Gnus -- Minor tweak define #'time-to-seconds

[packages] / xemacs-packages / calc / calc.texinfo

\input texinfo                  @c -*-texinfo-*-
@comment %**start of header (This is for running Texinfo on a region.)
@c smallbook
@setfilename calc.info
@c [title]
@settitle GNU Emacs Calc 2.1 Manual
@comment %**end of header (This is for running Texinfo on a region.)
@setchapternewpage odd

@ignore

@tex
% Some special kludges to make TeX formatting prettier.
% Because makeinfo.c exists, we can't just define new commands.
% So instead, we take over little-used existing commands.
%
% Redefine @cite{text} to act like $text$ in regular TeX.
% Info will typeset this same as @samp{text}.
\gdef\goodtex{\tex \let\rm\goodrm \let\t\ttfont \turnoffactive}
\gdef\goodrm{\fam0\tenrm}
\gdef\cite{\goodtex$\citexxx}
\gdef\citexxx#1{#1$\Etex}
\global\let\oldxrefX=\xrefX
\gdef\xrefX[#1]{\begingroup\let\cite=\dfn\oldxrefX[#1]\endgroup}
%
% Redefine @i{text} to be equivalent to @cite{text}, i.e., to use math mode.
% This looks the same in TeX but omits the surrounding ` ' in Info.
\global\let\i=\cite
%
% Redefine @c{tex-stuff} \n @whatever{info-stuff}.
\gdef\c{\futurelet\next\mycxxx}
\gdef\mycxxx{%
  \ifx\next\bgroup \goodtex\let\next\mycxxy
  \else\ifx\next\mindex \let\next\relax
  \else\ifx\next\kindex \let\next\relax
  \else\ifx\next\starindex \let\next\relax \else \let\next\comment
  \fi\fi\fi\fi \next
}
\gdef\mycxxy#1#2{#1\Etex\mycxxz}
\gdef\mycxxz#1{}
@end tex

@c Fix some things to make math mode work properly.
@iftex
@textfont0=@tenrm
@font@teni=cmmi10 scaled @magstephalf   @textfont1=@teni
@font@seveni=cmmi7 scaled @magstephalf  @scriptfont1=@seveni
@font@fivei=cmmi5 scaled @magstephalf   @scriptscriptfont1=@fivei
@font@tensy=cmsy10 scaled @magstephalf  @textfont2=@tensy
@font@sevensy=cmsy7 scaled @magstephalf @scriptfont2=@sevensy
@font@fivesy=cmsy5 scaled @magstephalf  @scriptscriptfont2=@fivesy
@font@tenex=cmex10 scaled @magstephalf  @textfont3=@tenex
@scriptfont3=@tenex  @scriptscriptfont3=@tenex
@textfont7=@tentt  @scriptfont7=@tentt  @scriptscriptfont7=@tentt
@end iftex

@c Fix some other things specifically for this manual.
@iftex
@finalout
@mathcode`@:=`@:  @c Make Calc fractions come out right in math mode
@tocindent=.5pc   @c Indent subsections in table of contents less
@rightskip=0pt plus 2pt  @c Favor short lines rather than overfull hboxes
@tex
\gdef\coloneq{\mathrel{\mathord:\mathord=}}
\ifdim\parskip>17pt
  \global\parskip=12pt   % Standard parskip looks a bit too large
\fi
\gdef\internalBitem{\parskip=7pt\kyhpos=\tableindent\kyvpos=0pt
\smallbreak\parsearg\itemzzy}
\gdef\itemzzy#1{\itemzzz{#1}\relax\ifvmode\kern-7pt\fi}
\gdef\trademark{${}^{\rm TM}$}
\gdef\group{%
  \par\vskip8pt\begingroup
  \def\Egroup{\egroup\endgroup}%
  \let\aboveenvbreak=\relax  % so that nothing gets between vtop and first box
  \def\singlespace{\baselineskip=\singlespaceskip}%
  \vtop\bgroup
}
%
%\global\abovedisplayskip=0pt
%\global\abovedisplayshortskip=-10pt
%\global\belowdisplayskip=7pt
%\global\belowdisplayshortskip=2pt
\gdef\beforedisplay{\vskip-10pt}
\gdef\afterdisplay{\vskip-5pt}
\gdef\beforedisplayh{\vskip-25pt}
\gdef\afterdisplayh{\vskip-10pt}
%
\gdef\printindex{\parsearg\calcprintindex}
\gdef\calcprintindex#1{%
  \doprintindex{#1}%
  \openin1 \jobname.#1s
  \ifeof1{\let\s=\indexskip \csname indexsize#1\endcsname}\fi
  \closein1
}
\gdef\indexskip{(This page intentionally left blank)\vfill\eject}
\gdef\indexsizeky{\s\s\s\s\s\s\s\s}
\gdef\indexsizepg{\s\s\s\s\s\s}
\gdef\indexsizetp{\s\s\s\s\s\s}
\gdef\indexsizecp{\s\s\s\s}
\gdef\indexsizevr{}
\gdef\indexsizefn{\s\s}
\gdef\langle#1\rangle{\it XXX}   % Avoid length mismatch with true expansion
%
% Ensure no indentation at beginning of sections, and avoid club paragraphs.
\global\let\calcchapternofonts=\chapternofonts
\gdef\chapternofonts{\aftergroup\calcfixclub\calcchapternofonts}
\gdef\calcfixclub{\calcclubpenalty=10000\noindent}
\global\let\calcdobreak=\dobreak
\gdef\dobreak{{\penalty-9999\dimen0=\pagetotal\advance\dimen0by1.5in
\ifdim\dimen0>\pagegoal\vfill\eject\fi}\calcdobreak}
%
\gdef\kindex{\def\indexname{ky}\futurelet\next\calcindexer}
\gdef\tindex{\def\indexname{tp}\futurelet\next\calcindexer}
\gdef\mindex{\let\indexname\relax\futurelet\next\calcindexer}
\gdef\calcindexer{\catcode`\ =\active\parsearg\calcindexerxx}
\gdef\calcindexerxx#1{%
  \catcode`\ =10%
  \ifvmode \indent \fi \setbox0=\lastbox \advance\kyhpos\wd0 \fixoddpages \box0
  \setbox0=\hbox{\ninett #1}%
  \calcindexersh{\llap{\hbox to 4em{\bumpoddpages\lower\kyvpos\box0\hss}\hskip\kyhpos}}%
  \global\let\calcindexersh=\calcindexershow
  \advance\clubpenalty by 5000%
  \ifx\indexname\relax \else
    \singlecodeindexer{#1\indexstar}%
    \global\def\indexstar{}%
  \fi
  \futurelet\next\calcindexerxxx
}
\gdef\indexstar{}
\gdef\bumpoddpages{\ifodd\calcpageno\hskip7.3in\fi}
%\gdef\bumpoddpages{\hskip7.3in}   % for marginal notes on right side always
%\gdef\bumpoddpages{}              % for marginal notes on left side always
\gdef\fixoddpages{%
\global\calcpageno=\pageno
{\dimen0=\pagetotal
\advance\dimen0 by2\baselineskip
\ifdim\dimen0>\pagegoal
\global\advance\calcpageno by 1
\vfill\eject\noindent
\fi}%
}
\gdef\calcindexershow#1{\smash{#1}\advance\kyvpos by 11pt}
\gdef\calcindexernoshow#1{}
\global\let\calcindexersh=\calcindexershow
\gdef\calcindexerxxx{%
  \ifx\indexname\relax
    \ifx\next\kindex \global\let\calcindexersh=\calcindexernoshow \fi
    \ifx\next\tindex \global\let\calcindexersh=\calcindexernoshow \fi
  \fi
  \calcindexerxxxx
}
\gdef\calcindexerxxxx#1{\next}
\gdef\indexstarxx{\thinspace{\rm *}}
\gdef\starindex{\global\let\indexstar=\indexstarxx}
\gdef\calceverypar{%
\kyhpos=\leftskip\kyvpos=0pt\clubpenalty=\calcclubpenalty
\calcclubpenalty=1000\relax
}
\gdef\idots{{\indrm...}}
@end tex
@newdimen@kyvpos @kyvpos=0pt
@newdimen@kyhpos @kyhpos=0pt
@newcount@calcclubpenalty @calcclubpenalty=1000
@newcount@calcpageno
@newtoks@calcoldeverypar @calcoldeverypar=@everypar
@everypar={@calceverypar@the@calcoldeverypar}
@ifx@turnoffactive@undefinedzzz@def@turnoffactive{}@fi
@ifx@ninett@undefinedzzz@font@ninett=cmtt9@fi
@catcode`@\=0 \catcode`\@=11
\r@ggedbottomtrue
\catcode`\@=0 @catcode`@\=@active
@end iftex

