upstream

33 files changed, 1167 insertions, 1265 deletions

diff --git a/doc/emacs/ChangeLog b/doc/emacs/ChangeLog
index b796acd8b39..6e687bcefc9 100644
--- a/doc/emacs/ChangeLog
+++ b/doc/emacs/ChangeLog
@@ -1,3 +1,12 @@
+2011-11-21  Chong Yidong  <cyd@gnu.org>
+
+        * mark.texi (Global Mark Ring): Fix description of global mark
+        ring (Bug#10032).
+
+2011-11-20  Juanma Barranquero  <lekktu@gmail.com>
+
+        * msdog.texi (Windows Fonts): Fix typo.
+
 2011-11-17  Glenn Morris  <rgm@gnu.org>
 
         * regs.texi (Bookmarks): Small fixes related to saving.  (Bug#10058)
diff --git a/doc/emacs/ack.texi b/doc/emacs/ack.texi
index 6801c7f1e0e..d7022ba739b 100644
--- a/doc/emacs/ack.texi
+++ b/doc/emacs/ack.texi
@@ -549,7 +549,7 @@ Taichi Kawabata added support for Devanagari script and the Indian
 languages, and wrote @file{ucs-normalize.el} for Unicode normalization.
 
 @item
-Taro Kawagishi implented the MD4 Message Digest Algorithm in Lisp; and
+Taro Kawagishi implemented the MD4 Message Digest Algorithm in Lisp; and
 wrote @file{ntlm.el} and @file{sasl-ntlm.el} for NT LanManager
 authentication support.
 
diff --git a/doc/emacs/mark.texi b/doc/emacs/mark.texi
index 0eccef41711..7d65719e5f0 100644
--- a/doc/emacs/mark.texi
+++ b/doc/emacs/mark.texi
@@ -354,9 +354,12 @@ Positions in Registers}).
 @vindex global-mark-ring-max
   In addition to the ordinary mark ring that belongs to each buffer,
 Emacs has a single @dfn{global mark ring}.  Each time you set a mark,
-in any buffer, this is recorded in the global mark ring in addition to
-the current buffer's own mark ring.  The length of this ring can be
-controlled by @code{global-mark-ring-max}, and is 16 by default.
+this is recorded in the global mark ring in addition to the current
+buffer's own mark ring, if you have switched buffers since the
+previous mark setting.  Hence, the global mark ring records a sequence
+of buffers that you have been in, and, for each buffer, a place where
+you set the mark.  The length of the global mark ring is controlled by
+@code{global-mark-ring-max}, and is 16 by default.
 
 @kindex C-x C-@key{SPC}
 @findex pop-global-mark
diff --git a/doc/emacs/msdog.texi b/doc/emacs/msdog.texi
index bbaf31ade85..e3c9b8d4fc2 100644
--- a/doc/emacs/msdog.texi
+++ b/doc/emacs/msdog.texi
@@ -914,7 +914,7 @@ as a fallback with the font family left unspecified.
 @vindex w32-charset-info-alist
 @item registry
 Specifies the character set registry that the font is
-expected to cover.  Most TrueType and OpenType fonts will be unicode fonts
+expected to cover.  Most TrueType and OpenType fonts will be Unicode fonts
 that cover several national character sets, but you can narrow down the
 selection of fonts to those that support a particular character set by
 using a specific registry from @code{w32-charset-info-alist} here.
@@ -936,9 +936,9 @@ Options specific to @code{GDI} fonts:
 @table @code
 
 @cindex font scripts (MS Windows)
-@cindex font unicode subranges (MS Windows)
+@cindex font Unicode subranges (MS Windows)
 @item script
-Specifies a unicode subrange the font should support.
+Specifies a Unicode subrange the font should support.
 
 The following scripts are recognized on Windows: @code{latin}, @code{greek},
 @code{coptic}, @code{cyrillic}, @code{armenian}, @code{hebrew}, @code{arabic},
diff --git a/doc/emacs/windows.texi b/doc/emacs/windows.texi
index ad2040c9047..c44b67454a2 100644
--- a/doc/emacs/windows.texi
+++ b/doc/emacs/windows.texi
@@ -34,11 +34,11 @@ has its own value of point.
 
 @cindex selected window
   At any time, one Emacs window is the @dfn{selected window}; the
-buffer this window is displaying is the current buffer.  Each window
-has its own value of point.  On graphical displays, the point is
-indicated by a solid blinking cursor in the selected window, and by a
-hollow box in non-selected windows.  On text-only terminals, the
-cursor is drawn only in the selected window.  @xref{Cursor Display}.
+buffer this window is displaying is the current buffer.  On graphical
+displays, the point is indicated by a solid blinking cursor in the
+selected window, and by a hollow box in non-selected windows.  On
+text-only terminals, the cursor is drawn only in the selected window.
+@xref{Cursor Display}.
 
   Commands to move point affect the value of point for the selected
 Emacs window only.  They do not change the value of point in other
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/ChangeLog b/doc/lispref/ChangeLog
index 0fa50492481..293f253c545 100644
--- a/doc/lispref/ChangeLog
+++ b/doc/lispref/ChangeLog
@@ -1,3 +1,43 @@
+2011-11-21  Martin Rudalics  <rudalics@gmx.at>
+
+        * windows.texi (Windows and Frames, Splitting Windows): Fix
+        typos.
+
+2011-11-21  Chong Yidong  <cyd@gnu.org>
+
+        * windows.texi (Splitting Windows): Fix error in documentation of
+        window-combination-limit.
+        (Cyclic Window Ordering): Minor fixes to next-window,
+        one-window-p, and get-lru-window docs.  Don't document
+        window-list-1.
+        (Buffers and Windows): Copyedits.
+        (Choosing Window): Document special handling of special-display-*.
+        (Choosing Window Options): Fix display-buffer-reuse-frames doc.
+        Don't document even-window-heights, which is going away.  Clarify
+        which options are obeyed by which action functions.
+
+2011-11-20  Stefan Monnier  <monnier@iro.umontreal.ca>
+
+        * display.texi (Invisible Text): Clarify point adjustment (bug#10072).
+
+2011-11-20  Martin Rudalics  <rudalics@gmx.at>
+
+        * windows.texi (Resizing Windows, Splitting Windows):
+        Remove term "status" when talking about combination limits.
+
+2011-11-20  Juanma Barranquero  <lekktu@gmail.com>
+
+        * compile.texi (Compiler Errors):
+        * help.texi (Help Functions): Fix typos.
+
+2011-11-19  Chong Yidong  <cyd@gnu.org>
+
+        * windows.texi (Splitting Windows): Clarify role of window
+        parameters in split-window.  Shorten the example.
+        (Deleting Windows): Rewrite intro to handle internal windows.
+        Fix delete-windows-on doc.
+        (Selecting Windows): Copyedits.
+
 2011-11-17  Martin Rudalics  <rudalics@gmx.at>
 
         * windows.texi (Resizing Windows, Splitting Windows)
@@ -6,8 +46,8 @@
 
 2011-11-16  Martin Rudalics  <rudalics@gmx.at>
 
-        * windows.texi (Resizing Windows, Splitting Windows): Rename
-        occurrences of window-nest to window-combination-limit.
+        * windows.texi (Resizing Windows, Splitting Windows):
+        Rename occurrences of window-nest to window-combination-limit.
 
 2011-11-14  Juanma Barranquero  <lekktu@gmail.com>
 
@@ -15,8 +55,8 @@
 
 2011-11-12  Martin Rudalics  <rudalics@gmx.at>
 
-        * windows.texi (Splitting Windows, Deleting Windows): Remove
-        references to splits status of windows.
+        * windows.texi (Splitting Windows, Deleting Windows):
+        Remove references to splits status of windows.
 
 2011-11-10  Glenn Morris  <rgm@gnu.org>
 
@@ -68,8 +108,8 @@
         (Windows and Frames): Various clarifications, e.g. non-live
         windows also belong to frames.  Fix window-list description.
         Simplify window nesting example.
-        (Splitting Windows, Window Configurations): Use
-        split-window-below.
+        (Splitting Windows, Window Configurations):
+        Use split-window-below.
 
 2011-11-04  Eli Zaretskii  <eliz@gnu.org>
 
@@ -119,8 +159,8 @@
 
 2011-10-05  Chong Yidong  <cyd@stupidchicken.com>
 
-        * display.texi (Low-Level Font, Face Attributes, Font Lookup): Fix
-        Emacs manual xref (Bug#9675).
+        * display.texi (Low-Level Font, Face Attributes, Font Lookup):
+        Fix Emacs manual xref (Bug#9675).
 
 2011-10-01  Chong Yidong  <cyd@stupidchicken.com>
 
@@ -159,8 +199,8 @@
         * windows.texi (Window History): New node.  Move text here from
         Buffers and Windows.
         (Switching Buffers): Rename from Displaying Buffers, since we
-        don't document display-buffer here; callers changed.  Document
-        FORCE-SAME-WINDOW arg to switch-to-buffer and
+        don't document display-buffer here; callers changed.
+        Document FORCE-SAME-WINDOW arg to switch-to-buffer and
         switch-to-buffer-other-frame.  Delete duplicate
         replace-buffer-in-windows doc.
         (Choosing Window): Document display actions.
@@ -191,10 +231,10 @@
         Provide examples.  Describe window-nest and window-splits
         options.
         (Deleting Windows): Minor rewrite.
-        (Selecting Windows): Minor rewrite.  Describe
-        frame-selected-window and set-frame-selected-window here.
-        (Cyclic Window Ordering): Minor rewrite.  Describe
-        window-list-1.
+        (Selecting Windows): Minor rewrite.
+        Describe frame-selected-window and set-frame-selected-window here.
+        (Cyclic Window Ordering): Minor rewrite.
+        Describe window-list-1.
         (Buffers and Windows): Rewrite.  Explain a window's previous and
         next buffers and the corresponding functions.
         (Window Tree): Merge into Windows and Frames section.
@@ -296,8 +336,8 @@
 
         * display.texi (Bidirectional Display): Document the pitfalls of
         concatenating strings with bidirectional content, with possible
-        solutions.  Document bidi-string-mark-left-to-right.  Mention
-        paragraph direction in modes that inherit from prog-mode.
+        solutions.  Document bidi-string-mark-left-to-right.
+        Mention paragraph direction in modes that inherit from prog-mode.
         Document use of `bidi-class' and `mirroring' properties as part of
         reordering.
 
@@ -353,8 +393,8 @@
         the next character, and doesn't affect longer sequences in
         particular (bug#8935).
 
-        * debugging.texi (Using Debugger): Mention
-        @code{eval-expression-debug-on-error} (bug#8549).
+        * debugging.texi (Using Debugger):
+        Mention @code{eval-expression-debug-on-error} (bug#8549).
 
 2011-07-14  Eli Zaretskii  <eliz@gnu.org>
 
@@ -503,7 +543,7 @@
 
 2011-06-15  Lars Magne Ingebrigtsen  <larsi@gnus.org>
 
-        * processes.texi (Process Information): Renamed `process-alive-p'
+        * processes.texi (Process Information): Rename `process-alive-p'
         to `process-live-p' for consistency with other `-live-p' functions.
 
 2011-06-03  Paul Eggert  <eggert@cs.ucla.edu>
@@ -520,8 +560,8 @@
 
 2011-05-31  Lars Magne Ingebrigtsen  <larsi@gnus.org>
 
-        * processes.texi (Process Information): Document
-        `process-alive-p'.
+        * processes.texi (Process Information):
+        Document `process-alive-p'.
 
 2011-05-29  Chong Yidong  <cyd@stupidchicken.com>
 
@@ -1919,8 +1959,8 @@
 
 2009-05-09  Eli Zaretskii  <eliz@gnu.org>
 
-        * nonascii.texi (Default Coding Systems): Document
-        find-auto-coding, set-auto-coding, and auto-coding-alist.
+        * nonascii.texi (Default Coding Systems):
+        Document find-auto-coding, set-auto-coding, and auto-coding-alist.
         Add indexing.
         (Lisp and Coding Systems): Add index entries.
 
