diff options
| author | Paul Eggert <eggert@cs.ucla.edu> | 2011-11-19 23:30:16 -0800 |
|---|---|---|
| committer | Paul Eggert <eggert@cs.ucla.edu> | 2011-11-19 23:30:16 -0800 |
| commit | 40ba43b4b71df1d51954bdad071e74243c4aea7c (patch) | |
| tree | e4cb03937e72463278264e9684481d68ece4698c | |
| parent | 24901d610c9ff524e7e7c132dca1cd4312368db0 (diff) | |
| download | emacs-40ba43b4b71df1d51954bdad071e74243c4aea7c.tar.gz | |
Spelling fixes.
71 files changed, 632 insertions, 632 deletions
diff --git a/admin/grammars/c.by b/admin/grammars/c.by index 004f0b5f30f..b49f8ce76c7 100644 --- a/admin/grammars/c.by +++ b/admin/grammars/c.by @@ -122,7 +122,7 @@ %put DELETE summary "delete <object>;" ;; Despite this, this parser can find templates by ignoring the TEMPLATE -;; keyword, and finding the class/method being templateized. +;; keyword, and finding the class/method being templatized. %token TEMPLATE "template" %put TEMPLATE summary "template <class TYPE ...> TYPE_OR_FUNCTION" diff --git a/doc/lispintro/emacs-lisp-intro.texi b/doc/lispintro/emacs-lisp-intro.texi index ef04626e95f..244d95d6937 100644 --- a/doc/lispintro/emacs-lisp-intro.texi +++ b/doc/lispintro/emacs-lisp-intro.texi @@ -887,7 +887,7 @@ but in this case, it is best to treat it as a novel or as a travel guide to a country not yet visited: interesting, but not the same as being there. -Much of this introduction is dedicated to walk-throughs or guided tours +Much of this introduction is dedicated to walkthroughs or guided tours of code used in GNU Emacs. These tours are designed for two purposes: first, to give you familiarity with real, working code (code you use every day); and, second, to give you familiarity with the way Emacs diff --git a/doc/lispref/spellfile b/doc/lispref/spellfile index a98f0427ef6..5c0a6d0f5ea 100644 --- a/doc/lispref/spellfile +++ b/doc/lispref/spellfile @@ -639,7 +639,7 @@ suspension' symbolp symlink syms -syntatic +syntactic tabname temacs temporarily' diff --git a/doc/misc/calc.texi b/doc/misc/calc.texi index 56f6b64c20b..290b120ea80 100644 --- a/doc/misc/calc.texi +++ b/doc/misc/calc.texi @@ -90,7 +90,7 @@ This file documents Calc, the GNU Emacs calculator. @end ifinfo @ifnotinfo -This file documents Calc, the GNU Emacs calculator, included with +This file documents Calc, the GNU Emacs calculator, included with GNU Emacs @value{EMACSVER}. @end ifnotinfo @@ -324,7 +324,7 @@ need to know. @c @cindex Marginal notes 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. +variables also have their own indices. @c @texline Each @c @infoline In the printed manual, each @c paragraph that is referenced in the Key or Function Index is marked @@ -338,7 +338,7 @@ the @kbd{h i} key sequence. Outside of the Calc window, you can press 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 +manual describing any Calc key, function, or variable using @w{@kbd{h k}}, @kbd{h f}, or @kbd{h v}, respectively. @xref{Help Commands}. @ifnottex @@ -437,12 +437,12 @@ Delete, and Space keys. then the command to operate on the numbers. @noindent -Type @kbd{2 @key{RET} 3 + Q} to compute +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 +Type @kbd{P 2 ^} to compute @texline @math{\pi^2 = 9.86960440109}. @infoline the value of `pi' squared, 9.86960440109. @@ -461,14 +461,14 @@ conventional ``algebraic'' notation. To enter an algebraic formula, use the apostrophe key. @noindent -Type @kbd{' sqrt(2+3) @key{RET}} to compute +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 +Type @kbd{' pi^2 @key{RET}} to enter @texline @math{\pi^2}. -@infoline `pi' squared. +@infoline `pi' squared. To evaluate this symbolic formula as a number, type @kbd{=}. @noindent @@ -526,10 +526,10 @@ 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 +Type @kbd{v t} to transpose this @texline @math{3\times2} -@infoline 3x2 -matrix into a +@infoline 3x2 +matrix into a @texline @math{2\times3} @infoline 2x3 matrix. Type @w{@kbd{v u}} to unpack the rows into two separate @@ -605,7 +605,7 @@ there are Quick mode, Keypad mode, and Embedded mode. @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}, +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 @@ -1154,9 +1154,9 @@ its initial state: Empty stack, and initial mode settings. @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 +the value of @texline @math{2^{32}}. -@infoline @expr{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 @@ -1213,7 +1213,7 @@ 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; +rules, and many other algebra features; @texline Fran\c{c}ois @infoline Francois Pinard, who contributed an early prototype of the Calc Summary appendix @@ -1226,7 +1226,7 @@ Randal Schwartz, who suggested the @code{calc-eval} function; Juha Sarlin, who first worked out how to split Calc into quickly-loading 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. +well as many other things. @cindex Bibliography @cindex Knuth, Art of Computer Programming @@ -1472,9 +1472,9 @@ Here's the first exercise: What will the keystrokes @kbd{1 @key{RET} 2 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 +(@bullet{}) @strong{Exercise 2.} Compute @texline @math{(2\times4) + (7\times9.4) + {5\over4}} -@infoline @expr{2*4 + 7*9.5 + 5/4} +@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 @@ -1889,7 +1889,7 @@ 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 +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 @@ -2149,7 +2149,7 @@ 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. +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, @@ -2550,13 +2550,13 @@ angle is measured in degrees. For example, @noindent The shift-@kbd{S} command computes the sine of an angle. The sine -of 45 degrees is +of 45 degrees is @texline @math{\sqrt{2}/2}; -@infoline @expr{sqrt(2)/2}; +@infoline @expr{sqrt(2)/2}; squaring this yields @expr{2/4 = 0.5}. However, there has been a slight -roundoff error because the representation of +roundoff error because the representation of @texline @math{\sqrt{2}/2} -@infoline @expr{sqrt(2)/2} +@infoline @expr{sqrt(2)/2} wasn't exact. The @kbd{c 1} command is a handy way to clean up numbers in this case; it temporarily reduces the precision by one digit while it re-rounds the number on the top of the stack. @@ -2595,9 +2595,9 @@ either radians or degrees, depending on the current angular mode. @end smallexample @noindent -Here we compute the Inverse Sine of +Here we compute the Inverse Sine of @texline @math{\sqrt{0.5}}, -@infoline @expr{sqrt(0.5)}, +@infoline @expr{sqrt(0.5)}, first in radians, then in degrees. Use @kbd{c d} and @kbd{c r} to convert a number from radians to degrees @@ -2783,9 +2783,9 @@ logarithm). These can be modified by the @kbd{I} (inverse) and @kbd{H} (hyperbolic) prefix keys. Let's compute the sine and cosine of an angle, and verify the -identity +identity @texline @math{\sin^2x + \cos^2x = 1}. -@infoline @expr{sin(x)^2 + cos(x)^2 = 1}. +@infoline @expr{sin(x)^2 + cos(x)^2 = 1}. We'll arbitrarily pick @mathit{-64} degrees as a good value for @expr{x}. With the angular mode set to degrees (type @w{@kbd{m d}}), do: @@ -2806,7 +2806,7 @@ You can of course do these calculations to any precision you like.) Remember, @kbd{f h} is the @code{calc-hypot}, or square-root of sum of squares, command. -Another identity is +Another identity is @texline @math{\displaystyle\tan x = {\sin x \over \cos x}}. @infoline @expr{tan(x) = sin(x) / cos(x)}. @smallexample @@ -2871,7 +2871,7 @@ the top two stack elements right after the @kbd{U U}, then a pair of A similar identity is supposed to hold for hyperbolic sines and cosines, except that it is the @emph{difference} @texline @math{\cosh^2x - \sinh^2x} -@infoline @expr{cosh(x)^2 - sinh(x)^2} +@infoline @expr{cosh(x)^2 - sinh(x)^2} that always equals one. Let's try to verify this identity. @smallexample @@ -2993,7 +2993,7 @@ factorial function defined in terms of Euler's Gamma function @end smallexample @noindent -Here we verify the identity +Here we verify the identity @texline @math{n! = \Gamma(n+1)}. @infoline @expr{@var{n}!@: = gamma(@var{n}+1)}. @@ -3283,11 +3283,11 @@ rows in the matrix is different from the number of elements in the vector. (@bullet{}) @strong{Exercise 1.} Use @samp{*} to sum along the rows -of the above +of the above @texline @math{2\times3} -@infoline 2x3 +@infoline 2x3 matrix to get @expr{[6, 15]}. Now use @samp{*} to sum along the columns -to get @expr{[5, 7, 9]}. +to get @expr{[5, 7, 9]}. @xref{Matrix Answer 1, 1}. (@bullet{}) @cindex Identity matrix @@ -3432,7 +3432,7 @@ the matrix and vector. If we multiplied in the other order, Calc would assume the vector was a row vector in order to make the dimensions come out right, and the answer would be incorrect. If you don't feel safe letting Calc take either interpretation of your -vectors, use explicit +vectors, use explicit @texline @math{N\times1} @infoline Nx1 or @@ -3482,9 +3482,9 @@ on the left by the transpose of @expr{A}: @tex $A^T A \, X = A^T B$, where $A^T$ is the transpose \samp{trn(A)}. @end tex -Now +Now @texline @math{A^T A} -@infoline @expr{trn(A)*A} +@infoline @expr{trn(A)*A} is a square matrix so a solution is possible. It turns out that the @expr{X} vector you compute in this way will be a ``least-squares'' solution, which can be regarded as the ``closest'' solution to the set @@ -3577,9 +3577,9 @@ other a plain number.) In the final step, we take the square root of each element. (@bullet{}) @strong{Exercise 1.} Compute a vector of powers of two -from +from @texline @math{2^{-4}} -@infoline @expr{2^-4} +@infoline @expr{2^-4} to @expr{2^4}. @xref{List Answer 1, 1}. (@bullet{}) You can also @dfn{reduce} a binary operator across a vector. @@ -3780,9 +3780,9 @@ $$ m = {N \sum x y - \sum x \sum y \over @end tex @noindent -where +where @texline @math{\sum x} -@infoline @expr{sum(x)} +@infoline @expr{sum(x)} represents the sum of all the values of @expr{x}. While there is an actual @code{sum} function in Calc, it's easier to sum a vector using a simple reduction. First, let's compute the four different sums that @@ -3883,9 +3883,9 @@ $$ b = {\sum y - m \sum x \over N} $$ @end group @end smallexample -Let's ``plot'' this straight line approximation, +Let's ``plot'' this straight line approximation, @texline @math{y \approx m x + b}, -@infoline @expr{m x + b}, +@infoline @expr{m x + b}, and compare it with the original data. @smallexample @@ -3959,7 +3959,7 @@ Next, let's add the line we got from our least-squares fit. (If you are reading this tutorial on-line while running Calc, typing @kbd{g a} may cause the tutorial to disappear from its window and be replaced by a buffer named @samp{*Gnuplot Commands*}. The tutorial -will reappear when you terminate GNUPLOT by typing @kbd{g q}.) +will reappear when you terminate GNUPLOT by typing @kbd{g q}.) @end ifinfo @smallexample @@ -4138,7 +4138,7 @@ command to enable multi-line display of vectors.) @c [fix-ref Numerical Solutions] (@bullet{}) @strong{Exercise 8.} Compute a list of values of Bessel's @texline @math{J_1(x)} -@infoline @expr{J1} +@infoline @expr{J1} function @samp{besJ(1,x)} for @expr{x} from 0 to 5 in steps of 0.25. Find the value of @expr{x} (from among the above set of values) for which @samp{besJ(1,x)} is a maximum. Use an ``automatic'' method, @@ -4150,7 +4150,7 @@ of thing automatically; @pxref{Numerical Solutions}.) @cindex Digits, vectors of (@bullet{}) @strong{Exercise 9.} You are given an integer in the range @texline @math{0 \le N < 10^m} -@infoline @expr{0 <= N < 10^m} +@infoline @expr{0 <= N < 10^m} for @expr{m=12} (i.e., an integer of less than twelve digits). Convert this integer into a vector of @expr{m} digits, each in the range from 0 to 9. In vector-of-digits notation, @@ -4164,12 +4164,12 @@ to try is 25129925999. @xref{List Answer 9, 9}. (@bullet{}) happened? How would you do this test? @xref{List Answer 10, 10}. (@bullet{}) (@bullet{}) @strong{Exercise 11.} The area of a circle of radius one -is @cpi{}. The area of the +is @cpi{}. The area of the @texline @math{2\times2} @infoline 2x2 square that encloses that circle is 4. So if we throw @var{n} darts at random points in the square, about @cpiover{4} of them will land inside -the circle. This gives us an entertaining way to estimate the value of +the circle. This gives us an entertaining way to estimate the value of @cpi{}. The @w{@kbd{k r}} command picks a random number between zero and the value on the stack. We could get a random floating-point number between @mathit{-1} and 1 by typing @@ -4183,12 +4183,12 @@ points lie inside the unit circle. Hint: Use the @kbd{v b} command. another way to calculate @cpi{}. Say you have an infinite field of vertical lines with a spacing of one inch. Toss a one-inch matchstick onto the field. The probability that the matchstick will land crossing -a line turns out to be +a line turns out to be @texline @math{2/\pi}. -@infoline @expr{2/pi}. +@infoline @expr{2/pi}. Toss 100 matchsticks to estimate @cpi{}. (If you want still more fun, the probability that the GCD (@w{@kbd{k g}}) of two large integers is -one turns out to be +one turns out to be @texline @math{6/\pi^2}. @infoline @expr{6/pi^2}. That provides yet another way to estimate @cpi{}.) @@ -4488,7 +4488,7 @@ a 60% chance that the result is correct within 0.59 degrees. @cindex Torus, volume of (@bullet{}) @strong{Exercise 7.} The volume of a torus (a donut shape) is @texline @math{2 \pi^2 R r^2} -@infoline @w{@expr{2 pi^2 R r^2}} +@infoline @w{@expr{2 pi^2 R r^2}} where @expr{R} is the radius of the circle that defines the center of the tube and @expr{r} is the radius of the tube itself. Suppose @expr{R} is 20 cm and @expr{r} is 4 cm, each known to @@ -4569,7 +4569,7 @@ In this last step, Calc has divided by 5 modulo 24; i.e., it has found a new number which, when multiplied by 5 modulo 24, produces the original number, 21. If @var{m} is prime and the divisor is not a multiple of @var{m}, it is always possible to find such a number. For non-prime -@var{m} like 24, it is only sometimes possible. +@var{m} like 24, it is only sometimes possible. @smallexample @group @@ -4587,7 +4587,7 @@ that arises in the second one. @cindex Fermat, primality test of (@bullet{}) @strong{Exercise 10.} A theorem of Pierre de Fermat -says that +says that @texline @w{@math{x^{n-1} \bmod n = 1}} @infoline @expr{x^(n-1) mod n = 1} if @expr{n} is a prime number and @expr{x} is an integer less than @@ -4615,9 +4615,9 @@ of day on the stack as an HMS/modulo form. This calculation tells me it is six hours and 22 minutes until midnight. (@bullet{}) @strong{Exercise 11.} A rule of thumb is that one year -is about +is about @texline @math{\pi \times 10^7} -@infoline @w{@expr{pi * 10^7}} +@infoline @w{@expr{pi * 10^7}} seconds. What time will it be that many seconds from right now? @xref{Types Answer 11, 11}. (@bullet{}) @@ -5093,18 +5093,18 @@ One way to do it is again with vector mapping and reduction: @end smallexample (@bullet{}) @strong{Exercise 3.} Find the integral from 1 to @expr{y} -of +of @texline @math{x \sin \pi x} -@infoline @w{@expr{x sin(pi x)}} +@infoline @w{@expr{x sin(pi x)}} (where the sine is calculated in radians). Find the values of the integral for integers @expr{y} from 1 to 5. @xref{Algebra Answer 3, 3}. (@bullet{}) Calc's integrator can do many simple integrals symbolically, but many others are beyond its capabilities. Suppose we wish to find the area -under the curve +under the curve @texline @math{\sin x \ln x} -@infoline @expr{sin(x) ln(x)} +@infoline @expr{sin(x) ln(x)} over the same range of @expr{x}. If you entered this formula and typed @kbd{a i x @key{RET}} (don't bother to try this), Calc would work for a long time but would be unable to find a solution. In fact, there is no @@ -5242,10 +5242,10 @@ $$ h (f(a) + f(a+h) + f(a+2h) + f(a+3h) + \cdots \afterdisplay @end tex -Compute the integral from 1 to 2 of +Compute the integral from 1 to 2 of @texline @math{\sin x \ln x} -@infoline @expr{sin(x) ln(x)} -using Simpson's rule with 10 slices. +@infoline @expr{sin(x) ln(x)} +using Simpson's rule with 10 slices. @xref{Algebra Answer 4, 4}. (@bullet{}) Calc has a built-in @kbd{a I} command for doing numerical integration. @@ -5396,7 +5396,7 @@ having to retype it. To edit a variable, type @kbd{s e} and the variable name, use regular Emacs editing commands as necessary, then type @kbd{C-c C-c} to store -the edited value back into the variable. +the edited value back into the variable. You can also use @w{@kbd{s e}} to create a new variable if you wish. Notice that the first time you use each rule, Calc puts up a ``compiling'' @@ -5780,7 +5780,7 @@ in @samp{a + 1} for @samp{x} in the defining formula. @tindex Si (@bullet{}) @strong{Exercise 1.} The ``sine integral'' function @texline @math{{\rm Si}(x)} -@infoline @expr{Si(x)} +@infoline @expr{Si(x)} is defined as the integral of @samp{sin(t)/t} for @expr{t = 0} to @expr{x} in radians. (It was invented because this integral has no solution in terms of basic functions; if you give it @@ -5857,9 +5857,9 @@ the following functions: @enumerate @item -Compute +Compute @texline @math{\displaystyle{\sin x \over x}}, -@infoline @expr{sin(x) / x}, +@infoline @expr{sin(x) / x}, where @expr{x} is the number on the top of the stack. @item @@ -5923,15 +5923,15 @@ key if you have one, makes a copy of the number in level 2.) @cindex Golden ratio @cindex Phi, golden ratio A fascinating property of the Fibonacci numbers is that the @expr{n}th -Fibonacci number can be found directly by computing +Fibonacci number can be found directly by computing @texline @math{\phi^n / \sqrt{5}} @infoline @expr{phi^n / sqrt(5)} -and then rounding to the nearest integer, where +and then rounding to the nearest integer, where @texline @math{\phi} (``phi''), -@infoline @expr{phi}, -the ``golden ratio,'' is +@infoline @expr{phi}, +the ``golden ratio,'' is @texline @math{(1 + \sqrt{5}) / 2}. -@infoline @expr{(1 + sqrt(5)) / 2}. +@infoline @expr{(1 + sqrt(5)) / 2}. (For convenience, this constant is available from the @code{phi} variable, or the @kbd{I H P} command.) @@ -5946,19 +5946,19 @@ variable, or the @kbd{I H P} command.) @cindex Continued fractions (@bullet{}) @strong{Exercise 5.} The @dfn{continued fraction} -representation of +representation of @texline @math{\phi} -@infoline @expr{phi} -is +@infoline @expr{phi} +is @texline @math{1 + 1/(1 + 1/(1 + 1/( \ldots )))}. @infoline @expr{1 + 1/(1 + 1/(1 + 1/( ...@: )))}. We can compute an approximate value by carrying this however far -and then replacing the innermost +and then replacing the innermost @texline @math{1/( \ldots )} -@infoline @expr{1/( ...@: )} +@infoline @expr{1/( ...@: )} by 1. Approximate @texline @math{\phi} -@infoline @expr{phi} +@infoline @expr{phi} using a twenty-term continued fraction. @xref{Programming Answer 5, 5}. (@bullet{}) @@ -6056,9 +6056,9 @@ survive past the @kbd{Z '} command. The @dfn{Bernoulli numbers} are a sequence with the interesting property that all of the odd Bernoulli numbers are zero, and the even ones, while difficult to compute, can be roughly approximated -by the formula +by the formula @texline @math{\displaystyle{2 n! \over (2 \pi)^n}}. -@infoline @expr{2 n!@: / (2 pi)^n}. +@infoline @expr{2 n!@: / (2 pi)^n}. Let's write a keyboard macro to compute (approximate) Bernoulli numbers. (Calc has a command, @kbd{k b}, to compute exact Bernoulli numbers, but this command is very slow for large @expr{n} since the higher Bernoulli @@ -6166,7 +6166,7 @@ Z` ;; calc-kbd-push (Save local values) 0 ;; calc digits (Push a zero onto the stack) st ;; calc-store-into (Store it in the following variable) 1 ;; calc quick variable (Quick variable q1) -1 ;; calc digits (Initial value for the loop) +1 ;; calc digits (Initial value for the loop) TAB ;; calc-roll-down (Swap initial and final) Z( ;; calc-kbd-for (Begin the "for" loop) & ;; calc-inv (Take the reciprocal) @@ -6193,10 +6193,10 @@ Press @kbd{C-c C-c} to finish editing and return to the Calculator. The @file{edmacro} package defines a handy @code{read-kbd-macro} command which reads the current region of the current buffer as a sequence of -keystroke names, and defines that sequence on the @kbd{X} +keystroke names, and defines that sequence on the @kbd{X} (and @kbd{C-x e}) key. Because this is so useful, Calc puts this command on the @kbd{C-x * m} key. Try reading in this macro in the -following form: Press @kbd{C-@@} (or @kbd{C-@key{SPC}}) at +following form: Press @kbd{C-@@} (or @kbd{C-@key{SPC}}) at one end of the text below, then type @kbd{C-x * m} at the other. @example @@ -6230,12 +6230,12 @@ $$ x_{\rm new} = x - {f(x) \over f^{\prime}(x)} $$ where @expr{f'(x)} is the derivative of @expr{f}. The @expr{x} values will quickly converge to a solution, i.e., eventually @texline @math{x_{\rm new}} -@infoline @expr{new_x} +@infoline @expr{new_x} and @expr{x} will be equal to within the limits of the current precision. Write a program which takes a formula involving the variable @expr{x}, and an initial guess @expr{x_0}, on the stack, and produces a value of @expr{x} for which the formula -is zero. Use it to find a solution of +is zero. Use it to find a solution of @texline @math{\sin(\cos x) = 0.5} @infoline @expr{sin(cos(x)) = 0.5} near @expr{x = 4.5}. (Use angles measured in radians.) Note that @@ -6245,12 +6245,12 @@ method when it is able. @xref{Programming Answer 8, 8}. (@bullet{}) @cindex Digamma function @cindex Gamma constant, Euler's @cindex Euler's gamma constant -(@bullet{}) @strong{Exercise 9.} The @dfn{digamma} function +(@bullet{}) @strong{Exercise 9.