@end ignore

@ifinfo
@direntry
* Calc: (calc).               Scientific, financial, and symbolic calculator
                              for Emacs
@end direntry

This file documents Calc, the GNU Emacs calculator.

Copyright (C) 1990, 1991 Free Software Foundation, Inc.

Permission is granted to make and distribute verbatim copies of this
manual provided the copyright notice and this permission notice are
preserved on all copies.

@ignore
Permission is granted to process this file through TeX and print the
results, provided the printed document carries copying permission notice
identical to this one except for the removal of this paragraph (this
paragraph not being relevant to the printed manual).

@end ignore
Permission is granted to copy and distribute modified versions of this
manual under the conditions for verbatim copying, provided also that the
section entitled ``GNU General Public License'' is included exactly as
in the original, and provided that the entire resulting derived work is
distributed under the terms of a permission notice identical to this one.

Permission is granted to copy and distribute translations of this manual
into another language, under the above conditions for modified versions,
except that the section entitled ``GNU General Public License'' may be
included in a translation approved by the author instead of in the
original English.
@end ifinfo

@titlepage
@sp 6
@center @titlefont{Calc Manual}
@sp 4
@center GNU Emacs Calc Version 2.1
@c [volume]
@sp 1
@center January 1992
@sp 5
@center Dave Gillespie
@page

@vskip 0pt plus 1filll
Copyright @copyright{} 1990, 1991 Free Software Foundation, Inc.

Permission is granted to make and distribute verbatim copies of
this manual provided the copyright notice and this permission notice
are preserved on all copies.

@ignore
Permission is granted to process this file through TeX and print the
results, provided the printed document carries copying permission notice
identical to this one except for the removal of this paragraph (this
paragraph not being relevant to the printed manual).

@end ignore
Permission is granted to copy and distribute modified versions of this
manual under the conditions for verbatim copying, provided also that the
section entitled ``GNU General Public License'' is included exactly as
in the original, and provided that the entire resulting derived work is
distributed under the terms of a permission notice identical to this one.

Permission is granted to copy and distribute translations of this manual
into another language, under the above conditions for modified versions,
except that the section entitled ``GNU General Public License'' may be
included in a translation approved by the author instead of in the
original English.
@end titlepage

@c [begin]
@ifnottex
@node Top, Copying,, (dir)
@chapter The GNU Emacs Calculator

@noindent
@dfn{Calc} is an advanced desk calculator and mathematical tool
that runs as part of the GNU Emacs environment.

This manual is divided into three major parts: "Getting Started," the
"Calc Tutorial," and the "Calc Reference."  The Tutorial introduces all
the major aspects of Calculator use in an easy, hands-on way.  The
remainder of the manual is a complete reference to the features of the
Calculator.

For help in the Emacs Info system (which you are using to read this
file), type @kbd{?}.  (You can also type @kbd{h} to run through a
longer Info tutorial.)

@end ifnottex
@menu
* Copying::               How you can copy and share Calc.

* Getting Started::       General description and overview.
@ifinfo
* Interactive Tutorial::  Same as tutorial.
@end ifinfo
* Tutorial::              A step-by-step introduction for beginners.

* Introduction::          Introduction to the Calc reference manual.
* Data Types::            Types of objects manipulated by Calc.
* Stack and Trail::       Manipulating the stack and trail buffers.
* Mode Settings::         Adjusting display format and other modes.
* Arithmetic::            Basic arithmetic functions.
* Scientific Functions::  Transcendentals and other scientific functions.
* Matrix Functions::      Operations on vectors and matrices.
* Algebra::               Manipulating expressions algebraically.
* Units::                 Operations on numbers with units.
* Store and Recall::      Storing and recalling variables.
* Graphics::              Commands for making graphs of data.
* Kill and Yank::         Moving data into and out of Calc.
* Embedded Mode::         Working with formulas embedded in a file.
* Programming::           Calc as a programmable calculator.

* Summary::               Summary of Calc commands and functions.

* Key Index::             The standard Calc key sequences.
* Command Index::         The interactive Calc commands.
* Function Index::        Functions (in algebraic formulas).
* Concept Index::         General concepts.
* Variable Index::        Variables used by Calc (both user and internal).
* Lisp Function Index::   Internal Lisp math functions.
@end menu

@node Copying, Getting Started, Top, Top
@unnumbered GNU GENERAL PUBLIC LICENSE
@include gpl.texi

@node Getting Started, Tutorial, Copying, Top
@chapter Getting Started

@noindent
This chapter provides a general overview of Calc, the GNU Emacs
Calculator:  What it is, how to start it and how to exit from it,
and what are the various ways that it can be used.

