@c $Id: mathematics.texinfo,v 1.18 2002/01/09 16:59:51 m Exp m $
@node Mathematics, , Reminders, Productivity
@comment  node-name,  next,  previous,  up
@chapter Mathematics
@cindex mathematics

@noindent
Tools and techniques for dealing with numbers are the subject of this
chapter: listing them in sequence or randomly, calculating arithmetic,
and converting between units. Larger applications, such as spreadsheets
and plotting tools, are also mentioned.

@menu
* Arithmetic::                  Calculating arithmetic.
* Random Numbers::              Output a random number.
* Number Sequence::             Listing a sequence of numbers.
* Prime Factors::               Getting prime factors.
* Converting Numbers::          Converting between units of scale.
* Math Tools::                  Other math tools.
@end menu


@node Arithmetic, Random Numbers, Mathematics, Mathematics
@comment  node-name,  next,  previous,  up
@section Calculating Arithmetic
@cindex calculating arithmetic
@cindex arithmetic, calculating

@noindent
As you might expect, there are many tools for making arithmetic
calculations in Linux. The following recipes describe how to use two of
them for two common scenarios; a list of other calculator tools,
including a visual calculator, appears at the end of this chapter
(@pxref{Math Tools, , Other Math Tools}).

@menu
* Quick Math::                  Quick math on the input line.
* Bc::                          A command-line calculator.
@end menu


@node Quick Math, Bc, Arithmetic, Arithmetic
@comment  node-name,  next,  previous,  up
@subsection Making a Quick Arithmetic Calculation
@cindex making a quick arithmetic calculation
@cindex arithmetic calculation, making a quick 
@pindex calc

@flushleft
@sf{WWW}: @url{http://dsl.org/comp/tinyutils/}
@end flushleft
@*
@noindent
To do a quick calculation that requires only addition, subtraction,
multiplication, or division, use @code{calc}. It takes as an argument a
simple mathematical expression, and it outputs the answer.

Use @samp{*} for a multiplication sign and @samp{/} for division; to
output the remainder, use @samp{%}. You can use parenthesis to group
expressions---but when you do, be sure to quote them (@pxref{Quoting, ,
Passing Special Characters to Commands}).

@itemize @bullet
@item
To output the result of 50 times 10, type:

@example
@cartouche
$ @kbd{calc 50*10 @key{RET}}
500
$
@end cartouche
@end example

@item
To output the result of 100 times the sum of 4 plus 420, type:

@example
@cartouche
$ @kbd{calc '100*(4+420)' @key{RET}}
42400
$
@end cartouche
@end example

@item
To output the remainder of 10 divided by 3, type:

@example
@cartouche
$ @kbd{calc 10%3 @key{RET}}
1
$
@end cartouche
@end example
@end itemize

@sp .25
@noindent
@strong{NOTE:} This tool is useful for quickly computing a simple
arithmetic equation, but it has several drawbacks: it only outputs whole
integers, its operators are limited, and complex expressions must be
quoted. For doing anything more than the simplest operations, see the
next recipe, which describes @code{bc}.


@node Bc, , Quick Math, Arithmetic
@comment  node-name,  next,  previous,  up
@subsection Making Many Arithmetic Calculations
@cindex making many arithmetic calculations
@cindex arithmetic calculations, making many 
@pindex bc

@flushleft
@sf{Debian}: @file{bc}
@sf{WWW}: @url{ftp://src.doc.ic.ac.uk:/pub/gnu/bc-1.05a.tar.gz}
@end flushleft
@*
@noindent
When you have a lot of calculations to make, or when you must compute
numbers with decimals, use @code{bc}, a calculation language that
supports arbitrary precision numbers. Type @kbd{bc} to perform
arithmetic operations interactively, just like you would with a
calculator.

Type each statement to evaluate on a line by itself, typing @key{RET} at
the end the statement; the evaluation of what you type is output on the
following line. Each line you type will be evaluated by @code{bc} as an
arithmetic expression. To exit, type @kbd{quit} on a line by itself.