} The @dfn{digamma} function @texline @math{\psi(z) (``psi'')} @infoline @expr{psi(z)} -is defined as the derivative of +is defined as the derivative of @texline @math{\ln \Gamma(z)}. -@infoline @expr{ln(gamma(z))}. +@infoline @expr{ln(gamma(z))}. For large values of @expr{z}, it can be approximated by the infinite sum @ifnottex @@ -6267,9 +6267,9 @@ $$ @end tex @noindent -where +where @texline @math{\sum} -@infoline @expr{sum} +@infoline @expr{sum} represents the sum over @expr{n} from 1 to infinity (or to some limit high enough to give the desired accuracy), and the @code{bern} function produces (exact) Bernoulli numbers. @@ -6277,27 +6277,27 @@ While this sum is not guaranteed to converge, in practice it is safe. An interesting mathematical constant is Euler's gamma, which is equal to about 0.5772. One way to compute it is by the formula, @texline @math{\gamma = -\psi(1)}. -@infoline @expr{gamma = -psi(1)}. +@infoline @expr{gamma = -psi(1)}. Unfortunately, 1 isn't a large enough argument for the above formula to work (5 is a much safer value for @expr{z}). -Fortunately, we can compute +Fortunately, we can compute @texline @math{\psi(1)} -@infoline @expr{psi(1)} -from +@infoline @expr{psi(1)} +from @texline @math{\psi(5)} -@infoline @expr{psi(5)} -using the recurrence +@infoline @expr{psi(5)} +using the recurrence @texline @math{\psi(z+1) = \psi(z) + {1 \over z}}. -@infoline @expr{psi(z+1) = psi(z) + 1/z}. -Your task: Develop a program to compute +@infoline @expr{psi(z+1) = psi(z) + 1/z}. +Your task: Develop a program to compute @texline @math{\psi(z)}; -@infoline @expr{psi(z)}; +@infoline @expr{psi(z)}; it should ``pump up'' @expr{z} if necessary to be greater than 5, then use the above summation formula. Use looping commands to compute the sum. Use your function -to compute +to compute @texline @math{\gamma} -@infoline @expr{gamma} +@infoline @expr{gamma} to twelve decimal places. (Calc has a built-in command for Euler's constant, @kbd{I P}, which you can use to check your answer.) @xref{Programming Answer 9, 9}. (@bullet{}) @@ -6470,7 +6470,7 @@ This section includes answers to all the exercises in the Calc tutorial. @noindent @kbd{1 @key{RET} 2 @key{RET} 3 @key{RET} 4 + * -} -The result is +The result is @texline @math{1 - (2 \times (3 + 4)) = -13}. @infoline @expr{1 - (2 * (3 + 4)) = -13}. @@ -6481,9 +6481,9 @@ The result is @texline @math{2\times4 + 7\times9.5 + {5\over4} = 75.75} @infoline @expr{2*4 + 7*9.5 + 5/4 = 75.75} -After computing the intermediate term +After computing the intermediate term @texline @math{2\times4 = 8}, -@infoline @expr{2*4 = 8}, +@infoline @expr{2*4 = 8}, you can leave that result on the stack while you compute the second term. With both of these results waiting on the stack you can then compute the final term, then press @kbd{+ +} to add everything up. @@ -6790,7 +6790,7 @@ Dividing two integers that are larger than the current precision may give a floating-point result that is inaccurate even when rounded down to an integer. Consider @expr{123456789 / 2} when the current precision is 6 digits. The true answer is @expr{61728394.5}, but -with a precision of 6 this will be rounded to +with a precision of 6 this will be rounded to @texline @math{12345700.0/2.0 = 61728500.0}. @infoline @expr{12345700.@: / 2.@: = 61728500.}. The result, when converted to an integer, will be off by 106. @@ -6900,18 +6900,18 @@ Type @kbd{d N} to return to Normal display mode afterwards. @subsection Matrix Tutorial Exercise 3 @noindent -To solve +To solve @texline @math{A^T A \, X = A^T B}, -@infoline @expr{trn(A) * A * X = trn(A) * B}, +@infoline @expr{trn(A) * A * X = trn(A) * B}, first we compute @texline @math{A' = A^T A} -@infoline @expr{A2 = trn(A) * A} -and +@infoline @expr{A2 = trn(A) * A} +and @texline @math{B' = A^T B}; -@infoline @expr{B2 = trn(A) * B}; -now, we have a system +@infoline @expr{B2 = trn(A) * B}; +now, we have a system @texline @math{A' X = B'} -@infoline @expr{A2 * X = B2} +@infoline @expr{A2 * X = B2} which we can solve using Calc's @samp{/} command. @ifnottex @@ -6942,7 +6942,7 @@ $$ The first step is to enter the coefficient matrix. We'll store it in quick variable number 7 for later reference. Next, we compute the @texline @math{B'} -@infoline @expr{B2} +@infoline @expr{B2} vector. @smallexample @@ -6958,9 +6958,9 @@ vector. @end smallexample @noindent -Now we compute the matrix +Now we compute the matrix @texline @math{A'} -@infoline @expr{A2} +@infoline @expr{A2} and divide. @smallexample @@ -6979,16 +6979,16 @@ and divide. (The actual computed answer will be slightly inexact due to round-off error.) -Notice that the answers are similar to those for the +Notice that the answers are similar to those for the @texline @math{3\times3} @infoline 3x3 -system solved in the text. That's because the fourth equation that was +system solved in the text. That's because the fourth equation that was added to the system is almost identical to the first one multiplied by two. (If it were identical, we would have gotten the exact same -answer since the +answer since the @texline @math{4\times3} @infoline 4x3 -system would be equivalent to the original +system would be equivalent to the original @texline @math{3\times3} @infoline 3x3 system.) @@ -7064,7 +7064,7 @@ $$ m \times x + b \times 1 = y $$ \afterdisplay @end tex -Thus we want a +Thus we want a @texline @math{19\times2} @infoline 19x2 matrix with our @expr{x} vector as one column and @@ -7083,12 +7083,12 @@ we combine the two columns to form our @expr{A} matrix. @end smallexample @noindent -Now we compute +Now we compute @texline @math{A^T y} -@infoline @expr{trn(A) * y} -and +@infoline @expr{trn(A) * y} +and @texline @math{A^T A} -@infoline @expr{trn(A) * A} +@infoline @expr{trn(A) * A} and divide. @smallexample @@ -7114,9 +7114,9 @@ and divide. @end group @end smallexample -Since we were solving equations of the form +Since we were solving equations of the form @texline @math{m \times x + b \times 1 = y}, -@infoline @expr{m*x + b*1 = y}, +@infoline @expr{m*x + b*1 = y}, these numbers should be @expr{m} and @expr{b}, respectively. Sure enough, they agree exactly with the result computed using @kbd{V M} and @kbd{V R}! @@ -7177,9 +7177,9 @@ then raise the number to that power.) @subsection List Tutorial Exercise 4 @noindent -A number @expr{j} is a divisor of @expr{n} if +A number @expr{j} is a divisor of @expr{n} if @texline @math{n \mathbin{\hbox{\code{\%}}} j = 0}. -@infoline @samp{n % j = 0}. +@infoline @samp{n % j = 0}. The first step is to get a vector that identifies the divisors. @smallexample @@ -7248,9 +7248,9 @@ so that the mapping operation works; no prime factor will ever be zero, so adding zeros on the left and right is safe. From then on the job is pretty straightforward. -Incidentally, Calc provides the +Incidentally, Calc provides the @texline @dfn{M@"obius} @math{\mu} -@infoline @dfn{Moebius mu} +@infoline @dfn{Moebius mu} function which is zero if and only if its argument is square-free. It would be a much more convenient way to do the above test in practice. @@ -7282,7 +7282,7 @@ exercise and type @kbd{1 -} to subtract one from all the elements. The numbers down the lefthand edge of the list we desire are called the ``triangular numbers'' (now you know why!). The @expr{n}th triangular number is the sum of the integers from 1 to @expr{n}, and -can be computed directly by the formula +can be computed directly by the formula @texline @math{n (n+1) \over 2}. @infoline @expr{n * (n+1) / 2}. @@ -7378,7 +7378,7 @@ A way to isolate the maximum value is to compute the maximum using @noindent It's a good idea to verify, as in the last step above, that only -one value is equal to the maximum. (After all, a plot of +one value is equal to the maximum. (After all, a plot of @texline @math{\sin x} @infoline @expr{sin(x)} might have many points all equal to the maximum value, 1.) @@ -7650,12 +7650,12 @@ return to full-sized display of vectors. This problem can be made a lot easier by taking advantage of some symmetries. First of all, after some thought it's clear that the @expr{y} axis can be ignored altogether. Just pick a random @expr{x} -component for one end of the match, pick a random direction +component for one end of the match, pick a random direction @texline @math{\theta}, @infoline @expr{theta}, -and see if @expr{x} and +and see if @expr{x} and @texline @math{x + \cos \theta} -@infoline @expr{x + cos(theta)} +@infoline @expr{x + cos(theta)} (which is the @expr{x} coordinate of the other endpoint) cross a line. The lines are at integer coordinates, so this happens when the two numbers surround an integer. @@ -7670,9 +7670,9 @@ In fact, since the field of lines is infinite we can choose the coordinates 0 and 1 for the lines on either side of the leftmost endpoint. The rightmost endpoint will be between 0 and 1 if the match does not cross a line, or between 1 and 2 if it does. So: -Pick random @expr{x} and +Pick random @expr{x} and @texline @math{\theta}, -@infoline @expr{theta}, +@infoline @expr{theta}, compute @texline @math{x + \cos \theta}, @infoline @expr{x + cos(theta)}, @@ -8997,7 +8997,7 @@ Each of these functions can be computed using the stack, or using algebraic entry, whichever way you prefer: @noindent -Computing +Computing @texline @math{\displaystyle{\sin x \over x}}: @infoline @expr{sin(x) / x}: @@ -9068,7 +9068,7 @@ C-x ( ' [0, 1; 1, 1] ^ ($-1) * [1, 1] @key{RET} v u @key{DEL} C-x ) @noindent This program is quite efficient because Calc knows how to raise a -matrix (or other value) to the power @expr{n} in only +matrix (or other value) to the power @expr{n} in only @texline @math{\log_2 n} @infoline @expr{log(n,2)} steps. For example, this program can compute the 1000th Fibonacci @@ -9122,7 +9122,7 @@ harmonic number is 4.02. @noindent The first step is to compute the derivative @expr{f'(x)} and thus -the formula +the formula @texline @math{\displaystyle{x - {f(x) \over f'(x)}}}. @infoline @expr{x - f(x)/f'(x)}. @@ -9239,12 +9239,12 @@ method (among others) to look for numerical solutions to any equation. @noindent The first step is to adjust @expr{z} to be greater than 5. A simple ``for'' loop will do the job here. If @expr{z} is less than 5, we -reduce the problem using +reduce the problem using @texline @math{\psi(z) = \psi(z+1) - 1/z}. @infoline @expr{psi(z) = psi(z+1) - 1/z}. We go -on to compute +on to compute @texline @math{\psi(z+1)}, -@infoline @expr{psi(z+1)}, +@infoline @expr{psi(z+1)}, and remember to add back a factor of @expr{-1/z} when we're done. This step is repeated until @expr{z > 5}. @@ -9283,7 +9283,7 @@ are exactly equal, not just equal to within the current precision.) @end group @end smallexample -Now we compute the initial part of the sum: +Now we compute the initial part of the sum: @texline @math{\ln z - {1 \over 2z}} @infoline @expr{ln(z) - 1/2z} minus the adjustment factor. @@ -9326,9 +9326,9 @@ up the value of @expr{2 n}. (Calc does have a summation command, @end group @end smallexample -This is the value of +This is the value of @texline @math{-\gamma}, -@infoline @expr{- gamma}, +@infoline @expr{- gamma}, with a slight bit of roundoff error. To get a full 12 digits, let's use a higher precision: @@ -9361,9 +9361,9 @@ C-x ) @noindent Taking the derivative of a term of the form @expr{x^n} will produce -a term like +a term like @texline @math{n x^{n-1}}. -@infoline @expr{n x^(n-1)}. +@infoline @expr{n x^(n-1)}. Taking the derivative of a constant produces zero. From this it is easy to see that the @expr{n}th derivative of a polynomial, evaluated at @expr{x = 0}, will equal the @@ -9652,7 +9652,7 @@ still exists and is updated silently. @xref{Trail Commands}. @mindex @null @end ignore In most installations, the @kbd{C-x * c} key sequence is a more -convenient way to start the Calculator. Also, @kbd{C-x * *} +convenient way to start the Calculator. Also, @kbd{C-x * *} is a synonym for @kbd{C-x * c} unless you last used Calc in its Keypad mode. @@ -9908,9 +9908,9 @@ additional notes from the summary that apply to this command. The @kbd{h f} (@code{calc-describe-function}) command looks up an algebraic function or a command name in the Calc manual. Enter an algebraic function name to look up that function in the Function -Index or enter a command name beginning with @samp{calc-} to look it +Index or enter a command name beginning with @samp{calc-} to look it up in the Command Index. This command will also look up operator -symbols that can appear in algebraic formulas, like @samp{%} and +symbols that can appear in algebraic formulas, like @samp{%} and @samp{=>}. @kindex h v @@ -10038,7 +10038,7 @@ During numeric entry, the only editing key available is @key{DEL}. @cindex Formulas, entering The @kbd{'} (@code{calc-algebraic-entry}) command can be used to enter calculations in algebraic form. This is accomplished by typing the -apostrophe key, ', followed by the expression in standard format: +apostrophe key, ', followed by the expression in standard format: @example ' 2+3*4 @key{RET}. @@ -10047,7 +10047,7 @@ apostrophe key, ', followed by the expression in standard format: @noindent This will compute @texline @math{2+(3\times4) = 14} -@infoline @expr{2+(3*4) = 14} +@infoline @expr{2+(3*4) = 14} and push it on the stack. If you wish you can ignore the RPN aspect of Calc altogether and simply enter algebraic expressions in this way. You may want to use @key{DEL} every so often to @@ -10453,9 +10453,9 @@ is greater than this, it will recompute @cpi{} using a series approximation. This value will not need to be recomputed ever again unless you raise the precision still further. Many operations such as logarithms and sines make use of similarly cached values such as -@cpiover{4} and +@cpiover{4} and @texline @math{\ln 2}. -@infoline @expr{ln(2)}. +@infoline @expr{ln(2)}. The visible effect of caching is that high-precision computations may seem to do extra work the first time. Other things cached include powers of two (for the binary arithmetic @@ -10612,10 +10612,10 @@ form). The numerator and denominator always use the same radix. A floating-point number or @dfn{float} is a number stored in scientific notation. The number of significant digits in the fractional part is governed by the current floating precision (@pxref{Precision}). The -range of acceptable values is from +range of acceptable values is from @texline @math{10^{-3999999}} -@infoline @expr{10^-3999999} -(inclusive) to +@infoline @expr{10^-3999999} +(inclusive) to @texline @math{10^{4000000}} @infoline @expr{10^4000000} (exclusive), plus the corresponding negative values and zero. @@ -10690,18 +10690,18 @@ polar. The default format is rectangular, displayed in the form Rectangular complex numbers can also be displayed in @samp{@var{a}+@var{b}i} notation; @pxref{Complex Formats}. -Polar complex numbers are displayed in the form +Polar complex numbers are displayed in the form @texline `@tfn{(}@var{r}@tfn{;}@math{\theta}@tfn{)}' @infoline `@tfn{(}@var{r}@tfn{;}@var{theta}@tfn{)}' -where @var{r} is the nonnegative magnitude and +where @var{r} is the nonnegative magnitude and @texline @math{\theta} -@infoline @var{theta} -is the argument or phase angle. The range of +@infoline @var{theta} +is the argument or phase angle. The range of @texline @math{\theta} -@infoline @var{theta} +@infoline @var{theta} depends on the current angular mode (@pxref{Angular Modes}); it is generally between @mathit{-180} and @mathit{+180} degrees or the equivalent range -in radians. +in radians. Complex numbers are entered in stages using incomplete objects. @xref{Incomplete Objects}. @@ -10742,9 +10742,9 @@ really mean is that @expr{1 / x}, as @expr{x} becomes larger and larger, becomes arbitrarily close to zero. So you can imagine that if @expr{x} got ``all the way to infinity,'' then @expr{1 / x} would go all the way to zero. Similarly, when they say that -@samp{exp(inf) = inf}, they mean that +@samp{exp(inf) = inf}, they mean that @texline @math{e^x} -@infoline @expr{exp(x)} +@infoline @expr{exp(x)} grows without bound as @expr{x} grows. The symbol @samp{-inf} likewise stands for an infinitely negative real value; for example, we say that @samp{exp(-inf) = 0}. You can have an infinity pointing in any @@ -10839,7 +10839,7 @@ of its elements. @end ignore @tindex vec Algebraic functions for building vectors include @samp{vec(a, b, c)} -to build @samp{[a, b, c]}, @samp{cvec(a, n, m)} to build an +to build @samp{[a, b, c]}, @samp{cvec(a, n, m)} to build an @texline @math{n\times m} @infoline @var{n}x@var{m} matrix of @samp{a}s, and @samp{index(n)} to build a vector of integers @@ -11184,9 +11184,9 @@ there is no solution to this equation (which can happen only when division is left in symbolic form. Other operations, such as square roots, are not yet supported for modulo forms. (Note that, although @w{`@tfn{(}@var{a} @tfn{mod} @var{M}@tfn{)^.5}'} will compute a ``modulo square root'' -in the sense of reducing +in the sense of reducing @texline @math{\sqrt a} -@infoline @expr{sqrt(a)} +@infoline @expr{sqrt(a)} modulo @expr{M}, this is not a useful definition from the number-theoretical point of view.) @@ -11220,11 +11220,11 @@ The algebraic function @samp{makemod(a, m)} builds the modulo form @cindex Standard deviations An @dfn{error form} is a number with an associated standard deviation, as in @samp{2.3 +/- 0.12}. The notation -@texline `@var{x} @tfn{+/-} @math{\sigma}' -@infoline `@var{x} @tfn{+/-} sigma' +@texline `@var{x} @tfn{+/-} @math{\sigma}' +@infoline `@var{x} @tfn{+/-} sigma' stands for an uncertain value which follows a normal or Gaussian distribution of mean @expr{x} and standard -deviation or ``error'' +deviation or ``error'' @texline @math{\sigma}. @infoline @expr{sigma}. Both the mean and the error can be either numbers or @@ -11235,7 +11235,7 @@ regular number by the Calculator. All arithmetic and transcendental functions accept error forms as input. Operations on the mean-value part work just like operations on regular -numbers. The error part for any function @expr{f(x)} (such as +numbers. The error part for any function @expr{f(x)} (such as @texline @math{\sin x} @infoline @expr{sin(x)}) is defined by the error of @expr{x} times the derivative of @expr{f} @@ -11267,35 +11267,35 @@ Consult a good text on error analysis for a discussion of the proper use of standard deviations. Actual errors often are neither Gaussian-distributed nor uncorrelated, and the above formulas are valid only when errors are small. As an example, the error arising from -@texline `@tfn{sin(}@var{x} @tfn{+/-} @math{\sigma}@tfn{)}' -@infoline `@tfn{sin(}@var{x} @tfn{+/-} @var{sigma}@tfn{)}' -is -@texline `@math{\sigma} @tfn{abs(cos(}@var{x}@tfn{))}'. -@infoline `@var{sigma} @tfn{abs(cos(}@var{x}@tfn{))}'. +@texline `@tfn{sin(}@var{x} @tfn{+/-} @math{\sigma}@tfn{)}' +@infoline `@tfn{sin(}@var{x} @tfn{+/-} @var{sigma}@tfn{)}' +is +@texline `@math{\sigma} @tfn{abs(cos(}@var{x}@tfn{))}'. +@infoline `@var{sigma} @tfn{abs(cos(}@var{x}@tfn{))}'. When @expr{x} is close to zero, @texline @math{\cos x} -@infoline @expr{cos(x)} -is close to one so the error in the sine is close to +@infoline @expr{cos(x)} +is close to one so the error in the sine is close to @texline @math{\sigma}; @infoline @expr{sigma}; -this makes sense, since +this makes sense, since @texline @math{\sin x} -@infoline @expr{sin(x)} +@infoline @expr{sin(x)} is approximately @expr{x} near zero, so a given error in @expr{x} will produce about the same error in the sine. Likewise, near 90 degrees @texline @math{\cos x} -@infoline @expr{cos(x)} +@infoline @expr{cos(x)} is nearly zero and so the computed error is small: The sine curve is nearly flat in that region, so an error in @expr{x} -has relatively little effect on the value of +has relatively little effect on the value of @texline @math{\sin x}. -@infoline @expr{sin(x)}. +@infoline @expr{sin(x)}. However, consider @samp{sin(90 +/- 1000)}. The cosine of 90 is zero, so Calc will report zero error! We get an obviously wrong result because we have violated the small-error approximation underlying the error analysis. If the error in @expr{x} had been small, the error in @texline @math{\sin x} -@infoline @expr{sin(x)} +@infoline @expr{sin(x)} would indeed have been negligible. @ignore @@ -11402,14 +11402,14 @@ contain zero inside them Calc is forced to give the result, While it may seem that intervals and error forms are similar, they are based on entirely different concepts of inexact quantities. An error -form -@texline `@var{x} @tfn{+/-} @math{\sigma}' -@infoline `@var{x} @tfn{+/-} @var{sigma}' +form +@texline `@var{x} @tfn{+/-} @math{\sigma}' +@infoline `@var{x} @tfn{+/-} @var{sigma}' means a variable is random, and its value could -be anything but is ``probably'' within one -@texline @math{\sigma} -@infoline @var{sigma} -of the mean value @expr{x}. An interval +be anything but is ``probably'' within one +@texline @math{\sigma} +@infoline @var{sigma} +of the mean value @expr{x}. An interval `@tfn{[}@var{a} @tfn{..