@menu
* What is Calc::
* About This Manual::
* Notations Used in This Manual::
* Using Calc::
* Demonstration of Calc::
* History and Acknowledgements::
@end menu

@node What is Calc, About This Manual, Getting Started, Getting Started
@section What is Calc?

@noindent
@dfn{Calc} is an advanced calculator and mathematical tool that runs as
part of the GNU Emacs environment.  Very roughly based on the HP-28/48
series of calculators, its many features include:

@itemize @bullet
@item
Choice of algebraic or RPN (stack-based) entry of calculations.

@item
Arbitrary precision integers and floating-point numbers.

@item
Arithmetic on rational numbers, complex numbers (rectangular and polar),
error forms with standard deviations, open and closed intervals, vectors
and matrices, dates and times, infinities, sets, quantities with units,
and algebraic formulas.

@item
Mathematical operations such as logarithms and trigonometric functions.

@item
Programmer's features (bitwise operations, non-decimal numbers).

@item
Financial functions such as future value and internal rate of return.

@item
Number theoretical features such as prime factorization and arithmetic
modulo @i{M} for any @i{M}.

@item
Algebraic manipulation features, including symbolic calculus.

@item
Moving data to and from regular editing buffers.

@item
``Embedded mode'' for manipulating Calc formulas and data directly
inside any editing buffer.

@item
Graphics using GNUPLOT, a versatile (and free) plotting program.

@item
Easy programming using keyboard macros, algebraic formulas,
algebraic rewrite rules, or extended Emacs Lisp.
@end itemize

Calc tries to include a little something for everyone; as a result it is
large and might be intimidating to the first-time user.  If you plan to
use Calc only as a traditional desk calculator, all you really need to
read is the ``Getting Started'' chapter of this manual and possibly the
first few sections of the tutorial.  As you become more comfortable with
the program you can learn its additional features.  In terms of efficiency,
scope and depth, Calc cannot replace a powerful tool like Mathematica.
@c Removed this per RMS' request:
@c Mathematica@c{\trademark} @asis{ (tm)}.
But Calc has the advantages of convenience, portability, and availability
of the source code.  And, of course, it's free!

@node About This Manual, Notations Used in This Manual, What is Calc, Getting Started
@section About This Manual

@noindent
This document serves as a complete description of the GNU Emacs
Calculator.  It works both as an introduction for novices, and as
a reference for experienced users.  While it helps to have some
experience with GNU Emacs in order to get the most out of Calc,
this manual ought to be readable even if you don't know or use Emacs
regularly.

The manual is divided into three major parts:@: the ``Getting
Started'' chapter you are reading now, the Calc tutorial
and the Calc reference manual (the remaining chapters and appendices).

If you are in a hurry to use Calc, there is a brief ``demonstration''
below which illustrates the major features of Calc in just a couple of
pages.  If you don't have time to go through the full tutorial, this
will show you everything you need to know to begin.
@xref{Demonstration of Calc}.

The tutorial chapter walks you through the various parts of Calc
with lots of hands-on examples and explanations.  If you are new
to Calc and you have some time, try going through at least the
beginning of the tutorial.  The tutorial includes about 70 exercises
with answers.  These exercises give you some guided practice with
Calc, as well as pointing out some interesting and unusual ways
to use its features.

The reference section discusses Calc in complete depth.  You can read
the reference from start to finish if you want to learn every aspect
of Calc.  Or, you can look in the table of contents or the Concept
Index to find the parts of the manual that discuss the things you
need to know.

@c [fix-ref Help Commands]
You can access this manual on-line at any time within Calc by
pressing the @kbd{h i} key sequence.  Outside of the Calc window,
you can press @kbd{M-# i} to read the manual on-line.  Also, you
can jump directly to the Tutorial by pressing @kbd{h t} or @kbd{M-# t},
or to the Summary by pressing @kbd{h s} or @kbd{M-# s}.  Within Calc,
you can also go to the part of the manual describing any Calc key,
function, or variable using @w{@kbd{h k}}, @kbd{h f}, or @kbd{h v},
respectively.  @xref{Help Commands}.

@c Printed copies of this manual are also available from the Free Software
@c Foundation.

@node Notations Used in This Manual, Demonstration of Calc, About This Manual, Getting Started
@section Notations Used in This Manual

@noindent
This section describes the various notations that are used
throughout the Calc manual.

In keystroke sequences, uppercase letters mean you must hold down
the shift key while typing the letter.  Keys pressed with Control
held down are shown as @kbd{C-x}.  Keys pressed with Meta held down
are shown as @kbd{M-x}.  Other notations are @key{RET} for the
Return key, @key{SPC} for the space bar, @key{TAB} for the Tab key,
@key{DEL} for the Delete key, and @key{LFD} for the Line-Feed key.

(If you don't have the @key{LFD} or @key{TAB} keys on your keyboard,
the @kbd{C-j} and @kbd{C-i} keys are equivalent to them, respectively.
If you don't have a Meta key, look for Alt or Extend Char.  You can
also press @key{ESC} or @key{C-[} first to get the same effect, so
that @kbd{M-x}, @kbd{ESC x}, and @kbd{C-[ x} are all equivalent.)

Sometimes the @key{RET} key is not shown when it is ``obvious''
that you must press @kbd{RET} to proceed.  For example, the @key{RET}
is usually omitted in key sequences like @kbd{M-x calc-keypad @key{RET}}.

Commands are generally shown like this:  @kbd{p} (@code{calc-precision})
or @kbd{M-# k} (@code{calc-keypad}).  This means that the command is
normally used by pressing the @kbd{p} key or @kbd{M-# k} key sequence,
but it also has the full-name equivalent shown, e.g., @kbd{M-x calc-precision}.

Commands that correspond to functions in algebraic notation
are written:  @kbd{C} (@code{calc-cos}) [@code{cos}].  This means
the @kbd{C} key is equivalent to @kbd{M-x calc-cos}, and that
the corresponding function in an algebraic-style formula would
be @samp{cos(@var{x})}.

A few commands don't have key equivalents:  @code{calc-sincos}
[@code{sincos}].@refill

@node Demonstration of Calc, Using Calc, Notations Used in This Manual, Getting Started
@section A Demonstration of Calc

@noindent
@cindex Demonstration of Calc
This section will show some typical small problems being solved with
Calc.  The focus is more on demonstration than explanation, but
everything you see here will be covered more thoroughly in the
Tutorial.

To begin, start Emacs if necessary (usually the command @code{emacs}
does this), and type @kbd{M-# c} (or @kbd{ESC # c}) to start the
Calculator.  (@xref{Starting Calc}, if this doesn't work for you.)