@@ -2237,7 +2277,7 @@
         (Future Local Variables): Node deleted.
 
         * objects.texi (General Escape Syntax): Update explanation of
-        unicode escape syntax.
+        Unicode escape syntax.
 
 2009-02-23  Chong Yidong  <cyd@stupidchicken.com>
 
@@ -5151,8 +5191,8 @@
         (Saving Buffers): Mention code and EOL conversions by file I/O
         primitives and subroutines.
 
-        * nonascii.texi (Lisp and Coding Systems): Document
-        coding-system-eol-type.  Add index entries for eol conversion.
+        * nonascii.texi (Lisp and Coding Systems):
+        Document coding-system-eol-type.  Add index entries for eol conversion.
 
         * display.texi (Defining Faces): Mention `mac', and add an xref to
         where window-system is described.
@@ -9102,7 +9142,7 @@
 
         * functions.texi (Defining Functions): Explain about redefining
         primitives.
-        (Function Safety): Renamed.  Minor changes.
+        (Function Safety): Rename.  Minor changes.
         Comment out the detailed criteria for what is safe.
 
 2003-06-22  Andreas Schwab  <schwab@suse.de>
@@ -9603,7 +9643,7 @@
 
         * Makefile (infodir, prefix): New vars.
         (install): Use infodir.
-        (emacsinfodir): Deleted.
+        (emacsinfodir): Delete.
 
 1993-05-27  Richard Stallman  (rms@mole.gnu.ai.mit.edu)
 
@@ -9614,7 +9654,7 @@
 
 1993-05-16  Jim Blandy  (jimb@wookumz.gnu.ai.mit.edu)
 
-        * Makefile (dist): Changed to use Gzip instead of compress.
+        * Makefile (dist): Change to use Gzip instead of compress.
 
 1993-04-23  Eric S. Raymond  (eric@mole.gnu.ai.mit.edu)
 
diff --git a/doc/lispref/compile.texi b/doc/lispref/compile.texi
index fe5563370c4..372c041ab7a 100644
--- a/doc/lispref/compile.texi
+++ b/doc/lispref/compile.texi
@@ -528,7 +528,7 @@ but the compiler does not issue warnings for anything that occurs
 inside @var{body}.
 
 We recommend that you use this construct around the smallest
-possible piece of code, to avoid missing possible warnings other than one
+possible piece of code, to avoid missing possible warnings other than
 one you intend to suppress.
 @end defspec
 
diff --git a/doc/lispref/display.texi b/doc/lispref/display.texi
index 034d92f78c3..9849420b1f5 100644
--- a/doc/lispref/display.texi
+++ b/doc/lispref/display.texi
@@ -870,15 +870,21 @@ ignore invisible newlines if @code{line-move-ignore-invisible} is
 non-@code{nil} (the default), but only because they are explicitly
 programmed to do so.
 
-  However, if a command ends with point inside or immediately before
-invisible text, the main editing loop moves point further forward or
-further backward (in the same direction that the command already moved
-it) until that condition is no longer true.  Thus, if the command
-moved point back into an invisible range, Emacs moves point back to
-the beginning of that range, and then back one more character.  If the
-command moved point forward into an invisible range, Emacs moves point
-forward up to the first visible character that follows the invisible
-text.
+  However, if a command ends with point inside or at the boundary of invisible
+text, the main editing loop moves point to one of the two ends of the invisible
+text.  Which end to move to is chosen based on the following factors: make sure
+that the overall movement of the command is still in the same direction, and
+prefer a position where an inserted char would not inherit the @code{invisible}
+property.  Additionally, if the text is not replaced by an ellipsis and the
+command only moved within the invisible text, then point is moved one extra
+character so as to try and reflect the command's movement by a visible movement
+of the cursor.
+
+  Thus, if the command moved point back to an invisible range (with the usual
+stickiness), Emacs moves point back to the beginning of that range.  If the
+command moved point forward into an invisible range, Emacs moves point forward
+to the first visible character that follows the invisible text and then forward
+one more character.
 
   Incremental search can make invisible overlays visible temporarily
 and/or permanently when a match includes invisible text.  To enable
@@ -4546,7 +4552,7 @@ you may prefer to use a different one for a given image type (which
 @c FIXME how is this priority determined?
 loader will be used in practice depends on the priority of the loaders).
 @c FIXME why are these uppercase when image-types is lower-case?
-@c FIXME what are the possibe options?  Are these actually file extensions?
+@c FIXME what are the possible options?  Are these actually file extensions?
 For example, if you never want to use the ImageMagick loader to use
 JPEG files, add @code{JPG} to this list.
 
diff --git a/doc/lispref/frames.texi b/doc/lispref/frames.texi
index d2e86a77112..dad1f28026e 100644
--- a/doc/lispref/frames.texi
+++ b/doc/lispref/frames.texi
@@ -953,7 +953,7 @@ variable, Emacs uses the latter.  By default,
 The @code{alpha} frame parameter can also be a cons cell
 @code{(@samp{active} . @samp{inactive})}, where @samp{active} is the
 opacity of the frame when it is selected, and @samp{inactive} is the
-opactity when it is not selected.
+opacity when it is not selected.
 @end table
 
 The following frame parameters are semi-obsolete in that they are
diff --git a/doc/lispref/help.texi b/doc/lispref/help.texi
index 0ce05d55a07..3426e81cdb3 100644
--- a/doc/lispref/help.texi
+++ b/doc/lispref/help.texi
@@ -653,7 +653,7 @@ buffer, which is used to regenerate the help information when the user
 clicks on the @samp{Back} or @samp{Forward} buttons.  Most commands
 that use the @samp{*Help*} buffer should invoke this function before
 clearing the buffer.  The @var{item} argument should have the form
-@code{(@var{funtion} . @var{args})}, where @var{funtion} is a function
+@code{(@var{function} . @var{args})}, where @var{function} is a function
 to call, with argument list @var{args}, to regenerate the help buffer.
 The @var{interactive-p} argument is non-@code{nil} if the calling
 command was invoked interactively; in that case, the stack of items
diff --git a/doc/lispref/searching.texi b/doc/lispref/searching.texi
index fe7c805c6f7..a601ed0c2c0 100644
--- a/doc/lispref/searching.texi
+++ b/doc/lispref/searching.texi
@@ -1213,7 +1213,7 @@ match data around it, to prevent it from being overwritten.
 
   Notice that all functions are allowed to overwrite the match data
 unless they're explicitly documented not to do so.  A consequence is
-that functions that are run implictly in the background
+that functions that are run implicitly in the background
 (@pxref{Timers}, and @ref{Idle Timers}) should likely save and restore
 the match data explicitly.
 
diff --git a/doc/lispref/spellfile b/doc/lispref/spellfile
index e66dcc88f71..5c0a6d0f5ea 100644
--- a/doc/lispref/spellfile
+++ b/doc/lispref/spellfile
@@ -376,7 +376,6 @@ inserting'
 integerp
 intermixed
 ints
-inturned
 irreversibly
 jum
 keymapp
@@ -530,7 +529,6 @@ pointer'
 pointm
 pos
 preallocate
-predicale
 preload
 prepend
 prepended
@@ -641,7 +639,7 @@ suspension'
 symbolp
 symlink
 syms
-syntatic
+syntactic
 tabname
 temacs
 temporarily'
diff --git a/doc/lispref/windows.texi b/doc/lispref/windows.texi
index 8c99a06909b..bb1b0524689 100644
--- a/doc/lispref/windows.texi
+++ b/doc/lispref/windows.texi
@@ -110,6 +110,7 @@ including for the case where @var{object} is a deleted window.
 @end defun
 
 @cindex selected window
+@cindex window selected within a frame
   In each frame, at any time, exactly one Emacs window is designated
 as @dfn{selected within the frame}.  For the selected frame, that
 window is called the @dfn{selected window}---the one in which most
@@ -148,10 +149,10 @@ the minibuffer window in the returned list.  If @var{minibuffer} is
 active.  If @var{minibuffer} is neither @code{nil} nor @code{t}, the
 minibuffer window is never included.
 
-The optional argument @var{window}, if non-@code{nil}, should be a
-live window on the specified frame; then @var{window} will be the
-first element in the returned list.  If @var{window} is omitted or
-@code{nil}, the window selected within the frame is first element.
+The optional argument @var{window}, if non-@code{nil}, should be a live
+window on the specified frame; then @var{window} will be the first
+element in the returned list.  If @var{window} is omitted or @code{nil},
+the window selected within the frame is the first element.
 @end defun
 
 @cindex window tree
@@ -634,9 +635,9 @@ function @code{window-resizable} above.
 
 The choice of which window edges this function alters depends on the
 values of the option @code{window-combination-resize} and the
-combination-limit status of the involved windows; in some cases, it may
-alter both edges.  @xref{Splitting Windows}.  To resize by moving only
-the bottom or right edge of a window, use the function
+combination limits of the involved windows; in some cases, it may alter
+both edges.  @xref{Splitting Windows}.  To resize by moving only the
+bottom or right edge of a window, use the function
 @code{adjust-window-trailing-edge}, below.
 @end defun
 
@@ -774,22 +775,24 @@ properties from it, including margins and scroll bars.  If
 @var{window} is an internal window, the new window inherits the
 properties of the window selected within @var{window}'s frame.
 
-If the variable @code{ignore-window-parameters} is non-@code{nil}
-(@pxref{Window Parameters}), this function ignores window parameters.
-Otherwise, it consults the @code{split-window} parameter of
-@var{window}; if this is @code{t}, it splits the window disregarding
-any other window parameters.  If the @code{split-window} parameter
-specifies a function, that function is called with the arguments
-@var{window}, @var{size}, and @var{side} to split @var{window}, in
-lieu of the usual action of @code{split-window}.
+The behavior of this function may be altered by the window parameters
+of @var{window}, so long as the variable
+@code{ignore-window-parameters} is non-@code{nil}.  If the value of
+the @code{split-window} window parameter is @code{t}, this function
+ignores all other window parameters.  Otherwise, if the value of the
+@code{split-window} window parameter is a function, that function is
+called with the arguments @var{window}, @var{size}, and @var{side}, in
+lieu of the usual action of @code{split-window}.  Otherwise, this
+function obeys the @code{window-atom} or @code{window-side} window
+parameter, if any.  @xref{Window Parameters}.
 @end deffn
 
-  As an example, we show a combination of @code{split-window} calls
-that yields the window configuration discussed in @ref{Windows and
-Frames}.  This example demonstrates splitting a live window as well as
-splitting an internal window.  We begin with a frame containing a
-single window (a live root window), which we denote by @var{W4}.
-Calling @code{(split-window W3)} yields this window configuration:
+  As an example, here is a sequence of @code{split-window} calls that
+yields the window configuration discussed in @ref{Windows and Frames}.
+This example demonstrates splitting a live window as well as splitting
+an internal window.  We begin with a frame containing a single window
+(a live root window), which we denote by @var{W4}.  Calling
+@code{(split-window W4)} yields this window configuration:
 
 @smallexample
 @group
@@ -841,9 +844,6 @@ A new live window @var{W2} is created, to the left of the internal
 window @var{W3}.  A new internal window @var{W1} is created, becoming
 the new root window.
 
-  The following two options can be used to modify the operation of
-@code{split-window}.
-
 @defopt window-combination-resize
 If this variable is @code{nil}, @code{split-window} can only split a
 window (denoted by @var{window}) if @var{window}'s screen area is
@@ -854,18 +854,17 @@ If this variable is non-@code{nil}, @code{split-window} tries to
 resize all windows that are part of the same combination as
 @var{window}, in order to accommodate the new window.  In particular,
 this may allow @code{split-window} to succeed even if @var{window} is
-a fixed-size window or too small to ordinarily split.
-
-Also if this variable is non-@code{nil}, subsequent resizing and
-deleting @var{window} will usually affect @emph{all} windows in
-@var{window}'s combination.
+a fixed-size window or too small to ordinarily split.  Furthermore,
+subsequently resizing or deleting @var{window} may resize all other
+windows in its combination.
 