@itemize @bullet
@item
To multiply 42 and 17, type:

@example
@cartouche
$ @kbd{bc @key{RET}}
bc 1.05
Copyright 1991, 1992, 1993, 1994, 1997, 1998 Free Software
Foundation, Inc. 
This is free software with ABSOLUTELY NO WARRANTY.
For details type `warranty'. 
@kbd{42 * 17 @key{RET}}
714
@kbd{quit @key{RET}}
$
@end cartouche
@end example
@end itemize

In this example, @code{bc} output its version number and warranty
information when it started; then, the statement @kbd{42 * 17} was typed
by the user, @code{bc} output the result (@samp{714}), and then the
user typed @kbd{quit} to exit @code{bc}.

By default, digits to the right of the decimal point are truncated from
the output---so dividing 10 by 3 would output @samp{3} as a result, and
outputting the remainder from this operation by typing @kbd{10%3} would
output a @samp{1}. However, @code{bc} is an arbitrary precision
calculator, and you can give the number of digits to use after the
decimal point by specifying the value of the @code{scale} variable; its
default value is 0.

@itemize @bullet
@item
To use @code{bc} to compute the result of 10 divided by 3, using 20
digits after the decimal point, type: 

@*
@*
@*

@example
@cartouche
$ @kbd{bc @key{RET}}
bc 1.05
Copyright 1991, 1992, 1993, 1994, 1997, 1998 Free Software
Foundation, Inc. 
This is free software with ABSOLUTELY NO WARRANTY.
For details type `warranty'. 
@kbd{scale=20 @key{RET}
10 / 3 @key{RET}}
3.33333333333333333333
@kbd{quit @key{RET}}
$
@end cartouche
@end example
@end itemize

The following table describes the symbols you can use to specify
mathematical operations.

@multitable @columnfractions .30 .70
@item @sc{Symbol}
@tab @sc{Operation}
@item @code{@var{expression} + @var{expression}}
@tab Add: output the sum of the two expressions.

@item @code{@var{expression} - @var{expression}}
@tab Subtract: output the difference of the two expressions.

@item @code{@var{expression} * @var{expression}}
@tab Multiply: output the product of the two expressions.

@item @code{@var{expression} / @var{expression}}
@tab Divide: output the quotient of the two expressions.

@item @code{@var{expression} % @var{expression}}
@tab Remainder: output the remainder resulting by dividing the two
expressions.

@item @code{@var{expression} ^ @var{expression}}
@tab Power: raise the first expression to the power of the second
expression.

@item @code{(@var{expressions})}
@tab Group an expression or expressions together, altering the standard
precedence of performing operations.

@item @code{sqrt(@var{expression})}
@tab Output the square root of @var{expression}.
@end multitable


@node Random Numbers, Number Sequence, Arithmetic, Mathematics
@comment  node-name,  next,  previous,  up
@section Outputting a Random Number
@cindex outputting a random number
@cindex random number, outputting a
@pindex random

@flushleft
@sf{WWW}: @url{http://dsl.org/comp/tinyutils/}
@end flushleft
@*
@noindent
To output a random number, use @code{random}. Give as an argument an
integer denoting the range of numbers to be output; @code{random} then
outputs a random number from 0 to the number you give, minus one.

@itemize @bullet
@item
To output a random number from 0 to 9, type:

@example
$ @kbd{random 10 @key{RET}}
@end example
@end itemize


@node Number Sequence, Prime Factors, Random Numbers, Mathematics
@comment  node-name,  next,  previous,  up
@section Listing a Sequence of Numbers
@cindex listing a sequence of numbers
@cindex numbers, listing a sequence of 
@pindex seq
@pindex cat

@noindent
Use @code{seq} to print a sequence of numbers. This is very useful for
getting a listing of numbers to use as arguments, or otherwise passing
sequences of numbers to other commands.

To output the sequence from 1 to any number, give that number as an
argument.

@itemize @bullet
@item
To output the sequence of numbers from one to seven, type:

@example
$ @kbd{seq 7 @key{RET}}
@end example

@item
To output the sequence of numbers from one to negative seven, type:

@example
$ @kbd{seq -7 @key{RET}}
@end example
@end itemize

To output the sequence from any one number to another, give those
numbers as arguments.

@itemize @bullet
@item
To output the sequence of numbers from nine to zero, type:

@example
$ @kbd{seq 9 0 @key{RET}}
@end example

@item
To output the sequence of numbers from negative one to negative twenty, type:

@example
$ @kbd{seq -1 -20 @key{RET}}
@end example
@end itemize

To specify an increment other than one, give it as the @emph{second}
argument, between the starting and ending number.