@:} @var{b}@tfn{]}' means a variable's value is unknown, but guaranteed to lie in the specified range. Error forms are statistical or ``average case'' approximations; @@ -11641,7 +11641,7 @@ the C-style ``if'' operator @samp{a?b:c} [@code{if}]; @samp{=>} [@code{evalto}]. Note that, unlike in usual computer notation, multiplication binds more -strongly than division: @samp{a*b/c*d} is equivalent to +strongly than division: @samp{a*b/c*d} is equivalent to @texline @math{a b \over c d}. @infoline @expr{(a*b)/(c*d)}. @@ -11858,13 +11858,13 @@ next higher level. For example, with @samp{10 20 30 40 50} on the stack and the point on the line containing @samp{30}, @kbd{C-x C-t} creates @samp{10 20 40 30 50}. More generally, @kbd{C-x C-t} acts on the stack objects determined by the current point (and mark) similar -to how the text-mode command @code{transpose-lines} acts on +to how the text-mode command @code{transpose-lines} acts on lines. With argument @var{n}, @kbd{C-x C-t} will move the stack object at the level above the current point and move it past N other objects; for example, with @samp{10 20 30 40 50} on the stack and the point on -the line containing @samp{30}, @kbd{C-u 2 C-x C-t} creates +the line containing @samp{30}, @kbd{C-u 2 C-x C-t} creates @samp{10 40 20 30 50}. With an argument of 0, @kbd{C-x C-t} will switch -the stack objects at the levels determined by the point and the mark. +the stack objects at the levels determined by the point and the mark. @node Editing Stack Entries, Trail Commands, Stack Manipulation, Stack and Trail @section Editing Stack Entries @@ -12056,7 +12056,7 @@ the stack contains the arguments and the result: @samp{2 3 5}. With the exception of keyboard macros, this works for all commands that take arguments off the stack. (To avoid potentially unpleasant behavior, a @kbd{K} prefix before a keyboard macro will be ignored. A @kbd{K} -prefix called @emph{within} the keyboard macro will still take effect.) +prefix called @emph{within} the keyboard macro will still take effect.) As another example, @kbd{K a s} simplifies a formula, pushing the simplified version of the formula onto the stack after the original formula (rather than replacing the original formula). Note that you @@ -12064,7 +12064,7 @@ could get the same effect by typing @kbd{@key{RET} a s}, copying the formula and then simplifying the copy. One difference is that for a very large formula the time taken to format the intermediate copy in @kbd{@key{RET} a s} could be noticeable; @kbd{K a s} would avoid this -extra work. +extra work. Even stack manipulation commands are affected. @key{TAB} works by popping two values and pushing them back in the opposite order, @@ -12155,7 +12155,7 @@ discussion of the @code{calc-settings-file} variable; @pxref{Customizing Calc}. If the file name you give is your user init file (typically @file{~/.emacs}), @kbd{m F} will not automatically load the new file. This is because your user init file may contain other things you don't want -to reread. You can give +to reread. You can give a numeric prefix argument of 1 to @kbd{m F} to force it to read the file no matter what. Conversely, an argument of @mathit{-1} tells @kbd{m F} @emph{not} to read the new file. An argument of 2 or @mathit{-2} @@ -12274,7 +12274,7 @@ corresponding base command (@code{calc-sin} in this case). @pindex calc-option The @kbd{O} key (@code{calc-option}) sets another flag, the @dfn{Option Flag}, which also can alter the subsequent Calc command in -various ways. +various ways. The Inverse, Hyperbolic and Option flags apply only to the next Calculator command, after which they are automatically cleared. (They @@ -12366,7 +12366,7 @@ result cannot be expressed as an integer. In some cases you would rather get an exact fractional answer. One way to accomplish this is to use the @kbd{:} (@code{calc-fdiv}) [@code{fdiv}] command, which divides the two integers on the top of the stack to produce a fraction: -@kbd{6 @key{RET} 4 :} produces @expr{3:2} even though +@kbd{6 @key{RET} 4 :} produces @expr{3:2} even though @kbd{6 @key{RET} 4 /} produces @expr{1.5}. @kindex m f @@ -13155,11 +13155,11 @@ represent the integer and no more. The @kbd{d z} (@code{calc-leading-zeros}) command causes integers to be padded out with leading zeros according to the current binary word size. (@xref{Binary Functions}, for a discussion of word size.) If the absolute value of the word size is @expr{w}, all integers -are displayed with at least enough digits to represent +are displayed with at least enough digits to represent @texline @math{2^w-1} -@infoline @expr{(2^w)-1} +@infoline @expr{(2^w)-1} in the current radix. (Larger integers will still be displayed in their -entirety.) +entirety.) @cindex Two's complements Calc can display @expr{w}-bit integers using two's complement @@ -13181,7 +13181,7 @@ the integers from @expr{0} to are represented by themselves and the integers from @texline @math{-2^{w-1}} @infoline @expr{-2^(w-1)} -to @expr{-1} are represented by the integers from +to @expr{-1} are represented by the integers from @texline @math{2^{w-1}} @infoline @expr{2^(w-1)} to @expr{2^w-1} (the integer @expr{k} is represented by @expr{k+2^w}). @@ -13190,7 +13190,7 @@ Calc will display a two's complement integer by the radix (either representation (including any leading zeros necessary to include all @expr{w} bits). In a two's complement display mode, numbers that are not displayed in two's complement notation (i.e., that aren't -integers from +integers from @texline @math{-2^{w-1}} @infoline @expr{-2^(w-1)} to @@ -14095,13 +14095,13 @@ the @samp{$} sign has the same meaning it always does in algebraic formulas (a reference to an existing entry on the stack). Complex numbers are displayed as in @samp{3 + 4i}. Fractions and -quotients are written using @code{\over} in @TeX{} mode (as in +quotients are written using @code{\over} in @TeX{} mode (as in @code{@{a \over b@}}) and @code{\frac} in La@TeX{} mode (as in @code{\frac@{a@}@{b@}}); binomial coefficients are written with @code{\choose} in @TeX{} mode (as in @code{@{a \choose b@}}) and @code{\binom} in La@TeX{} mode (as in @code{\binom@{a@}@{b@}}). Interval forms are written with @code{\ldots}, and error forms are -written with @code{\pm}. Absolute values are written as in +written with @code{\pm}. Absolute values are written as in @samp{|x + 1|}, and the floor and ceiling functions are written with @code{\lfloor}, @code{\rfloor}, etc. The words @code{\left} and @code{\right} are ignored when reading formulas in @TeX{} and La@TeX{} @@ -14114,10 +14114,10 @@ and La@TeX{} have special names (like @code{\sin}) will use curly braces instead of parentheses for very simple arguments. During input, curly braces and parentheses work equally well for grouping, but when the document is formatted the curly braces will be invisible. Thus the -printed result is +printed result is @texline @math{\sin{2 x}} -@infoline @expr{sin 2x} -but +@infoline @expr{sin 2x} +but @texline @math{\sin(2 + x)}. @infoline @expr{sin(2 + x)}. @@ -14131,7 +14131,7 @@ italic letters in the printed document. If you invoke @kbd{d T} or @kbd{d L} with a positive numeric prefix argument, names of more than one character will instead be enclosed in a protective commands that will prevent them from being typeset in the math italics; they will be -written @samp{\hbox@{@var{name}@}} in @TeX{} mode and +written @samp{\hbox@{@var{name}@}} in @TeX{} mode and @samp{\text@{@var{name}@}} in La@TeX{} mode. The @samp{\hbox@{ @}} and @samp{\text@{ @}} notations are ignored during reading. If you use a negative prefix argument, such function names are @@ -14143,7 +14143,7 @@ any @TeX{} mode.) During reading, text of the form @samp{\matrix@{ ...@: @}} is replaced by @samp{[ ...@: ]}. The same also applies to @code{\pmatrix} and -@code{\bmatrix}. In La@TeX{} mode this also applies to +@code{\bmatrix}. In La@TeX{} mode this also applies to @samp{\begin@{matrix@} ... \end@{matrix@}}, @samp{\begin@{bmatrix@} ... \end@{bmatrix@}}, @samp{\begin@{pmatrix@} ... \end@{pmatrix@}}, as well as @@ -14151,12 +14151,12 @@ by @samp{[ ...@: ]}. The same also applies to @code{\pmatrix} and The symbol @samp{&} is interpreted as a comma, and the symbols @samp{\cr} and @samp{\\} are interpreted as semicolons. During output, matrices are displayed in @samp{\matrix@{ a & b \\ c & d@}} -format in @TeX{} mode and in +format in @TeX{} mode and in @samp{\begin@{pmatrix@} a & b \\ c & d \end@{pmatrix@}} format in La@TeX{} mode; you may need to edit this afterwards to change to your preferred matrix form. If you invoke @kbd{d T} or @kbd{d L} with an argument of 2 or -2, then matrices will be displayed in two-dimensional -form, such as +form, such as @example \begin@{pmatrix@} @@ -14300,25 +14300,25 @@ in Calc, @TeX{}, La@TeX{} and @dfn{eqn} (described in the next section): @example Calc TeX LaTeX eqn ---- --- ----- --- -acute \acute \acute -Acute \Acute +acute \acute \acute +Acute \Acute bar \bar \bar bar Bar \Bar -breve \breve \breve -Breve \Breve -check \check \check -Check \Check +breve \breve \breve +Breve \Breve +check \check \check +Check \Check dddot \dddot ddddot \ddddot dot \dot \dot dot Dot \Dot dotdot \ddot \ddot dotdot -DotDot \Ddot +DotDot \Ddot dyad dyad -grave \grave \grave -Grave \Grave +grave \grave \grave +Grave \Grave hat \hat \hat hat -Hat \Hat +Hat \Hat Prime prime tilde \tilde \tilde tilde Tilde \Tilde @@ -14363,7 +14363,7 @@ reading is: Note that, because these symbols are ignored, reading a @TeX{} or La@TeX{} formula into Calc and writing it back out may lose spacing and -font information. +font information. Also, the ``discretionary multiplication sign'' @samp{\*} is read the same as @samp{*}. @@ -14542,7 +14542,7 @@ are treated the same as curly braces: @samp{sqrt "1+x"} is equivalent to of quotes in @dfn{eqn}, but it is good enough for most uses. Accent codes (@samp{@var{x} dot}) are handled by treating them as -function calls (@samp{dot(@var{x})}) internally. +function calls (@samp{dot(@var{x})}) internally. @xref{TeX and LaTeX Language Modes}, for a table of these accent functions. The @code{prime} accent is treated specially if it occurs on a variable or function name: @samp{f prime prime @w{( x prime )}} is @@ -14572,7 +14572,7 @@ if the matrix justification mode so specifies. The @kbd{d Y} (@code{calc-yacas-language}) command selects the conventions of Yacas, a free computer algebra system. While the operators and functions in Yacas are similar to those of Calc, the names -of built-in functions in Yacas are capitalized. The Calc formula +of built-in functions in Yacas are capitalized. The Calc formula @samp{sin(2 x)}, for example, is entered and displayed @samp{Sin(2 x)} in Yacas mode, and `@samp{arcsin(x^2)} is @samp{ArcSin(x^2)} in Yacas mode. Complex numbers are written are written @samp{3 + 4 I}. @@ -14581,9 +14581,9 @@ The standard special constants are written @code{Pi}, @code{E}, represents both @code{inf} and @code{uinf}, and @code{Undefined} represents @code{nan}. -Certain operators on functions, such as @code{D} for differentiation +Certain operators on functions, such as @code{D} for differentiation and @code{Integrate} for integration, take a prefix form in Yacas. For -example, the derivative of @w{@samp{e^x sin(x)}} can be computed with +example, the derivative of @w{@samp{e^x sin(x)}} can be computed with @w{@samp{D(x) Exp(x)*Sin(x)}}. Other notable differences between Yacas and standard Calc expressions @@ -14602,7 +14602,7 @@ use square brackets. If, for example, @samp{A} represents the list The @kbd{d X} (@code{calc-maxima-language}) command selects the conventions of Maxima, another free computer algebra system. The function names in Maxima are similar, but not always identical, to Calc. -For example, instead of @samp{arcsin(x)}, Maxima will use +For example, instead of @samp{arcsin(x)}, Maxima will use @samp{asin(x)}. Complex numbers are written @samp{3 + 4 %i}. The standard special constants are written @code{%pi}, @code{%e}, @code{%i}, @code{%phi} and @code{%gamma}. In Maxima, @code{inf} means @@ -14610,8 +14610,8 @@ the same as in Calc, but @code{infinity} represents Calc's @code{uinf}. Underscores as well as percent signs are allowed in function and variable names in Maxima mode. The underscore again is equivalent to -the @samp{#} in Normal mode, and the percent sign is equivalent to -@samp{o'o}. +the @samp{#} in Normal mode, and the percent sign is equivalent to +@samp{o'o}. Maxima uses square brackets for lists and vectors, and matrices are written as calls to the function @code{matrix}, given the row vectors of @@ -14629,7 +14629,7 @@ conventions of Giac, another free computer algebra system. The function names in Giac are similar to Maxima. Complex numbers are written @samp{3 + 4 i}. The standard special constants in Giac are the same as in Calc, except that @code{infinity} represents both Calc's @code{inf} -and @code{uinf}. +and @code{uinf}. Underscores are allowed in function and variable names in Giac mode. Brackets are used for subscripts. In Giac, indexing of lists begins at @@ -15786,9 +15786,9 @@ Command is @kbd{m p}. @item Matrix/Scalar mode. Default value is @mathit{-1}. Value is 0 for Scalar mode, @mathit{-2} for Matrix mode, @mathit{-3} for square Matrix mode, -or @var{N} for +or @var{N} for @texline @math{N\times N} -@infoline @var{N}x@var{N} +@infoline @var{N}x@var{N} Matrix mode. Command is @kbd{m v}. @item @@ -16178,7 +16178,7 @@ whereas @w{@samp{[-2 ..@: 3] ^ 2}} is @samp{[0 ..@: 9]}. @mindex @null @end ignore @tindex / -The @kbd{/} (@code{calc-divide}) command divides two numbers. +The @kbd{/} (@code{calc-divide}) command divides two numbers. When combining multiplication and division in an algebraic formula, it is good style to use parentheses to distinguish between possible @@ -16187,7 +16187,7 @@ interpretations; the expression @samp{a/b*c} should be written parentheses, Calc will interpret @samp{a/b*c} as @samp{a/(b*c)}, since in algebraic entry Calc gives division a lower precedence than multiplication. (This is not standard across all computer languages, and -Calc may change the precedence depending on the language mode being used. +Calc may change the precedence depending on the language mode being used. @xref{Language Modes}.) This default ordering can be changed by setting the customizable variable @code{calc-multiplication-has-precedence} to @code{nil} (@pxref{Customizing Calc}); this will give multiplication and @@ -16373,7 +16373,7 @@ all the arguments.) The @kbd{f M} (@code{calc-mant-part}) [@code{mant}] function extracts the ``mantissa'' part @expr{m} of its floating-point argument; @kbd{f X} (@code{calc-xpon-part}) [@code{xpon}] extracts the ``exponent'' part -@expr{e}. The original number is equal to +@expr{e}. The original number is equal to @texline @math{m \times 10^e}, @infoline @expr{m * 10^e}, where @expr{m} is in the interval @samp{[1.0 ..@: 10.0)} except that @@ -16406,9 +16406,9 @@ floating-point numbers, the change is by one unit in the last place. For example, incrementing @samp{12.3456} when the current precision is 6 digits yields @samp{12.3457}. If the current precision had been 8 digits, the result would have been @samp{12.345601}. Incrementing -@samp{0.0} produces +@samp{0.0} produces @texline @math{10^{-p}}, -@infoline @expr{10^-p}, +@infoline @expr{10^-p}, where @expr{p} is the current precision. These operations are defined only on integers and floats. With numeric prefix arguments, they change the number by @expr{n} units. @@ -16852,7 +16852,7 @@ The last two arguments default to zero if omitted. The @kbd{t J} (@code{calc-julian}) [@code{julian}] command converts a date form into a Julian day count, which is the number of days since noon (GMT) on Jan 1, 4713 BC. A pure date is converted to an -integer Julian count representing noon of that day. A date/time form +integer Julian count representing noon of that day. A date/time form is converted to an exact floating-point Julian count, adjusted to interpret the date form in the current time zone but the Julian day count in Greenwich Mean Time. A numeric prefix argument allows @@ -17294,12 +17294,12 @@ With no arguments, @code{calc-time-zone} or @samp{tzone()} will by default get the time zone and daylight saving information from the calendar (@pxref{Daylight Saving,Calendar/Diary,The Calendar and the Diary, emacs,The GNU Emacs Manual}). To use a different time zone, or if the -calendar does not give the desired result, you can set the Calc variable +calendar does not give the desired result, you can set the Calc variable @code{TimeZone} (which is by default @code{nil}) to an appropriate time zone name. (The easiest way to do this is to edit the @code{TimeZone} variable using Calc's @kbd{s T} command, then use the @kbd{s p} (@code{calc-permanent-variable}) command to save the value of -@code{TimeZone} permanently.) +@code{TimeZone} permanently.) If the time zone given by @code{TimeZone} is a generalized time zone, e.g., @code{EGT}, Calc examines the date being converted to tell whether to use standard or daylight saving time. But if the current time zone @@ -17311,12 +17311,12 @@ from the calendar. The @kbd{t J} and @code{t U} commands with no numeric prefix arguments do the same thing as @samp{tzone()}; namely, use the -information from the calendar if @code{TimeZone} is @code{nil}, +information from the calendar if @code{TimeZone} is @code{nil}, otherwise use the time zone given by @code{TimeZone}. @vindex math-daylight-savings-hook @findex math-std-daylight-savings -When Calc computes the daylight saving information itself (i.e., when +When Calc computes the daylight saving information itself (i.e., when the @code{TimeZone} variable is set), it will by default consider daylight saving time to begin at 2 a.m.@: on the second Sunday of March (for years from 2007 on) or on the last Sunday in April (for years @@ -17392,7 +17392,7 @@ falls in this hour results in a time value for the following hour, from 3 a.m.@: to 4 a.m. At the end of daylight saving time, the hour from 1 a.m.@: to 2 a.m.@: repeats itself; converting a date/time form that falls in this hour results in a time value for the first -manifestation of that time (@emph{not} the one that occurs one hour +manifestation of that time (@emph{not} the one that occurs one hour later). If @code{math-daylight-savings-hook} is @code{nil}, then the @@ -17995,12 +17995,12 @@ particular, negative arguments are converted to positive integers modulo @expr{2^w} by all binary functions. If the word size is negative, binary operations produce twos-complement -integers from +integers from @texline @math{-2^{-w-1}} -@infoline @expr{-(2^(-w-1))} -to +@infoline @expr{-(2^(-w-1))} +to @texline @math{2^{-w-1}-1} -@infoline @expr{2^(-w-1)-1} +@infoline @expr{2^(-w-1)-1} inclusive. Either mode accepts inputs in any range; the sign of @expr{w} affects only the results produced. @@ -18182,13 +18182,13 @@ flag keys must be used to get some of these functions from the keyboard. One miscellaneous command is shift-@kbd{P} (@code{calc-pi}), which pushes the value of @cpi{} (at the current precision) onto the stack. With the Hyperbolic flag, it pushes the value @expr{e}, the base of natural logarithms. -With the Inverse flag, it pushes Euler's constant +With the Inverse flag, it pushes Euler's constant @texline @math{\gamma} -@infoline @expr{gamma} +@infoline @expr{gamma} (about 0.5772). With both Inverse and Hyperbolic, it -pushes the ``golden ratio'' +pushes the ``golden ratio'' @texline @math{\phi} -@infoline @expr{phi} +@infoline @expr{phi} (about 1.618). (At present, Euler's constant is not available to unlimited precision; Calc knows only the first 100 digits.) In Symbolic mode, these commands push the @@ -18266,7 +18266,7 @@ The @kbd{H L} (@code{calc-log10}) [@code{log10}] command computes the common (base-10) logarithm of a number. (With the Inverse flag [@code{exp10}], it raises ten to a given power.) Note that the common logarithm of a complex number is computed by taking the natural logarithm and dividing -by +by @texline @math{\ln10}. @infoline @expr{ln(10)}. @@ -18278,7 +18278,7 @@ by The @kbd{B} (@code{calc-log}) [@code{log}] command computes a logarithm to any base. For example, @kbd{1024 @key{RET} 2 B} produces 10, since @texline @math{2^{10} = 1024}. -@infoline @expr{2^10 = 1024}. +@infoline @expr{2^10 = 1024}. In certain cases like @samp{log(3,9)}, the result will be either @expr{1:2} or @expr{0.5} depending on the current Fraction mode setting. With the Inverse flag [@code{alog}], this command is @@ -18300,11 +18300,11 @@ integer arithmetic is used; otherwise, this is equivalent to @tindex expm1 The @kbd{f E} (@code{calc-expm1}) [@code{expm1}] command computes @texline @math{e^x - 1}, -@infoline @expr{exp(x)-1}, +@infoline @expr{exp(x)-1}, but using an algorithm that produces a more accurate -answer when the result is close to zero, i.e., when +answer when the result is close to zero, i.e., when @texline @math{e^x} -@infoline @expr{exp(x)} +@infoline @expr{exp(x)} is close to one. @kindex f L @@ -18312,7 +18312,7 @@ is close to one. @tindex lnp1 The @kbd{f L} (@code{calc-lnp1}) [@code{lnp1}] command computes @texline @math{\ln(x+1)}, -@infoline @expr{ln(x+1)}, +@infoline @expr{ln(x+1)}, producing a more accurate answer when @expr{x} is close to zero. @node Trigonometric and Hyperbolic Functions, Advanced Math Functions, Logarithmic Functions, Scientific Functions @@ -18515,9 +18515,9 @@ The @kbd{f g} (@code{calc-gamma}) [@code{gamma}] command computes the Euler gamma function. For positive integer arguments, this is related to the factorial function: @samp{gamma(n+1) = fact(n)}. For general complex arguments the gamma function can be defined by the following definite -integral: +integral: @texline @math{\Gamma(a) = \int_0^\infty t^{a-1} e^t dt}. -@infoline @expr{gamma(a) = integ(t^(a-1) exp(t), t, 0, inf)}. +@infoline @expr{gamma(a) = integ(t^(a-1) exp(t), t, 0, inf)}. (The actual implementation uses far more efficient computational methods.) @kindex f G @@ -18549,7 +18549,7 @@ integral: @tindex gammaG The @kbd{f G} (@code{calc-inc-gamma}) [@code{gammaP}] command computes the incomplete gamma function, denoted @samp{P(a,x)}. This is defined by -the integral, +the integral, @texline @math{P(a,x) = \left( \int_0^x t^{a-1} e^t dt \right) / \Gamma(a)}. @infoline @expr{gammaP(a,x) = integ(t^(a-1) exp(t), t, 0, x) / gamma(a)}. This implies that @samp{gammaP(a,inf) = 1} for any @expr{a} (see the @@ -18583,7 +18583,7 @@ You can obtain these using the \kbd{H f G} [\code{gammag}] and The @kbd{f b} (@code{calc-beta}) [@code{beta}] command computes the Euler beta function, which is defined in terms of the gamma function as @texline @math{B(a,b) = \Gamma(a) \Gamma(b) / \Gamma(a+b)}, -@infoline @expr{beta(a,b) = gamma(a) gamma(b) / gamma(a+b)}, +@infoline @expr{beta(a,b) = gamma(a) gamma(b) / gamma(a+b)}, or by @texline @math{B(a,b) = \int_0^1 t^{a-1} (1-t)^{b-1} dt}. @infoline @expr{beta(a,b) = integ(t^(a-1) (1-t)^(b-1), t, 0, 1)}. @@ -18606,7 +18606,7 @@ un-normalized version [@code{betaB}]. @tindex erf @tindex erfc The @kbd{f e} (@code{calc-erf}) [@code{erf}] command computes the -error function +error function @texline @math{\hbox{erf}(x) = {2 \over \sqrt{\pi}} \int_0^x e^{-t^2} dt}. @infoline @expr{erf(x) = 2 integ(exp(-(t^2)), t, 0, x) / sqrt(pi)}. The complementary error function @kbd{I f e} (@code{calc-erfc}) [@code{erfc}] @@ -18784,9 +18784,9 @@ The @kbd{k r} (@code{calc-random}) [@code{random}] command produces random numbers of various sorts. Given a positive numeric prefix argument @expr{M}, it produces a random -integer @expr{N} in the range +integer @expr{N} in the range @texline @math{0 \le N < M}. -@infoline @expr{0 <= N < M}. +@infoline @expr{0 <= N < M}. Each possible value @expr{N} appears with equal probability. With no numeric prefix argument, the @kbd{k r} command takes its argument @@ -18794,17 +18794,17 @@ from the stack instead. Once again, if this is a positive integer @expr{M} the result is a random integer less than @expr{M}. However, note that while numeric prefix arguments are limited to six digits or so, an @expr{M} taken from the stack can be arbitrarily large. If @expr{M} is negative, -the result is a random integer in the range +the result is a random integer in the range @texline @math{M < N \le 