-The setting of this variable has no effect if
-@code{window-combination-limit} (see below) is non-@code{nil}.
+This variable has no effect if @code{window-combination-limit} is
+non-@code{nil} (see below).
 @end defopt
 
-To illustrate the use of @code{window-combination-resize} consider the
-following window configuration:
+  To illustrate the effect of @code{window-combination-resize},
+consider the following window configuration:
+
 @smallexample
 @group
      ______________________________________
@@ -886,9 +885,10 @@ following window configuration:
 @end group
 @end smallexample
 
-Splitting window @code{W3} with @code{window-combination-resize}
-@code{nil} produces a configuration where the size of @code{W2} remains
-unchanged:
+@noindent
+If @code{window-combination-resize} is @code{nil}, splitting window
+@code{W3} leaves the size of @code{W2} unchanged:
+
 @smallexample
 @group
      ______________________________________
@@ -909,8 +909,11 @@ unchanged:
 @end group
 @end smallexample
 
-Splitting @code{W3} with @code{window-combination-resize} non-@code{nil}
-instead steals the space for @code{W4} from both @code{W2} and @code{W3}:
+@noindent
+If @code{window-combination-resize} is non-@code{nil}, splitting
+@code{W3} instead leaves all three live windows with approximately the
+same height:
+
 @smallexample
 @group
      ______________________________________
@@ -932,53 +935,51 @@ instead steals the space for @code{W4} from both @code{W2} and @code{W3}:
 @end smallexample
 
 @defopt window-combination-limit
-If this variable is @code{nil}, @code{split-window} creates a new parent
-window if and only if the old window has no parent window or shall be
-split orthogonally to the combination it is part of.  If this variable
-is @code{t}, @code{split-window} always creates a new parent window.  If
-this variable is always @code{t}, a frame's window tree is a binary tree
-so every window but the frame's root window has exactly one sibling.
-Other values are reserved for future use.
-
-The value of this variable is also assigned to the combination-limit
-status of the new parent window.  The combination-limit status of any
-window can be retrieved via the function @code{window-combination-limit}
-and altered by the function @code{set-window-combination-limit}, see
-below.
+If the value of this variable is @code{t}, the @code{split-window}
+function always creates a new internal window.  If the value is
+@code{nil}, the new live window is allowed to share the existing
+parent window, if one exists, provided the split occurs in the same
+direction as the existing window combination (otherwise, a new
+internal window is created anyway).  The default is @code{nil}.  Other
+values are reserved for future use.
+
+Thus, if the value is always @code{t}, each window tree is a binary
+tree: each window except the root window has exactly one sibling.
+
+Furthermore, @code{split-window} calls
+@code{set-window-combination-limit} on the newly-created internal
+window, recording the current value of this variable.  This affects
+how the window tree is rearranged when the child windows are deleted
+(see below).
 @end defopt
 
-@defun window-combination-limit &optional window
-This function returns the combination-limit status of @var{window}.  The
-argument @var{window} can be any window and defaults to the selected
-one.  Note, however, that the combination-limit status is currently
-meaningful for internal windows only.
-
-@cindex combination-limit status
-The @dfn{combination-limit status} of a window specifies whether that
-window may be removed and its child windows recombined with that
-window's siblings when such a sibling's child window is deleted.  The
-combination-limit status is initially assigned by @code{split-window}
-from the current value of the variable @code{window-combination-limit}
-(see above) and can be reset by the function
-@code{set-window-combination-limit} (see below).
-
-If the return value is @code{nil}, child windows of @var{window} may be
-recombined with @var{window}'s siblings when a window gets deleted.  A
-return value of @code{nil} means that child windows of @var{window} are
-never (re-)combined with @var{window}'s siblings in such a case.
-@end defun
-
-@defun set-window-combination-limit window &optional status
-This functions sets the combination-limit status (see above) of
-@var{window} to @var{status}.  The argument @var{window} can be any
-window and defaults to the selected one.  Note that setting the
-combination-limit status is meaningful for internal windows only.  The
-return value is @var{status}.
-@end defun
-
-To illustrate the use of @code{window-combination-limit} consider the
-following configuration (throughout the following examples we shall
-assume that @code{window-combination-resize} invariantly is @code{nil}).
+@cindex window combination limit
+@defun set-window-combination-limit window limit
+This functions sets the @dfn{combination limit} of the window
+@var{window} to @var{limit}.  This value can be retrieved via the
+function @code{window-combination-limit}.  See below for its effects;
+note that it is only meaningful for internal windows.  The
+@code{split-window} function automatically calls this function, passing
+the value of the variable @code{window-combination-limit} as
+@var{limit}.
+@end defun
+
+@defun window-combination-limit window
+This function returns the combination limit for @var{window}.
+
+The combination limit is meaningful only for an internal window.  If
+it is @code{nil}, then Emacs is allowed to automatically delete
+@var{window}, in response to a window deletion, in order to group the
+child windows of @var{window} with its sibling windows to form a new
+window combination.  If the combination limit is @code{t}, the child
+windows of @var{window} are never automatically re-combined with its
+siblings.
+@end defun
+
+  To illustrate the effect of @code{window-combination-limit},
+consider the following configuration (throughout this example, we will
+assume that @code{window-combination-resize} is @code{nil}):
+
 @smallexample
 @group
      ______________________________________
@@ -999,31 +1000,10 @@ assume that @code{window-combination-resize} invariantly is @code{nil}).
 @end group
 @end smallexample
 
-Splitting @code{W2} into two windows above each other with
-@code{window-combination-limit} equal @code{nil} will get you a
-configuration like:
-@smallexample
-@group
-     ______________________________________
-    | ____________________________________ |
-    ||                                    ||
-    ||                                    ||
-    ||_________________W2_________________||
-    | ____________________________________ |
-    ||                                    ||
-    ||                                    ||
-    ||_________________W4_________________||
-    | ____________________________________ |
-    ||                                    ||
-    ||                                    ||
-    ||_________________W3_________________||
-    |__________________W1__________________|
-
-@end group
-@end smallexample
+@noindent
+If @code{window-combination-limit} is @code{nil}, splitting @code{W2}
+into two windows, one above the other, yields
 
-If you now enlarge window @code{W4}, Emacs steals the necessary space
-from window @code{W3} resulting in a configuration like:
 @smallexample
 @group
      ______________________________________
@@ -1034,43 +1014,24 @@ from window @code{W3} resulting in a configuration like:
     | ____________________________________ |
     ||                                    ||
     ||                                    ||
-    ||                                    ||
     ||_________________W4_________________||
     | ____________________________________ |
     ||                                    ||
+    ||                                    ||
     ||_________________W3_________________||
     |__________________W1__________________|
 
 @end group
 @end smallexample
 
-Deleting window @code{W4}, will return its space to @code{W2} as
-follows:
-@smallexample
-@group
-     ______________________________________
-    | ____________________________________ |
-    ||                                    ||
-    ||                                    ||
-    ||                                    ||
-    ||                                    ||
-    ||                                    ||
-    ||                                    ||
-    ||                                    ||
-    ||_________________W2_________________||
-    | ____________________________________ |
-    ||                                    ||
-    ||_________________W3_________________||
-    |__________________W1__________________|
+@noindent
+The newly-created window, @code{W4}, shares the same internal window
+@code{W1}.  If @code{W4} is resized, it is allowed to resize the other
+live window, @code{W3}.
 
-@end group
-@end smallexample
+  If @code{window-combination-limit} is @code{t}, splitting @code{W2}
+in the initial configuration would instead have produced this:
 
-Hence, with respect to the initial configuration, window @code{W2} has
-grown at the expense of window @code{W3}.  If, however, in the initial
-configuration you had split @code{W2} with
-@code{window-combination-limit} bound to @code{t}, a new internal window
-@code{W5} would have been created as depicted below.
 @smallexample
 @group
      ______________________________________
@@ -1091,143 +1052,110 @@ configuration you had split @code{W2} with
 @end group
 @end smallexample
 
-Enlarging @code{W4} would now have stolen the necessary space from
-@code{W2} instead of @code{W3} as
-@smallexample
-@group
-     ______________________________________
-    | ____________________________________ |
-    || __________________________________ ||
-    |||________________W2________________|||
-    || __________________________________ ||
-    |||                                  |||
-    |||                                  |||
-    |||________________W4________________|||
-    ||_________________W5_________________||
-    | ____________________________________ |
-    ||                                    ||
-    ||                                    ||
-    ||_________________W3_________________||
-    |__________________W1__________________|
-
-@end group
-@end smallexample
+@noindent
+A new internal window @code{W5} has been created; its children are
+@code{W2} and the new live window @code{W4}.  Now, @code{W2} is the
+only sibling of @code{W4}, so resizing @code{W4} will resize
+@code{W2}, leaving @code{W3} unaffected.
 
-and the subsequent deletion of @code{W4} would have restored the initial
-configuration.
+  For interactive use, Emacs provides two commands which always split
+the selected window.  These call @code{split-window} internally.
 
-For interactive use, Emacs provides two commands which always split the
-selected window.
+@deffn Command split-window-right &optional size
+This function splits the selected window into two side-by-side
+windows, putting the selected window on the left.  If @var{size} is
+positive, the left window gets @var{size} columns; if @var{size} is
+negative, the right window gets @minus{}@var{size} columns.
+@end deffn
 
 @deffn Command split-window-below &optional size
-This function splits the selected window into two windows, one above the
-other, leaving the upper of the two windows selected, with @var{size}
-lines.  (If @var{size} is negative, then the lower of the two windows
-gets @minus{}@var{size} lines and the upper window gets the rest, but
-the upper window is still the one selected.)  However, if
-@code{split-window-keep-point} (see below) is @code{nil}, then either
-window can be selected.
-
-   In other respects, this function is similar to @code{split-window}.
-In particular, the upper window is the original one and the return value
-is the new, lower window.
+This function splits the selected window into two windows, one above
+the other, leaving the upper window selected.  If @var{size} is
+positive, the upper window gets @var{size} lines; if @var{size} is
+negative, the lower window gets @minus{}@var{size} lines.
 @end deffn
 
 @defopt split-window-keep-point
-If this variable is non-@code{nil} (the default), then
+If the value of this variable is non-@code{nil} (the default),
 @code{split-window-below} behaves as described above.
 
-   If it is @code{nil}, then @code{split-window-below} adjusts point
-in each of the two windows to avoid scrolling.  (This is useful on
-slow terminals.)  It selects whichever window contains the screen line
-that point was previously on.  Other functions are not affected by
-this variable.
+If it is @code{nil}, @code{split-window-below} adjusts point in each
+of the two windows to minimize redisplay.  (This is useful on slow
+terminals.)  It selects whichever window contains the screen line that
+point was previously on.  Note that this only affects
+@code{split-window-below}, not the lower-level @code{split-window}
+function.
 @end defopt
 
-@deffn Command split-window-right &optional size
-This function splits the selected window into two windows
-side-by-side, leaving the selected window on the left with @var{size}
-columns.  If @var{size} is negative, the rightmost window gets
-@minus{}@var{size} columns, but the leftmost window still remains
-selected.
-@end deffn
-
-
 @node Deleting Windows
 @section Deleting Windows
 @cindex deleting windows
 
-A window remains visible on its frame unless you @dfn{delete} it by
-calling certain functions that delete windows.  A deleted window cannot
-appear on the screen, but continues to exist as a Lisp object until
-there are no references to it.  There is no way to cancel the deletion
-of a window aside from restoring a saved window configuration
-(@pxref{Window Configurations}).  Restoring a window configuration also
-deletes any windows that aren't part of that configuration.  Erroneous
-information may result from using a deleted window as if it were live.
+  @dfn{Deleting} a window removes it from the frame's window tree.  If
+the window is a live window, it disappears from the screen.  If the
+window is an internal window, its child windows are deleted too.
 