Be sure to type all the sample input exactly, especially noting the
difference between lower-case and upper-case letters.  Remember,
@kbd{RET}, @kbd{TAB}, @kbd{DEL}, and @kbd{SPC} are the Return, Tab,
Delete, and Space keys.

@strong{RPN calculation.}  In RPN, you type the input number(s) first,
then the command to operate on the numbers.

@noindent
Type @kbd{2 RET 3 + Q} to compute @c{$\sqrt{2+3} = 2.2360679775$}
@asis{the square root of 2+3, which is 2.2360679775}.

@noindent
Type @kbd{P 2 ^} to compute @c{$\pi^2 = 9.86960440109$}
@asis{the value of `pi' squared, 9.86960440109}.

@noindent
Type @kbd{TAB} to exchange the order of these two results.

@noindent
Type @kbd{- I H S} to subtract these results and compute the Inverse
Hyperbolic sine of the difference, 2.72996136574.

@noindent
Type @kbd{DEL} to erase this result.

@strong{Algebraic calculation.}  You can also enter calculations using
conventional ``algebraic'' notation.  To enter an algebraic formula,
use the apostrophe key.

@noindent
Type @kbd{' sqrt(2+3) RET} to compute @c{$\sqrt{2+3}$}
@asis{the square root of 2+3}.

@noindent
Type @kbd{' pi^2 RET} to enter @c{$\pi^2$}
@asis{`pi' squared}.  To evaluate this symbolic
formula as a number, type @kbd{=}.

@noindent
Type @kbd{' arcsinh($ - $$) RET} to subtract the second-most-recent
result from the most-recent and compute the Inverse Hyperbolic sine.

@strong{Keypad mode.}  If you are using the X window system, press
@w{@kbd{M-# k}} to get Keypad mode.  (If you don't use X, skip to
the next section.)

@noindent
Click on the @key{2}, @key{ENTER}, @key{3}, @key{+}, and @key{SQRT}
``buttons'' using your left mouse button.

@noindent
Click on @key{PI}, @key{2}, and @t{y^x}.

@noindent
Click on @key{INV}, then @key{ENTER} to swap the two results.

@noindent
Click on @key{-}, @key{INV}, @key{HYP}, and @key{SIN}.

@noindent
Click on @key{<-} to erase the result, then click @key{OFF} to turn
the Keypad Calculator off.

@strong{Grabbing data.}  Type @kbd{M-# x} if necessary to exit Calc.
Now select the following numbers as an Emacs region:  ``Mark'' the
front of the list by typing control-@kbd{SPC} there,
then move to the other end of the list.  (Either get this list from
the on-line copy of this manual, accessed by @w{@kbd{M-# i}}, or just
type these numbers into a scratch file.)  Now type @kbd{M-# g} to
``grab'' these numbers into Calc.

@example
@group
1.23  1.97
1.6   2
1.19  1.08
@end group
@end example

@noindent
The result @samp{[1.23, 1.97, 1.6, 2, 1.19, 1.08]} is a Calc ``vector.''
Type @w{@kbd{V R +}} to compute the sum of these numbers.

@noindent
Type @kbd{U} to Undo this command, then type @kbd{V R *} to compute
the product of the numbers.

@noindent
You can also grab data as a rectangular matrix.  Place the cursor on
the upper-leftmost @samp{1} and set the mark, then move to just after
the lower-right @samp{8} and press @kbd{M-# r}.

@noindent
Type @kbd{v t} to transpose this @c{$3\times2$}
@asis{3x2} matrix into a @c{$2\times3$}
@asis{2x3} matrix.  Type
@w{@kbd{v u}} to unpack the rows into two separate vectors.  Now type
@w{@kbd{V R + TAB V R +}} to compute the sums of the two original columns.
(There is also a special grab-and-sum-columns command, @kbd{M-# :}.)

@strong{Units conversion.}  Units are entered algebraically.
Type @w{@kbd{' 43 mi/hr RET}} to enter the quantity 43 miles-per-hour.
Type @w{@kbd{u c km/hr RET}}.  Type @w{@kbd{u c m/s RET}}.

@strong{Date arithmetic.}  Type @kbd{t N} to get the current date and
time.  Type @kbd{90 +} to find the date 90 days from now.  Type
@kbd{' <25 dec 87> RET} to enter a date, then @kbd{- 7 /} to see how
many weeks have passed since then.

@strong{Algebra.}  Algebraic entries can also include formulas
or equations involving variables.  Type @kbd{' [x + y = a, x y = 1] RET}
to enter a pair of equations involving three variables.
(Note the leading apostrophe in this example; also, note that the space
between @samp{x y} is required.)  Type @w{@kbd{a S x,y RET}} to solve
these equations for the variables @cite{x} and @cite{y}.@refill

@noindent
Type @kbd{d B} to view the solutions in more readable notation.
Type @w{@kbd{d C}} to view them in C language notation, @kbd{d T}
to view them in the notation for the @TeX{} typesetting system, and
@kbd{d L} to view them in @LaTeX{} notation.
Type @kbd{d N} to return to the normal Calc notation.

@noindent
Type @kbd{7.5}, then @kbd{s l a RET} to let @cite{a = 7.5} in these formulas.
(That's a letter @kbd{l}, not a numeral @kbd{1}.)

@iftex
@strong{Help functions.}  You can read about any command in the on-line
manual.  Type @kbd{M-# c} to return to Calc after each of these
commands: @kbd{h k t N} to read about the @kbd{t N} command,
@kbd{h f sqrt RET} to read about the @code{sqrt} function, and
@kbd{h s} to read the Calc summary.
@end iftex
@ifnottex
@strong{Help functions.}  You can read about any command in the on-line
manual.  Remember to type the letter @kbd{l} (once or twice), then @kbd{M-# c}, to
return here after each of these commands: @w{@kbd{h k t N}} to read
about the @w{@kbd{t N}} command, @kbd{h f sqrt RET} to read about the
@code{sqrt} function, and @kbd{h s} to read the Calc summary.
@end ifnottex

Press @kbd{DEL} repeatedly to remove any leftover results from the stack.
To exit from Calc, press @kbd{q} or @kbd{M-# c} again.

@node Using Calc, History and Acknowledgements, Demonstration of Calc, Getting Started
@section Using Calc

@noindent
Calc has several user interfaces that are specialized for
different kinds of tasks.  As well as Calc's standard interface,
there are Quick Mode, Keypad Mode, and Embedded Mode.