0}. @infoline @expr{M < N <= 0}. If the value on the stack is a floating-point number @expr{M}, the result -is a random floating-point number @expr{N} in the range +is a random floating-point number @expr{N} in the range @texline @math{0 \le N < M} @infoline @expr{0 <= N < M} -or +or @texline @math{M < N \le 0}, -@infoline @expr{M < N <= 0}, +@infoline @expr{M < N <= 0}, according to the sign of @expr{M}. If @expr{M} is zero, the result is a Gaussian-distributed random real @@ -18812,14 +18812,14 @@ number; the distribution has a mean of zero and a standard deviation of one. The algorithm used generates random numbers in pairs; thus, every other call to this function will be especially fast. -If @expr{M} is an error form +If @expr{M} is an error form @texline @math{m} @code{+/-} @math{\sigma} -@infoline @samp{m +/- s} -where @var{m} and +@infoline @samp{m +/- s} +where @var{m} and @texline @math{\sigma} -@infoline @var{s} +@infoline @var{s} are both real numbers, the result uses a Gaussian distribution with mean -@var{m} and standard deviation +@var{m} and standard deviation @texline @math{\sigma}. @infoline @var{s}. @@ -18932,9 +18932,9 @@ generators that are typically used to implement @code{random}. If @code{RandSeed} contains an integer, Calc uses this integer to seed an ``additive congruential'' method (Knuth's algorithm 3.2.2A, -computing +computing @texline @math{X_{n-55} - X_{n-24}}. -@infoline @expr{X_n-55 - X_n-24}). +@infoline @expr{X_n-55 - X_n-24}). This method expands the seed value into a large table which is maintained internally; the variable @code{RandSeed} is changed from, e.g., 42 to the vector @expr{[42]} @@ -18970,18 +18970,18 @@ value. To create a random floating-point number with precision @var{p}, Calc simply creates a random @var{p}-digit integer and multiplies by @texline @math{10^{-p}}. -@infoline @expr{10^-p}. +@infoline @expr{10^-p}. The resulting random numbers should be very clean, but note that relatively small numbers will have few significant random digits. In other words, with a precision of 12, you will occasionally get -numbers on the order of +numbers on the order of @texline @math{10^{-9}} -@infoline @expr{10^-9} -or +@infoline @expr{10^-9} +or @texline @math{10^{-10}}, -@infoline @expr{10^-10}, +@infoline @expr{10^-10}, but those numbers will only have two or three random digits since they -correspond to small integers times +correspond to small integers times @texline @math{10^{-12}}. @infoline @expr{10^-12}. @@ -19032,7 +19032,7 @@ numbers. @tindex egcd The @kbd{k E} (@code{calc-extended-gcd}) [@code{egcd}] command computes the GCD of two integers @expr{x} and @expr{y} and returns a vector -@expr{[g, a, b]} where +@expr{[g, a, b]} where @texline @math{g = \gcd(x,y) = a x + b y}. @infoline @expr{g = gcd(x,y) = a x + b y}. @@ -19119,11 +19119,11 @@ functions. @tindex stir1 @tindex stir2 The @kbd{k s} (@code{calc-stirling-number}) [@code{stir1}] command -computes a Stirling number of the first +computes a Stirling number of the first @texline kind@tie{}@math{n \brack m}, @infoline kind, given two integers @expr{n} and @expr{m} on the stack. The @kbd{H k s} -[@code{stir2}] command computes a Stirling number of the second +[@code{stir2}] command computes a Stirling number of the second @texline kind@tie{}@math{n \brace m}. @infoline kind. These are the number of @expr{m}-cycle permutations of @expr{n} objects, @@ -19202,7 +19202,7 @@ analogously finds the next prime less than a given number. @pindex calc-totient @tindex totient The @kbd{k t} (@code{calc-totient}) [@code{totient}] command computes the -Euler ``totient'' +Euler ``totient'' @texline function@tie{}@math{\phi(n)}, @infoline function, the number of integers less than @expr{n} which @@ -19277,7 +19277,7 @@ recover the original arguments but substitute a new value for @expr{x}.) @tindex ltpc The @samp{utpc(x,v)} function uses the chi-square distribution with @texline @math{\nu} -@infoline @expr{v} +@infoline @expr{v} degrees of freedom. It is the probability that a model is correct if its chi-square statistic is @expr{x}. @@ -19293,10 +19293,10 @@ correct if its chi-square statistic is @expr{x}. @end ignore @tindex ltpf The @samp{utpf(F,v1,v2)} function uses the F distribution, used in -various statistical tests. The parameters +various statistical tests. The parameters @texline @math{\nu_1} -@infoline @expr{v1} -and +@infoline @expr{v1} +and @texline @math{\nu_2} @infoline @expr{v2} are the degrees of freedom in the numerator and denominator, @@ -19314,9 +19314,9 @@ respectively, used in computing the statistic @expr{F}. @end ignore @tindex ltpn The @samp{utpn(x,m,s)} function uses a normal (Gaussian) distribution -with mean @expr{m} and standard deviation +with mean @expr{m} and standard deviation @texline @math{\sigma}. -@infoline @expr{s}. +@infoline @expr{s}. It is the probability that such a normal-distributed random variable would exceed @expr{x}. @@ -19347,20 +19347,20 @@ Poisson random events will occur. @end ignore @tindex ltpt The @samp{utpt(t,v)} function uses the Student's ``t'' distribution -with +with @texline @math{\nu} -@infoline @expr{v} +@infoline @expr{v} degrees of freedom. It is the probability that a t-distributed random variable will be greater than @expr{t}. -(Note: This computes the distribution function +(Note: This computes the distribution function @texline @math{A(t|\nu)} @infoline @expr{A(t|v)} -where +where @texline @math{A(0|\nu) = 1} -@infoline @expr{A(0|v) = 1} -and +@infoline @expr{A(0|v) = 1} +and @texline @math{A(\infty|\nu) \to 0}. -@infoline @expr{A(inf|v) -> 0}. +@infoline @expr{A(inf|v) -> 0}. The @code{UTPT} operation on the HP-48 uses a different definition which returns half of Calc's value: @samp{UTPT(t,v) = .5*utpt(t,v)}.) @@ -19670,7 +19670,7 @@ prefix, if specified, must match the size of the vector. If the value on the stack is a scalar, it is used for each element on the diagonal, and the prefix argument is required. -To build a constant square matrix, e.g., a +To build a constant square matrix, e.g., a @texline @math{3\times3} @infoline 3x3 matrix filled with ones, use @kbd{0 M-3 v d 1 +}, i.e., build a zero @@ -19911,7 +19911,7 @@ command. With the Hyperbolic flag, @kbd{H v l} [@code{mdims}] computes a vector of the dimensions of a vector, matrix, or higher-order object. For example, @samp{mdims([[a,b,c],[d,e,f]])} returns @samp{[2, 3]} since -its argument is a +its argument is a @texline @math{2\times3} @infoline 2x3 matrix. @@ -19945,17 +19945,17 @@ If the number of columns does not evenly divide the number of elements in the vector, the last row will be short and the result will not be suitable for use as a matrix. For example, with the matrix @samp{[[1, 2], @w{[3, 4]}]} on the stack, @kbd{v a 4} produces -@samp{[[1, 2, 3, 4]]} (a +@samp{[[1, 2, 3, 4]]} (a @texline @math{1\times4} @infoline 1x4 -matrix), @kbd{v a 1} produces @samp{[[1], [2], [3], [4]]} (a +matrix), @kbd{v a 1} produces @samp{[[1], [2], [3], [4]]} (a @texline @math{4\times1} @infoline 4x1 -matrix), @kbd{v a 2} produces @samp{[[1, 2], [3, 4]]} (the original +matrix), @kbd{v a 2} produces @samp{[[1, 2], [3, 4]]} (the original @texline @math{2\times2} @infoline 2x2 matrix), @w{@kbd{v a 3}} produces @samp{[[1, 2, 3], [4]]} (not a -matrix), and @kbd{v a 0} produces the flattened list +matrix), and @kbd{v a 0} produces the flattened list @samp{[1, 2, @w{3, 4}]}. @cindex Sorting data @@ -20040,9 +20040,9 @@ If no prefix is given, then you will be prompted for a vector which will be used to determine the bins. (If a positive integer is given at this prompt, it will be still treated as if it were given as a prefix.) Each bin will consist of the interval of numbers closest to -the corresponding number of this new vector; if the vector -@expr{[a, b, c, ...]} is entered at the prompt, the bins will be -@expr{(-inf, (a+b)/2]}, @expr{((a+b)/2, (b+c)/2]}, etc. The result of +the corresponding number of this new vector; if the vector +@expr{[a, b, c, ...]} is entered at the prompt, the bins will be +@expr{(-inf, (a+b)/2]}, @expr{((a+b)/2, (b+c)/2]}, etc. The result of this command will be a vector counting how many elements of the original vector are in each bin. @@ -20313,10 +20313,10 @@ and only if it is in both of the input sets. Thus if the input sets are disjoint, i.e., if they share no common elements, the result will be the empty vector @samp{[]}. Note that the characters @kbd{V} and @kbd{^} were chosen to be close to the conventional mathematical -notation for set +notation for set @texline union@tie{}(@math{A \cup B}) @infoline union -and +and @texline intersection@tie{}(@math{A \cap B}). @infoline intersection. @@ -20432,7 +20432,7 @@ the same set. The set may include positive infinity, but must not include any negative numbers. The input is interpreted as a set of integers in the sense of @kbd{V F} (@code{vfloor}). Beware that a simple input like @samp{[100]} can result in a huge integer -representation +representation @texline (@math{2^{100}}, a 31-digit integer, in this case). @infoline (@expr{2^100}, a 31-digit integer, in this case). @@ -20544,10 +20544,10 @@ plus or minus infinity. @cindex Mean of data values The @kbd{u M} (@code{calc-vector-mean}) [@code{vmean}] command computes the average (arithmetic mean) of the data values. -If the inputs are error forms +If the inputs are error forms @texline @math{x \pm \sigma}, -@infoline @samp{x +/- s}, -this is the weighted mean of the @expr{x} values with weights +@infoline @samp{x +/- s}, +this is the weighted mean of the @expr{x} values with weights @texline @math{1 /\sigma^2}. @infoline @expr{1 / s^2}. @tex @@ -20558,9 +20558,9 @@ If the inputs are not error forms, this is simply the sum of the values divided by the count of the values. Note that a plain number can be considered an error form with -error +error @texline @math{\sigma = 0}. -@infoline @expr{s = 0}. +@infoline @expr{s = 0}. If the input to @kbd{u M} is a mixture of plain numbers and error forms, the result is the mean of the plain numbers, ignoring all values with non-zero errors. (By the @@ -20662,7 +20662,7 @@ for a vector of numbers simply by using the @kbd{A} command. @cindex Standard deviation @cindex Sample statistics The @kbd{u S} (@code{calc-vector-sdev}) [@code{vsdev}] command -computes the standard +computes the standard @texline deviation@tie{}@math{\sigma} @infoline deviation of the data values. If the values are error forms, the errors are used @@ -20677,9 +20677,9 @@ $$ \sigma^2 = {1 \over N - 1} \sum (x_i - \mu)^2 $$ This function also applies to distributions. The standard deviation of a single error form is simply the error part. The standard deviation of a continuous interval happens to equal the difference between the -limits, divided by +limits, divided by @texline @math{\sqrt{12}}. -@infoline @expr{sqrt(12)}. +@infoline @expr{sqrt(12)}. The standard deviation of an integer interval is the same as the standard deviation of a vector of those integers. @@ -20714,7 +20714,7 @@ population standard deviation of the equivalent vector of integers. The @kbd{H u S} (@code{calc-vector-variance}) [@code{vvar}] and @kbd{H I u S} (@code{calc-vector-pop-variance}) [@code{vpvar}] commands compute the variance of the data values. The variance -is the +is the @texline square@tie{}@math{\sigma^2} @infoline square of the standard deviation, i.e., the sum of the @@ -20738,7 +20738,7 @@ The functions in this section take two arguments, which must be vectors of equal size. The vectors are each flattened in the same way as by the single-variable statistical functions. Given a numeric prefix argument of 1, these functions instead take one object from -the stack, which must be an +the stack, which must be an @texline @math{N\times2} @infoline Nx2 matrix of data values. Once again, variable names can be used in place @@ -20996,7 +20996,7 @@ be prompted for the number of arguments to use. If any argument to @kbd{V M} is a matrix, the operator is normally mapped across all elements of the matrix. For example, given the matrix @expr{[[1, -2, 3], [-4, 5, -6]]}, @kbd{V M A} takes six absolute values to -produce another +produce another @texline @math{3\times2} @infoline 3x2 matrix, @expr{[[1, 2, 3], [4, 5, 6]]}. @@ -21612,8 +21612,8 @@ entire four-term sum. @pindex calc-break-selections The @kbd{j b} (@code{calc-break-selections}) command controls a mode in which the ``deep structure'' of these associative formulas shows -through. Calc actually stores the above formulas as -@samp{((a + b) - c) + d} and @samp{x * (y * z)}. (Note that for certain +through. Calc actually stores the above formulas as +@samp{((a + b) - c) + d} and @samp{x * (y * z)}. (Note that for certain obscure reasons, by default Calc treats multiplication as right-associative.) Once you have enabled @kbd{j b} mode, selecting with the cursor on the @samp{-} sign would only select the @samp{a + b - @@ -22098,7 +22098,7 @@ of a quotient you can call it with a zero prefix: @kbd{C-u 0 j *}. For example, if the formula on the stack is @samp{1 / (sqrt(a) + 1)}, you may wish to eliminate the square root in the denominator by multiplying the top and bottom by @samp{sqrt(a) - 1}. If you did this simply by using -a simple @kbd{j *} command, you would get +a simple @kbd{j *} command, you would get @samp{(sqrt(a)-1)/ (sqrt(a) (sqrt(a) - 1) + sqrt(a) - 1)}. Instead, you would probably want to use @kbd{C-u 0 j *}, which would expand the bottom and give you the desired result @samp{(sqrt(a)-1)/(a-1)}. More @@ -22405,7 +22405,7 @@ The most basic default simplification is the evaluation of functions. For example, @expr{2 + 3} is evaluated to @expr{5}, and @expr{@tfn{sqrt}(9)} is evaluated to @expr{3}. Evaluation does not occur if the arguments to a function are somehow of the wrong type @expr{@tfn{tan}([2,3,4])}), -range (@expr{@tfn{tan}(90)}), or number (@expr{@tfn{tan}(3,5)}), +range (@expr{@tfn{tan}(90)}), or number (@expr{@tfn{tan}(3,5)}), or if the function name is not recognized (@expr{@tfn{f}(5)}), or if Symbolic mode (@pxref{Symbolic Mode}) prevents evaluation (@expr{@tfn{sqrt}(2)}). @@ -22452,7 +22452,7 @@ Arithmetic operators like @kbd{+} and @kbd{*} always take two arguments in Calc's internal form. Sums and products of three or more terms are arranged by the associative law of algebra into a left-associative form for sums, @expr{((a + b) + c) + d}, and -(by default) a right-associative form for products, +(by default) a right-associative form for products, @expr{a * (b * (c * d))}. Formulas like @expr{(a + b) + (c + d)} are rearranged to left-associative form, though this rarely matters since Calc's algebra commands are designed to hide the inner structure of sums @@ -22533,7 +22533,7 @@ The product @expr{a (b + c)} is distributed over the sum only if rewritten to @expr{a (c - b)}. The distributive law of products and powers is used for adjacent -terms of the product: @expr{x^a x^b} goes to +terms of the product: @expr{x^a x^b} goes to @texline @math{x^{a+b}} @infoline @expr{x^(a+b)} where @expr{a} is a number, or an implicit 1 (as in @expr{x}), @@ -22544,9 +22544,9 @@ If the sum of the powers is zero, the product is simplified to @expr{1} or to @samp{idn(1)} if Matrix mode is enabled. The product of a negative power times anything but another negative -power is changed to use division: +power is changed to use division: @texline @math{x^{-2} y} -@infoline @expr{x^(-2) y} +@infoline @expr{x^(-2) y} goes to @expr{y / x^2} unless Matrix mode is in effect and neither @expr{x} nor @expr{y} are scalar (in which case it is considered unsafe to rearrange the order of the terms). @@ -22568,13 +22568,13 @@ The quotient @expr{x / 0} is left unsimplified or changed to an infinite quantity, as directed by the current infinite mode. @xref{Infinite Mode}. -The expression +The expression @texline @math{a / b^{-c}} -@infoline @expr{a / b^(-c)} +@infoline @expr{a / b^(-c)} is changed to @expr{a b^c}, where @expr{-c} is any negative-looking -power. Also, @expr{1 / b^c} is changed to +power. Also, @expr{1 / b^c} is changed to @texline @math{b^{-c}} -@infoline @expr{b^(-c)} +@infoline @expr{b^(-c)} for any power @expr{c}. Also, @expr{(-a) / b} and @expr{a / (-b)} go to @expr{-(a/b)}; @@ -22614,22 +22614,22 @@ are distributed to @expr{a^c b^c}, @expr{a^c / b^c} only if @expr{c} is an integer, or if either @expr{a} or @expr{b} are nonnegative real numbers. Powers of powers @expr{(a^b)^c} are simplified to @texline @math{a^{b c}} -@infoline @expr{a^(b c)} +@infoline @expr{a^(b c)} only when @expr{c} is an integer and @expr{b c} also evaluates to an integer. Without these restrictions these simplifications would not be safe because of problems with principal values. -(In other words, +(In other words, @texline @math{((-3)^{1/2})^2} -@infoline @expr{((-3)^1:2)^2} +@infoline @expr{((-3)^1:2)^2} is safe to simplify, but @texline @math{((-3)^2)^{1/2}} -@infoline @expr{((-3)^2)^1:2} +@infoline @expr{((-3)^2)^1:2} is not.) @xref{Declarations}, for ways to inform Calc that your variables satisfy these requirements. As a special case of this rule, @expr{@tfn{sqrt}(x)^n} is simplified to @texline @math{x^{n/2}} -@infoline @expr{x^(n/2)} +@infoline @expr{x^(n/2)} only for even integers @expr{n}. If @expr{a} is known to be real, @expr{b} is an even integer, and @@ -22642,13 +22642,13 @@ for any negative-looking expression @expr{-a}. Square roots @expr{@tfn{sqrt}(x)} generally act like one-half powers @texline @math{x^{1:2}} -@infoline @expr{x^1:2} +@infoline @expr{x^1:2} for the purposes of the above-listed simplifications. -Also, note that +Also, note that @texline @math{1 / x^{1:2}} -@infoline @expr{1 / x^1:2} -is changed to +@infoline @expr{1 / x^1:2} +is changed to @texline @math{x^{-1:2}}, @infoline @expr{x^(-1:2)}, but @expr{1 / @tfn{sqrt}(x)} is left alone. @@ -22660,9 +22660,9 @@ but @expr{1 / @tfn{sqrt}(x)} is left alone. Generic identity matrices (@pxref{Matrix Mode}) are simplified by the following rules: @expr{@tfn{idn}(a) + b} to @expr{a + b} if @expr{b} is provably scalar, or expanded out if @expr{b} is a matrix; -@expr{@tfn{idn}(a) + @tfn{idn}(b)} to @expr{@tfn{idn}(a + b)}; -@expr{-@tfn{idn}(a)} to @expr{@tfn{idn}(-a)}; @expr{a @tfn{idn}(b)} to -@expr{@tfn{idn}(a b)} if @expr{a} is provably scalar, or to @expr{a b} +@expr{@tfn{idn}(a) + @tfn{idn}(b)} to @expr{@tfn{idn}(a + b)}; +@expr{-@tfn{idn}(a)} to @expr{@tfn{idn}(-a)}; @expr{a @tfn{idn}(b)} to +@expr{@tfn{idn}(a b)} if @expr{a} is provably scalar, or to @expr{a b} if @expr{a} is provably non-scalar; @expr{@tfn{idn}(a) @tfn{idn}(b)} to @expr{@tfn{idn}(a b)}; analogous simplifications for quotients involving @code{idn}; and @expr{@tfn{idn}(a)^n} to @expr{@tfn{idn}(a^n)} where @@ -22683,7 +22683,7 @@ The expression @expr{@tfn{abs}(-x)} changes to @expr{@tfn{abs}(x)}. The expression @expr{@tfn{abs}(@tfn{abs}(x))} changes to @expr{@tfn{abs}(x)}; in fact, @expr{@tfn{abs}(x)} changes to @expr{x} or @expr{-x} if @expr{x} is provably nonnegative or nonpositive -(@pxref{Declarations}). +(@pxref{Declarations}). While most functions do not recognize the variable @code{i} as an imaginary number, the @code{arg} function does handle the two cases @@ -22693,7 +22693,7 @@ The expression @expr{@tfn{conj}(@tfn{conj}(x))} simplifies to @expr{x}. Various other expressions involving @code{conj}, @code{re}, and @code{im} are simplified, especially if some of the arguments are provably real or involve the constant @code{i}. For example, -@expr{@tfn{conj}(a + b i)} is changed to +@expr{@tfn{conj}(a + b i)} is changed to @expr{@tfn{conj}(a) - @tfn{conj}(b) i}, or to @expr{a - b i} if @expr{a} and @expr{b} are known to be real. @@ -22836,7 +22836,7 @@ several ways. (Note that these will be left unevaluated only in Symbolic mode.) First, square integer or rational factors are pulled out so that @expr{@tfn{sqrt}(8)} is rewritten as @texline @math{2\,@tfn{sqrt}(2)}. -@infoline @expr{2 sqrt(2)}. +@infoline @expr{2 sqrt(2)}. Conceptually speaking this implies factoring the argument into primes and moving pairs of primes out of the square root, but for reasons of efficiency Calc only looks for primes up to 29. @@ -22879,7 +22879,7 @@ declared to be an integer. Trigonometric functions are simplified in several ways. Whenever a products of two trigonometric functions can be replaced by a single function, the replacement is made; for example, -@expr{@tfn{tan}(x) @tfn{cos}(x)} is simplified to @expr{@tfn{sin}(x)}. +@expr{@tfn{tan}(x) @tfn{cos}(x)} is simplified to @expr{@tfn{sin}(x)}. Reciprocals of trigonometric functions are replaced by their reciprocal function; for example, @expr{1/@tfn{sec}(x)} is simplified to @expr{@tfn{cos}(x)}. The corresponding simplifications for the @@ -22887,7 +22887,7 @@ hyperbolic functions are also handled. Trigonometric functions of their inverse functions are simplified. The expression @expr{@tfn{sin}(@tfn{arcsin}(x))} is -simplified to @expr{x}, and similarly for @code{cos} and @code{tan}. +simplified to @expr{x}, and similarly for @code{cos} and @code{tan}. Trigonometric functions of inverses of different trigonometric functions can also be simplified, as in @expr{@tfn{sin}(@tfn{arccos}(x))} to @expr{@tfn{sqrt}(1 - x^2)}. @@ -22905,30 +22905,30 @@ No simplifications for inverse trigonometric and hyperbolic functions are known, except for negative arguments of @code{arcsin}, @code{arctan}, @code{arcsinh}, and @code{arctanh}. Note that @expr{@tfn{arcsin}(@tfn{sin}(x))} can @emph{not} safely change to -@expr{x}, since this only correct within an integer multiple of +@expr{x}, since this only correct within an integer multiple of @texline @math{2 \pi} -@infoline @expr{2 pi} +@infoline @expr{2 pi} radians or 360 degrees. However, @expr{@tfn{arcsinh}(@tfn{sinh}(x))} is simplified to @expr{x} if @expr{x} is known to be real. Several simplifications that apply to logarithms and exponentials -are that @expr{@tfn{exp}(@tfn{ln}(x))}, +are that @expr{@tfn{exp}(@tfn{ln}(x))}, @texline @tfn{e}@math{^{\ln(x)}}, -@infoline @expr{e^@tfn{ln}(x)}, +@infoline @expr{e^@tfn{ln}(x)}, and @texline @math{10^{{\rm log10}(x)}} -@infoline @expr{10^@tfn{log10}(x)} +@infoline @expr{10^@tfn{log10}(x)} all reduce to @expr{x}. Also, @expr{@tfn{ln}(@tfn{exp}(x))}, etc., can reduce to @expr{x} if @expr{x} is provably real. The form @expr{@tfn{exp}(x)^y} is