@itemize @bullet
@item
To output the sequence of numbers from -1 to 14, incrementing by 3,
type:

@example
$ @kbd{seq -1 3 14 @key{RET}}
@end example
@end itemize

Use the @samp{-w} option to pad numbers with leading zeros so that
they're all output with the same width.

Specify a separator string to be output between numbers as an argument
to the @samp{-s} option; the default is a newline character, which
outputs each number in the sequence on its own line.

@itemize @bullet
@item
To output the sequence of numbers from 9 to 999, incrementing by 23,
with numbers padded with zeros so that they're all of equal width, type:

@example
$ @kbd{seq -w 9 23 999 @key{RET}}
@end example

@item
To output the sequence of numbers from 1 to 23, with a space character
between each, type:

@example
$ @kbd{seq -s ' ' 1 23 @key{RET}}
@end example
@end itemize

To pass a sequence of numbers as arguments to a command, pipe the output
of @code{seq} using a space character as a separator.

@itemize @bullet
@item
To concatenate all the files in the current directory, whose names are
numbers from 25 through 75, into a new file called @file{selected-mail},
type:

@example
$ @kbd{cat `seq -s " " 25 75` > selected-mail @key{RET}}
@end example
@end itemize


@node Prime Factors, Converting Numbers, Number Sequence, Mathematics
@comment  node-name,  next,  previous,  up
@section Finding Prime Factors
@cindex finding prime factors
@cindex prime factors, finding
@pindex factor

@noindent
The @code{factor} tool calculates and outputs the prime factors of
numbers passed as arguments.

@itemize @bullet
@item
To output the prime factors of 2000, type:

@example
@cartouche
$ @kbd{factor 2000 @key{RET}}
2000: 2 2 2 2 5 5 5
$
@end cartouche
@end example
@end itemize

@sp .25
@noindent
@strong{NOTE:} If no number is given, @code{factor} reads numbers from
standard input; numbers should be separated by space, tab, or newline
characters.


@node Converting Numbers, Math Tools, Prime Factors, Mathematics
@comment  node-name,  next,  previous,  up
@section Converting Numbers
@cindex converting numbers
@cindex numbers, converting

@noindent
The following recipes are for converting numbers in various ways.

@menu
* Converting Units::            Converting units of measurement.
* Converting Arabic::           Converting Arabic numerals to text.
@end menu


@node Converting Units, Converting Arabic, Converting Numbers, Converting Numbers
@comment  node-name,  next,  previous,  up
@subsection Converting an Amount between Units of Measurement
@cindex converting an amount between units of measurement
@cindex measurement, converting an amount between units of
@cindex units of measurement, converting an amount between
@pindex units

@flushleft
@sf{Debian}: @file{units}
@sf{WWW}: @url{http://www.gnu.org/software/units/units.html}
@end flushleft
@*
@noindent
Use the @code{units} tool to convert units of measurement between
scales. Give two quoted arguments: the number and name of the units you
have, and the name of the units to convert to. It outputs two values:
the number of the second units you have, and how many of the second kind
of unit can make up the quantity of the first that you've specified.

@itemize @bullet
@item
To output the number of ounces in 50 grams, type:

@example
@cartouche
$ @kbd{units '50 grams' 'ounces' @key{RET}}
        * 1.7636981
        / 0.56699046
$
@end cartouche
@end example
@end itemize

In this example, the output indicates that there are about 1.7636981
ounces in 50 grams, and that conversely, one ounce is about 0.56699046
times 50 grams.

The @code{units} tool understands a great many different kinds of
units---from Celsius and Fahrenheit to pounds, hectares, the speed of
light, and a ``baker's dozen.'' All understood units are kept in a text
file database; use the @samp{-V} option to output the location of this
database on your system, which you can then peruse or search through to
see the units your version supports.

@itemize @bullet
@item
To determine the location of the @code{units} database, type:

@example
@cartouche
$ @kbd{units -V @key{RET}}
units version 1.55 with readline, units database in
/usr/share/misc/units.dat 
$
@end cartouche
@end example
@end itemize

In this example, the @code{units} database is located in the file 
@file{/usr/share/misc/units.dat}, which is the file to peruse to list
all of the units data.