-@deffn Command delete-window &optional window
-This function removes @var{window} from display and returns @code{nil}.
-The argument @var{window} can denote any window and defaults to the
-selected one.  An error is signaled if @var{window} is the only window
-on its frame.  Hence @var{window} must have at least one sibling window
-(@pxref{Windows and Frames}) in order to get deleted.  If @var{window}
-is the selected window on its frame, this function selects the most
-recently selected live window on that frame instead.
-
-If the variable @code{ignore-window-parameters} (@pxref{Window
-Parameters}) is non-@code{nil}, this function ignores all parameters of
-@var{window}.  Otherwise, if the @code{delete-window} parameter of
-@var{window} is @code{t}, it deletes the window disregarding other
-window parameters.  If the @code{delete-window} parameter specifies a
-function, that function is called with @var{window} as its sole
-argument.
+  Even after a window is deleted, it continues to exist as a Lisp
+object, until there are no more references to it.  Window deletion can
+be reversed, by restoring a saved window configuration (@pxref{Window
+Configurations}).
 
-If @code{window-combination-resize} (@pxref{Splitting Windows}) is
-@code{nil}, the space @var{window} took up is given to its left sibling
-if such a window exists and to its right sibling otherwise.  If
-@code{window-combination-resize} is non-@code{nil}, the space of
-@var{window} is proportionally distributed among the remaining windows
-in the same combination.
+@deffn Command delete-window &optional window
+This function removes @var{window} from display and returns
+@code{nil}.  If @var{window} is omitted or @code{nil}, it defaults to
+the selected window.  If deleting the window would leave no more
+windows in the window tree (e.g. if it is the only live window in the
+frame), an error is signaled.
+
+By default, the space taken up by @var{window} is given to one of its
+adjacent sibling windows, if any.  However, if the variable
+@code{window-combination-resize} is non-@code{nil}, the space is
+proportionally distributed among any remaining windows in the window
+combination.  @xref{Splitting Windows}.
+
+The behavior of this function may be altered by the window parameters
+of @var{window}, so long as the variable
+@code{ignore-window-parameters} is non-@code{nil}.  If the value of
+the @code{delete-window} window parameter is @code{t}, this function
+ignores all other window parameters.  Otherwise, if the value of the
+@code{delete-window} window parameter is a function, that function is
+called with the argument @var{window}, in lieu of the usual action of
+@code{delete-window}.  Otherwise, this function obeys the
+@code{window-atom} or @code{window-side} window parameter, if any.
+@xref{Window Parameters}.
 @end deffn
 
 @deffn Command delete-other-windows &optional window
-This function makes @var{window} fill its frame and returns @code{nil}.
-The argument @var{window} can denote an arbitrary window and defaults to
-the selected one.  Upon exit, @var{window} will be the selected window
-on its frame.
-
-If the variable @code{ignore-window-parameters} (@pxref{Window
-Parameters}) is non-@code{nil}, this function ignores all parameters of
-@var{window}.  Otherwise, if the @code{delete-other-windows} parameter
-of @var{window} equals @code{t}, it deletes all other windows
-disregarding any remaining window parameters.  If the
-@code{delete-other-windows} parameter of @var{window} specifies a
-function, it calls that function with @var{window} as its sole argument.
+This function makes @var{window} fill its frame, by deleting other
+windows as necessary.  If @var{window} is omitted or @code{nil}, it
+defaults to the selected window.  The return value is @code{nil}.
+
+The behavior of this function may be altered by the window parameters
+of @var{window}, so long as the variable
+@code{ignore-window-parameters} is non-@code{nil}.  If the value of
+the @code{delete-other-windows} window parameter is @code{t}, this
+function ignores all other window parameters.  Otherwise, if the value
+of the @code{delete-other-windows} window parameter is a function,
+that function is called with the argument @var{window}, in lieu of the
+usual action of @code{delete-other-windows}.  Otherwise, this function
+obeys the @code{window-atom} or @code{window-side} window parameter,
+if any.  @xref{Window Parameters}.
 @end deffn
 
 @deffn Command delete-windows-on &optional buffer-or-name frame
-This function deletes all windows showing @var{buffer-or-name}.  If
-there are no windows showing @var{buffer-or-name}, it does nothing.
-The optional argument @var{buffer-or-name} may be a buffer or the name
-of an existing buffer and defaults to the current buffer.  Invoking
-this command on a minibuffer signals an error.
-
-The function @code{delete-windows-on} operates by calling
-@code{delete-window} for each window showing @var{buffer-or-name}.  If a
-frame has several windows showing different buffers, then those showing
-@var{buffer-or-name} are removed, and the other windows expand to fill
-the space.
-
-If all windows in some frame are showing @var{buffer-or-name} (including
-the case where there is only one window), then that frame is deleted
-provided there are other frames left.
-
-The optional argument @var{frame} specifies which frames to operate on.
-This function does not use it in quite the same way as the other
-functions which scan all live windows (@pxref{Cyclic Window Ordering});
-specifically, the values @code{t} and @code{nil} have the opposite of
-their meanings in the other functions.  Here are the full details:
+This function deletes all windows showing @var{buffer-or-name}, by
+calling @code{delete-window} on those windows.  @var{buffer-or-name}
+should be a buffer, or the name of a buffer; if omitted or @code{nil},
+it defaults to the current buffer.  If there are no windows showing
+the specified buffer, this function does nothing.  If the specified
+buffer is a minibuffer, an error is signaled.
+
+If there is a dedicated window showing the buffer, and that window is
+the only one on its frame, this function also deletes that frame if it
+is not the only frame on the terminal.
+
+The optional argument @var{frame} specifies which frames to operate
+on:
 
 @itemize @bullet
 @item @code{nil}
@@ -1241,34 +1169,37 @@ means operate on all visible or iconified frames.
 @item A frame
 means operate on that frame.
 @end itemize
-@end deffn
 
+Note that this argument does not have the same meaning as in other
+functions which scan all live windows (@pxref{Cyclic Window
+Ordering}).  Specifically, the values @code{t} and @code{nil} have the
+opposite of their meanings in those other functions.
+@end deffn
 
 @node Selecting Windows
 @section Selecting Windows
 @cindex selecting a window
 
 @defun select-window window &optional norecord
-This function makes @var{window} the selected window, see @ref{Basic
-Windows}.  Unless @var{window} already is the selected window, this also
-makes @var{window}'s buffer (@pxref{Buffers and Windows}) the current
-buffer.  Moreover, the cursor for selected windows will be displayed in
-@var{window} after the next redisplay.  This function returns
-@var{window}.
+This function makes @var{window} the selected window, as well as the
+window selected within its frame (@pxref{Basic Windows}).
+@var{window} must be a live window.  Unless @var{window} already is the
+selected window, its buffer becomes the current buffer (@pxref{Buffers
+and Windows}).  The return value is @var{window}.
 
-Normally, @var{window}'s selected buffer is moved to the front of the
-buffer list (@pxref{The Buffer List}) and @var{window} becomes the most
-recently selected window.  But if the optional argument @var{norecord}
-is non-@code{nil}, the buffer list remains unchanged and @var{window}
-does not become the most recently selected one.
+By default, this function also moves @var{window}'s selected buffer to
+the front of the buffer list (@pxref{The Buffer List}), and makes
+@var{window} the most recently selected window.  However, if the
+optional argument @var{norecord} is non-@code{nil}, these additional
+actions are omitted.
 @end defun
 
 @cindex most recently selected windows
-The sequence of calls to @code{select-window} with a non-@code{nil}
+  The sequence of calls to @code{select-window} with a non-@code{nil}
 @var{norecord} argument determines an ordering of windows by their
 selection time.  The function @code{get-lru-window} can be used to
-retrieve the least recently selected live window in this ordering, see
-@ref{Cyclic Window Ordering}.
+retrieve the least recently selected live window (@pxref{Cyclic Window
+Ordering}).
 
 @defmac save-selected-window forms@dots{}
 This macro records the selected frame, as well as the selected window
@@ -1300,33 +1231,26 @@ The order of recently selected windows and the buffer list are not
 changed by this macro.
 @end defmac
 
-@cindex frame selected window
-@cindex window selected within frame
-Earlier (@pxref{Basic Windows}) we mentioned that at any time, exactly
-one window on any frame is selected within the frame.  The significance
-of this designation is that selecting the frame also selects this
-window.  Conversely, selecting a window for Emacs with
-@code{select-window} also makes that window selected within its frame.
-
-@defun frame-selected-window  &optional frame
-This function returns the window on @var{frame} that is selected within
-@var{frame}.  The optional argument @var{frame} must denote a live frame
-and defaults to the selected one.
+@defun frame-selected-window &optional frame
+This function returns the window on @var{frame} that is selected
+within that frame.  @var{frame} should be a live frame; if omitted or
+@code{nil}, it defaults to the selected frame.
 @end defun
 
 @defun set-frame-selected-window frame window &optional norecord
-This function sets the selected window of frame @var{frame} to
-@var{window}.  The argument @var{frame} must denote a live frame and
-defaults to the selected one.  If @var{frame} is the selected frame,
-this also makes @var{window} the selected window.  The argument
-@var{window} must denote a live window.  This function returns
-@var{window}.
+This function makes @code{window} the window selected within the frame
+@var{frame}.  @var{frame} should be a live frame; if omitted or
+@code{nil}, it defaults to the selected frame.  @var{window} should be
+a live window; if omitted or @code{nil}, it defaults to the selected
+window.
 
-Optional argument @var{norecord} non-@code{nil} means to neither change
-the list of most recently selected windows (@pxref{Selecting Windows})
-nor the buffer list (@pxref{The Buffer List}).
-@end defun
+If @var{frame} is the selected frame, this makes @var{window} the
+selected window.
 
+If the optional argument @var{norecord} is non-@code{nil}, this
+function does not alter the list of most recently selected windows,
+nor the buffer list.
+@end defun
 
 @node Cyclic Window Ordering
 @section Cyclic Ordering of Windows
@@ -1334,28 +1258,22 @@ nor the buffer list (@pxref{The Buffer List}).
 @cindex ordering of windows, cyclic
 @cindex window ordering, cyclic
 
-When you use the command @kbd{C-x o} (@code{other-window}) to select
+  When you use the command @kbd{C-x o} (@code{other-window}) to select
 some other window, it moves through live windows in a specific order.
-For any given configuration of windows, this order never varies.  It is
-called the @dfn{cyclic ordering of windows}.
-
-   For a particular frame, this ordering is determined by the window
-tree of that frame, see @ref{Windows and Frames}.  More precisely, the
-ordering is obtained by a depth-first traversal of the frame's window
-tree supplemented, if requested, by the frame's minibuffer window.
+For any given configuration of windows, this order never varies.  It
+is called the @dfn{cyclic ordering of windows}.
 
-   If there's just one live frame, the cyclic ordering is the ordering
-for that frame.  Otherwise, the cyclic ordering is obtained by appending
-the orderings for individual frames in order of the list of all live
-frames, @ref{Finding All Frames}.  In any case, the ordering is made
-``cyclic'' by having the last window precede the first window in the
-ordering.
+  The ordering is determined by a depth-first traversal of the frame's
+window tree, retrieving the live windows which are the leaf nodes of
+the tree (@pxref{Windows and Frames}).  If the minibuffer is active,
+the minibuffer window is included too.  The ordering is cyclic, so the
+last window in the sequence is followed by the first one.
 
 @defun next-window &optional window minibuf all-frames
 @cindex minibuffer window, and @code{next-window}
-This function returns the window following @var{window} in the cyclic
-ordering of windows.  The argument @var{window} must specify a live
-window and defaults to the selected one.
+This function returns a live window, the one following @var{window} in
+the cyclic ordering of windows.  @var{window} should be a live window;
+if omitted or @code{nil}, it defaults to the selected window.
 
