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authorJay Belanger2010-05-13 17:33:11 -0500
committerJay Belanger2010-05-13 17:33:11 -0500
commit14914c431498a802e271ad42cdd6f06175ae4b4a (patch)
tree95bee6775e02daa38277a26ac56e96d83e0241d3 /doc
parent2ef3c1449c876f7c9fb327e90c59b6f4df4e4df0 (diff)
downloademacs-14914c431498a802e271ad42cdd6f06175ae4b4a.tar.gz
emacs-14914c431498a802e271ad42cdd6f06175ae4b4a.zip
calc.texi: Remove "\turnoffactive" commands throughout.
Diffstat (limited to 'doc')
-rw-r--r--doc/misc/ChangeLog4
-rw-r--r--doc/misc/calc.texi43
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 @@
12010-05-13 Jay Belanger <jay.p.belanger@gmail.com>
2
3 * calc.texi: Remove "\turnoffactive" commands througout.
4
12010-05-08 Štěpán Němec <stepnem@gmail.com> (tiny change) 52010-05-08 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
3489Now 3483Now
@@ -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
3824These are $\sum x$, $\sum x^2$, $\sum y$, and $\sum x y$, 3815These are $\sum x$, $\sum x^2$, $\sum y$, and $\sum x y$,
3825respectively. (We could have used \kbd{*} to compute $\sum x^2$ and 3816respectively. (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 $$
@@ -18591,7 +18564,6 @@ letter gamma). You can obtain these using the @kbd{H f G} [@code{gammag}]
18591and @kbd{H I f G} [@code{gammaG}] commands. 18564and @kbd{H I f G} [@code{gammaG}] commands.
18592@end ifnottex 18565@end ifnottex
18593@tex 18566@tex
18594\turnoffactive
18595The functions corresponding to the integrals that define $P(a,x)$ 18567The functions corresponding to the integrals that define $P(a,x)$
18596and $Q(a,x)$ but without the normalizing $1/\Gamma(a)$ 18568and $Q(a,x)$ but without the normalizing $1/\Gamma(a)$
18597factor are called $\gamma(a,x)$ and $\Gamma(a,x)$, respectively. 18569factor are called $\gamma(a,x)$ and $\Gamma(a,x)$, respectively.
@@ -20559,7 +20531,6 @@ this is the weighted mean of the @expr{x} values with weights
20559@texline @math{1 /\sigma^2}. 20531@texline @math{1 /\sigma^2}.
20560@infoline @expr{1 / s^2}. 20532@infoline @expr{1 / s^2}.
20561@tex 20533@tex
20562\turnoffactive
20563$$ \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 } } $$
20565@end tex 20536@end tex
@@ -20593,7 +20564,6 @@ root of the reciprocal of the sum of the reciprocals of the squares
20593of the input errors. (I.e., the variance is the reciprocal of the 20564of the input errors. (I.e., the variance is the reciprocal of the
20594sum of the reciprocals of the variances.) 20565sum of the reciprocals of the variances.)
20595@tex 20566@tex
20596\turnoffactive
20597$$ \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}} $$
20598@end tex 20568@end tex
20599If the inputs are plain 20569If the inputs are plain
@@ -20603,7 +20573,6 @@ out to be equivalent to calculating the standard deviation and
20603then assuming each value's error is equal to this standard 20573then assuming each value's error is equal to this standard
20604deviation.) 20574deviation.)
20605@tex 20575@tex
20606\turnoffactive
20607$$ \sigma_\mu^2 = {\sigma^2 \over N} $$ 20576$$ \sigma_\mu^2 = {\sigma^2 \over N} $$
20608@end tex 20577@end tex
20609 20578
@@ -20636,7 +20605,6 @@ command computes the harmonic mean of the data values. This is
20636defined as the reciprocal of the arithmetic mean of the reciprocals 20605defined as the reciprocal of the arithmetic mean of the reciprocals
20637of the values. 20606of the values.
20638@tex 20607@tex
20639\turnoffactive
20640$$ { N \over \displaystyle \sum {1 \over x_i} } $$ 20608$$ { N \over \displaystyle \sum {1 \over x_i} } $$
20641@end tex 20609@end tex
20642 20610
@@ -20650,7 +20618,6 @@ is the @var{n}th root of the product of the values. This is also
20650equal to the @code{exp} of the arithmetic mean of the logarithms 20618equal to the @code{exp} of the arithmetic mean of the logarithms
20651of the data values. 20619of the data values.
20652@tex 20620@tex
20653\turnoffactive
20654$$ \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} $$
20656@end tex 20623@end tex
@@ -20662,7 +20629,6 @@ mean'' of two numbers taken from the stack. This is computed by
20662replacing the two numbers with their arithmetic mean and geometric 20629replacing the two numbers with their arithmetic mean and geometric
20663mean, then repeating until the two values converge. 20630mean, then repeating until the two values converge.
20664@tex 20631@tex
20665\turnoffactive
20666$$ 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} $$
20667@end tex 20633@end tex
20668 20634
@@ -20685,7 +20651,6 @@ deviation, whose value is the square root of the sum of the squares of
20685the differences between the values and the mean of the @expr{N} values, 20651the differences between the values and the mean of the @expr{N} values,
20686divided by @expr{N-1}. 20652divided by @expr{N-1}.
20687@tex 20653@tex
20688\turnoffactive
20689$$ \sigma^2 = {1 \over N - 1} \sum (x_i - \mu)^2 $$ 20654$$ \sigma^2 = {1 \over N - 1} \sum (x_i - \mu)^2 $$
20690@end tex 20655@end tex
20691 20656
@@ -20712,7 +20677,6 @@ is used when the input represents a sample of the set of all
20712data values, so that the mean computed from the input is itself 20677data values, so that the mean computed from the input is itself
20713only an estimate of the true mean. 20678only an estimate of the true mean.
20714@tex 20679@tex
20715\turnoffactive
20716$$ \sigma^2 = {1 \over N} \sum (x_i - \mu)^2 $$ 20680$$ \sigma^2 = {1 \over N} \sum (x_i - \mu)^2 $$
20717@end tex 20681@end tex
20718 20682
@@ -20777,7 +20741,6 @@ are composed of error forms, the error for a given data point
20777is taken as the square root of the sum of the squares of the two 20741is taken as the square root of the sum of the squares of the two
20778input errors. 20742input errors.
20779@tex 20743@tex
20780\turnoffactive
20781$$ \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$$ \sigma_{x\!y}^2 =
20783 {\displaystyle {1 \over N-1} 20746 {\displaystyle {1 \over N-1}
@@ -20805,7 +20768,6 @@ This is defined by the covariance of the vectors divided by the
20805product of their standard deviations. (There is no difference 20768product of their standard deviations. (There is no difference
20806between sample or population statistics here.) 20769between sample or population statistics here.)
20807@tex 20770@tex
20808\turnoffactive
20809$$ 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 $$
24619\afterdisplay 24577\afterdisplay
@@ -25388,7 +25346,6 @@ any later ones are answered by reading additional elements from
25388the stack. Thus, @kbd{' k^2 @key{RET} ' k @key{RET} 1 @key{RET} 5 @key{RET} a + @key{RET}} 25346the stack. Thus, @kbd{' k^2 @key{RET} ' k @key{RET} 1 @key{RET} 5 @key{RET} a + @key{RET}}
25389produces the result 55. 25347produces the result 55.
25390@tex 25348@tex
25391\turnoffactive
25392$$ \sum_{k=1}^5 k^2 = 55 $$ 25349$$ \sum_{k=1}^5 k^2 = 55 $$
25393@end tex 25350@end tex
25394 25351