@menu
* Starting Calc::
* The Standard Interface::
* Quick Mode Overview::
* Keypad Mode Overview::
* Standalone Operation::
* Embedded Mode Overview::
* Other M-# Commands::
@end menu

@node Starting Calc, The Standard Interface, Using Calc, Using Calc
@subsection Starting Calc

@noindent
On most systems, you can type @kbd{M-#} to start the Calculator.
The notation @kbd{M-#} is short for Meta-@kbd{#}.  On most
keyboards this means holding down the Meta (or Alt) and
Shift keys while typing @kbd{3}.

@cindex META key
Once again, if you don't have a Meta key on your keyboard you can type
@key{ESC} first, then @kbd{#}, to accomplish the same thing.  If you
don't even have an @key{ESC} key, you can fake it by holding down
Control or @key{CTRL} while typing a left square bracket
(that's @kbd{C-[} in Emacs notation).@refill

@kbd{M-#} is a @dfn{prefix key}; when you press it, Emacs waits for
you to press a second key to complete the command.  In this case,
you will follow @kbd{M-#} with a letter (upper- or lower-case, it
doesn't matter for @kbd{M-#}) that says which Calc interface you
want to use.

You can change the prefix key used for starting Calc by putting
@example
(global-set-key "PREFIXKEY" 'calc-dispatch)
@end example
in your .emacs file.  This manual will assume that you are using
the default prefix @kbd{M-#}; if you change the prefix, use your
new prefix whenever you see @kbd{M-#}.

To get Calc's standard interface, type @kbd{M-# c}.  To get
Keypad Mode, type @kbd{M-# k}.  Type @kbd{M-# ?} to get a brief
list of the available options, and type a second @kbd{?} to get
a complete list.

To ease typing, @kbd{M-# M-#} (or @kbd{M-# #} if that's easier)
also works to start Calc.  (You can also type your prefix key
followed by one of @kbd{=}, @kbd{&}, @kbd{\}, @kbd{/}, @kbd{+},
@kbd{-} or @kbd{*}, to make it more convenient if you have changed
the prefix.)

It starts the same interface (either
@kbd{M-# c} or @w{@kbd{M-# k}}) that you last used, selecting the
@kbd{M-# c} interface by default.  (If your installation has
a special function key set up to act like @kbd{M-#}, hitting that
function key twice is just like hitting @kbd{M-# M-#}.)

By default, @kbd{M-#} is bound to the command @code{calc-dispatch}.
If you decide to bind another key or key-sequence to 
@code{calc-dispatch}, then typing that key followed by your choice
of @kbd{#}, @kbd{&}, @kbd{\}, @kbd{=}, @kbd{*}, 
@kbd{/}, @kbd{+} or @kbd{-} will act like @kbd{M-# M-#}.

If @kbd{M-#} doesn't work for you, you can always type explicit
commands like @kbd{M-x calc} (for the standard user interface) or
@w{@kbd{M-x calc-keypad}} (for Keypad Mode).  First type @kbd{M-x}
(that's Meta with the letter @kbd{x}), then, at the prompt,
type the full command (like @kbd{calc-keypad}) and press Return.

If you type @kbd{M-x calc} and Emacs still doesn't recognize the
command (it will say @samp{[No match]} when you try to press
@key{RET}), then Calc has not been properly installed.

The same commands (like @kbd{M-# c} or @kbd{M-# M-#}) that start
the Calculator also turn it off if it is already on.

@node The Standard Interface, Quick Mode Overview, Starting Calc, Using Calc
@subsection The Standard Calc Interface

@noindent
@cindex Standard user interface
Calc's standard interface acts like a traditional RPN calculator,
operated by the normal Emacs keyboard.  When you type @kbd{M-# c}
to start the Calculator, the Emacs screen splits into two windows
with the file you were editing on top and Calc on the bottom.

@iftex
@advance@hsize20pt
@end iftex
@smallexample
@group

...
--**-Emacs: myfile             (Fundamental)----All----------------------
--- Emacs Calculator Mode ---                   |Emacs Calculator Trail
2:  17.3                                        |    17.3
1:  -5                                          |    3
    .                                           |    2
                                                |    4
                                                |  * 8
                                                |  ->-5
                                                |
--%%-Calc: 12 Deg       (Calculator)----All----- --%%-Emacs: *Calc Trail*
@end group
@end smallexample

In this figure, the mode-line for @file{myfile} has moved up and the
``Calculator'' window has appeared below it.  As you can see, Calc
actually makes two windows side-by-side.  The lefthand one is
called the @dfn{stack window} and the righthand one is called the
@dfn{trail window.}  The stack holds the numbers involved in the
calculation you are currently performing.  The trail holds a complete
record of all calculations you have done.  In a desk calculator with
a printer, the trail corresponds to the paper tape that records what
you do.

In this case, the trail shows that four numbers (17.3, 3, 2, and 4)
were first entered into the Calculator, then the 2 and 4 were
multiplied to get 8, then the 3 and 8 were subtracted to get @i{-5}.
(The @samp{>} symbol shows that this was the most recent calculation.)
The net result is the two numbers 17.3 and @i{-5} sitting on the stack.

Most Calculator commands deal explicitly with the stack only, but
there is a set of commands that allow you to search back through
the trail and retrieve any previous result.

Calc commands use the digits, letters, and punctuation keys.
Shifted (i.e., upper-case) letters are different from lowercase
letters.  Some letters are @dfn{prefix} keys that begin two-letter
commands.  For example, @kbd{e} means ``enter exponent'' and shifted
@kbd{E} means @cite{e^x}.  With the @kbd{d} (``display modes'') prefix
the letter ``e'' takes on very different meanings:  @kbd{d e} means
``engineering notation'' and @kbd{d E} means ``@dfn{eqn} language mode.''

There is nothing stopping you from switching out of the Calc
window and back into your editing window, say by using the Emacs
@w{@kbd{C-x o}} (@code{other-window}) command.  When the cursor is
inside a regular window, Emacs acts just like normal.  When the
cursor is in the Calc stack or trail windows, keys are interpreted
as Calc commands.

When you quit by pressing @kbd{M-# c} a second time, the Calculator
windows go away but the actual Stack and Trail are not gone, just
hidden.  When you press @kbd{M-# c} once again you will get the
same stack and trail contents you had when you last used the
Calculator.

The Calculator does not remember its state between Emacs sessions.
Thus if you quit Emacs and start it again, @kbd{M-# c} will give you
a fresh stack and trail.  There is a command (@kbd{m m}) that lets
you save your favorite mode settings between sessions, though.
One of the things it saves is which user interface (standard or
Keypad) you last used; otherwise, a freshly started Emacs will
always treat @kbd{M-# M-#} the same as @kbd{M-# c}.

The @kbd{q} key is another equivalent way to turn the Calculator off.