 The optional argument @var{minibuf} specifies whether minibuffer windows
 shall be included in the cyclic ordering.  Normally, when @var{minibuf}
@@ -1369,139 +1287,100 @@ minibuffer windows.  If @var{minibuf} is neither @code{t} nor
 @code{nil}, minibuffer windows are not included even if they are active.
 
 The optional argument @var{all-frames} specifies which frames to
-consider.  Here are the possible values and their meanings:
+consider:
 
 @itemize @bullet
 @item @code{nil}
-means consider all windows on @var{window}'s frame, plus the minibuffer
-window used by that frame even if it lies in some other frame.  If the
-minibuffer counts (as determined by @var{minibuf}), then all windows on
-all frames that share that minibuffer count too.
+means to consider windows on @var{window}'s frame.  If the minibuffer
+window is considered (as specified by the @var{minibuf} argument),
+then frames that share the minibuffer window are considered too.
 
 @item @code{t}
-means consider all windows on all existing frames.
+means to consider windows on all existing frames.
 
 @item @code{visible}
-means consider all windows on all visible frames.  (To get useful
-results, ensure that @var{window} is on a visible frame.)
+means to consider windows on all visible frames.
 
 @item 0
-means consider all windows on all visible or iconified frames.
+means to consider windows on all visible or iconified frames.
 
 @item A frame
-means consider all windows on that frame.
+means to consider windows on that specific frame.
 
 @item Anything else
-means consider the windows on @var{window}'s frame, and no others.
+means to consider windows on @var{window}'s frame, and no others.
 @end itemize
 
-This example assumes there are two windows, both displaying the
-buffer @samp{windows.texi}:
-
-@example
-@group
-(selected-window)
-     @result{} #<window 56 on windows.texi>
-@end group
-@group
-(next-window (selected-window))
-     @result{} #<window 52 on windows.texi>
-@end group
-@group
-(next-window (next-window (selected-window)))
-     @result{} #<window 56 on windows.texi>
-@end group
-@end example
+If more than one frame is considered, the cyclic ordering is obtained
+by appending the orderings for those frames, in the same order as the
+list of all live frames (@pxref{Finding All Frames}).
 @end defun
 
 @defun previous-window &optional window minibuf all-frames
-This function returns the window preceding @var{window} in the cyclic
-ordering of windows.  The other arguments specify which windows to
-consider as in @code{next-window}.
+This function returns a live window, the one preceding @var{window} in
+the cyclic ordering of windows.  The other arguments are handled like
+in @code{next-window}.
 @end defun
 
 @deffn Command other-window count &optional all-frames
-This function selects another window in the cyclic ordering of windows.
-@var{count} specifies the number of windows to skip in the ordering,
-starting with the selected window, before making the selection.  If
-@var{count} is a positive number, it skips @var{count} windows forwards.
-@var{count} negative means skip @minus{}@var{count} windows backwards.
-If @var{count} is zero, it does not skip any window, thus re-selecting
-the selected window.  In an interactive call, @var{count} is the numeric
-prefix argument.
+This function selects a live window, one @var{count} places from the
+selected window in the cyclic ordering of windows.  If @var{count} is
+a positive number, it skips @var{count} windows forwards; if
+@var{count} is negative, it skips @minus{}@var{count} windows
+backwards; if @var{count} is zero, that simply re-selects the selected
+window.  When called interactively, @var{count} is the numeric prefix
+argument.
 
 The optional argument @var{all-frames} has the same meaning as in
-@code{next-window}, but the @var{minibuf} argument of @code{next-window}
-is always effectively @code{nil}.  This function returns @code{nil}.
+@code{next-window}, like a @code{nil} @var{minibuf} argument to
+@code{next-window}.
 
 This function does not select a window that has a non-@code{nil}
 @code{no-other-window} window parameter (@pxref{Window Parameters}).
 @end deffn
 
-The following function returns a copy of the list of windows in the
-cyclic ordering.
+@defun walk-windows fun &optional minibuf all-frames
+This function calls the function @var{fun} once for each live window,
+with the window as the argument.
 
-@defun window-list-1 &optional window &optional minibuf &optional all_frames
-This function returns a list of live windows.  The optional arguments
-@var{minibuf} and @var{all-frames} specify the set of windows to include
-in the list.  See the description of @code{next-window} for details.
+It follows the cyclic ordering of windows.  The optional arguments
+@var{minibuf} and @var{all-frames} specify the set of windows
+included; these have the same arguments as in @code{next-window}.  If
+@var{all-frames} specifies a frame, the first window walked is the
+first window on that frame (the one returned by
+@code{frame-first-window}), not necessarily the selected window.
 
-The optional argument @var{window} specifies the first window to list
-and defaults to the selected window.  If @var{window} is not on the list
-of windows returned, some other window will be listed first but no error
-is signaled.
+If @var{fun} changes the window configuration by splitting or deleting
+windows, that does not alter the set of windows walked, which is
+determined prior to calling @var{fun} for the first time.
 @end defun
 
-The functions described below use @code{window-list-1} for generating a
-copy of the list of all relevant windows.  Hence, any change of the
-window configuration that occurs while one of these functions is
-executed is @emph{not} reflected in the list of windows investigated.
-
-@defun walk-windows proc &optional minibuf all-frames
-This function cycles through live windows.  It calls the function
-@var{proc} once for each window, with the window as its sole argument.
-
-The optional arguments @var{minibuf} and @var{all-frames} specify the
-set of windows to include in the walk, see @code{next-window} above.  If
-@var{all-frames} specifies a frame, the first window walked is the first
-window on that frame as returned by @code{frame-first-window} and not
-necessarily the selected window.
-
-If @var{proc} changes the window configuration by splitting or deleting
-windows, that change is not reflected in the set of windows walked.
-That set is determined entirely by the set of live windows at the time
-this function was invoked.
-@end defun
-
-The following function allows to determine whether a specific window is
-the only live window.
-
 @defun one-window-p &optional no-mini all-frames
-This function returns non-@code{nil} if the selected window is the only
-window.
+This function returns @code{t} if the selected window is the only live
+window, and @code{nil} otherwise.
 
-The optional argument @var{no-mini}, if non-@code{nil}, means don't
-count the minibuffer even if it is active; otherwise, the minibuffer
-window is counted when it is active.  The optional argument
-@var{all-frames} has the same meaning as for @code{next-window}, see
-above.
+If the minibuffer window is active, it is normally considered (so that
+this function returns @code{nil}).  However, if the optional argument
+@var{no-mini} is non-@code{nil}, the minibuffer window is ignored even
+if active.  The optional argument @var{all-frames} has the same
+meaning as for @code{next-window}.
 @end defun
 
 @cindex finding windows
-  The following functions choose (but do not select) one of the windows
-on the screen, offering various criteria for the choice.
+  The following functions return a window which satisfies some
+criterion, without selecting it:
 
 @cindex least recently used window
 @defun get-lru-window &optional all-frames dedicated
-This function returns the window least recently ``used'' (that is,
-selected).  If any full-width windows are present, it only considers
-these.  The optional argument @var{all-frames} has the same meaning as
-in @code{next-window}.
+This function returns a live window which is heuristically the ``least
+recently used'' window.  The optional argument @var{all-frames} has
+the same meaning as in @code{next-window}.
 
-The selected window is returned if it is the only candidate.  A
-minibuffer window is never a candidate.  A dedicated window
-(@pxref{Dedicated Windows}) is never a candidate unless the optional
-argument @var{dedicated} is non-@code{nil}.
+If any full-width windows are present, only those windows are
+considered.  The selected window is never returned, unless it is the
+only candidate.  A minibuffer window is never a candidate.  A
+dedicated window (@pxref{Dedicated Windows}) is never a candidate
+unless the optional argument @var{dedicated} is non-@code{nil}.
 @end defun
 
 @cindex largest window
@@ -1515,22 +1394,23 @@ If there are two candidate windows of the same size, this function
 prefers the one that comes first in the cyclic ordering of windows,
 starting from the selected window.
 
-The optional argument @var{all-frames} specifies which set of windows to
-consider as with @code{next-window}, see above.
+The optional argument @var{all-frames} specifies the windows to
+search, and has the same meaning as in @code{next-window}.
 @end defun
 
 @cindex window that satisfies a predicate
 @cindex conditional selection of windows
 @defun get-window-with-predicate predicate &optional minibuf all-frames default
-This function returns a window satisfying @var{predicate}.  It cycles
-through all visible windows calling @var{predicate} on each one of them
-with that window as its argument.  The function returns the first window
-for which @var{predicate} returns a non-@code{nil} value; if that never
-happens, it returns @var{default} (which defaults to @code{nil}).
+This function calls the function @var{predicate} for each of the
+windows in the cyclic order of windows in turn, passing it the window
+as an argument.  If the predicate returns non-@code{nil} for any
+window, this function stops and returns that window.  If no such
+window is found, the return value is @var{default} (which defaults to
+@code{nil}).
 
 The optional arguments @var{minibuf} and @var{all-frames} specify the
-set of windows to investigate.  See the description of
-@code{next-window} for details.
+windows to search, and have the same meanings as in
+@code{next-window}.
 @end defun
 
 @node Buffers and Windows
@@ -1539,47 +1419,41 @@ set of windows to investigate.  See the description of
 @cindex windows, controlling precisely
 @cindex buffers, controlled in windows
 
-To find out which buffer is displayed in a given window the following
-function is used.
+  This section describes low-level functions for examining and setting
+the contents of windows.  @xref{Switching Buffers}, for higher-level
+functions for displaying a specific buffer in a window.
 
 @defun window-buffer &optional window
-This function returns the buffer that @var{window} is displaying.  The
-argument @var{window} can be any window and defaults to the selected
-one.  If @var{window} is an internal window, this function returns
+This function returns the buffer that @var{window} is displaying.  If
+@var{window} is omitted or @code{nil} it defaults to the selected
+window.  If @var{window} is an internal window, this function returns
 @code{nil}.
 @end defun
 
-The basic, low-level function to associate a window with a buffer is
-@code{set-window-buffer}.  Higher-level functions like
-@code{switch-to-buffer} and @code{display-buffer} try to obey a number
-of user customizations regulating which windows are supposed to
-display which buffers.  @xref{Switching Buffers}.  When writing an
-application, you should avoid using @code{set-window-buffer} unless
-you are sure you need it.
-
 @defun set-window-buffer window buffer-or-name &optional keep-margins
-This function makes @var{window} display @var{buffer-or-name} and
-returns @code{nil}.  The argument @var{window} has to denote a live
-window and defaults to the selected one.  The argument
-@var{buffer-or-name} must specify a buffer or the name of an existing
-buffer.  An error is signaled when @var{window} is @dfn{strongly}
-dedicated to its buffer (@pxref{Dedicated Windows}) and does not already
-display @var{buffer-or-name}.
-
-Normally, displaying @var{buffer-or-name} in @var{window} resets the
-window's position, display margins, fringe widths, and scroll bar
-settings based on the local variables of the specified buffer.  However,
-if the optional argument @var{keep-margins} is non-@code{nil}, display
-margins and fringe widths of @var{window} remain unchanged.
-@xref{Fringes}.
-
-This function is the fundamental primitive for changing which buffer is
-displayed in a window, and all ways of doing that call this function.
-Neither the selected window nor the current buffer are changed by this
-function.
+This function makes @var{window} display @var{buffer-or-name}.
+@var{window} should be a live window; if @code{nil}, it defaults to
+the selected window.  @var{buffer-or-name} should be a buffer, or the
+name of an existing buffer.  This function does not change which
+window is selected, nor does it directly change which buffer is
+current (@pxref{Current Buffer}).  Its return value is @code{nil}.
 