simplified to @expr{@tfn{exp}(x y)}. If @expr{x} -is a suitable multiple of -@texline @math{\pi i} +is a suitable multiple of +@texline @math{\pi i} @infoline @expr{pi i} (as described above for the trigonometric functions), then @expr{@tfn{exp}(x)} or @expr{e^x} will be expanded. Finally, @expr{@tfn{ln}(x)} is simplified to a form involving @code{pi} and @code{i} where @expr{x} is provably negative, positive imaginary, or -negative imaginary. +negative imaginary. The error functions @code{erf} and @code{erfc} are simplified when their arguments are negative-looking or are calls to the @code{conj} @@ -23006,18 +23006,18 @@ values of @expr{x} in a certain range; outside that range, values are folded down to the 360-degree range that the inverse trigonometric functions always produce. -Powers of powers @expr{(x^a)^b} are simplified to +Powers of powers @expr{(x^a)^b} are simplified to @texline @math{x^{a b}} @infoline @expr{x^(a b)} for all @expr{a} and @expr{b}. These results will be valid only -in a restricted range of @expr{x}; for example, in +in a restricted range of @expr{x}; for example, in @texline @math{(x^2)^{1:2}} @infoline @expr{(x^2)^1:2} the powers cancel to get @expr{x}, which is valid for positive values of @expr{x} but not for negative or complex values. Similarly, @expr{@tfn{sqrt}(x^a)} and @expr{@tfn{sqrt}(x)^a} are both -simplified (possibly unsafely) to +simplified (possibly unsafely) to @texline @math{x^{a/2}}. @infoline @expr{x^(a/2)}. @@ -23027,7 +23027,7 @@ Forms like @expr{@tfn{sqrt}(1 - sin(x)^2)} are simplified to, e.g., Arguments of square roots are partially factored to look for squared terms that can be extracted. For example, -@expr{@tfn{sqrt}(a^2 b^3 + a^3 b^2)} simplifies to +@expr{@tfn{sqrt}(a^2 b^3 + a^3 b^2)} simplifies to @expr{a b @tfn{sqrt}(a+b)}. The simplifications of @expr{@tfn{ln}(@tfn{exp}(x))}, @@ -23093,9 +23093,9 @@ number for an answer, then the quotient simplifies to that number. For powers and square roots, the ``unsafe'' simplifications @expr{(a b)^c} to @expr{a^c b^c}, @expr{(a/b)^c} to @expr{a^c / b^c}, -and @expr{(a^b)^c} to +and @expr{(a^b)^c} to @texline @math{a^{b c}} -@infoline @expr{a^(b c)} +@infoline @expr{a^(b c)} are done if the powers are real numbers. (These are safe in the context of units because all numbers involved can reasonably be assumed to be real.) @@ -23108,12 +23108,12 @@ according to the previous paragraph. For example, @samp{acre^1.5} is simplified by noting that @expr{1.5 = 3:2}, that @samp{acre} is defined in terms of @samp{m^2}, and that the 2 in the power of @code{m} is a multiple of 2 in @expr{3:2}. Thus, @code{acre^1.5} is -replaced by approximately +replaced by approximately @texline @math{(4046 m^2)^{1.5}} -@infoline @expr{(4046 m^2)^1.5}, -which is then changed to +@infoline @expr{(4046 m^2)^1.5}, +which is then changed to @texline @math{4046^{1.5} \, (m^2)^{1.5}}, -@infoline @expr{4046^1.5 (m^2)^1.5}, +@infoline @expr{4046^1.5 (m^2)^1.5}, then to @expr{257440 m^3}. The functions @code{float}, @code{frac}, @code{clean}, @code{abs}, @@ -23401,7 +23401,7 @@ answer! If you use the @code{deriv} function directly in an algebraic formula, you can write @samp{deriv(f,x,x0)} which represents the derivative -of @expr{f} with respect to @expr{x}, evaluated at the point +of @expr{f} with respect to @expr{x}, evaluated at the point @texline @math{x=x_0}. @infoline @expr{x=x0}. @@ -23441,7 +23441,7 @@ respect to a prompted-for variable. The integrator is not guaranteed to work for all integrable functions, but it is able to integrate several large classes of formulas. In particular, any polynomial or rational function (a polynomial divided by a polynomial) is acceptable. -(Rational functions don't have to be in explicit quotient form, however; +(Rational functions don't have to be in explicit quotient form, however; @texline @math{x/(1+x^{-2})} @infoline @expr{x/(1+x^-2)} is not strictly a quotient of polynomials, but it is equivalent to @@ -23472,7 +23472,7 @@ integral $\int_a^b f(x) \, dx$. Please note that the current implementation of Calc's integrator sometimes produces results that are significantly more complex than they need to -be. For example, the integral Calc finds for +be. For example, the integral Calc finds for @texline @math{1/(x+\sqrt{x^2+1})} @infoline @expr{1/(x+sqrt(x^2+1))} is several times more complicated than the answer Mathematica @@ -23480,11 +23480,11 @@ returns for the same input, although the two forms are numerically equivalent. Also, any indefinite integral should be considered to have an arbitrary constant of integration added to it, although Calc does not write an explicit constant of integration in its result. For example, -Calc's solution for +Calc's solution for @texline @math{1/(1+\tan x)} -@infoline @expr{1/(1+tan(x))} +@infoline @expr{1/(1+tan(x))} differs from the solution given in the @emph{CRC Math Tables} by a -constant factor of +constant factor of @texline @math{\pi i / 2} @infoline @expr{pi i / 2}, due to a different choice of constant of integration. @@ -23544,9 +23544,9 @@ in your @code{IntegRules}. @tindex Ei As a more serious example, the expression @samp{exp(x)/x} cannot be integrated in terms of the standard functions, so the ``exponential -integral'' function +integral'' function @texline @math{{\rm Ei}(x)} -@infoline @expr{Ei(x)} +@infoline @expr{Ei(x)} was invented to describe it. We can get Calc to do this integral in terms of a made-up @code{Ei} function by adding the rule @samp{[integtry(exp(x)/x, x) := Ei(x)]} @@ -23717,18 +23717,18 @@ form @expr{X = 0}. This command also works for inequalities, as in @expr{y < 3x + 6}. Some inequalities cannot be solved where the analogous equation could -be; for example, solving +be; for example, solving @texline @math{a < b \, c} -@infoline @expr{a < b c} +@infoline @expr{a < b c} for @expr{b} is impossible without knowing the sign of @expr{c}. In this case, @kbd{a S} will -produce the result +produce the result @texline @math{b \mathbin{\hbox{\code{!=}}} a/c} -@infoline @expr{b != a/c} +@infoline @expr{b != a/c} (using the not-equal-to operator) to signify that the direction of the -inequality is now unknown. The inequality +inequality is now unknown. The inequality @texline @math{a \le b \, c} -@infoline @expr{a <= b c} +@infoline @expr{a <= b c} is not even partially solved. @xref{Declarations}, for a way to tell Calc that the signs of the variables in a formula are in fact known. @@ -24186,13 +24186,13 @@ value of the variable which minimizes the formula's value, along with the minimum value itself. Note that this command looks for a @emph{local} minimum. Many functions -have more than one minimum; some, like +have more than one minimum; some, like @texline @math{x \sin x}, -@infoline @expr{x sin(x)}, +@infoline @expr{x sin(x)}, have infinitely many. In fact, there is no easy way to define the -``global'' minimum of +``global'' minimum of @texline @math{x \sin x} -@infoline @expr{x sin(x)} +@infoline @expr{x sin(x)} but Calc can still locate any particular local minimum for you. Calc basically goes downhill from the initial guess until it finds a point at which the function's value is greater both to the left @@ -24271,7 +24271,7 @@ to be determined. For a typical set of measured data there will be no single @expr{m} and @expr{b} that exactly fit the data; in this case, Calc chooses values of the parameters that provide the closest possible fit. The model formula can be entered in various ways after -the key sequence @kbd{a F} is pressed. +the key sequence @kbd{a F} is pressed. If the letter @kbd{P} is pressed after @kbd{a F} but before the model description is entered, the data as well as the model formula will be @@ -24319,7 +24319,7 @@ the @dfn{parameters} of the model. The @kbd{a F} command takes the data set to be fitted from the stack. By default, it expects the data in the form of a matrix. For example, -for a linear or polynomial fit, this would be a +for a linear or polynomial fit, this would be a @texline @math{2\times N} @infoline 2xN matrix where the first row is a list of @expr{x} values and the second @@ -24327,10 +24327,10 @@ row has the corresponding @expr{y} values. For the multilinear fit shown above, the matrix would have four rows (@expr{x_1}, @expr{x_2}, @expr{x_3}, and @expr{y}, respectively). -If you happen to have an +If you happen to have an @texline @math{N\times2} @infoline Nx2 -matrix instead of a +matrix instead of a @texline @math{2\times N} @infoline 2xN matrix, just press @kbd{v t} first to transpose the matrix. @@ -24425,13 +24425,13 @@ $$ \chi^2 = \sum_{i=1}^N (y_i - (a + b x_i))^2 $$ which is clearly zero if @expr{a + b x} exactly fits all data points, and increases as various @expr{a + b x_i} values fail to match the corresponding @expr{y_i} values. There are several reasons why the -summand is squared, one of them being to ensure that +summand is squared, one of them being to ensure that @texline @math{\chi^2 \ge 0}. @infoline @expr{chi^2 >= 0}. Least-squares fitting simply chooses the values of @expr{a} and @expr{b} -for which the error +for which the error @texline @math{\chi^2} -@infoline @expr{chi^2} +@infoline @expr{chi^2} is as small as possible. Other kinds of models do the same thing but with a different model @@ -24593,9 +24593,9 @@ contain error forms. The data values must either all include errors or all be plain numbers. Error forms can go anywhere but generally go on the numbers in the last row of the data matrix. If the last row contains error forms -@texline `@var{y_i}@w{ @tfn{+/-} }@math{\sigma_i}', -@infoline `@var{y_i}@w{ @tfn{+/-} }@var{sigma_i}', -then the +@texline `@var{y_i}@w{ @tfn{+/-} }@math{\sigma_i}', +@infoline `@var{y_i}@w{ @tfn{+/-} }@var{sigma_i}', +then the @texline @math{\chi^2} @infoline @expr{chi^2} statistic is now, @@ -24617,9 +24617,9 @@ the fitting operation. If there are error forms on other rows of the data matrix, all the errors for a given data point are combined; the square root of the -sum of the squares of the errors forms the +sum of the squares of the errors forms the @texline @math{\sigma_i} -@infoline @expr{sigma_i} +@infoline @expr{sigma_i} used for the data point. Both @kbd{a F} and @kbd{H a F} can accept error forms in the input @@ -24627,19 +24627,19 @@ matrix, although if you are concerned about error analysis you will probably use @kbd{H a F} so that the output also contains error estimates. -If the input contains error forms but all the +If the input contains error forms but all the @texline @math{\sigma_i} -@infoline @expr{sigma_i} +@infoline @expr{sigma_i} values are the same, it is easy to see that the resulting fitted model -will be the same as if the input did not have error forms at all +will be the same as if the input did not have error forms at all @texline (@math{\chi^2} @infoline (@expr{chi^2} -is simply scaled uniformly by +is simply scaled uniformly by @texline @math{1 / \sigma^2}, -@infoline @expr{1 / sigma^2}, +@infoline @expr{1 / sigma^2}, which doesn't affect where it has a minimum). But there @emph{will} be a difference in the estimated errors of the coefficients reported by -@kbd{H a F}. +@kbd{H a F}. Consult any text on statistical modeling of data for a discussion of where these error estimates come from and how they should be @@ -24671,18 +24671,18 @@ will have length @expr{M = d+1} with the constant term first. The covariance matrix @expr{C} computed from the fit. This is an @var{m}x@var{m} symmetric matrix; the diagonal elements @texline @math{C_{jj}} -@infoline @expr{C_j_j} -are the variances +@infoline @expr{C_j_j} +are the variances @texline @math{\sigma_j^2} -@infoline @expr{sigma_j^2} +@infoline @expr{sigma_j^2} of the parameters. The other elements are covariances -@texline @math{\sigma_{ij}^2} -@infoline @expr{sigma_i_j^2} +@texline @math{\sigma_{ij}^2} +@infoline @expr{sigma_i_j^2} that describe the correlation between pairs of parameters. (A related -set of numbers, the @dfn{linear correlation coefficients} +set of numbers, the @dfn{linear correlation coefficients} @texline @math{r_{ij}}, @infoline @expr{r_i_j}, -are defined as +are defined as @texline @math{\sigma_{ij}^2 / \sigma_i \, \sigma_j}.) @infoline @expr{sigma_i_j^2 / sigma_i sigma_j}.) @@ -24693,35 +24693,35 @@ will instead be an empty vector; this is always the case for the polynomial and multilinear fits described so far. @item -The value of +The value of @texline @math{\chi^2} -@infoline @expr{chi^2} +@infoline @expr{chi^2} for the fit, calculated by the formulas shown above. This gives a measure of the quality of the fit; statisticians consider @texline @math{\chi^2 \approx N - M} -@infoline @expr{chi^2 = N - M} +@infoline @expr{chi^2 = N - M} to indicate a moderately good fit (where again @expr{N} is the number of data points and @expr{M} is the number of parameters). @item A measure of goodness of fit expressed as a probability @expr{Q}. This is computed from the @code{utpc} probability distribution -function using +function using @texline @math{\chi^2} -@infoline @expr{chi^2} +@infoline @expr{chi^2} with @expr{N - M} degrees of freedom. A value of 0.5 implies a good fit; some texts recommend that often @expr{Q = 0.1} or even 0.001 can signify an acceptable fit. In -particular, +particular, @texline @math{\chi^2} -@infoline @expr{chi^2} +@infoline @expr{chi^2} statistics assume the errors in your inputs follow a normal (Gaussian) distribution; if they don't, you may have to accept smaller values of @expr{Q}. The @expr{Q} value is computed only if the input included error estimates. Otherwise, Calc will report the symbol @code{nan} -for @expr{Q}. The reason is that in this case the +for @expr{Q}. The reason is that in this case the @texline @math{\chi^2} @infoline @expr{chi^2} value has effectively been used to estimate the original errors @@ -24763,7 +24763,7 @@ Power law. @mathit{a x^b y^c}. @item q Quadratic. @mathit{a + b (x-c)^2 + d (x-e)^2}. @item g -Gaussian. +Gaussian. @texline @math{{a \over b \sqrt{2 \pi}} \exp\left( -{1 \over 2} \left( x - c \over b \right)^2 \right)}. @infoline @mathit{(a / b sqrt(2 pi)) exp(-0.5*((x-c)/b)^2)}. @item s @@ -24788,7 +24788,7 @@ the parameter values from the vector that is placed in the trail.) All models except Gaussian, logistics, Hubbert and polynomials can generalize as shown to any number of independent variables. Also, all -the built-in models except for the logistic and Hubbert curves have an +the built-in models except for the logistic and Hubbert curves have an additive or multiplicative parameter shown as @expr{a} in the above table which can be replaced by zero or one, as appropriate, by typing @kbd{h} before the model key. @@ -24893,9 +24893,9 @@ form @samp{arcsin(y) = a t + b}. The @code{arcsin} function always returns results in the range from @mathit{-90} to 90 degrees (or the equivalent range in radians). Suppose you had data that you believed to represent roughly three oscillations of a sine wave, -so that the argument of the sine might go from zero to +so that the argument of the sine might go from zero to @texline @math{3\times360} -@infoline @mathit{3*360} +@infoline @mathit{3*360} degrees. The above model would appear to be a good way to determine the true frequency and phase of the sine wave, but in practice it @@ -24955,18 +24955,18 @@ ln(y) = ln(a) + b ln(x) @end example @noindent -which matches the desired form with +which matches the desired form with @texline @math{Y = \ln(y)}, -@infoline @expr{Y = ln(y)}, +@infoline @expr{Y = ln(y)}, @texline @math{A = \ln(a)}, @infoline @expr{A = ln(a)}, -@expr{F = 1}, @expr{B = b}, and +@expr{F = 1}, @expr{B = b}, and @texline @math{G = \ln(x)}. -@infoline @expr{G = ln(x)}. +@infoline @expr{G = ln(x)}. Calc thus computes the logarithms of your @expr{y} and @expr{x} values, -does a linear fit for @expr{A} and @expr{B}, then solves to get -@texline @math{a = \exp(A)} -@infoline @expr{a = exp(A)} +does a linear fit for @expr{A} and @expr{B}, then solves to get +@texline @math{a = \exp(A)} +@infoline @expr{a = exp(A)} and @expr{b = B}. Another interesting example is the ``quadratic'' model, which can @@ -25015,7 +25015,7 @@ from the list of parameters when you answer the variables prompt. A last desperate step would be to use the general-purpose @code{minimize} function rather than @code{fit}. After all, both -functions solve the problem of minimizing an expression (the +functions solve the problem of minimizing an expression (the @texline @math{\chi^2} @infoline @expr{chi^2} sum) by adjusting certain parameters in the expression. The @kbd{a F} @@ -25026,9 +25026,9 @@ command can do the same thing by brute force. A compromise would be to pick out a few parameters without which the fit is linearizable, and use @code{minimize} on a call to @code{fit} which efficiently takes care of the rest of the parameters. The thing -to be minimized would be the value of +to be minimized would be the value of @texline @math{\chi^2} -@infoline @expr{chi^2} +@infoline @expr{chi^2} returned as the fifth result of the @code{xfit} function: @smallexample @@ -25086,13 +25086,13 @@ of the sum of the squares of the errors. It then changes @expr{x} and @expr{y} to be plain numbers, and makes @expr{z} into an error form with this combined error. The @expr{Y(x,y,z)} part of the linearized model is evaluated, and the result should be an error -form. The error part of that result is used for +form. The error part of that result is used for @texline @math{\sigma_i} -@infoline @expr{sigma_i} -for the data point. If for some reason @expr{Y(x,y,z)} does not return -an error form, the combined error from @expr{z} is used directly for +@infoline @expr{sigma_i} +for the data point. If for some reason @expr{Y(x,y,z)} does not return +an error form, the combined error from @expr{z} is used directly for @texline @math{\sigma_i}. -@infoline @expr{sigma_i}. +@infoline @expr{sigma_i}. Finally, @expr{z} is also stripped of its error for use in computing @expr{F(x,y,z)}, @expr{G(x,y,z)} and so on; the righthand side of the linearized model is computed in regular @@ -25104,7 +25104,7 @@ depends only on the dependent variable @expr{z}, and in fact is often simply equal to @expr{z}. For common cases like polynomials and multilinear models, the combined error is simply used as the @texline @math{\sigma} -@infoline @expr{sigma} +@infoline @expr{sigma} for the data point with no further ado.) @tex @@ -25481,7 +25481,7 @@ this would be a division by zero. But at @expr{k = k_0}, this formula works out to the indeterminate form @expr{0 / 0}, which Calc will not assume is zero. Better would be to use @samp{(k != k_0) ? 1/(k-k_0) : 0}; the @samp{? :} operator does -an ``if-then-else'' test: This expression says, ``if +an ``if-then-else'' test: This expression says, ``if @texline @math{k \ne k_0}, @infoline @expr{k != k_0}, then @expr{1/(k-k_0)}, else zero.'' Now the formula @expr{1/(k-k_0)} @@ -26496,16 +26496,16 @@ f(a b) := a f(b) :: real(a)]} is stored in variable @samp{linearF}, then the rule set @samp{[f(0) := 0, import(linearF)]} will apply all three rules. It is possible to modify the imported rules slightly: @samp{import(x, v1, x1, v2, x2, @dots{})} imports -the rule set @expr{x} with all occurrences of +the rule set @expr{x} with all occurrences of @texline @math{v_1}, -@infoline @expr{v1}, -as either a variable name or a function name, replaced with +@infoline @expr{v1}, +as either a variable name or a function name, replaced with @texline @math{x_1} -@infoline @expr{x1} -and so on. (If +@infoline @expr{x1} +and so on. (If @texline @math{v_1} -@infoline @expr{v1} -is used as a function name, then +@infoline @expr{v1} +is used as a function name, then @texline @math{x_1} @infoline @expr{x1} must be either a function name itself or a @w{@samp{< >}} nameless @@ -27609,7 +27609,7 @@ the keyboard macro @kbd{' tri($) @key{RET}} to make a command that applies @code{tri} to the value on the top of the stack. @xref{Programming}. @cindex Quaternions -The following rule set, contributed by +The following rule set, contributed by @texline Fran\c cois @infoline Francois Pinard, implements @dfn{quaternions}, a generalization of the concept of @@ -27764,9 +27764,9 @@ equivalent temperature on the Fahrenheit scale. While many of Calc's conversion factors are exact, some are necessarily approximate. If Calc is in fraction mode (@pxref{Fraction Mode}), then unit conversions will try to give exact, rational conversions, but it -isn't always possible. Given @samp{55 mph} in fraction mode, typing -@kbd{u c m/s @key{RET}} produces @samp{15367:625 m/s}, for example, -while typing @kbd{u c au/yr @key{RET}} produces +isn't always possible. Given @samp{55 mph} in fraction mode, typing +@kbd{u c m/s @key{RET}} produces @samp{15367:625 m/s}, for example, +while typing @kbd{u c au/yr @key{RET}} produces @samp{5.18665819999e-3 au/yr}. If the units you request are inconsistent with the original units, the @@ -27994,7 +27994,7 @@ defined by the @TeX{} typesetting system: @samp{72.27 texpt = 1 in}. Other units used by @TeX{} are available; they are @code{texpc} (a pica), @code{texbp} (a ``big point'', equal to a standard point which is larger than the point used by @TeX{}), @code{texdd} (a Didot point), -@code{texcc} (a Cicero) and @code{texsp} (a scaled @TeX{} point, +@code{texcc} (a Cicero) and @code{texsp} (a scaled @TeX{} point, all dimensions representable in @TeX{} are multiples of this value). When Calc is using the @TeX{} or La@TeX{} language mode (@pxref{TeX @@ -28131,17 +28131,17 @@ The units @code{dB} (decibels) and @code{Np} (nepers) are logarithmic units which are manipulated differently than standard units. Calc provides commands to work with these logarithmic units. -Decibels and nepers are used to measure power quantities as well as +Decibels and nepers are used to measure power quantities as well as field quantities (quantities whose squares are proportional to power); these two types of quantities are handled slightly different from each other. By default the Calc commands work as if power quantities are being used; with the @kbd{H} prefix the Calc commands work as if field quantities are being used. -The decibel level of a power +The decibel level of a power @infoline @math{P1}, @texline @math{P_1}, -relative to a reference power +relative to a reference power @infoline @math{P0}, @texline @math{P_0}, is defined to be @@ -28151,10 +28151,10 @@ is defined to be one-tenth of a bel. The bel, named after Alexander Graham Bell, was considered to be too large of a unit and was effectively replaced by the decibel.) If @math{F} is a field quantity with power -@math{P=k F^2}, then a reference quantity of +@math{P=k F^2}, then a reference quantity of @infoline @math{F0} @texline @math{F_0} -would correspond to a power of +would correspond to a power of @infoline @math{P0=k F0^2}. @texline @math{P_{0}=kF_{0}^2}. If @@ -28163,7 +28163,7 @@ If then @ifnottex -@example +@example 10 log10(P1/P0) = 10 log10(F1^2/F0^2) = 20 log10(F1/F0). @end example @end ifnottex @@ -28175,42 +28175,42 @@ $$ 10 \log_{10}(P_1/P_0) = 10 \log_{10}(F_1^2/F_0^2) = 20 @noindent In order to get the same decibel level regardless of whether a field quantity or the corresponding power quantity is used, the decibel -level of a field quantity +level of a field quantity @infoline @math{F1}, -@texline @math{F_1}, -relative to a reference +@texline @math{F_1}, +relative to a reference @infoline @math{F0}, -@texline @math{F_0}, +@texline @math{F_0}, is defined as @infoline @math{20 log10(F1/F0) dB}. @texline @math{20 \log_{10}(F_{1}/F_{0}) {\rm dB}}. -For example, the decibel value of a sound pressure level of +For example, the decibel value of a sound pressure level of @infoline @math{60 uPa} @texline @math{60 \mu{\rm Pa}} -relative to +relative to @infoline @math{20 uPa} @texline @math{20 \mu{\rm Pa}} -(the threshhold of human hearing) is +(the threshold of human hearing) is @infoline @math{20 log10(60 uPa/ 20 uPa) dB = 20 log10(3) dB}, @texline @math{20 \log_{10}(60 \mu{\rm Pa}/20 \mu{\rm Pa}) {\rm dB} = 20 \log_{10}(3) {\rm dB}}, -which is about +which is about @infoline @math{9.54 dB}. @texline @math{9.54 {\rm dB}}. Note that in taking the ratio, the original units cancel and so these -logarithmic units are dimensionless. +logarithmic units are dimensionless. Nepers (named after John Napier, who is credited with inventing the logarithm) are similar to bels except they use natural logarithms instead -of common logarithms. The neper level of a power +of common logarithms. The neper level of a power @infoline @math{P1}, @texline @math{P_1}, -relative to a reference power +relative to a reference power @infoline @math{P0}, @texline @math{P_0}, is @infoline @math{(1/2) ln(P1/P0) Np}. @texline @math{(1/2) \ln(P_1/P_0) {\rm Np}}. -The neper level of a field +The neper level of a field @infoline @math{F1}, @texline @math{F_1}, relative to a reference field @@ -28223,13 +28223,13 @@ is @vindex calc-lu-power-reference @vindex calc-lu-field-reference For power quantities, Calc uses -@infoline @math{1 mW} +@infoline @math{1 mW} @texline @math{1 {\rm mW}} -as the default reference quantity; this default can be changed by changing +as the default reference quantity; this default can be changed by changing the value of the customizable variable @code{calc-lu-power-reference} (@pxref{Customizing Calc}). -For field quantities, Calc uses -@infoline @math{20 uPa} +For field quantities, Calc uses +@infoline @math{20 uPa} @texline @math{20 \mu{\rm Pa}} as the default reference quantity; this is the value used in acoustics which is where decibels are commonly encountered. This default can be @@ -28247,9 +28247,9 @@ command computes the power quantity corresponding to a given number of logarithmic units. With the capital @kbd{O} prefix, @kbd{O l q}, the reference level will be read from the top of the stack. (In an algebraic formula, @code{lupquant} can be given an optional second -argument which will be used for the reference level.) For example, -@code{20 dB @key{RET} l q} will return @code{100 mW}; -@code{20 dB @key{RET} 4 W @key{RET} O l q} will return @code{400 W}. +argument which will be used for the reference level.) For example, +@code{20 dB @key{RET} l q} will return @code{100 mW}; +@code{20 dB @key{RET} 4 W @key{RET} O l q} will return @code{400 W}. The @kbd{H l q} [@code{lufquant}] command behaves like @kbd{l q} but computes field quantities instead of power quantities. @@ -28288,13 +28288,13 @@ the reference level can be given as an optional second argument. @tindex lufdiv The sum of two power or field quantities doesn't correspond to the sum of the corresponding decibel or neper levels. If the powers -corresponding to decibel levels -@infoline @math{D1} -@texline @math{D_1} -and -@infoline @math{D2} -@texline @math{D_2} -are added, the corresponding decibel level ``sum'' will be +corresponding to decibel levels +@infoline @math{D1} +@texline @math{D_1} +and +@infoline @math{D2} +@texline @math{D_2} +are added, the corresponding decibel level ``sum'' will be @ifnottex @example @@ -28338,7 +28338,7 @@ $$ D + 10 \log_{10}(N) {\rm dB},$$ @noindent if a field quantity is multiplied by @math{N} the corresponding decibel level -will be +will be @ifnottex @example @@ -28375,31 +28375,31 @@ operating on notes. Scientific pitch notation refers to a note by giving a letter A through G, possibly followed by a flat or sharp) with a subscript indicating an octave number. Each octave starts with C and ends with -B and +B and @c increasing each note by a semitone will result @c in the sequence @expr{C}, @expr{C} sharp, @expr{D}, @expr{E} flat, @expr{E}, @c @expr{F}, @expr{F} sharp, @expr{G}, @expr{A} flat, @expr{A}, @expr{B} -@c flat and @expr{B}. +@c flat and @expr{B}. the octave numbered 0 was chosen to correspond to the lowest audible frequency. Using this system, middle C (about 261.625 Hz) corresponds to the note @expr{C} in octave 4 and is denoted @expr{C_4}. Any frequency can be described by giving a note plus an offset in cents (where a cent is a ratio of frequencies so that a -semitone consists of 100 cents). +semitone consists of 100 cents). The midi note number system assigns numbers to notes so that @expr{C_(-1)} corresponds to the midi note number 0 and @expr{G_9} corresponds to the midi note number 127. A midi controller can have up to 128 keys and each midi note number from 0 to 127 corresponds to -a possible key. +a possible key. @kindex l s @pindex calc-spn @tindex spn The @kbd{l s} (@code{calc-spn}) [@code{spn}] command converts either a frequency or a midi number to scientific pitch notation. For -example, @code{500 Hz} gets converted to -@code{B_4 + 21.3094853649 cents} and @code{84} to @code{C_6}. +example, @code{500 Hz} gets converted to +@code{B_4 + 21.3094853649 cents} and @code{84} to @code{C_6}. @kindex l m @@ -28464,7 +28464,7 @@ The @kbd{s s} (@code{calc-store}) command stores the value at the top of the stack into a specified variable. It prompts you to enter the name of the variable. If you press a single digit, the value is stored immediately in one of the ``quick'' variables @code{q0} through -@code{q9}. Or you can enter any variable name. +@code{q9}. Or you can enter any variable name. @kindex s t @pindex calc-store-into @@ -28554,12 +28554,12 @@ and @kbd{s ]} which decrease or increase a variable by one. All the arithmetic stores accept the Inverse prefix to reverse the order of the operands. If @expr{v} represents the contents of the variable, and @expr{a} is the value drawn from the stack, then regular -@w{@kbd{s -}} assigns +@w{@kbd{s -}} assigns @texline @math{v \coloneq v - a}, -@infoline @expr{v := v - a}, +@infoline @expr{v := v - a}, but @kbd{I s -} assigns @texline @math{v \coloneq a - v}. -@infoline @expr{v := a - v}. +@infoline @expr{v := a - v}. While @kbd{I s *} might seem pointless, it is useful if matrix multiplication is involved. Actually, all the arithmetic stores use formulas designed to behave usefully both @@ -28668,7 +28668,7 @@ magic property is preserved, however, when a variable is copied with @kindex s k @pindex calc-copy-special-constant If one of the ``special constants'' is redefined (or undefined) so that -it no longer has its magic property, the property can be restored with +it no longer has its magic property, the property can be restored with @kbd{s k} (@code{calc-copy-special-constant}). This command will prompt for a special constant and a variable to store it in, and so a special constant can be stored in any variable. Here, the special constant that @@ -28850,7 +28850,7 @@ explicitly naming them in an @kbd{s p} command.) The @kbd{s i} (@code{calc-insert-variables}) command writes the values of all Calc variables into a specified buffer. The variables are written with the prefix @code{var-} in the form of -Lisp @code{setq} commands +Lisp @code{setq} commands which store the values in string form. You can place these commands in your Calc init file (or @file{.emacs}) if you wish, though in this case it would be easier to use @kbd{s p @key{RET}}. (Note that @kbd{s i} @@ -29159,9 +29159,9 @@ In the first case, ``x'' and ``y'' are each vectors (not necessarily of the same length); either or both may instead be interval forms. The ``z'' value must be a matrix with the same number of rows as elements in ``x'', and the same number of columns as elements in ``y''. The -result is a surface plot where +result is a surface plot where @texline @math{z_{ij}} -@infoline @expr{z_ij} +@infoline @expr{z_ij} is the height of the point at coordinate @expr{(x_i, y_j)} on the surface. The 3D graph will be displayed from a certain default viewpoint; you can change this @@ -29270,9 +29270,9 @@ that don't have common ``x'' values. (Of course, the range of ``x'' values covered by all the curves ought to be roughly the same if they are to look nice on the same graph.) -For example, to plot +For example, to plot @texline @math{\sin n x} -@infoline @expr{sin(n x)} +@infoline @expr{sin(n x)} for integers @expr{n} from 1 to 5, you could use @kbd{v x} to create a vector of integers (@expr{n}), then @kbd{V M '} or @kbd{V M $} to map @samp{sin(n x)} @@ -29510,8 +29510,8 @@ available for any device. The @kbd{g S} (@code{calc-graph-point-style}) command similarly turns the symbols at the data points on or off, or sets the point style. If you turn both lines and points off, the data points will show as -tiny dots. If the ``y'' values being plotted contain error forms and -the connecting lines are turned off, then this command will also turn +tiny dots. If the ``y'' values being plotted contain error forms and +the connecting lines are turned off, then this command will also turn the error bars on or off. @cindex @code{LineStyles} variable @@ -29563,7 +29563,7 @@ terminals with no special graphics facilities. It writes a crude picture of the graph composed of characters like @code{-} and @code{|} to a buffer called @samp{*Gnuplot Trail*}, which Calc then displays. The graph is made the same size as the Emacs screen, which on most -dumb terminals will be +dumb terminals will be @texline @math{80\times24} @infoline 80x24 characters. The graph is displayed in @@ -29820,7 +29820,7 @@ difference.) @pindex calc-prepend-to-register @pindex calc-append-to-register @cindex Registers -An alternative to killing and yanking stack entries is using +An alternative to killing and yanking stack entries is using registers in Calc. Saving stack entries in registers is like saving text in normal Emacs registers; although, like Calc's kill commands, register commands always operate on whole stack @@ -29935,7 +29935,7 @@ separately as a matrix element. If a line contained would correctly split the line into two error forms. @xref{Matrix Functions}, to see how to pull the matrix apart into its -constituent rows and columns. (If it is a +constituent rows and columns. (If it is a @texline @math{1\times1} @infoline 1x1 matrix, just hit @kbd{v u} (@code{calc-unpack}) twice.) @@ -30273,7 +30273,7 @@ same limit as last time. @key{INV GCD} computes the LCM (least common multiple) function. -@key{INV FACT} is the gamma function. +@key{INV FACT} is the gamma function. @texline @math{\Gamma(x) = (x-1)!}. @infoline @expr{gamma(x) = (x-1)!}. @@ -30490,7 +30490,7 @@ Similarly, Calc will use @TeX{} language for @code{tex-mode}, @code{plain-tex-mode} and @code{context-mode}, C language for @code{c-mode} and @code{c++-mode}, FORTRAN language for @code{fortran-mode} and @code{f90-mode}, Pascal for @code{pascal-mode}, -and eqn for @code{nroff-mode} (@pxref{Customizing Calc}). +and eqn for @code{nroff-mode} (@pxref{Customizing Calc}). These can be overridden with Calc's mode changing commands (@pxref{Mode Settings in Embedded Mode}). If no suitable language is available, Calc will continue with its current language. @@ -30670,13 +30670,13 @@ version. Plain formulas are preceded and followed by @samp{%%%} signs by default. This notation has the advantage that the @samp{%} -character begins a comment in @TeX{} and La@TeX{}, so if your formula is +character begins a comment in @TeX{} and La@TeX{}, so if your formula is embedded in a @TeX{} or La@TeX{} document its plain version will be invisible in the final printed copy. Certain major modes have different -delimiters to ensure that the ``plain'' version will be -in a comment for those modes, also. +delimiters to ensure that the ``plain'' version will be +in a comment for those modes, also. See @ref{Customizing Embedded Mode} to see how to change the ``plain'' -formula delimiters. +formula delimiters. There are several notations which Calc's parser for ``big'' formatted formulas can't yet recognize. In particular, it can't @@ -31178,7 +31178,7 @@ We would have to go down to the other formula and press @kbd{C-x * u} on it in order to get it to notice the new annotation. Two more mode-recording modes selectable by @kbd{m R} are available -which are also available outside of Embedded mode. +which are also available outside of Embedded mode. (@pxref{General Mode Commands}.) They are @code{Save}, in which mode settings are recorded permanently in your Calc init file (the file given by the variable @code{calc-settings-file}, typically @file{~/.emacs.d/calc.el}) @@ -31195,11 +31195,11 @@ for @code{Save} have no effect. @noindent You can modify Embedded mode's behavior by setting various Lisp -variables described here. These variables are customizable +variables described here. These variables are customizable (@pxref{Customizing Calc}), or you can use @kbd{M-x set-variable} or @kbd{M-x edit-options} to adjust a variable on the fly. (Another possibility would be to use a file-local variable annotation at -the end of the file; +the end of the file; @pxref{File Variables, , Local Variables in Files, emacs, the Emacs manual}.) Many of the variables given mentioned here can be set to depend on the major mode of the editing buffer (@pxref{Customizing Calc}). @@ -31334,7 +31334,7 @@ Calc never scans for this string; Calc always looks for the annotation itself. But this is the string that is inserted before the opening bracket when Calc adds an annotation on its own. The default is @code{"% "}, but may be different for different major -modes. +modes. @vindex calc-embedded-close-mode The @code{calc-embedded-close-mode} variable is a string which @@ -31459,7 +31459,7 @@ without its key binding, type @kbd{M-x} and enter a function name. (The (If the command you give implies a function, the function will be saved, and if the function has any display formats, those will be saved, but not the other way around: Saving a function will not save any commands -or key bindings associated with the function.) +or key bindings associated with the function.) @kindex Z E @pindex calc-user-define-edit @@ -31542,7 +31542,7 @@ Once you have bound your keyboard macro to a key, you can use @cindex Keyboard macros, editing The @kbd{Z E} (@code{calc-user-define-edit}) command on a key that has been defined by a keyboard macro tries to use the @code{edmacro} package -edit the macro. Type @kbd{C-c C-c} to finish editing and update +edit the macro. Type @kbd{C-c C-c} to finish editing and update the definition stored on the key, or, to cancel the edit, kill the buffer with @kbd{C-x k}. The special characters @code{RET}, @code{LFD}, @code{TAB}, @code{SPC}, @@ -31552,7 +31552,7 @@ sequences, written in all uppercase, as must the prefixes @code{C-} and copied verbatim into the keyboard macro. Basically, the notation is the same as is used in all of this manual's examples, except that the manual takes some liberties with spaces: When we say @kbd{' [1 2 3] @key{RET}}, -we take it for granted that it is clear we really mean +we take it for granted that it is clear we really mean @kbd{' [1 @key{SPC} 2 @key{SPC} 3] @key{RET}}. @kindex C-x * m @@ -31823,7 +31823,7 @@ prompt for the @kbd{Z #} command; it will not play any role in any subsequent calculations.) This command allows your keyboard macros to accept numbers or formulas as interactive input. -As an example, +As an example, @kbd{2 @key{RET} "Power: " @key{RET} Z # 3 @key{RET} ^} will prompt for input with ``Power: '' in the minibuffer, then return 2 to the provided power. (The response to the prompt that's given, 3 in this example, @@ -31900,7 +31900,7 @@ The third prompt is for an algebraic function name. The default is to use the same name as the command name but without the @samp{calc-} prefix. (If this is of the form @samp{User-m}, the hyphen is removed so it won't be taken for a minus sign in algebraic formulas.) -This is the name you will use if you want to enter your +This is the name you will use if you want to enter your new function in an algebraic formula. Suppose we enter @kbd{yow @key{RET}}. Then the new function can be invoked by pushing two numbers on the stack and typing @kbd{z m} or @kbd{x spam}, or by entering the algebraic @@ -32695,7 +32695,7 @@ same thing with a single division by 512. @end ignore @tindex mysin A somewhat limited sine function could be defined as follows, using the -well-known Taylor series expansion for +well-known Taylor series expansion for @texline @math{\sin x}: @infoline @samp{sin(x)}: @@ -35241,7 +35241,7 @@ to use a different prefix, you can put @end example @noindent -in your .emacs file. +in your .emacs file. (@xref{Key Bindings,,Customizing Key Bindings,emacs, The GNU Emacs Manual}, for more information on binding keys.) A convenient way to start Calc is with @kbd{C-x * *}; to make it equally @@ -35269,7 +35269,7 @@ to see how regular expressions work. @defvar calc-settings-file The variable @code{calc-settings-file} holds the file name in which commands like @kbd{m m} and @kbd{Z P} store ``permanent'' -definitions. +definitions. If @code{calc-settings-file} is not your user init file (typically @file{~/.emacs}) and if the variable @code{calc-loaded-settings-file} is @code{nil}, then Calc will automatically load your settings file (if it @@ -35314,7 +35314,7 @@ enabled, it will try to use the current major mode to determine what language should be used. (This can be overridden using Calc's mode changing commands, @xref{Mode Settings in Embedded Mode}.) The variable @code{calc-language-alist} consists of a list of pairs of -the form @code{(@var{MAJOR-MODE} . @var{LANGUAGE})}; for example, +the form @code{(@var{MAJOR-MODE} . @var{LANGUAGE})}; for example, @code{(latex-mode . latex)} is one such pair. If Calc embedded is activated in a buffer whose major mode is @var{MAJOR-MODE}, it will set itself to use the language @var{LANGUAGE}. @@ -35342,7 +35342,7 @@ what formulas @kbd{C-x * a} will activate in a buffer. It is a regular expression, and when activating embedded formulas with @kbd{C-x * a}, it will tell Calc that what follows is a formula to be activated. (Calc also uses other patterns to find formulas, such as -@samp{=>} and @samp{:=}.) +@samp{=>} and @samp{:=}.) The default pattern is @code{"%Embed\n\\(% .*\n\\)*"}, which checks for @samp{%Embed} followed by any number of lines beginning with @@ -35367,7 +35367,7 @@ It consists of a list of pairs of the form @code{(@var{MAJOR-MODE} . (texinfo-mode . "@@c Embed\n\\(@@c .*\n\\)*")) @end example Any major modes added to @code{calc-embedded-announce-formula-alist} -should also be added to @code{calc-embedded-open-close-plain-alist} +should also be added to @code{calc-embedded-open-close-plain-alist} and @code{calc-embedded-open-close-mode-alist}. @end defvar @@ -35378,7 +35378,7 @@ See @ref{Customizing Embedded Mode}.@* The variables @code{calc-embedded-open-formula} and @code{calc-embedded-close-formula} control the region that Calc will activate as a formula when Embedded mode is entered with @kbd{C-x * e}. -They are regular expressions; +They are regular expressions; Calc normally scans backward and forward in the buffer for the nearest text matching these regular expressions to be the ``formula delimiters''. @@ -35403,7 +35403,7 @@ The variable @code{calc-embedded-open-close-formula-alist} is used to set @code{calc-embedded-open-formula} and @code{calc-embedded-close-formula} to different regular expressions depending on the major mode of the editing buffer. -It consists of a list of lists of the form +It consists of a list of lists of the form @code{(@var{MAJOR-MODE} @var{OPEN-FORMULA-REGEXP} @var{CLOSE-FORMULA-REGEXP})}, and its default value is @code{nil}. @@ -35422,7 +35422,7 @@ The default value of @code{calc-embedded-word-regexp} is The variable @code{calc-embedded-word-regexp-alist} is used to set @code{calc-embedded-word-regexp} to a different regular expression depending on the major mode of the editing buffer. -It consists of a list of lists of the form +It consists of a list of lists of the form @code{(@var{MAJOR-MODE} @var{WORD-REGEXP})}, and its default value is @code{nil}. @end defvar @@ -35437,8 +35437,8 @@ formulas. Note that these are actual strings, not regular expressions, because Calc must be able to write these string into a buffer as well as to recognize them. -The default string for @code{calc-embedded-open-plain} is -@code{"%%% "}, note the trailing space. The default string for +The default string for @code{calc-embedded-open-plain} is +@code{"%%% "}, note the trailing space. The default string for @code{calc-embedded-close-plain} is @code{" %%%\n"}, without the trailing newline here, the first line of a Big mode formula that followed might be shifted over with respect to the other lines. @@ -35447,7 +35447,7 @@ The variable @code{calc-embedded-open-close-plain-alist} is used to set @code{calc-embedded-open-plain} and @code{calc-embedded-close-plain} to different strings depending on the major mode of the editing buffer. -It consists of a list of lists of the form +It consists of a list of lists of the form @code{(@var{MAJOR-MODE} @var{OPEN-PLAIN-STRING} @var{CLOSE-PLAIN-STRING})}, and its default value is @example @@ -35490,7 +35490,7 @@ The variable @code{calc-embedded-open-close-new-formula-alist} is used to set @code{calc-embedded-open-new-formula} and @code{calc-embedded-close-new-formula} to different strings depending on the major mode of the editing buffer. -It consists of a list of lists of the form +It consists of a list of lists of the form @code{(@var{MAJOR-MODE} @var{OPEN-NEW-FORMULA-STRING} @var{CLOSE-NEW-FORMULA-STRING})}, and its default value is @code{nil}. @@ -35508,7 +35508,7 @@ necessary to add them to user-written annotations. The default value of @code{calc-embedded-open-mode} is @code{"% "} and the default value of @code{calc-embedded-close-mode} is -@code{"\n"}. +@code{"\n"}. If you change the value of @code{calc-embedded-close-mode}, it is a good idea still to end with a newline so that mode annotations will appear on lines by themselves. @@ -35517,7 +35517,7 @@ The variable @code{calc-embedded-open-close-mode-alist} is used to set @code{calc-embedded-open-mode} and @code{calc-embedded-close-mode} to different strings expressions depending on the major mode of the editing buffer. -It consists of a list of lists of the form +It consists of a list of lists of the form @code{(@var{MAJOR-MODE} @var{OPEN-MODE-STRING} @var{CLOSE-MODE-STRING})}, and its default value is @example @@ -35548,7 +35548,7 @@ units. The default value of @code{calc-lu-power-reference} is @code{"mW"} and the default value of @code{calc-lu-field-reference} is -@code{"20 uPa"}. +@code{"20 uPa"}. @end defvar @defvar calc-note-threshold @@ -35564,15 +35564,15 @@ The default value of @code{calc-note-threshold} is 1. @defvarx calc-selected-face @defvarx calc-nonselected-face See @ref{Displaying Selections}.