If you type @kbd{M-# b} first and then @kbd{M-# c}, you get a
full-screen version of Calc (@code{full-calc}) in which the stack and
trail windows are still side-by-side but are now as tall as the whole
Emacs screen.  When you press @kbd{q} or @kbd{M-# c} again to quit,
the file you were editing before reappears.  The @kbd{M-# b} key
switches back and forth between ``big'' full-screen mode and the
normal partial-screen mode.

Finally, @kbd{M-# o} (@code{calc-other-window}) is like @kbd{M-# c}
except that the Calc window is not selected.  The buffer you were
editing before remains selected instead.  @kbd{M-# o} is a handy
way to switch out of Calc momentarily to edit your file; type
@kbd{M-# c} to switch back into Calc when you are done.

@node Quick Mode Overview, Keypad Mode Overview, The Standard Interface, Using Calc
@subsection Quick Mode (Overview)

@noindent
@dfn{Quick Mode} is a quick way to use Calc when you don't need the
full complexity of the stack and trail.  To use it, type @kbd{M-# q}
(@code{quick-calc}) in any regular editing buffer.

Quick Mode is very simple:  It prompts you to type any formula in
standard algebraic notation (like @samp{4 - 2/3}) and then displays
the result at the bottom of the Emacs screen (@i{3.33333333333}
in this case).  You are then back in the same editing buffer you
were in before, ready to continue editing or to type @kbd{M-# q}
again to do another quick calculation.  The result of the calculation
will also be in the Emacs ``kill ring'' so that a @kbd{C-y} command
at this point will yank the result into your editing buffer.

Calc mode settings affect Quick Mode, too, though you will have to
go into regular Calc (with @kbd{M-# c}) to change the mode settings.

@c [fix-ref Quick Calculator mode]
@xref{Quick Calculator}, for further information.

@node Keypad Mode Overview, Standalone Operation, Quick Mode Overview, Using Calc
@subsection Keypad Mode (Overview)

@noindent
@dfn{Keypad Mode} is a mouse-based interface to the Calculator.
It is designed for use with the X window system.  If you don't
have X, you will have to operate keypad mode with your arrow
keys (which is probably more trouble than it's worth).

Type @kbd{M-# k} to turn Keypad Mode on or off.  Once again you
get two new windows, this time on the righthand side of the screen
instead of at the bottom.  The upper window is the familiar Calc
Stack; the lower window is a picture of a typical calculator keypad.

@tex
\dimen0=\pagetotal%
\advance \dimen0 by 24\baselineskip%
\ifdim \dimen0>\pagegoal \vfill\eject \fi%
\medskip
@end tex
@smallexample
                                        |--- Emacs Calculator Mode ---
                                        |2:  17.3
                                        |1:  -5
                                        |    .
                                        |--%%-Calc: 12 Deg       (Calcul
                                        |----+-----Calc 2.00-----+----1
                                        |FLR |CEIL|RND |TRNC|CLN2|FLT |
                                        |----+----+----+----+----+----|
                                        | LN |EXP |    |ABS |IDIV|MOD |
                                        |----+----+----+----+----+----|
                                        |SIN |COS |TAN |SQRT|y^x |1/x |
                                        |----+----+----+----+----+----|
                                        |  ENTER  |+/- |EEX |UNDO| <- |
                                        |-----+---+-+--+--+-+---++----|
                                        | INV |  7  |  8  |  9  |  /  |
                                        |-----+-----+-----+-----+-----|
                                        | HYP |  4  |  5  |  6  |  *  |
                                        |-----+-----+-----+-----+-----|
                                        |EXEC |  1  |  2  |  3  |  -  |
                                        |-----+-----+-----+-----+-----|
                                        | OFF |  0  |  .  | PI  |  +  |
                                        |-----+-----+-----+-----+-----+
@end smallexample
@iftex
@begingroup
@ifdim@hsize=5in
@vskip-3.7in
@advance@hsize-2.2in
@else
@vskip-3.89in
@advance@hsize-3.05in
@advance@vsize.1in
@fi
@end iftex

Keypad Mode is much easier for beginners to learn, because there
is no need to memorize lots of obscure key sequences.  But not all
commands in regular Calc are available on the Keypad.  You can
always switch the cursor into the Calc stack window to use
standard Calc commands if you need.  Serious Calc users, though,
often find they prefer the standard interface over Keypad Mode.

To operate the Calculator, just click on the ``buttons'' of the
keypad using your left mouse button.  To enter the two numbers
shown here you would click @w{@kbd{1 7 .@: 3 ENTER 5 +/- ENTER}}; to
add them together you would then click @kbd{+} (to get 12.3 on
the stack).

If you click the right mouse button, the top three rows of the
keypad change to show other sets of commands, such as advanced
math functions, vector operations, and operations on binary
numbers.

@iftex
@endgroup
@end iftex
Because Keypad Mode doesn't use the regular keyboard, Calc leaves
the cursor in your original editing buffer.  You can type in
this buffer in the usual way while also clicking on the Calculator
keypad.  One advantage of Keypad Mode is that you don't need an
explicit command to switch between editing and calculating.

If you press @kbd{M-# b} first, you get a full-screen Keypad Mode
(@code{full-calc-keypad}) with three windows:  The keypad in the lower
left, the stack in the lower right, and the trail on top.

@c [fix-ref Keypad Mode]
@xref{Keypad Mode}, for further information.

@node Standalone Operation, Embedded Mode Overview, Keypad Mode Overview, Using Calc
@subsection Standalone Operation

@noindent
@cindex Standalone Operation
If you are not in Emacs at the moment but you wish to use Calc,
you must start Emacs first.  If all you want is to run Calc, you
can give the commands:

@example
emacs -f full-calc
@end example

@noindent
or

@example
emacs -f full-calc-keypad
@end example

@noindent
which run a full-screen Calculator (as if by @kbd{M-# b M-# c}) or
a full-screen X-based Calculator (as if by @kbd{M-# b M-# k}).
In standalone operation, quitting the Calculator (by pressing
@kbd{q} or clicking on the keypad @key{EXIT} button) quits Emacs
itself.

@node Embedded Mode Overview, Other M-# Commands, Standalone Operation, Using Calc
@subsection Embedded Mode (Overview)

@noindent
@dfn{Embedded Mode} is a way to use Calc directly from inside an
editing buffer.  Suppose you have a formula written as part of a
document like this:

@smallexample
@group
The derivative of

                                   ln(ln(x))

is
@end group
@end smallexample

@noindent
and you wish to have Calc compute and format the derivative for
you and store this derivative in the buffer automatically.  To
do this with Embedded Mode, first copy the formula down to where
you want the result to be:

@smallexample
@group
The derivative of

                                   ln(ln(x))

is

                                   ln(ln(x))
@end group
@end smallexample

Now, move the cursor onto this new formula and press @kbd{M-# e}.
Calc will read the formula (using the surrounding blank lines to
tell how much text to read), then push this formula (invisibly)
onto the Calc stack.  The cursor will stay on the formula in the
editing buffer, but the buffer's mode line will change to look
like the Calc mode line (with mode indicators like @samp{12 Deg}
and so on).  Even though you are still in your editing buffer,
the keyboard now acts like the Calc keyboard, and any new result
you get is copied from the stack back into the buffer.  To take
the derivative, you would type @kbd{a d x @key{RET}}.