-This function runs @code{window-scroll-functions} before running
-@code{window-configuration-change-hook}, see @ref{Window Hooks}.
+If @var{window} is @dfn{strongly dedicated} to a buffer and
+@var{buffer-or-name} does not specify that buffer, this function
+signals an error.  @xref{Dedicated Windows}.
+
+By default, this function resets @var{window}'s position, display
+margins, fringe widths, and scroll bar settings, based on the local
+variables in the specified buffer.  However, if the optional argument
+@var{keep-margins} is non-@code{nil}, it leaves the display margins
+and fringe widths unchanged.
+
+When writing an application, you should normally use the higher-level
+functions described in @ref{Switching Buffers}, instead of calling
+@code{set-window-buffer} directly.
+
+This function runs @code{window-scroll-functions}, followed by
+@code{window-configuration-change-hook}.  @xref{Window Hooks}.
 @end defun
 
 @defvar buffer-display-count
@@ -1589,28 +1463,26 @@ displayed in a window.  It is incremented each time
 @end defvar
 
 @defvar buffer-display-time
-This variable records the time at which a buffer was last made visible
-in a window.  It is always local in each buffer; each time
-@code{set-window-buffer} is called, it sets this variable to
-@code{(current-time)} in the specified buffer (@pxref{Time of Day}).
-When a buffer is first created, @code{buffer-display-time} starts out
-with the value @code{nil}.
+This buffer-local variable records the time at which a buffer was last
+displayed in a window.  The value is @code{nil} if the buffer has
+never been displayed.  It is updated each time
+@code{set-window-buffer} is called for the buffer, with the value
+returned by @code{current-time} (@pxref{Time of Day}).
 @end defvar
 
 @defun get-buffer-window &optional buffer-or-name all-frames
-This function returns a window displaying @var{buffer-or-name}, or
-@code{nil} if there is none.  If there are several such windows, then
-the function returns the first one in the cyclic ordering of windows,
-starting from the selected window, @xref{Cyclic Window Ordering}.
+This function returns the first window displaying @var{buffer-or-name}
+in the cyclic ordering of windows, starting from the selected window
+(@pxref{Cyclic Window Ordering}).  If no such window exists, the
+return value is @code{nil}.
 
-The argument @var{buffer-or-name} may be a buffer or a buffer name and
-defaults to the current buffer.  The optional argument @var{all-frames}
-specifies which windows to consider:
+@var{buffer-or-name} should be a buffer or the name of a buffer; if
+omitted or @code{nil}, it defaults to the current buffer.  The
+optional argument @var{all-frames} specifies which windows to
+consider:
 
 @itemize @bullet
 @item
-@code{nil} means consider windows on the selected frame.
-@item
 @code{t} means consider windows on all existing frames.
 @item
 @code{visible} means consider windows on all visible frames.
@@ -1618,44 +1490,45 @@ specifies which windows to consider:
 0 means consider windows on all visible or iconified frames.
 @item
 A frame means consider windows on that frame only.
+@item
+Any other value means consider windows on the selected frame.
 @end itemize
 
-Observe that the behavior of @code{get-buffer-window} may differ from
-that of @code{next-window} (@pxref{Cyclic Window Ordering}) when
-@var{all-frames} equals @code{nil} or any value not listed here.
-Perhaps we will change @code{get-buffer-window} in the future to make it
-compatible with the other functions.
+Note that these meanings differ slightly from those of the
+@var{all-frames} argument to @code{next-window} (@pxref{Cyclic Window
+Ordering}).  This function may be changed in a future version of Emacs
+to eliminate this discrepancy.
 @end defun
 
 @defun get-buffer-window-list &optional buffer-or-name minibuf all-frames
 This function returns a list of all windows currently displaying
-@var{buffer-or-name}.  The argument @var{buffer-or-name} may be a buffer
-or the name of an existing buffer and defaults to the current buffer.
+@var{buffer-or-name}.  @var{buffer-or-name} should be a buffer or the
+name of an existing buffer.  If omitted or @code{nil}, it defaults to
+the current buffer.
 
-The two remaining arguments work like the same-named arguments of
-@code{next-window} (@pxref{Cyclic Window Ordering}); they are @emph{not}
-like the optional arguments of @code{get-buffer-window}.
+The arguments @var{minibuf} and @var{all-frames} have the same
+meanings as in the function @code{next-window} (@pxref{Cyclic Window
+Ordering}).  Note that the @var{all-frames} argument does @emph{not}
+behave exactly like in @code{get-buffer-window}.
 @end defun
 
 @deffn Command replace-buffer-in-windows &optional buffer-or-name
 This command replaces @var{buffer-or-name} with some other buffer, in
-all windows displaying it.  For each such window, it choose another
-buffer using @code{switch-to-prev-buffer} (@pxref{Window History}).
-
-The argument @var{buffer-or-name} may be a buffer, or the name of an
-existing buffer; it defaults to the current buffer.
-
-If a window displaying @var{buffer-or-name} is dedicated
-(@pxref{Dedicated Windows}) and is not the only window on its frame,
-that window is deleted.  If that window is the only window on its frame
-and there are other frames on the frame's terminal, that frame is dealt
-with by the function specified by @code{frame-auto-hide-function}
-(@pxref{Quitting Windows}).  Otherwise, the buffer provided by the
-function @code{switch-to-prev-buffer} (@pxref{Window History}) is
-displayed in the window instead.
+all windows displaying it.  @var{buffer-or-name} should be a buffer,
+or the name of an existing buffer; if omitted or @code{nil}, it
+defaults to the current buffer.
+
+The replacement buffer in each window is chosen via
+@code{switch-to-prev-buffer} (@pxref{Window History}).  Any dedicated
+window displaying @var{buffer-or-name} is deleted (@pxref{Dedicated
+Windows}), unless it is the only window on its frame---if it is the
+only window, and that frame is not the only frame on its terminal, the
+frame is ``dismissed'' by calling the function specified by
+@code{frame-auto-hide-function} (@pxref{Quitting Windows}).  If the
+dedicated window is the only window on the only frame on its terminal,
+the buffer is replaced anyway.
 @end deffn
 
-
 @node Switching Buffers
 @section Switching to a Buffer in a Window
 @cindex switching to a buffer
@@ -1731,9 +1604,12 @@ The @var{buffer-or-name} and @var{norecord} arguments have the same
 meanings as in @code{switch-to-buffer}.
 @end deffn
 
-The above commands use @code{pop-to-buffer}, which is the function
-used by Lisp programs to flexibly display a buffer in some window and
-select that window for editing:
+The above commands use the function @code{pop-to-buffer}, which
+flexibly displays a buffer in some window and selects that window for
+editing.  In turn, @code{pop-to-buffer} uses @code{display-buffer} for
+displaying the buffer.  Hence, all the variables affecting
+@code{display-buffer} will affect it as well.  @xref{Choosing Window},
+for the documentation of @code{display-buffer}.
 
 @defun pop-to-buffer buffer-or-name &optional action norecord
 This function makes @var{buffer-or-name} the current buffer and
@@ -1743,10 +1619,6 @@ on a different graphical frame, that frame is given input focus if
 possible (@pxref{Input Focus}).  The return value is the buffer that
 was switched to.
 
-This function uses @code{display-buffer} to display the buffer, so all
-the variables affecting @code{display-buffer} will affect it as well.
-@xref{Choosing Window}.
-
 If @var{buffer-or-name} is @code{nil}, it defaults to the buffer
 returned by @code{other-buffer} (@pxref{The Buffer List}).  If
 @var{buffer-or-name} is a string that is not the name of any existing
@@ -1775,8 +1647,8 @@ used as a subroutine by many functions and commands, including
 Buffers}).
 
 @cindex display action
-@cindex action function, for display-buffer
-@cindex action alist, for display-buffer
+@cindex action function, for @code{display-buffer}
+@cindex action alist, for @code{display-buffer}
   This command performs several complex steps to find a window to
 display in.  These steps are described by means of @dfn{display
 actions}, which have the form @code{(@var{function} . @var{alist})}.
@@ -1815,6 +1687,11 @@ The variable @code{display-buffer-overriding-action}.
 The user option @code{display-buffer-alist}.
 
 @item
+A special action for handling @code{special-display-buffer-names} and
+@code{special-display-regexps}, if either of those variables is
+non-@code{nil}.  @xref{Choosing Window Options}.
+
+@item
 The @var{action} argument.
 
 @item
@@ -1886,10 +1763,9 @@ This function tries to ``display'' @var{buffer} by finding a window
 that is already displaying it.
 
 If @var{alist} has a non-@code{nil} @code{inhibit-same-window} entry,
-the selected window is not eligible for reuse.
-
-If @var{alist} contains a @code{reusable-frames} entry, its value
-determines which frames to search for a reusable window:
+the selected window is not eligible for reuse.  If @var{alist}
+contains a @code{reusable-frames} entry, its value determines which
+frames to search for a reusable window:
 
 @itemize @bullet
 @item
@@ -1910,17 +1786,28 @@ normally searches just the selected frame; however, if either the
 variable @code{display-buffer-reuse-frames} or the variable
 @code{pop-up-frames} is non-@code{nil}, it searches all frames on the
 current terminal.  @xref{Choosing Window Options}.
+
+If this function chooses a window on another frame, it makes that
+frame visible and raises it if necessary.
 @end defun
 
 @defun display-buffer-pop-up-frame buffer alist
 This function creates a new frame, and displays the buffer in that
-frame's window.
+frame's window.  It actually performs the frame creation by calling
+the function specified in @code{pop-up-frame-function}
+(@pxref{Choosing Window Options}).
 @end defun
 
 @defun display-buffer-pop-up-window buffer alist
 This function tries to display @var{buffer} by splitting the largest
-or least recently-used window.  It uses @code{split-window-sensibly}
-as a subroutine (@pxref{Choosing Window Options}).
+or least recently-used window (typically one on the selected frame).
+It actually performs the split by calling the function specified in
+@code{split-window-preferred-function} (@pxref{Choosing Window
+Options}).
+
+It can fail if no window splitting can be performed for some reason
+(e.g. if there is just one frame and it has an @code{unsplittable}
+frame parameter; @pxref{Buffer Parameters}).
 @end defun
 
 @defun display-buffer-use-some-window buffer alist
@@ -1937,142 +1824,108 @@ The behavior of the standard display actions of @code{display-buffer}
 options.
 