@node Converting Arabic, , Converting Units, Converting Numbers
@comment  node-name,  next,  previous,  up
@subsection Converting an Arabic Numeral to English
@cindex converting an Arabic numeral to English
@cindex numeral, converting an Arabic to English
@pindex number

@flushleft
@sf{Debian}: @file{bsdgames}
@end flushleft
@*
@noindent
Use @code{number} to convert Arabic numerals to English text. Give a
numeral as an argument; with no argument, @code{number} reads a numeral
from the standard input.

@itemize @bullet
@item
To output the English text equivalent of 100,000, type:

@example
$ @kbd{number 100000 @key{RET}}
@end example
@end itemize


@node Math Tools, , Converting Numbers, Mathematics
@comment  node-name,  next,  previous,  up
@section Other Math Tools
@cindex other math tools
@cindex math tools, other
@cindex GnuCash
@pindex dome
@pindex dc
@pindex calc
@pindex gnucash
@pindex xcalc

@noindent
The following table lists some of the other mathematics tools available
for Linux. It is by no means a complete list.

@multitable @columnfractions .30 .70
@item @sc{Tool}
@tab @sc{Description}
@item @code{calc}
@tab @code{calc} is a scientific calculator tool for Emacs.

@noindent
{@sf{Debian}}: @file{calc}

@item @code{dc}
@tab Like @code{bc}, the @code{dc} tool is an arbitrary-precision
calculator language, but it is a @dfn{reverse-polish} calculator, where
numbers are pushed on a stack. When you give an arithmetic operation
symbol, @code{dc} pops numbers off the stack for their operands, and
then it pushes the evaluation on the stack.

@noindent
{@sf{Debian}}: @file{dc}

@item @code{dome}
@tab Richard J. Bono's @code{dome} is a geodesic math tool for
calculating the properties of a geodesic dome symmetry triangle---it can
calculate chord factors, vertex coordinates, and topological abundance
of various dome types, including ``Buckyball'' formations and elliptical
geodesics.

@noindent
{@sf{Debian}}: @file{dome}

@noindent
{@sf{WWW}}: @url{http://www.cris.com/~rjbono/html/domes.html}

@item @code{gnucash}
@tab GnuCash is an intuitive personal finance application. Use it for
managing finances, including bank accounts, stocks, income, and
expenses; it's ``based on professional accounting principles'' to ensure
accuracy in computation and reporting.

@noindent
{@sf{Debian}}: @file{gnucash}

@noindent
{@sf{WWW}}: @url{http://www.gnucash.org/}

@item @code{gnumeric}
@tab Gnumeric is the GNOME spreadsheet application. It is powerful, and
somewhat reminiscent of Excel.

@noindent
{@sf{Debian}}: @file{gnumeric}

@noindent
{@sf{WWW}}: @url{http://www.gnu.org/software/gnumeric/gnumeric.html}

@item @code{gnuplot}
@tab The @code{gnuplot} tool can be used for data visualization, making
2-D and 3-D graphs, and plotting functions.

@noindent
{@sf{Debian}}: @file{gnuplot}

@noindent
{@sf{WWW}}: @url{ftp://ftp.gnu.org/pub/gnu/gnuplot/}

@item @code{oleo}
@tab GNU Oleo is a spreadsheet application. It can run in both X and in
the console, has Emacs-like key bindings, and can generate PostScript 
output.

@noindent
{@sf{Debian}}: @file{oleo}

@noindent
{@sf{WWW}}: @url{http://www.gnu.org/software/oleo/oleo.html}

@item @code{sc}
@tab @code{sc} is a small spreadsheet tool that runs in the console; it
provides formulas and other basic features you would expect from a
minimal spreadsheet.

@item @code{xcalc}
@tab @code{xcalc} is a visual scientific calculator for the X Window
System---it draws a calculator on the screen, and you can use the mouse
or keyboard to use it. It is capable of emulating the TI-30 and HP-10C
calculators.

@item @code{xspread}
@tab @code{xspread} is the X client front-end to @code{sc}.

@noindent
{@sf{Debian}}: @file{xspread}
@end multitable