@smallexample
@group
The derivative of

                                   ln(ln(x))

is

1 / (x ln(x))
@end group
@end smallexample

To make this look nicer, you might want to press @kbd{d =} to center
the formula, and even @kbd{d B} to use ``big'' display mode.

@smallexample
@group
The derivative of

                                   ln(ln(x))

is
% [calc-mode: justify: center]
% [calc-mode: language: big]

                                       1
                                    -------
                                    x ln(x)
@end group
@end smallexample

Calc has added annotations to the file to help it remember the modes
that were used for this formula.  They are formatted like comments
in the @TeX{} typesetting language, just in case you are using @TeX{} 
or @LaTeX{}. (In this example @TeX{} is not being used, so you might 
want to move these comments up to the top of the file or otherwise put 
them out of the way.)

As an extra flourish, we can add an equation number using a
righthand label:  Type @kbd{d @} (1) RET}.

@smallexample
@group
% [calc-mode: justify: center]
% [calc-mode: language: big]
% [calc-mode: right-label: " (1)"]

                                       1
                                    -------                      (1)
                                    x ln(x)
@end group
@end smallexample

To leave Embedded Mode, type @kbd{M-# e} again.  The mode line
and keyboard will revert to the way they were before.  (If you have
actually been trying this as you read along, you'll want to press
@kbd{M-# 0} [with the digit zero] now to reset the modes you changed.)

The related command @kbd{M-# w} operates on a single word, which
generally means a single number, inside text.  It uses any
non-numeric characters rather than blank lines to delimit the
formula it reads.  Here's an example of its use:

@smallexample
A slope of one-third corresponds to an angle of 1 degrees.
@end smallexample

Place the cursor on the @samp{1}, then type @kbd{M-# w} to enable
Embedded Mode on that number.  Now type @kbd{3 /} (to get one-third),
and @kbd{I T} (the Inverse Tangent converts a slope into an angle),
then @w{@kbd{M-# w}} again to exit Embedded mode.

@smallexample
A slope of one-third corresponds to an angle of 18.4349488229 degrees.
@end smallexample

@c [fix-ref Embedded Mode]
@xref{Embedded Mode}, for full details.

@node Other M-# Commands, , Embedded Mode Overview, Using Calc
@subsection Other @kbd{M-#} Commands

@noindent
Two more Calc-related commands are @kbd{M-# g} and @kbd{M-# r},
which ``grab'' data from a selected region of a buffer into the
Calculator.  The region is defined in the usual Emacs way, by
a ``mark'' placed at one end of the region, and the Emacs
cursor or ``point'' placed at the other.

The @kbd{M-# g} command reads the region in the usual left-to-right,
top-to-bottom order.  The result is packaged into a Calc vector
of numbers and placed on the stack.  Calc (in its standard
user interface) is then started.  Type @kbd{v u} if you want
to unpack this vector into separate numbers on the stack.  Also,
@kbd{C-u M-# g} interprets the region as a single number or
formula.

The @kbd{M-# r} command reads a rectangle, with the point and
mark defining opposite corners of the rectangle.  The result
is a matrix of numbers on the Calculator stack.

Complementary to these is @kbd{M-# y}, which ``yanks'' the
value at the top of the Calc stack back into an editing buffer.
If you type @w{@kbd{M-# y}} while in such a buffer, the value is
yanked at the current position.  If you type @kbd{M-# y} while
in the Calc buffer, Calc makes an educated guess as to which
editing buffer you want to use.  The Calc window does not have
to be visible in order to use this command, as long as there
is something on the Calc stack.

Here, for reference, is the complete list of @kbd{M-#} commands.
The shift, control, and meta keys are ignored for the keystroke
following @kbd{M-#}.

@noindent
Commands for turning Calc on and off:

@table @kbd
@item #
Turn Calc on or off, employing the same user interface as last time.

@item C
Turn Calc on or off using its standard bottom-of-the-screen
interface.  If Calc is already turned on but the cursor is not
in the Calc window, move the cursor into the window.

@item O
Same as @kbd{C}, but don't select the new Calc window.  If
Calc is already turned on and the cursor is in the Calc window,
move it out of that window.

@item B
Control whether @kbd{M-# c} and @kbd{M-# k} use the full screen.

@item Q
Use Quick Mode for a single short calculation.

@item K
Turn Calc Keypad mode on or off.

@item E
Turn Calc Embedded mode on or off at the current formula.

@item J
Turn Calc Embedded mode on or off, select the interesting part.

@item W
Turn Calc Embedded mode on or off at the current word (number).

@item Z
Turn Calc on in a user-defined way, as defined by a @kbd{Z I} command.

@item X
Quit Calc; turn off standard, Keypad, or Embedded mode if on.
(This is like @kbd{q} or @key{OFF} inside of Calc.)
@end table
@iftex
@sp 2
@end iftex

@c @group
@noindent
Commands for moving data into and out of the Calculator:

@table @kbd
@item G
Grab the region into the Calculator as a vector.

@item R
Grab the rectangular region into the Calculator as a matrix.

@item :
Grab the rectangular region and compute the sums of its columns.

@item _
Grab the rectangular region and compute the sums of its rows.

@item Y
Yank a value from the Calculator into the current editing buffer.
@end table
@iftex
@sp 2
@end iftex
@c @end group

@c @group
@noindent
Commands for use with Embedded Mode:

@table @kbd
@item A
``Activate'' the current buffer.  Locate all formulas that
contain @samp{:=} or @samp{=>} symbols and record their locations
so that they can be updated automatically as variables are changed.

@item D
Duplicate the current formula immediately below and select
the duplicate.

@item F
Insert a new formula at the current point.

@item N
Move the cursor to the next active formula in the buffer.

@item P
Move the cursor to the previous active formula in the buffer.

@item U
Update (i.e., as if by the @kbd{=} key) the formula at the current point.

@item `
Edit (as if by @code{calc-edit}) the formula at the current point.
@end table
@iftex
@sp 2
@end iftex
@c @end group

@c @group
@noindent
Miscellaneous commands:

@table @kbd
@item I
Run the Emacs Info system to read the Calc manual.
(This is the same as @kbd{h i} inside of Calc.)