 @defopt display-buffer-reuse-frames
-If this variable is non-@code{nil}, @code{display-buffer} searches
-visible and iconified frames for a window displaying
-@var{buffer-or-name}.  If there is such a window, @code{display-buffer}
-makes that window's frame visible and raises it if necessary, and
-returns the window.  If there is no such window or
-@code{display-buffer-reuse-frames} is @code{nil}, the behavior of
-@code{display-buffer} is determined by the variables described next.
+If the value of this variable is non-@code{nil}, @code{display-buffer}
+may search all frames on the current terminal when looking for a
+window already displaying the specified buffer.  The default is
+@code{nil}.  This variable is consulted by the action function
+@code{display-buffer-reuse-window} (@pxref{Display Action Functions}).
 @end defopt
 
 @defopt pop-up-windows
-This variable specifies whether @code{display-buffer} is allowed to
-split (@pxref{Splitting Windows}) an existing window.  If this variable
-is non-@code{nil}, @code{display-buffer} tries to split the largest or
-least recently used window on the selected frame.  (If the selected
-frame is a minibuffer-only frame, @code{display-buffer} tries to split a
-window on another frame instead.)  If this variable is @code{nil} or the
-variable @code{pop-up-frames} (see below) is non-@code{nil},
-@code{display-buffer} does not split any window.
+If the value of this variable is non-@code{nil}, @code{display-buffer}
+is allowed to split an existing window to make a new window for
+displaying in.  This is the default.
+
+This variable is provided mainly for backward compatibility.  It is
+obeyed by @code{display-buffer} via a special mechanism in
+@code{display-buffer-fallback-action}, which only calls the action
+function @code{display-buffer-pop-up-window} (@pxref{Display Action
+Functions}) when the value is @code{nil}.  It is not consulted by
+@code{display-buffer-pop-up-window} itself, which the user may specify
+directly in @code{display-buffer-alist} etc.
 @end defopt
 
 @defopt split-window-preferred-function
-This variable must specify a function with one argument, which is a
-window.  The @code{display-buffer} routines will call this function with
-one or more candidate windows when they look for a window to split.  The
-function is expected to split that window and return the new window.  If
-the function returns @code{nil}, this means that the argument window
-cannot (or shall not) be split.
-
-The default value of @code{split-window-preferred-function} is the
-function @code{split-window-sensibly} described below.  If you
-customize this option, bear in mind that the @code{display-buffer}
-routines may call your function up to two times when trying to split a
-window.  The argument of the first call is the largest window on the
-chosen frame (as returned by @code{get-largest-window}).  If that call
-fails to return a live window, your function is called a second time
-with the least recently used window on that frame (as returned by
-@code{get-lru-window}).
-
-The function specified by this option may try to split any other window
-instead of the argument window.  Note that the window selected at the
-time @code{display-buffer} was invoked is still selected when your
-function is called.  Hence, you can split the selected window (instead
-of the largest or least recently used one) by simply ignoring the window
-argument in the body of your function.  You can even choose to not split
-any window as long as the return value of your function specifies a live
-window or @code{nil}, but you are not encouraged to do so
-unconditionally.  If you want @code{display-buffer} to never split any
-windows, set @code{pop-up-windows} to @code{nil}.
+This variable specifies a function for splitting a window, in order to
+make a new window for displaying a buffer.  It is used by the
+@code{display-buffer-pop-up-window} action function to actually split
+the window (@pxref{Display Action Functions}).
+
+The default value is @code{split-window-sensibly}, which is documented
+below.  The value must be a function that takes one argument, a
+window, and return either a new window (which is used to display the
+desired buffer) or @code{nil} (which means the splitting failed).
 @end defopt
 
 @defun split-window-sensibly window
-This function takes a window as argument and tries to split that window
-in a suitable way.  The two variables described next are useful for
-tuning the behavior of this function.
+This function tries to split @code{window}, and return the newly
+created window.  If @code{window} cannot be split, it returns
+@code{nil}.
+
+This function obeys the usual rules that determine when a window may
+be split (@pxref{Splitting Windows}).  It first tries to split by
+placing the new window below, subject to the restriction imposed by
+@code{split-height-threshold} (see below) in addition to any other
+restrictions.  If that fails, it tries to split by placing the new
+window to the right, subject to @code{split-width-threshold} (see
+below).  If that fails, and the window is the only window on its
+frame, this function again tries to split and place the new window
+below, disregarding @code{split-height-threshold}.  If this fails as
+well, this function gives up and returns @code{nil}.
 @end defun
 
 @defopt split-height-threshold
-This variable specifies whether @code{split-window-sensibly} may split
-windows vertically.  If it is an integer, @code{split-window-sensibly}
-tries to vertically split a window only if it has at least this many
-lines.  If the window has less lines, splitting fails, or the value of
-this variable is @code{nil}, @code{split-window-sensibly} will try to
-split the window horizontally, subject to restrictions of
-@code{split-width-threshold} (see below).  If splitting horizontally
-fails too and the window is the only window on its frame,
-@code{split-window-sensibly} will try to split the window vertically
-disregarding the value of @code{split-height-threshold}.  If this fails
-as well, @code{split-window-sensibly} returns @code{nil}.
-
-@code{split-window-sensibly} does not split vertically a window whose
-height is fixed (@pxref{Resizing Windows}).  Also, it vertically splits
-a window only if the space taken up by that window can accommodate two
-windows one above the other that are both at least
-@code{window-min-height} lines tall.  Moreover, if the window that shall
-be split has a mode line, @code{split-window-sensibly} does not split
-the window unless the new window can accommodate a mode line too.
+This variable, used by @code{split-window-sensibly}, specifies whether
+to split the window placing the new window below.  If it is an
+integer, that means to split only if the original window has at least
+that many lines.  If it is @code{nil}, that means not to split this
+way.
 @end defopt
 
 @defopt split-width-threshold
-This variable specifies whether @code{split-window-sensibly} may split
-windows horizontally.  If it is an integer, @code{split-window-sensibly}
-tries to horizontally split a window only if it has at least this many
-columns.  If it is @code{nil}, @code{split-window-sensibly} will not
-split the window horizontally.  (It still might split the window
-vertically, though, see above.)
-
-@code{split-window-sensibly} does not split horizontally a window if
-that window's width is fixed (@pxref{Resizing Windows}).  Also, it
-horizontally splits a window only if the space that window takes up can
-accommodate two windows side by side that are both at least
-@code{window-min-width} columns wide.
+This variable, used by @code{split-window-sensibly}, specifies whether
+to split the window placing the new window to the right.  If the value
+is an integer, that means to split only if the original window has at
+least that many columns.  If the value is @code{nil}, that means not
+to split this way.
 @end defopt
 
-@defopt even-window-heights
-This variable specifies whether @code{display-buffer} should even out
-window heights if the buffer gets displayed in an existing window, above
-or beneath another window.  If @code{even-window-heights} is
-non-@code{nil}, the default, window heights will be evened out.  If
-either of the involved window has fixed height (@pxref{Resizing
-Windows}) or @code{even-window-heights} is @code{nil}, the original
-window heights will be left alone.
-@end defopt
-
-@c Emacs 19 feature
 @defopt pop-up-frames
-This variable specifies whether @code{display-buffer} should make new
-frames.  If it is non-@code{nil}, @code{display-buffer} looks for a
-window already displaying @var{buffer-or-name} on any visible or
-iconified frame.  If it finds such a window, it makes that window's
-frame visible and raises it if necessary, and returns the window.
-Otherwise it makes a new frame, unless the variable's value is
-@code{graphic-only} and the selected frame is not on a graphic display.
-@xref{Frames}, for more information.
-
-Note that the value of @code{pop-up-windows} does not matter if
-@code{pop-up-frames} is non-@code{nil}.  If @code{pop-up-frames} is
-@code{nil}, then @code{display-buffer} either splits a window or reuses
-one.
+If the value of this variable is non-@code{nil}, that means
+@code{display-buffer} may display buffers by making new frames.  The
+default is @code{nil}.
+
+A non-@code{nil} value also means that when @code{display-buffer} is
+looking for a window already displaying @var{buffer-or-name}, it can
+search any visible or iconified frame, not just the selected frame.
+
+This variable is provided mainly for backward compatibility.  It is
+obeyed by @code{display-buffer} via a special mechanism in
+@code{display-buffer-fallback-action}, which calls the action function
+@code{display-buffer-pop-up-frame} (@pxref{Display Action Functions})
+if the value is non-@code{nil}.  (This is done before attempting to
+split a window.)  This variable is not consulted by
+@code{display-buffer-pop-up-frame} itself, which the user may specify
+directly in @code{display-buffer-alist} etc.
 @end defopt
 
-@c Emacs 19 feature
 @defopt pop-up-frame-function
-This variable specifies how to make a new frame if @code{pop-up-frames}
-is non-@code{nil}.
-
-The value of this variable must be a function of no arguments.  When
-@code{display-buffer} makes a new frame, it does so by calling that
-function, which should return a frame.  The default value of this
-variable is a function that creates a frame using the parameters
-specified by @code{pop-up-frame-alist} described next.
+This variable specifies a function for creating a new frame, in order
+to make a new window for displaying a buffer.  It is used by the
+@code{display-buffer-pop-up-frame} action function (@pxref{Display
+Action Functions}).
+
+The value should be a function that takes no arguments and returns a
+frame, or @code{nil} if no frame could be created.  The default value
+is a function that creates a frame using the parameters specified by
+@code{pop-up-frame-alist} (see below).
 @end defopt
 
 @defopt pop-up-frame-alist
-This variable holds an alist specifying frame parameters used by the
-default value of @code{pop-up-frame-function} for making new frames.
-@xref{Frame Parameters}, for more information about frame parameters.
+This variable holds an alist of frame parameters (@pxref{Frame
+Parameters}), which is used by the default function in
+@code{pop-up-frame-function} to make a new frame.  The default is
+@code{nil}.
 @end defopt
 
 @defopt special-display-buffer-names
@@ -2193,12 +2046,6 @@ This variable takes precedence over all the other options described
 above.
 @end defopt
 
-If all options described above fail to produce a suitable window,
-@code{display-buffer} tries to reuse an existing window.  As a last
-resort, it will try to display @var{buffer-or-name} on a separate frame.
-In that case, the value of @code{pop-up-frames} is disregarded.
-
-
 @node Window History
 @section Window History
 @cindex window history
diff --git a/doc/misc/ChangeLog b/doc/misc/ChangeLog
index 924f3501bfa..43d9ba1b1e6 100644
--- a/doc/misc/ChangeLog
+++ b/doc/misc/ChangeLog
@@ -1,3 +1,19 @@
+2011-11-20  Glenn Morris  <rgm@gnu.org>
+
+        * gnus.texi (Group Information):
+        Remove gnus-group-fetch-faq, command deleted 2010-09-24.
+
+2011-11-20  Juanma Barranquero  <lekktu@gmail.com>
+
+        * gnus-coding.texi (Gnus Maintenance Guide):
+        Rename from "Gnus Maintainance Guide".
+
+        * ede.texi (ede-compilation-program, ede-compiler, ede-linker):
+        * eieio.texi (Customizing):
+        * gnus.texi (Article Washing):
+        * gnus-news.texi:
+        * sem-user.texi (Smart Jump): Fix typos.
+
 2011-11-16  Juanma Barranquero  <lekktu@gmail.com>
 
         * org.texi (Agenda commands, Exporting Agenda Views): Fix typos.
diff --git a/doc/misc/ada-mode.texi b/doc/misc/ada-mode.texi
index 374158c2c78..0eb20d01324 100644
--- a/doc/misc/ada-mode.texi
+++ b/doc/misc/ada-mode.texi
@@ -1357,7 +1357,7 @@ specifies the casing of one word or word fragment. Comments may be
 included, separated from the word by a space.
 
 If the word starts with an asterisk (@key{*}), it defines the casing
-af a word fragment (or ``substring''); part of a word between two
+as a word fragment (or ``substring''); part of a word between two
 underscores or word boundary.
 
 For example:
diff --git a/doc/misc/autotype.texi b/doc/misc/autotype.texi
index 2e66c78a3cb..ecf4c7e47b2 100644
--- a/doc/misc/autotype.texi
+++ b/doc/misc/autotype.texi
@@ -156,7 +156,7 @@ the point is normally left after that skeleton is inserted (@pxref{Using
 Skeletons}).  The point (@pxref{(emacs)Point}) is left at the next
 interesting spot in the skeleton instead.
 