@* -The variable @code{calc-highlight-selections-with-faces} +The variable @code{calc-highlight-selections-with-faces} determines how selected sub-formulas are distinguished. -If @code{calc-highlight-selections-with-faces} is nil, then +If @code{calc-highlight-selections-with-faces} is nil, then a selected sub-formula is distinguished either by changing every character not part of the sub-formula with a dot or by changing every -character in the sub-formula with a @samp{#} sign. +character in the sub-formula with a @samp{#} sign. If @code{calc-highlight-selections-with-faces} is t, then a selected sub-formula is distinguished either by displaying the -non-selected portion of the formula with @code{calc-nonselected-face} +non-selected portion of the formula with @code{calc-nonselected-face} or by displaying the selected sub-formula with @code{calc-nonselected-face}. @end defvar @@ -36651,9 +36651,9 @@ input data set. Each entry may be a single value or a vector of values. @c 20 @item -With a prefix argument of 1, take a single +With a prefix argument of 1, take a single @texline @var{n}@math{\times2} -@infoline @mathit{@var{N}x2} +@infoline @mathit{@var{N}x2} matrix from the stack instead of two separate data vectors. @c 21 @@ -36754,7 +36754,7 @@ Variable name may be a single digit or a full name. @c 30 @item -Editing occurs in a separate buffer. Press @kbd{C-c C-c} (or +Editing occurs in a separate buffer. Press @kbd{C-c C-c} (or @key{LFD}, or in some cases @key{RET}) to finish the edit, or kill the buffer with @kbd{C-x k} to cancel the edit. The @key{LFD} key prevents evaluation of the result of the edit. @@ -36854,7 +36854,7 @@ to evaluate variables. @item The variable is replaced by the formula shown on the right. The Inverse flag reverses the order of the operands, e.g., @kbd{I s - x} -assigns +assigns @texline @math{x \coloneq a-x}. @infoline @expr{x := a-x}. diff --git a/doc/misc/cc-mode.texi b/doc/misc/cc-mode.texi index 55c2c4c0ae8..d5f403e5cdb 100644 --- a/doc/misc/cc-mode.texi +++ b/doc/misc/cc-mode.texi @@ -912,7 +912,7 @@ construct, should the point start inside it. If @ccmode fails to find function beginnings or ends inside the current declaration scope, it will search the enclosing scopes. If you want @ccmode to recognize functions only at the top level@footnote{this was @ccmode{}'s -behavior prior to version 5.32.}, set @code{c-defun-tatic} to +behavior prior to version 5.32.}, set @code{c-defun-tactic} to @code{t}. These functions are analogous to the Emacs built-in commands diff --git a/doc/misc/faq.texi b/doc/misc/faq.texi index 262c3d734fe..15c9232d4b6 100644 --- a/doc/misc/faq.texi +++ b/doc/misc/faq.texi @@ -627,7 +627,7 @@ translations of the reference card into several languages; look for files named @file{etc/refcards/@var{lang}-refcard.*}, where @var{lang} is a two-letter code of the language. For example, the German version of the reference card is in the files @file{etc/refcards/de-refcard.tex} -and @file{etc/recards/de-refcard.pdf}. +and @file{etc/refcards/de-refcard.pdf}. @item There are many other commands in Emacs for getting help and diff --git a/doc/misc/gnus.texi b/doc/misc/gnus.texi index 3bfa5a89e79..327fb392242 100644 --- a/doc/misc/gnus.texi +++ b/doc/misc/gnus.texi @@ -25471,7 +25471,7 @@ Write @code{spam-check-blackbox} if Blackbox can check incoming mail. Write @code{spam-blackbox-register-routine} and @code{spam-blackbox-unregister-routine} using the bogofilter -register/unregister routines as a start, or other restister/unregister +register/unregister routines as a start, or other register/unregister routines more appropriate to Blackbox, if Blackbox can register/unregister spam and ham. diff --git a/etc/NEWS.1-17 b/etc/NEWS.1-17 index 9a72089859e..dc9922ed989 100644 --- a/etc/NEWS.1-17 +++ b/etc/NEWS.1-17 @@ -775,7 +775,7 @@ to the value of `minibuffer-help-form'. `help-form' is expected at all times to contain either `nil' or an expression to be executed when C-h is typed (overriding -teh definition of C-h as a command). `minibuffer-help-form' +the definition of C-h as a command). `minibuffer-help-form' can be used to provide a different default way of handling C-h while in the minibuffer. @@ -1870,7 +1870,7 @@ Changes in Emacs 1.9 * The variable global-minor-modes is used to display strings in the mode line of all buffers. It should be - a list of elements thaht are conses whose cdrs are strings + a list of elements that are conses whose cdrs are strings to be displayed. This complements the variable minor-modes, which has the same effect but has a separate value in each buffer. diff --git a/etc/NEWS.18 b/etc/NEWS.18 index ce1f6b12fb3..820103e3110 100644 --- a/etc/NEWS.18 +++ b/etc/NEWS.18 @@ -1303,7 +1303,7 @@ changing the file's uid or gid. The default value of this variable is `nil', because usually it is useful to have the uid of a file change according to who edited it -last. I recommend thet this variable be left normally `nil' and +last. I recommend that this variable be left normally `nil' and changed with a local variables list in those particular files where the uid needs to be preserved. diff --git a/etc/NEWS.19 b/etc/NEWS.19 index 88e5849f136..16a9d9dc4cb 100644 --- a/etc/NEWS.19 +++ b/etc/NEWS.19 @@ -5484,7 +5484,7 @@ non-nil. ** M-x revert-buffer no longer offers to revert from a recent auto-save file unless you give it a prefix argument. Otherwise it always reverts from the real file regardless of whether there has been an -auto-save since thenm. (Reverting from the auto-save file is no longer +auto-save since then. (Reverting from the auto-save file is no longer very useful now that the undo capacity is larger.) ** M-x recover-file no longer turns off Auto Save mode when it reads diff --git a/etc/THE-GNU-PROJECT b/etc/THE-GNU-PROJECT index 80dde864901..f3d554e45bf 100644 --- a/etc/THE-GNU-PROJECT +++ b/etc/THE-GNU-PROJECT @@ -762,7 +762,7 @@ Those of us who value free software for freedom's sake will stay with free software anyway. We will manage to get work done without the patented features. But those who value free software because they - expect it to be techically superior are likely to call it a failure + expect it to be technically superior are likely to call it a failure when a patent holds it back. Thus, while it is useful to talk about the practical effectiveness of the "cathedral" model of development (1), and the reliability and power of some free software, we must not stop diff --git a/leim/quail/sgml-input.el b/leim/quail/sgml-input.el index 3b569879404..a8c335afa33 100644 --- a/leim/quail/sgml-input.el +++ b/leim/quail/sgml-input.el @@ -916,7 +916,7 @@ E.g.: á -> á" ("θ" ?\θ) ;; GREEK SMALL LETTER THETA ("Θ" ?\Θ) ;; GREEK CAPITAL LETTER THETA ("&thetas;" ?\θ) ;; GREEK SMALL LETTER THETA - ("&thetasyLsymbol;" ?\ϑ) ;; GREEK THETA SYMBOL + ("ϑ" ?\ϑ) ;; GREEK THETA SYMBOL ("ϑ" ?\ϑ) ;; GREEK THETA SYMBOL ("&THgr;" ?\Θ) ;; GREEK CAPITAL LETTER THETA ("&thgr;" ?\θ) ;; GREEK SMALL LETTER THETA diff --git a/lisp/allout.el b/lisp/allout.el index bd2094da253..e701d9685a1 100644 --- a/lisp/allout.el +++ b/lisp/allout.el @@ -612,7 +612,7 @@ headers look like comments in the programming language. It will also use the comment-start string, with an '_' appended, for `allout-primary-bullet'. String values are used as literals, not regular expressions, so -do not escape any regulare-expression characters. +do not escape any regular-expression characters. Value t means to first check for assoc value in `allout-mode-leaders' alist, then use comment-start string, if any, then use default (`.'). diff --git a/lisp/cedet/ede/generic.el b/lisp/cedet/ede/generic.el index d73a32a8bcb..69570771546 100644 --- a/lisp/cedet/ede/generic.el +++ b/lisp/cedet/ede/generic.el @@ -359,7 +359,7 @@ the new configuration." (defun ede-generic-new-autoloader (internal-name external-name projectfile class) "Add a new EDE Autoload instance for identifying a generic project. -INTERNAL-NAME is a long name that identifies thsi project type. +INTERNAL-NAME is a long name that identifies this project type. EXTERNAL-NAME is a shorter human readable name to describe the project. PROJECTFILE is a file name that identifies a project of this type to EDE, such as a Makefile, or SConstruct file. diff --git a/lisp/cedet/ede/pconf.el b/lisp/cedet/ede/pconf.el index 05290158189..ae503e836d8 100644 --- a/lisp/cedet/ede/pconf.el +++ b/lisp/cedet/ede/pconf.el @@ -82,7 +82,7 @@ don't do it. A value of nil means to just do it.") (directory-file-name (ede-subproject-relative-path sp top-level-project-local))))) (when (string= dir "./") (setq dir "")) - ;; Use concat, because expand-file-name removes the relativeness. + ;; Use concat, because expand-file-name removes the relativity. (concat dir "Makefile") ))))) ;; ;; NOTE TO SELF. TURN THIS INTO THE OFFICIAL LIST diff --git a/lisp/cedet/ede/project-am.el b/lisp/cedet/ede/project-am.el index 316309092e7..033a486f1a7 100644 --- a/lisp/cedet/ede/project-am.el +++ b/lisp/cedet/ede/project-am.el @@ -284,7 +284,7 @@ buffer being in order to provide a smart default target type." (progn (forward-line -1) (end-of-line) (insert "\n")) - ;; If the above search fails, thats ok. We'd just want to be at + ;; If the above search fails, that's ok. We'd just want to be at ;; point-min anyway. ) (makefile-insert-macro (car (cdr (cdr ntype)))))) diff --git a/lisp/cedet/semantic/analyze.el b/lisp/cedet/semantic/analyze.el index 43e998b852e..ae199703c80 100644 --- a/lisp/cedet/semantic/analyze.el +++ b/lisp/cedet/semantic/analyze.el @@ -161,7 +161,7 @@ be just a string in some circumstances.") (defclass semantic-analyze-context-return (semantic-analyze-context) () ; No extra data. "Analysis class for return data. -Return data methods identify the requred type by the return value +Return data methods identify the required type by the return value of the parent function.") ;;; METHODS diff --git a/lisp/cedet/semantic/bovine/c.el b/lisp/cedet/semantic/bovine/c.el index 7de0011ce92..686113c23e2 100644 --- a/lisp/cedet/semantic/bovine/c.el +++ b/lisp/cedet/semantic/bovine/c.el @@ -954,7 +954,7 @@ now. (nth 1 (car names)) ; name "typedef" (semantic-tag-type-members tag) - ;; parent is just tbe name of what + ;; parent is just the name of what ;; is passed down as a tag. (list (semantic-tag-name diff --git a/lisp/cedet/semantic/complete.el b/lisp/cedet/semantic/complete.el index 2b3841bd594..aaec4cb30ff 100644 --- a/lisp/cedet/semantic/complete.el +++ b/lisp/cedet/semantic/complete.el @@ -1478,7 +1478,7 @@ one in the source buffer." (tag (cdr nt)) (table (car nt)) ) - ;; If we fail to normalize, resete. + ;; If we fail to normalize, reset. (when (not tag) (setq table rtable tag rtag)) ;; Do the focus. (let ((buf (or (semantic-tag-buffer tag) diff --git a/lisp/cedet/semantic/db-javascript.el b/lisp/cedet/semantic/db-javascript.el index 716bbc9d00a..e662290340d 100644 --- a/lisp/cedet/semantic/db-javascript.el +++ b/lisp/cedet/semantic/db-javascript.el @@ -137,7 +137,7 @@ Create one of our special tables that can act as an intermediary." (defmethod semanticdb-get-tags ((table semanticdb-table-javascript )) "Return the list of tags belonging to TABLE." - ;; NOTE: Omniscient databases probably don't want to keep large tabes + ;; NOTE: Omniscient databases probably don't want to keep large tables ;; lolly-gagging about. Keep internal Emacs tables empty and ;; refer to alternate databases when you need something. semanticdb-javascript-tags) diff --git a/lisp/cedet/semantic/edit.el b/lisp/cedet/semantic/edit.el index 0780a628254..a2c8c5efd40 100644 --- a/lisp/cedet/semantic/edit.el +++ b/lisp/cedet/semantic/edit.el @@ -649,7 +649,7 @@ This function is for internal use by `semantic-edits-incremental-parser'." parent-tag (aref tmp 2)) ;; We can calculate parse begin/end by checking ;; out what is in TAGS. The one near start is - ;; always first. Make sure the reprase includes + ;; always first. Make sure the reparse includes ;; the `whitespace' around the snarfed tags. ;; Since cache-list is positioned properly, use it ;; to find that boundary. @@ -707,7 +707,7 @@ This function is for internal use by `semantic-edits-incremental-parser'." ;; since that is how the multi-tag parser works. Grab ;; the reparse symbol from the first of the returned tags. ;; - ;; Feb '06 - If repase-symbol is nil, then they are top level + ;; Feb '06 - If reparse-symbol is nil, then they are top level ;; tags. (I'm guessing.) Is this right? (setq reparse-symbol (semantic--tag-get-property (car (or tags cache-list)) diff --git a/lisp/cedet/semantic/fw.el b/lisp/cedet/semantic/fw.el index ca3015c5941..479044ec518 100644 --- a/lisp/cedet/semantic/fw.el +++ b/lisp/cedet/semantic/fw.el @@ -251,7 +251,7 @@ later installation should be done in MODE hook." (defmacro semantic-exit-on-input (symbol &rest forms) "Using SYMBOL as an argument to `throw', execute FORMS. -If FORMS includes a call to `semantic-thow-on-input', then +If FORMS includes a call to `semantic-throw-on-input', then if a user presses any key during execution, this form macro will exit with the value passed to `semantic-throw-on-input'. If FORMS completes, then the return value is the same as `progn'." diff --git a/lisp/cedet/semantic/scope.el b/lisp/cedet/semantic/scope.el index 16deb245527..ea4903c70ea 100644 --- a/lisp/cedet/semantic/scope.el +++ b/lisp/cedet/semantic/scope.el @@ -303,7 +303,7 @@ are from nesting data types." (miniscope (semantic-scope-cache "mini")) ptag) - ;; Find the next entry in the refereneced type for + ;; Find the next entry in the referenced type for ;; our function, and append to return list till our ;; returnlist is empty. (while snlist diff --git a/lisp/cedet/semantic/tag.el b/lisp/cedet/semantic/tag.el index 82b23d8d1cd..f8538ef7901 100644 --- a/lisp/cedet/semantic/tag.el +++ b/lisp/cedet/semantic/tag.el @@ -919,7 +919,7 @@ That is the value of the attribute `:system-flag'." "Return a filename representation of TAG. The default action is to return the `semantic-tag-name'. Some languages do not use full filenames in their include statements. -Override this method to translate the code represenation +Override this method to translate the code representation into a filename. (A relative filename if necessary.) See `semantic-dependency-tag-file' to expand an include diff --git a/lisp/cedet/srecode/document.el b/lisp/cedet/srecode/document.el index 134b5310ab3..e25905ead83 100644 --- a/lisp/cedet/srecode/document.el +++ b/lisp/cedet/srecode/document.el @@ -698,7 +698,7 @@ allocating something based on its type." (cdr (car al))))) (setq al nil))) (setq al (cdr al))) - ;; add tailers to names which are obviously returning something. + ;; add trailers to names which are obviously returning something. (if tailit (progn (setq al srecode-document-autocomment-return-last-alist) diff --git a/lisp/comint.el b/lisp/comint.el index 3b874c48f27..c0b02e5a230 100644 --- a/lisp/comint.el +++ b/lisp/comint.el @@ -1980,7 +1980,7 @@ Make backspaces delete the previous character." ;; The point should float after any insertion we do. (saved-point (copy-marker (point) t))) - ;; We temporarly remove any buffer narrowing, in case the + ;; We temporarily remove any buffer narrowing, in case the ;; process mark is outside of the restriction (save-restriction (widen) diff --git a/lisp/dframe.el b/lisp/dframe.el index b7c29d8f992..b1eb2d636b9 100644 --- a/lisp/dframe.el +++ b/lisp/dframe.el @@ -82,7 +82,7 @@ ;; c) If successful (your -frame variable has a value), call ;; timer setup if applicable. ;; your-frame-reposition- -- Function to call from after-create-hook to -;; reposition your frame with `dframe-repsoition-frame'. +;; reposition your frame with `dframe-reposition-frame'. ;; your-mode -- Set up the major mode of the buffer for your app. ;; Set these variables: dframe-track-mouse-function, ;; dframe-help-echo-function, @@ -726,7 +726,7 @@ who requested the timer. NULL-ON-ERROR is ignored." (if timeout (add-to-list 'dframe-client-functions fn) (setq dframe-client-functions (delete fn dframe-client-functions))) - ;; Now decided what to do about the timout. + ;; Now decided what to do about the timeout. (if (or ;; We have a timer, restart the timer with the new time. timeout diff --git a/lisp/emacs-lisp/avl-tree.el b/lisp/emacs-lisp/avl-tree.el index e8b7a1f9a8b..9ecd4e12020 100644 --- a/lisp/emacs-lisp/avl-tree.el +++ b/lisp/emacs-lisp/avl-tree.el @@ -206,7 +206,7 @@ Return t if the height of the tree has shrunk." Return cons cell (SHRUNK . DATA), where SHRUNK is t if the height of the tree has shrunk and nil otherwise, and DATA is -the releted data." +the related data." (let ((br (avl-tree--node-branch root branch))) (cond ;; DATA not in tree. diff --git a/lisp/emacs-lisp/elint.el b/lisp/emacs-lisp/elint.el index dd3e02b8388..ba04a27021e 100644 --- a/lisp/emacs-lisp/elint.el +++ b/lisp/emacs-lisp/elint.el @@ -335,7 +335,7 @@ Will be local in linted buffers.") Is measured in buffer-modified-ticks and is local in linted buffers.") ;; This is a minor optimization. It is local to every buffer, and so -;; does not prevent recursive requirs. It does not list the requires +;; does not prevent recursive requires. It does not list the requires ;; of requires. (defvar elint-features nil "List of all libraries this buffer has required, or that have been provided.") diff --git a/lisp/emulation/viper-init.el b/lisp/emulation/viper-init.el index c069c387003..b0c37ed28e4 100644 --- a/lisp/emulation/viper-init.el +++ b/lisp/emulation/viper-init.el @@ -205,7 +205,7 @@ designated buffers.") (viper-deflocalvar viper-insert-diehard-minor-mode nil "Minor mode that simulates Vi very closely. -Not recommened, except for the novice user.") +Not recommended, except for the novice user.") (viper-deflocalvar viper-insert-kbd-minor-mode nil "Minor mode for Ex command macros Insert state. @@ -679,7 +679,7 @@ to a new place after repeating previous Vi command." :group 'viper-search) (defcustom viper-search-scroll-threshold 2 - "*If search lands within this threshnold from the window top/bottom, + "*If search lands within this threshold from the window top/bottom, the window will be scrolled up or down appropriately, to reveal context. If you want Viper search to behave as usual in Vi, set this variable to a negative number." diff --git a/lisp/erc/ChangeLog.01 b/lisp/erc/ChangeLog.01 index f4e10d05981..2b29acf5a25 100644 --- a/lisp/erc/ChangeLog.01 +++ b/lisp/erc/ChangeLog.01 @@ -93,7 +93,7 @@ * erc.el: * erc-insert-hook: Changed strategy completely, no start end parameters any more. - We narrow-to-region now, thats much cleaner. + We narrow-to-region now, that's much cleaner. * rename erc-fill-region to erc-fill and change the autoload ** You'll probably need to restart Emacs @@ -221,7 +221,7 @@ * Applied antifuchs/mhp patches, the latest on erc-help, unmodified * New variable: erc-reuse-buffers default to t. * Modified erc-generate-new-buffer-name to use it. it checks if server and port are the same, - then one can assume thats the same channel/query target again. + then one can assume that's the same channel/query target again. 