@item T
Run the Emacs Info system to read the Calc Tutorial.

@item S
Run the Emacs Info system to read the Calc Summary.

@item L
Load Calc entirely into memory.  (Normally the various parts
are loaded only as they are needed.)

@item M
Read a region of written keystroke names (like @samp{C-n a b c RET})
and record them as the current keyboard macro.

@item 0
(This is the ``zero'' digit key.)  Reset the Calculator to
its default state:  Empty stack, and default mode settings.
With any prefix argument, reset everything but the stack.
@end table
@c @end group

@node History and Acknowledgements, , Using Calc, Getting Started
@section History and Acknowledgements

@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 @c{$2^{32}$}
@cite{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 digits even though we knew they were there in the
program's memory!  I was so annoyed, I vowed to write a calculator
of my own, once and for all.

I chose Emacs Lisp, a) because I had always been curious about it
and b) because, being only a text editor extension language after
all, Emacs Lisp would surely reach its limits long before the project
got too far out of hand.

To make a long story short, Emacs Lisp turned out to be a distressingly
solid implementation of Lisp, and the humble task of calculating
turned out to be more open-ended than one might have expected.

Emacs Lisp doesn't have built-in floating point 
math@footnote{This has changed; all modern Emacsen now have floating
point support as well as support for larger integers.  
In addition, SXEmacs has support for many different number types.}, 
so it had to be
simulated in software.  In fact, Emacs integers will only comfortably
fit six decimal digits or so---not enough for a decent calculator.  So
I had to write my own high-precision integer code as well, and once I had
this I figured that arbitrary-size integers were just as easy as large
integers.  Arbitrary floating-point precision was the logical next step.
Also, since the large integer arithmetic was there anyway it seemed only
fair to give the user direct access to it, which in turn made it practical
to support fractions as well as floats.  All these features inspired me
to look around for other data types that might be worth having.

Around this time, my friend Rick Koshi showed me his nifty new HP-28
calculator.  It allowed the user to manipulate formulas as well as
numerical quantities, and it could also operate on matrices.  I decided
that these would be good for Calc to have, too.  And once things had
gone this far, I figured I might as well take a look at serious algebra
systems like Mathematica, Macsyma, and Maple for further ideas.  Since
these systems did far more than I could ever hope to implement, I decided
to focus on rewrite rules and other programming features so that users
could implement what they needed for themselves.

Rick complained that matrices were hard to read, so I put in code to
format them in a 2D style.  Once these routines were in place, Big mode
was obligatory.  Gee, what other language modes would be useful?

Scott Hemphill and Allen Knutson, two friends with a strong mathematical
bent, contributed ideas and algorithms for a number of Calc features
including modulo forms, primality testing, and float-to-fraction conversion.

Units were added at the eager insistence of Mass Sivilotti.  Later,
Ulrich Mueller at CERN and Przemek Klosowski at NIST provided invaluable
expert assistance with the units table.  As far as I can remember, the
idea of using algebraic formulas and variables to represent units dates
back to an ancient article in Byte magazine about muMath, an early
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; @c{Fran\c cois}
@asis{Francois} Pinard, who contributed
an early prototype of the Calc Summary appendix as well as providing
valuable suggestions in many other areas of Calc; Carl Witty, whose eagle
eyes discovered many typographical and factual errors in the Calc manual;
Tim Kay, who drove the development of Embedded mode; Ove Ewerlid, who
made many suggestions relating to the algebra commands and contributed
some code for polynomial operations; Randal Schwartz, who suggested the
@code{calc-eval} function; Robert J. Chassell, who suggested the Calc
Tutorial and exercises; and Juha Sarlin, who first worked out how to split
Calc into quickly-loading parts.  Bob Weiner helped immensely with the
Lucid Emacs port.

@cindex Bibliography
@cindex Knuth, Art of Computer Programming
@cindex Numerical Recipes
@c Should these be expanded into more complete references?
Among the books used in the development of Calc were Knuth's @emph{Art
of Computer Programming} (especially volume II, @emph{Seminumerical
Algorithms}); @emph{Numerical Recipes} by Press, Flannery, Teukolsky,
and Vetterling; Bevington's @emph{Data Reduction and Error Analysis for
the Physical Sciences}; @emph{Concrete Mathematics} by Graham, Knuth,
and Patashnik; Steele's @emph{Common Lisp, the Language}; the @emph{CRC
Standard Math Tables} (William H. Beyer, ed.); and Abramowitz and
Stegun's venerable @emph{Handbook of Mathematical Functions}.  I
consulted the user's manuals for the HP-28 and HP-48 calculators, as
well as for the programs Mathematica, SMP, Macsyma, Maple, MathCAD,
Gnuplot, and others.  Also, of course, Calc could not have been written
without the excellent @emph{GNU Emacs Lisp Reference Manual}, by Bil
Lewis and Dan LaLiberte.

Final thanks go to Richard Stallman, without whose fine implementations
of the Emacs editor, language, and environment, Calc would have been
finished in two weeks.

@c [tutorial]

@ifinfo
@c This node is accessed by the `M-# t' command.
@node Interactive Tutorial, , , Top
@chapter Tutorial

@noindent
Some brief instructions on using the Emacs Info system for this tutorial:

Press the space bar and Delete keys to go forward and backward in a
section by screenfuls (or use the regular Emacs scrolling commands
for this).

Press @kbd{n} or @kbd{p} to go to the Next or Previous section.
If the section has a @dfn{menu}, press a digit key like @kbd{1}
or @kbd{2} to go to a sub-section from the menu.  Press @kbd{u} to
go back up from a sub-section to the menu it is part of.

Exercises in the tutorial all have cross-references to the
appropriate page of the ``answers'' section.  Press @kbd{f}, then
the exercise number, to see the answer to an exercise.  After
you have followed a cross-reference, you can press the letter
@kbd{l} to return to where you were before.

You can press @kbd{?} at any time for a brief summary of Info commands.

Press @kbd{1} now to enter the first section of the Tutorial.

@menu
* Tutorial::
@end menu
@end ifinfo

@node Tutorial, Introduction, Getting Started, Top
@chapter Tutorial

@noindent
This chapter explains how to use Calc and its many features, in
a step-by-step, tutorial way.  You are encouraged to run Calc and
work along with the examples as you read (@pxref{Starting Calc}).
If you are already familiar with advanced calculators, you may wish
@c [not-split]
to skip on to the rest of this manual.
@c [when-split]
@c to skip on to volume II of this manual, the @dfn{Calc Reference}.

@c [fix-ref Embedded Mode]
This tutorial describes the standard user interface of Calc only.
The ``Quick Mode'' and ``Keypad Mode'' interfaces are fairly