-  A negative prefix means to do something similar with that many precedingly
+  A negative prefix means to do something similar with that many previously
 marked interregions (@pxref{(emacs)Mark}).  In the simplest case, if you type
 @kbd{M--} just before issuing the skeleton command, that will wrap the
 skeleton around the current region, just like a positive argument would have
diff --git a/doc/misc/calc.texi b/doc/misc/calc.texi
index 5a1ee872a2b..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.
@@ -10666,7 +10666,7 @@ and displayed in any radix just like integers and fractions.  Since a
 float that is entered in a radix other that 10 will be converted to
 decimal, the number that Calc stores may not be exactly the number that
 was entered, it will be the closest decimal approximation given the
-current precison.  The notation @samp{@var{radix}#@var{ddd}.@var{ddd}}
+current precision.  The notation @samp{@var{radix}#@var{ddd}.@var{ddd}}
 is a floating-point number whose digits are in the specified radix.
 Note that the @samp{.}  is more aptly referred to as a ``radix point''
 than as a decimal point in this case.  The number @samp{8#123.4567} is
@@ -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/dbus.texi b/doc/misc/dbus.texi
index 79c7ada3b0b..88b068ccd5b 100644
--- a/doc/misc/dbus.texi
+++ b/doc/misc/dbus.texi
@@ -332,7 +332,7 @@ Example:
 @code{method}, @code{signal}, and @code{property} elements.  Unlike
 properties, which can change their values during lifetime of a D-Bus
 object, annotations are static.  Often they are used for code
-generators of D-Bus langugae bindings.  Example:
+generators of D-Bus language bindings.  Example:
 
 @example
 <annotation name="de.berlios.Pinot.GetStatistics" value="pinotDBus"/>
diff --git a/doc/misc/dired-x.texi b/doc/misc/dired-x.texi
index 99530e6356d..a026c63e25b 100644
--- a/doc/misc/dired-x.texi
+++ b/doc/misc/dired-x.texi
@@ -476,7 +476,7 @@ in your @code{dired-mode-hook}.
 This Dired-X feature is obsolete as of Emacs 24.1.  The standard Emacs
 directory local variables mechanism (@pxref{Directory
 Variables,,,emacs,The Gnu Emacs manual}) replaces it.  For an example of
-the new mechanims, @pxref{Omitting Variables}.
+the new mechanisms, @pxref{Omitting Variables}.
 
 When Dired visits a directory, it looks for a file whose name is the
 value of variable @code{dired-local-variables-file} (default: @file{.dired}).
diff --git a/doc/misc/ede.texi b/doc/misc/ede.texi
index 55dc7f9a822..f8d757c2d87 100644
--- a/doc/misc/ede.texi
+++ b/doc/misc/ede.texi
@@ -3526,7 +3526,7 @@ use the same autoconf form.
 @item :objectextention
 Type: @code{string}
 
-A string which is the extention used for object files.
+A string which is the extension used for object files.
 For example, C code uses .o on unix, and Emacs Lisp uses .elc.
 @refill
 
@@ -3634,7 +3634,7 @@ it's rule definition.
 @item :objectextention
 Type: @code{string}
 
-A string which is the extention used for object files.
+A string which is the extension used for object files.
 For example, C code uses .o on unix, and Emacs Lisp uses .elc.
 @refill
 
@@ -3782,7 +3782,7 @@ it's rule definition.
 @item :objectextention
 Type: @code{string}
 
-A string which is the extention used for object files.
+A string which is the extension used for object files.
 For example, C code uses .o on unix, and Emacs Lisp uses .elc.
 @refill
 
diff --git a/doc/misc/eieio.texi b/doc/misc/eieio.texi
index 8ee40288fe0..7b4945027d3 100644
--- a/doc/misc/eieio.texi
+++ b/doc/misc/eieio.texi
@@ -1212,9 +1212,9 @@ This method does nothing by default, but that may change in the future.
 This would be the best way to make your objects persistent when using
 in-place editing.
 
-@section Widget extention
+@section Widget extension
 
-When widgets are being created, one new widget extention has been added,
+When widgets are being created, one new widget extension has been added,
 called the @code{:slotofchoices}.  When this occurs in a widget
 definition, all elements after it are removed, and the slot is specifies
 is queried and converted into a series of constants.
diff --git a/doc/misc/eshell.texi b/doc/misc/eshell.texi
index d2705155887..b0090f0fb84 100644
--- a/doc/misc/eshell.texi
+++ b/doc/misc/eshell.texi
@@ -61,7 +61,7 @@ developing GNU and promoting software freedom.''
 @node Top, What is Eshell?, (dir), (dir)
 @top Eshell
 
-Eshell is a shell-like command interpretor
+Eshell is a shell-like command interpreter
 implemented in Emacs Lisp.  It invokes no external processes except for
 those requested by the user.  It is intended to be a functional
 replacement for command shells such as @command{bash}, @command{zsh},
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-coding.texi b/doc/misc/gnus-coding.texi
index ab9c0232d3d..a79c68f0123 100644
--- a/doc/misc/gnus-coding.texi
+++ b/doc/misc/gnus-coding.texi
@@ -1,7 +1,7 @@
 \input texinfo
 
 @setfilename gnus-coding
-@settitle Gnus Coding Style and Maintainance Guide
+@settitle Gnus Coding Style and Maintenance Guide
 @syncodeindex fn cp
 @syncodeindex vr cp
 @syncodeindex pg cp
@@ -45,7 +45,7 @@ license to the document, as described in section 6 of the license.
 
 @ifnottex
 @node Top
-@top Gnus Coding Style and Maintainance Guide
+@top Gnus Coding Style and Maintenance Guide
 This manual describes @dots{}
 
 @insertcopying 
@@ -53,7 +53,7 @@ This manual describes @dots{}
 
 @menu
 * Gnus Coding Style:: Gnus Coding Style
-* Gnus Maintainance Guide:: Gnus Maintainance Guide
+* Gnus Maintenance Guide:: Gnus Maintenance Guide
 @end menu
 
 @c @ref{Gnus Reference Guide, ,Gnus Reference Guide, gnus, The Gnus Newsreader}
@@ -250,8 +250,8 @@ Emacs 20.7 and up.
 XEmacs 21.1 and up.
 @end itemize
 
-@node Gnus Maintainance Guide
-@chapter Gnus Maintainance Guide
+@node Gnus Maintenance Guide
+@chapter Gnus Maintenance Guide
 
 @section Stable and development versions
 
diff --git a/doc/misc/gnus-news.texi b/doc/misc/gnus-news.texi
index 62c1663508b..612ea14e2cf 100644
--- a/doc/misc/gnus-news.texi
+++ b/doc/misc/gnus-news.texi
@@ -107,7 +107,7 @@ EasyPG is included in Emacs 23 and available separately as well.
 @itemize @bullet
 
 @item
-Symbols like @code{gcc-self} now has the same presedence rules in
+Symbols like @code{gcc-self} now have the same precedence rules in
 @code{gnus-parameters} as other ``real'' variables: The last match
 wins instead of the first match.
 
diff --git a/doc/misc/gnus.texi b/doc/misc/gnus.texi
index a3a93c6ef61..f099dfd36d0 100644
--- a/doc/misc/gnus.texi
+++ b/doc/misc/gnus.texi
@@ -4491,23 +4491,6 @@ news.
 @table @kbd
 
 
-@item H f
-@kindex H f (Group)
-@findex gnus-group-fetch-faq
-@vindex gnus-group-faq-directory
-@cindex FAQ
-@cindex ange-ftp
-Try to fetch the @acronym{FAQ} for the current group
-(@code{gnus-group-fetch-faq}).  Gnus will try to get the @acronym{FAQ}
-from @code{gnus-group-faq-directory}, which is usually a directory on
-a remote machine.  This variable can also be a list of directories.
-In that case, giving a prefix to this command will allow you to choose
-between the various sites.  @code{ange-ftp} (or @code{efs}) will be
-used for fetching the file.
-
-If fetching from the first site is unsuccessful, Gnus will attempt to go
-through @code{gnus-group-faq-directory} and try to open them one by one.
-
 @item H d
 @itemx C-c C-d
 @c @icon{gnus-group-describe-group}
@@ -8992,7 +8975,7 @@ apostrophe or quotation mark, then try this wash.
 Translate many non-@acronym{ASCII} characters into their
 @acronym{ASCII} equivalents (@code{gnus-article-treat-non-ascii}).
 This is mostly useful if you're on a terminal that has a limited font
-and does't show accented characters, ``advanced'' punctuation, and the
+and doesn't show accented characters, ``advanced'' punctuation, and the
 like.  For instance, @samp{»} is tranlated into @samp{>>}, and so on.
 
 @item W Y f
@@ -21228,7 +21211,7 @@ features (inspired by the Google search input language):
 AND, OR, and NOT are supported, and parentheses can be used to control
 operator precedence, e.g. (emacs OR xemacs) AND linux. Note that
 operators must be written with all capital letters to be
-recognised. Also preceding a term with a - sign is equivalent to NOT
+recognized. Also preceding a term with a - sign is equivalent to NOT
 term.
 
 @item Automatic AND queries
@@ -21273,7 +21256,7 @@ Gmane queries follow a simple query language:
 AND, OR, NOT (or AND NOT), and XOR are supported, and brackets can be
 used to control operator precedence, e.g. (emacs OR xemacs) AND linux.
 Note that operators must be written with all capital letters to be
-recognised.
+recognized.
 
 @item Required and excluded terms
 + and - can be used to require or exclude terms, e.g. football -american
@@ -25471,7 +25454,7 @@ 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.
 
@@ -30030,7 +30013,7 @@ this:
 @subsection Score File Syntax
 
 Score files are meant to be easily parseable, but yet extremely
-mallable.  It was decided that something that had the same read syntax
+malleable.  It was decided that something that had the same read syntax
 as an Emacs Lisp list would fit that spec.
 
 Here's a typical score file:
diff --git a/doc/misc/message.texi b/doc/misc/message.texi
index 48d0028e452..4d828f69bbd 100644
--- a/doc/misc/message.texi
+++ b/doc/misc/message.texi
@@ -2120,7 +2120,7 @@ follows this line--} by default.
 
 @item message-directory
 @vindex message-directory
-Directory used by many mailey things.  The default is @file{~/Mail/}.
+Directory used by many mailish things.  The default is @file{~/Mail/}.
 All other mail file variables are derived from @code{message-directory}.
 
 @item message-auto-save-directory
diff --git a/doc/misc/org.texi b/doc/misc/org.texi
index cc925906c28..34a4ba4f8f3 100644
--- a/doc/misc/org.texi
+++ b/doc/misc/org.texi
@@ -15533,7 +15533,7 @@ chapter about publishing.
 @i{Jambunathan K} contributed the OpenDocumentText exporter.
 @item
 @i{Sebastien Vauban} reported many issues with LaTeX and BEAMER export and
-enabled source code highlighling in Gnus.
+enabled source code highlighting in Gnus.
 @item
 @i{Stefan Vollmar} organized a video-recorded talk at the
 Max-Planck-Institute for Neurology.  He also inspired the creation of a
diff --git a/doc/misc/sem-user.texi b/doc/misc/sem-user.texi
index 7a363523aa6..28d1cdb6eb8 100644
--- a/doc/misc/sem-user.texi
+++ b/doc/misc/sem-user.texi
@@ -880,7 +880,7 @@ command, like this:
 @end example
 @end defun
 
-These commands are often more accurate than than the @code{find-tag}
+These commands are often more accurate than the @code{find-tag}
 command (@pxref{Tags,,,emacs,Emacs manual}), because the Semantic
 Analyzer is context-sensitive.
 
diff --git a/doc/misc/semantic.texi b/doc/misc/semantic.texi
index ad6159feb1a..55b60937fb6 100644
--- a/doc/misc/semantic.texi
+++ b/doc/misc/semantic.texi
@@ -421,7 +421,7 @@ local variables, and tag lists in scope for various reasons, such as
 C++ using statements.
 
 @item semanticdb-typecache.el
-The typecache is part of @code{semanticdb}, but is used primarilly by
+The typecache is part of @code{semanticdb}, but is used primarily by
 the analyzer to look up datatypes and complex names.  The typecache is
 bound across source files and builds a master lookup table for data
 type names.
diff --git a/doc/misc/tramp.texi b/doc/misc/tramp.texi
index 0accc6fac43..e6b0f4fa235 100644
--- a/doc/misc/tramp.texi
+++ b/doc/misc/tramp.texi
@@ -3180,7 +3180,7 @@ names:
  '("^/xy" . "@trampfn{ssh, news, news.my.domain, /opt/news/etc/}"))
 @end lisp
 
-This shortens the file openening command to @kbd{C-x C-f /xy
+This shortens the file opening command to @kbd{C-x C-f /xy
 @key{RET}}.  The disadvantage is, again, that you cannot edit the file
 name, because the expansion happens after entering the file name only.