691 | 20656 | ||
| @@ -20712,7 +20677,6 @@ is used when the input represents a sample of the set of all | |||
| 20712 | data values, so that the mean computed from the input is itself | 20677 | data values, so that the mean computed from the input is itself |
| 20713 | only an estimate of the true mean. | 20678 | only an estimate of the true mean. |
| 20714 | @tex | 20679 | @tex |
| 20715 | \turnoffactive | ||
| 20716 | $$ \sigma^2 = {1 \over N} \sum (x_i - \mu)^2 $$ | 20680 | $$ \sigma^2 = {1 \over N} \sum (x_i - \mu)^2 $$ |
| 20717 | @end tex | 20681 | @end tex |
| 20718 | 20682 | ||
| @@ -20777,7 +20741,6 @@ are composed of error forms, the error for a given data point | |||
| 20777 | is taken as the square root of the sum of the squares of the two | 20741 | is taken as the square root of the sum of the squares of the two |
| 20778 | input errors. | 20742 | input errors. |
| 20779 | @tex | 20743 | @tex |
| 20780 | \turnoffactive | ||
| 20781 | $$ \sigma_{x\!y}^2 = {1 \over N-1} \sum (x_i - \mu_x) (y_i - \mu_y) $$ | 20744 | $$ \sigma_{x\!y}^2 = {1 \over N-1} \sum (x_i - \mu_x) (y_i - \mu_y) $$ |
| 20782 | $$ \sigma_{x\!y}^2 = | 20745 | $$ \sigma_{x\!y}^2 = |
| 20783 | {\displaystyle {1 \over N-1} | 20746 | {\displaystyle {1 \over N-1} |
| @@ -20805,7 +20768,6 @@ This is defined by the covariance of the vectors divided by the | |||
| 20805 | product of their standard deviations. (There is no difference | 20768 | product of their standard deviations. (There is no difference |
| 20806 | between sample or population statistics here.) | 20769 | between sample or population statistics here.) |
| 20807 | @tex | 20770 | @tex |
| 20808 | \turnoffactive | ||
| 20809 | $$ r_{x\!y} = { \sigma_{x\!y}^2 \over \sigma_x^2 \sigma_y^2 } $$ | 20771 | $$ r_{x\!y} = { \sigma_{x\!y}^2 \over \sigma_x^2 \sigma_y^2 } $$ |
| 20810 | @end tex | 20772 | @end tex |
| 20811 | 20773 | ||
| @@ -24361,8 +24323,6 @@ For example, suppose the data matrix | |||
| 24361 | @end example | 24323 | @end example |
| 24362 | @end ifnottex | 24324 | @end ifnottex |
| 24363 | @tex | 24325 | @tex |
| 24364 | \turnoffactive | ||
| 24365 | \turnoffactive | ||
| 24366 | \beforedisplay | 24326 | \beforedisplay |
| 24367 | $$ \pmatrix{ 1 & 2 & 3 & 4 & 5 \cr | 24327 | $$ \pmatrix{ 1 & 2 & 3 & 4 & 5 \cr |
| 24368 | 5 & 7 & 9 & 11 & 13 } | 24328 | 5 & 7 & 9 & 11 & 13 } |
| @@ -24422,7 +24382,6 @@ chi^2 = sum((y_i - (a + b x_i))^2, i, 1, N) | |||
| 24422 | @end example | 24382 | @end example |
| 24423 | @end ifnottex | 24383 | @end ifnottex |
| 24424 | @tex | 24384 | @tex |
| 24425 | \turnoffactive | ||
| 24426 | \beforedisplay | 24385 | \beforedisplay |
| 24427 | $$ \chi^2 = \sum_{i=1}^N (y_i - (a + b x_i))^2 $$ | 24386 | $$ \chi^2 = \sum_{i=1}^N (y_i - (a + b x_i))^2 $$ |
| 24428 | \afterdisplay | 24387 | \afterdisplay |
| @@ -24613,7 +24572,6 @@ chi^2 = sum(((y_i - (a + b x_i)) / sigma_i)^2, i, 1, N) | |||
| 24613 | @end example | 24572 | @end example |
| 24614 | @end ifnottex | 24573 | @end ifnottex |
| 24615 | @tex | 24574 | @tex |
| 24616 | \turnoffactive | ||
| 24617 | \beforedisplay | 24575 | \beforedisplay |
| 24618 | $$ \chi^2 = \sum_{i=1}^N \left(y_i - (a + b x_i) \over \sigma_i\right)^2 $$ | 24576 | $$ \chi^2 = \sum_{i=1}^N \left(y_i - (a + b x_i) \over \sigma_i\right)^2 $$ |
| 24619 | \afterdisplay | 24577 | \afterdisplay |
| @@ -25388,7 +25346,6 @@ any later ones are answered by reading additional elements from | |||
| 25388 | the stack. Thus, @kbd{' k^2 @key{RET} ' k @key{RET} 1 @key{RET} 5 @key{RET} a + @key{RET}} | 25346 | the stack. Thus, @kbd{' k^2 @key{RET} ' k @key{RET} 1 @key{RET} 5 @key{RET} a + @key{RET}} |
| 25389 | produces the result 55. | 25347 | produces the result 55. |
| 25390 | @tex | 25348 | @tex |
| 25391 | \turnoffactive | ||
| 25392 | $$ \sum_{k=1}^5 k^2 = 55 $$ | 25349 | $$ \sum_{k=1}^5 k^2 = 55 $$ |
| 25393 | @end tex | 25350 | @end tex |
| 25394 | 25351 | ||