2001-11-23 Mario Lang <mlang@delysid.org> @@ -415,7 +415,7 @@ * erc.el: only some code beautification * erc-imenu.el: - remove add-hook call, thats done in erc.el now for autoloadability + remove add-hook call, that's done in erc.el now for autoloadability * erc.el: * Make erc-imenu autoloadable diff --git a/lisp/ezimage.el b/lisp/ezimage.el index a3562944039..d0bbdfb2f8a 100644 --- a/lisp/ezimage.el +++ b/lisp/ezimage.el @@ -239,7 +239,7 @@ IMAGESPEC is the image data, and DOCSTRING is documentation for the image." ("[ ]" . ezimage-page) ("{+}" . ezimage-box-plus) ("{-}" . ezimage-box-minus) - ;; Some vaguely representitive entries + ;; Some vaguely representative entries ("*" . ezimage-checkout) ("#" . ezimage-object) ("!" . ezimage-object-out-of-date) diff --git a/lisp/faces.el b/lisp/faces.el index 7bc103ca699..f10c9f87f25 100644 --- a/lisp/faces.el +++ b/lisp/faces.el @@ -1925,7 +1925,7 @@ frame parameters in PARAMETERS." (progn ;; Initialize faces from face spec and custom theme. (face-spec-recalc face frame) - ;; X resouces for the default face are applied during + ;; X resources for the default face are applied during ;; `x-create-frame'. (and (not (eq face 'default)) window-system-p (make-face-x-resource-internal face frame)) diff --git a/lisp/follow.el b/lisp/follow.el index 7375b15ad16..852944a8061 100644 --- a/lisp/follow.el +++ b/lisp/follow.el @@ -562,7 +562,7 @@ Keys specific to Follow mode: ;; ;; Almost like the real thing, except when the cursor ends up outside ;; the top or bottom... In our case however, we end up outside the -;; window and hence we are recenterd. Should we let `recenter' handle +;; window and hence we are recentered. Should we let `recenter' handle ;; the point position we would never leave the selected window. To do ;; it ourselves we would need to do our own redisplay, which is easier ;; said than done. (Why didn't I do a real display abstraction from diff --git a/lisp/font-lock.el b/lisp/font-lock.el index d410b8eb51a..c319974fb41 100644 --- a/lisp/font-lock.el +++ b/lisp/font-lock.el @@ -981,7 +981,7 @@ The value of this variable is used when Font Lock mode is turned on." ;; rules one way and C code another. Neat! ;; ;; A further reason to use the fontification indirection feature is when the -;; default syntactual fontification, or the default fontification in general, +;; default syntactic fontification, or the default fontification in general, ;; is not flexible enough for a particular major mode. For example, perhaps ;; comments are just too hairy for `font-lock-fontify-syntactically-region' to ;; cope with. You need to write your own version of that function, e.g., diff --git a/lisp/gnus/gnus-group.el b/lisp/gnus/gnus-group.el index 4c527caff5c..6f146644115 100644 --- a/lisp/gnus/gnus-group.el +++ b/lisp/gnus/gnus-group.el @@ -1361,7 +1361,7 @@ if it is a string, only list groups matching REGEXP." ; We list groups with unread articles (and gnus-list-groups-with-ticked-articles (cdr (assq 'tick (gnus-info-marks info)))) - ; And groups with tickeds + ; And groups with ticked articles ;; Check for permanent visibility. (and gnus-permanently-visible-groups (string-match gnus-permanently-visible-groups diff --git a/lisp/gnus/gnus-sum.el b/lisp/gnus/gnus-sum.el index 5380595eadb..7cea88e7f54 100644 --- a/lisp/gnus/gnus-sum.el +++ b/lisp/gnus/gnus-sum.el @@ -1657,7 +1657,7 @@ For example: This variable is a list of FUNCTION or (REGEXP . FUNCTION). If item is FUNCTION, FUNCTION will be apply to all newsgroups. If item is a -\(REGEXP . FUNCTION), FUNCTION will be only apply to thes newsgroups +\(REGEXP . FUNCTION), FUNCTION will be applied only to the newsgroups whose names match REGEXP. For example: diff --git a/lisp/gnus/message.el b/lisp/gnus/message.el index 176857633e1..5d82faee20d 100644 --- a/lisp/gnus/message.el +++ b/lisp/gnus/message.el @@ -7167,7 +7167,7 @@ header line with the old Message-ID." (defun message-wash-subject (subject) "Remove junk like \"Re:\", \"(fwd)\", etc. added to subject string SUBJECT. -Previous forwarders, replyers, etc. may add it." +Previous forwarders, repliers, etc. may add it." (with-temp-buffer (insert subject) (goto-char (point-min)) diff --git a/lisp/gnus/nntp.el b/lisp/gnus/nntp.el index 325aa67f80d..9816c208fab 100644 --- a/lisp/gnus/nntp.el +++ b/lisp/gnus/nntp.el @@ -1681,7 +1681,7 @@ password contained in '~/.nntp-authinfo'." ;; for the first available article. Obviously, a client can ;; use that entry to avoid making unnecessary requests. The ;; only problem is for a client that assumes that the response - ;; will always be within the requested ranage. For such a + ;; will always be within the requested range. For such a ;; client, we can get N copies of the same entry (one for each ;; XOVER command sent to the server). diff --git a/lisp/gnus/smime.el b/lisp/gnus/smime.el index 128bda6f516..90af71404ef 100644 --- a/lisp/gnus/smime.el +++ b/lisp/gnus/smime.el @@ -180,7 +180,7 @@ File should contain certificates in PEM format." (defcustom smime-certificate-directory "~/Mail/certs/" "*Directory containing other people's certificates. It should contain files named to the X.509 hash of the certificate, -and the files themself should be in PEM format." +and the files themselves should be in PEM format." ;The S/MIME library provide simple functionality for fetching ;certificates into this directory, so there is no need to populate it ;manually. diff --git a/lisp/image-dired.el b/lisp/image-dired.el index 8c151d35ed2..4a164dfaa42 100644 --- a/lisp/image-dired.el +++ b/lisp/image-dired.el @@ -469,7 +469,7 @@ For more information, see the documentation for If non-nil, using `image-dired-next-line-and-display' and `image-dired-previous-line-and-display' will leave a trail of thumbnail images in the thumbnail buffer. If you enable this and want to clean -the thumbnail buffer because it is filled with too many thumbmnails, +the thumbnail buffer because it is filled with too many thumbnails, just call `image-dired-display-thumb' to display only the image at point. This value can be toggled using `image-dired-toggle-append-browsing'." :type 'boolean @@ -1605,7 +1605,7 @@ With prefix argument ARG, create thumbnails even if they already exist (setq thumb-name (image-dired-thumb-name curr-file)) ;; If the user overrides the exist check, we must clear the ;; image cache so that if the user wants to display the - ;; thumnail, it is not fetched from cache. + ;; thumbnail, it is not fetched from cache. (if arg (clear-image-cache)) (if (or (not (file-exists-p thumb-name)) @@ -2043,7 +2043,7 @@ function. The result is a couple of new files in files))) (defun image-dired-display-next-thumbnail-original () - "In thubnail buffer, move to next thumbnail and display the image." + "In thumbnail buffer, move to next thumbnail and display the image." (interactive) (image-dired-forward-image) (image-dired-display-thumbnail-original-image)) diff --git a/lisp/info-xref.el b/lisp/info-xref.el index 8a5cca18496..805bec064cf 100644 --- a/lisp/info-xref.el +++ b/lisp/info-xref.el @@ -413,7 +413,7 @@ and can take a long time." (unless (boundp 'viper-mode) (setq viper-mode nil)) ;; avoid viper.el ask about viperizing (unless (boundp 'gnus-registry-install) - (setq gnus-registry-install nil)) ;; avoid gnus-registery.el querying + (setq gnus-registry-install nil)) ;; avoid gnus-registry.el querying (mapatoms (lambda (symbol) diff --git a/lisp/international/titdic-cnv.el b/lisp/international/titdic-cnv.el index 757322aa0ce..0ba0b9085b9 100644 --- a/lisp/international/titdic-cnv.el +++ b/lisp/international/titdic-cnv.el @@ -1179,7 +1179,7 @@ the generated Quail package is saved." (setq tail (cdr tail))))) (defun batch-miscdic-convert () - "Run `miscdic-convert' on the files remaing on the command line. + "Run `miscdic-convert' on the files remaining on the command line. Use this from the command line, with `-batch'; it won't work in an interactive Emacs. If there's an argument \"-dir\", the next argument specifies a directory diff --git a/lisp/language/thai-util.el b/lisp/language/thai-util.el index b7dbcc1a956..e9943df12a8 100644 --- a/lisp/language/thai-util.el +++ b/lisp/language/thai-util.el @@ -124,7 +124,7 @@ (?ใ vowel-base "VOWEL SIGN SARA MAI MUAN") ; 0xE3 (?ไ vowel-base "VOWEL SIGN SARA MAI MALAI") ; 0xE4 (?ๅ vowel-base "LAK KHANG YAO") ; 0xE5 - (?ๆ special "MAI YAMOK (repetion)") ; 0xE6 + (?ๆ special "MAI YAMOK (repetition)") ; 0xE6 (?็ sign-upper "VOWEL SIGN MAI TAI KHU N/S-T") ; 0xE7 (?่ tone "TONE MAI EK N/S-T") ; 0xE8 (?้ tone "TONE MAI THO N/S-T") ; 0xE9 diff --git a/lisp/loadhist.el b/lisp/loadhist.el index da20e4cb7ca..51df6ecff0a 100644 --- a/lisp/loadhist.el +++ b/lisp/loadhist.el @@ -133,7 +133,7 @@ from a file." font-lock-unfontify-region-function kill-buffer-query-functions kill-emacs-query-functions lisp-indent-function mouse-position-function - redisplaylay-end-trigger-functions suspend-tty-functions + redisplay-end-trigger-functions suspend-tty-functions temp-buffer-show-function window-scroll-functions window-size-change-functions write-contents-functions write-file-functions write-region-annotate-functions) diff --git a/lisp/mail/feedmail.el b/lisp/mail/feedmail.el index 43d43617631..7167fa567d3 100644 --- a/lisp/mail/feedmail.el +++ b/lisp/mail/feedmail.el @@ -1010,7 +1010,7 @@ If it contains a \"%s\", that will be replaced with the value of (defcustom feedmail-ask-before-queue-reprompt "FQM: Please type q, i, d, or e; or ? for help [%s]: " - "A string which will be used for repompting after invalid input. + "A string which will be used for reprompting after invalid input. If it contains a \"%s\", that will be replaced with the value of `feedmail-ask-before-queue-default'." :group 'feedmail-queue diff --git a/lisp/mpc.el b/lisp/mpc.el index 238e8ad68ae..6c2556b1f39 100644 --- a/lisp/mpc.el +++ b/lisp/mpc.el @@ -1589,7 +1589,7 @@ when constructing the set of constraints." (defvar mpc--changed-selection) (defun mpc-reorder (&optional nodeactivate) - "Reorder entries based on thre currently active selections. + "Reorder entries based on the currently active selections. I.e. split the current browser buffer into a first part containing the entries included in the selection, then a separator, and then the entries not included in the selection. diff --git a/lisp/net/tramp-cmds.el b/lisp/net/tramp-cmds.el index fcf523a7068..998f62920a1 100644 --- a/lisp/net/tramp-cmds.el +++ b/lisp/net/tramp-cmds.el @@ -23,7 +23,7 @@ ;;; Commentary: -;; This package provides all interactive commands which are releated +;; This package provides all interactive commands which are related ;; to Tramp. ;;; Code: diff --git a/lisp/net/tramp-gw.el b/lisp/net/tramp-gw.el index 70b70004de9..4ddd63bc3b8 100644 --- a/lisp/net/tramp-gw.el +++ b/lisp/net/tramp-gw.el @@ -178,7 +178,7 @@ instead of the host name declared in TARGET-VEC." (tramp-file-name-host gw-vec))) ;; Declare the SOCKS server to be used. (socks-server - (list "Tramp tempory socks server list" + (list "Tramp temporary socks server list" ;; Host name. (tramp-file-name-real-host gw-vec) ;; Port number. diff --git a/lisp/net/tramp-sh.el b/lisp/net/tramp-sh.el index 51fc6e295f0..941b788ae4d 100644 --- a/lisp/net/tramp-sh.el +++ b/lisp/net/tramp-sh.el @@ -4905,7 +4905,7 @@ If no corresponding command is found, nil is returned." (defun tramp-get-inline-coding (vec prop size) "Return the coding command related to PROP. -PROP is either `remote-encoding', `remode-decoding', +PROP is either `remote-encoding', `remote-decoding', `local-encoding' or `local-decoding'. SIZE is the length of the file to be coded. Depending on SIZE, diff --git a/lisp/notifications.el b/lisp/notifications.el index a4e7fdd5425..e4e44fb0f67 100644 --- a/lisp/notifications.el +++ b/lisp/notifications.el @@ -163,7 +163,7 @@ Various PARAMS can be set: only URI schema supported right now) or a name in a freedesktop.org-compliant icon theme. :sound-file The path to a sound file to play when the notification pops up. - :sound-name A themeable named sound from the freedesktop.org sound naming + :sound-name A themable named sound from the freedesktop.org sound naming specification to play when the notification pops up. Similar to icon-name,only for sounds. An example would be \"message-new-instant\". diff --git a/lisp/org/org-capture.el b/lisp/org/org-capture.el index 24aea5d7eae..e3a87b77b5c 100644 --- a/lisp/org/org-capture.el +++ b/lisp/org/org-capture.el @@ -1449,7 +1449,7 @@ The template may still contain \"%?\" for cursor positioning." (goto-char (point-min)) (while (looking-at "[ \t]*\n") (replace-match "")) (if (re-search-forward "[ \t\n]*\\'" nil t) (replace-match "\n")) - ;; Return the expanded tempate and kill the temporary buffer + ;; Return the expanded template and kill the temporary buffer (untabify (point-min) (point-max)) (set-buffer-modified-p nil) (prog1 (buffer-string) (kill-buffer (current-buffer)))))) diff --git a/lisp/org/org-list.el b/lisp/org/org-list.el index 9184f0c3d54..cc8103e3c19 100644 --- a/lisp/org/org-list.el +++ b/lisp/org/org-list.el @@ -3008,7 +3008,7 @@ Valid parameters PARAMS are: Alternatively, each parameter can also be a form returning a string. These sexp can use keywords `counter' and `depth', -reprensenting respectively counter associated to the current +representing respectively counter associated to the current item, and depth of the current sub-list, starting at 0. Obviously, `counter' is only available for parameters applying to items." diff --git a/lisp/org/org-table.el b/lisp/org/org-table.el index 92c14f4cd59..76e4eae4b45 100644 --- a/lisp/org/org-table.el +++ b/lisp/org/org-table.el @@ -2641,7 +2641,7 @@ in the buffer and column1 and column2 are table column numbers." (prog1 (org-trim (org-table-get-field c1)) (if highlight (org-table-highlight-rectangle (point) (point))))) ;; A range, return a vector - ;; First sort the numbers to get a regular ractangle + ;; First sort the numbers to get a regular rectangle (if (< r2 r1) (setq tmp r1 r1 r2 r2 tmp)) (if (< c2 c1) (setq tmp c1 c1 c2 c2 tmp)) (if corners-only diff --git a/lisp/progmodes/cc-engine.el b/lisp/progmodes/cc-engine.el index 5ec0ab04f7f..c794cad65db 100644 --- a/lisp/progmodes/cc-engine.el +++ b/lisp/progmodes/cc-engine.el @@ -893,7 +893,7 @@ comment at the start of cc-engine.el for more info." ((eq sym 'while) ;; Is this a real while, or a do-while? ;; The next `when' triggers unless we are SURE that - ;; the `while' is not the tailend of a `do-while'. + ;; the `while' is not the tail end of a `do-while'. (when (or (not pptok) (memq (char-after pptok) delims) ;; The following kludge is to prevent @@ -9784,7 +9784,7 @@ comment at the start of cc-engine.el for more info." (c-beginning-of-statement-1 containing-sexp) (c-add-stmt-syntax 'statement nil t containing-sexp paren-state)) - ;;CASE 5N: We are at a tompmost continuation line and the only + ;;CASE 5N: We are at a topmost continuation line and the only ;;preceding items are annotations. ((and (c-major-mode-is 'java-mode) (setq placeholder (point)) diff --git a/lisp/progmodes/cperl-mode.el b/lisp/progmodes/cperl-mode.el index 88193d4d3fb..0e649480dda 100644 --- a/lisp/progmodes/cperl-mode.el +++ b/lisp/progmodes/cperl-mode.el @@ -1277,7 +1277,7 @@ versions of Emacs." "----" ["Ispell PODs" cperl-pod-spell ;; Better not to update syntaxification here: - ;; debugging syntaxificatio can be broken by this??? + ;; debugging syntaxification can be broken by this??? (or (get-text-property (point-min) 'in-pod) (< (progn diff --git a/lisp/ps-print.el b/lisp/ps-print.el index 6c80705f993..22f80aa5e82 100644 --- a/lisp/ps-print.el +++ b/lisp/ps-print.el @@ -5372,9 +5372,9 @@ Where: KIND is a valid value of `ps-n-up-filling'. XCOL YCOL are the relative position for the next column. XLIN YLIN are the relative position for the beginning of next line. -REPEAT is the number of repetions for external loop. -END is the number of repetions for internal loop and also the number of pages in - a row. +REPEAT is the number of repetitions for external loop. +END is the number of repetitions for internal loop and also the number + of pages in a row. XSTART YSTART are the relative position for the first page in a sheet.") diff --git a/lisp/startup.el b/lisp/startup.el index 877ba1987f6..06911e00d0d 100644 --- a/lisp/startup.el +++ b/lisp/startup.el @@ -943,7 +943,7 @@ opening the first frame (e.g. open a connection to an X server).") (normal-erase-is-backspace-setup-frame) ;; Register default TTY colors for the case the terminal hasn't a - ;; terminal init file. We do this regardles of whether the terminal + ;; terminal init file. We do this regardless of whether the terminal ;; supports colors or not and regardless the current display type, ;; since users can connect to color-capable terminals and also ;; switch color support on or off in mid-session by setting the diff --git a/lisp/textmodes/reftex-cite.el b/lisp/textmodes/reftex-cite.el index eb0e734080e..e0fd940208a 100644 --- a/lisp/textmodes/reftex-cite.el +++ b/lisp/textmodes/reftex-cite.el @@ -76,7 +76,7 @@ (get 'reftex-default-bibliography :reftex-expanded)) (defun reftex-bib-or-thebib () - ;; Tests if BibTeX or \begin{tehbibliography} should be used for the + ;; Tests if BibTeX or \begin{thebibliography} should be used for the ;; citation ;; Find the bof of the current file (let* ((docstruct (symbol-value reftex-docstruct-symbol)) diff --git a/lisp/thumbs.el b/lisp/thumbs.el index dad4731122e..6ffd256d0a0 100644 --- a/lisp/thumbs.el +++ b/lisp/thumbs.el @@ -235,7 +235,7 @@ reached." (setq dirsize (- dirsize (car (cdar files-list)))) (setq files-list (cdr files-list))))) -;; Check the thumbsnail directory size and clean it if necessary. +;; Check the thumbnail directory size and clean it if necessary. (when thumbs-thumbsdir-auto-clean (thumbs-cleanup-thumbsdir)) diff --git a/lisp/vc/ediff-mult.el b/lisp/vc/ediff-mult.el index cadcdec29b4..ce7818d5ef4 100644 --- a/lisp/vc/ediff-mult.el +++ b/lisp/vc/ediff-mult.el @@ -2164,7 +2164,7 @@ all marked sessions must be active." ;; If meta-buf doesn't exist, it is created. In that case, id doesn't have a ;; parent meta-buf ;; Check if META-BUF exists before calling this function -;; Optional MUST-REDRAW, if non-nil, would force redrawal of the whole meta +;; Optional MUST-REDRAW, if non-nil, would force redrawing of the whole meta ;; buffer. Otherwise, it will just go over the buffer and update activity marks ;; and session status. ;; SESSION-NUMBER, if specified, says which session caused the update. diff --git a/lisp/vc/vc-dispatcher.el b/lisp/vc/vc-dispatcher.el index 84c7f4a510b..7fe727bd179 100644 --- a/lisp/vc/vc-dispatcher.el +++ b/lisp/vc/vc-dispatcher.el @@ -103,7 +103,7 @@ ;; ;; When the client mode adds a local vc-mode-line-hook to a buffer, it ;; will be called with the buffer file name as argument whenever the -;; dispatcher resynchs the buffer. +;; dispatcher resyncs the buffer. ;; To do: ;; diff --git a/lisp/vc/vc.el b/lisp/vc/vc.el index 909585138fc..ed2bac17217 100644 --- a/lisp/vc/vc.el +++ b/lisp/vc/vc.el @@ -2690,7 +2690,7 @@ log entries should be gathered." (substring rev 0 index)))) (defun vc-default-responsible-p (backend file) - "Indicate whether BACKEND is reponsible for FILE. + "Indicate whether BACKEND is responsible for FILE. The default is to return nil always." nil) diff --git a/lwlib/xlwmenu.c b/lwlib/xlwmenu.c index 977f4a70b22..0128464d6e0 100644 --- a/lwlib/xlwmenu.c +++ b/lwlib/xlwmenu.c @@ -113,7 +113,7 @@ xlwMenuTranslations [] = <KeyUp>: key()\n\ "; -/* FIXME: Space should toggle toggleable menu item but not remove the menu +/* FIXME: Space should toggle togglable menu item but not remove the menu so you can toggle the next one without entering the menu again. */ /* FIXME: Should ESC close one level of menu structure or the complete menu? */ diff --git a/src/ChangeLog.11 b/src/ChangeLog.11 index 85f6c00eaaf..896f08916b3 100644 --- a/src/ChangeLog.11 +++ b/src/ChangeLog.11 @@ -7199,7 +7199,7 @@ 2010-06-27 Chong Yidong <cyd@stupidchicken.com> - * xfns.c (Fx_create_frame): Don't consult X resouces when setting + * xfns.c (Fx_create_frame): Don't consult X resources when setting menu-bar-lines and tool-bar-lines. Use menu-bar-mode and tool-bar-mode, which are now set using these X resources at startup, to determine the defaults (Bug#2249). @@ -29136,7 +29136,7 @@ * lisp.h (defvar_per_buffer, DEFVAR_PER_BUFFER): * lread.c (defvar_per_buffer): - * abbrev.c (syms_of_abbrev) <local-abbrev-tabl>: Move to buffer.c. + * abbrev.c (syms_of_abbrev) <local-abbrev-table>: Move to buffer.c. * window.c (candidate_window_p): Only consider as visible frames that are on the same terminal. diff --git a/src/ccl.c b/src/ccl.c index 2b4f04d1247..84d7a6a25ff 100644 --- a/src/ccl.c +++ b/src/ccl.c @@ -826,7 +826,7 @@ while (0) : (charset = CHARSET_FROM_ID ((id)), DECODE_CHAR (charset, (code)))) /* Encode character C by some of charsets in CHARSET_LIST. Set ID to - the id of the used charset, ENCODED to the resulf of encoding. + the id of the used charset, ENCODED to the result of encoding. Assume that we can use the variable `charset'. */ #define CCL_ENCODE_CHAR(c, charset_list, id, encoded) \ diff --git a/src/fontset.c b/src/fontset.c index e20d7957c7f..9697f62ea72 100644 --- a/src/fontset.c +++ b/src/fontset.c @@ -905,7 +905,7 @@ face_suitable_for_char_p (struct face *face, int c) /* Return ID of face suitable for displaying character C on frame F. - FACE must be reazlied for ASCII characters in advance. Called from + FACE must be realized for ASCII characters in advance. Called from the macro FACE_FOR_CHAR. */ int diff --git a/src/gtkutil.c b/src/gtkutil.c index 3df46afcd3a..7e6f5c3164d 100644 --- a/src/gtkutil.c +++ b/src/gtkutil.c @@ -2363,7 +2363,7 @@ xg_create_one_menuitem (widget_value *item, HIGHLIGHT_CB is the callback to call when entering/leaving menu items. POP_UP_P is non-zero if we shall create a popup menu. MENU_BAR_P is non-zero if we shall create a menu bar. - ADD_TEAROFF_P is non-zero if we shall add a teroff menu item. Ignored + ADD_TEAROFF_P is non-zero if we shall add a tearoff menu item. Ignored if MENU_BAR_P is non-zero. TOPMENU is the topmost GtkWidget that others shall be placed under. It may be NULL, in that case we create the appropriate widget diff --git a/src/sound.c b/src/sound.c index 39007574afc..4e9758d27df 100644 --- a/src/sound.c +++ b/src/sound.c @@ -267,7 +267,7 @@ struct sound read from the start of a sound file. */ char *header; - /* Number of bytes raed from sound file. This is always <= + /* Number of bytes read from sound file. This is always <= MAX_SOUND_HEADER_BYTES. */ int header_size; diff --git a/src/sysdep.c b/src/sysdep.c index d666f8dbb79..ae200308bf3 100644 --- a/src/sysdep.c +++ b/src/sysdep.c @@ -1663,7 +1663,7 @@ init_signals (void) sys_siglist[SIGQUIT] = "Quit"; # endif # ifdef SIGRETRACT - sys_siglist[SIGRETRACT] = "Need to relinguish monitor mode"; + sys_siglist[SIGRETRACT] = "Need to relinquish monitor mode"; # endif # ifdef SIGSAK sys_siglist[SIGSAK] = "Secure attention"; diff --git a/src/xfns.c b/src/xfns.c index 88e8ac595c5..c68149cce11 100644 --- a/src/xfns.c +++ b/src/xfns.c @@ -5914,7 +5914,7 @@ the tool bar buttons. */); x_gtk_whole_detached_tool_bar = 0; DEFVAR_BOOL ("x-gtk-use-system-tooltips", x_gtk_use_system_tooltips, - doc: /* *If non-nil with a Gtk+ built Emacs, the Gtk+ toolip is used. + doc: /* *If non-nil with a Gtk+ built Emacs, the Gtk+ tooltip is used. Otherwise use Emacs own tooltip implementation. When using Gtk+ tooltips, the tooltip face is not used. */); x_gtk_use_system_tooltips = 1; |