29. Mathematics
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.
29.1 Calculating Arithmetic
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
(see section Other Math Tools).
29.1.1 Making a Quick Arithmetic Calculation
@sf{WWW}: http://dsl.org/comp/tinyutils/
To do a quick calculation that requires only addition, subtraction,
multiplication, or division, use
calc. It takes as an argument a
simple mathematical expression, and it outputs the answer.
Use `*' for a multiplication sign and `/' for division; to
output the remainder, use `%'. You can use parenthesis to group
expressions--but when you do, be sure to quote them (see section Passing Special Characters to Commands).
-
To output the result of 50 times 10, type:
-
To output the result of 100 times the sum of 4 plus 420, type:
| | $ calc '100*(4+420)' RET
42400
$
|
-
To output the remainder of 10 divided by 3, type:
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 bc.
29.1.2 Making Many Arithmetic Calculations
@sf{Debian}: `bc'
@sf{WWW}: ftp://src.doc.ic.ac.uk:/pub/gnu/bc-1.05a.tar.gz
When you have a lot of calculations to make, or when you must compute
numbers with decimals, use
bc, a calculation language that
supports arbitrary precision numbers. Type
bc to perform
arithmetic operations interactively, just like you would with a
calculator.
Type each statement to evaluate on a line by itself, typing 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 bc as an
arithmetic expression. To exit, type quit on a line by itself.
-
To multiply 42 and 17, type:
| | $ bc 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'.
42 * 17 RET
714
quit RET
$
|
In this example, bc output its version number and warranty
information when it started; then, the statement 42 * 17 was typed
by the user, bc output the result (`714'), and then the
user typed quit to exit bc.
By default, digits to the right of the decimal point are truncated from
the output--so dividing 10 by 3 would output `3' as a result, and
outputting the remainder from this operation by typing 10%3 would
output a `1'. However, 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 scale variable; its
default value is 0.
-
To use
bc to compute the result of 10 divided by 3, using 20
digits after the decimal point, type:
| | $ bc 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'.
scale=20 RET
10 / 3 RET
3.33333333333333333333
quit RET
$
|
The following table describes the symbols you can use to specify
mathematical operations.
| SYMBOL |
OPERATION
|
expression + expression |
Add: output the sum of the two expressions.
|
expression - expression |
Subtract: output the difference of the two expressions.
|
expression * expression |
Multiply: output the product of the two expressions.
|
expression / expression |
Divide: output the quotient of the two expressions.
|
expression % expression |
Remainder: output the remainder resulting by dividing the two
expressions.
|
expression ^ expression |
Power: raise the first expression to the power of the second
expression.
|
(expressions) |
Group an expression or expressions together, altering the standard
precedence of performing operations.
|
sqrt(expression) |
Output the square root of expression.
|
29.2 Outputting a Random Number
@sf{WWW}: http://dsl.org/comp/tinyutils/
To output a random number, use
random. Give as an argument an
integer denoting the range of numbers to be output;
random then
outputs a random number from 0 to the number you give, minus one.
-
To output a random number from 0 to 9, type:
29.3 Listing a Sequence of Numbers
Use 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.
-
To output the sequence of numbers from one to seven, type:
-
To output the sequence of numbers from one to negative seven, type:
To output the sequence from any one number to another, give those
numbers as arguments.
-
To output the sequence of numbers from nine to zero, type:
-
To output the sequence of numbers from negative one to negative twenty, type:
To specify an increment other than one, give it as the second
argument, between the starting and ending number.
-
To output the sequence of numbers from -1 to 14, incrementing by 3,
type:
Use the `-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 `-s' option; the default is a newline character, which
outputs each number in the sequence on its own line.
-
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:
-
To output the sequence of numbers from 1 to 23, with a space character
between each, type:
To pass a sequence of numbers as arguments to a command, pipe the output
of seq using a space character as a separator.
-
To concatenate all the files in the current directory, whose names are
numbers from 25 through 75, into a new file called `selected-mail',
type:
| | $ cat `seq -s " " 25 75` > selected-mail RET
|
29.4 Finding Prime Factors
The factor tool calculates and outputs the prime factors of
numbers passed as arguments.
-
To output the prime factors of 2000, type:
| | $ factor 2000 RET
2000: 2 2 2 2 5 5 5
$
|
NOTE: If no number is given, factor reads numbers from
standard input; numbers should be separated by space, tab, or newline
characters.
29.5 Converting Numbers
The following recipes are for converting numbers in various ways.
29.5.1 Converting an Amount between Units of Measurement
@sf{Debian}: `units'
@sf{WWW}: http://www.gnu.org/software/units/units.html
Use the
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.
-
To output the number of ounces in 50 grams, type:
| | $ units '50 grams' 'ounces' RET
* 1.7636981
/ 0.56699046
$
|
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 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 `-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.
-
To determine the location of the
units database, type:
| | $ units -V RET
units version 1.55 with readline, units database in
/usr/share/misc/units.dat
$
|
In this example, the units database is located in the file
`/usr/share/misc/units.dat', which is the file to peruse to list
all of the units data.
29.5.2 Converting an Arabic Numeral to English
@sf{Debian}: `bsdgames'
Use
number to convert Arabic numerals to English text. Give a
numeral as an argument; with no argument,
number reads a numeral
from the standard input.
-
To output the English text equivalent of 100,000, type:
29.6 Other Math Tools
The following table lists some of the other mathematics tools available
for Linux. It is by no means a complete list.
| TOOL |
DESCRIPTION
|
calc |
calc is a scientific calculator tool for Emacs.
{@sf{Debian}}: `calc'
|
dc |
Like bc, the dc tool is an arbitrary-precision
calculator language, but it is a reverse-polish calculator, where
numbers are pushed on a stack. When you give an arithmetic operation
symbol, dc pops numbers off the stack for their operands, and
then it pushes the evaluation on the stack.
{@sf{Debian}}: `dc'
|
dome |
Richard J. Bono's 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.
{@sf{Debian}}: `dome'
{@sf{WWW}}: http://www.cris.com/~rjbono/html/domes.html
|
gnucash |
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.
{@sf{Debian}}: `gnucash'
{@sf{WWW}}: http://www.gnucash.org/
|
gnumeric |
Gnumeric is the GNOME spreadsheet application. It is powerful, and
somewhat reminiscent of Excel.
{@sf{Debian}}: `gnumeric'
{@sf{WWW}}: http://www.gnu.org/software/gnumeric/gnumeric.html
|
gnuplot |
The gnuplot tool can be used for data visualization, making
2-D and 3-D graphs, and plotting functions.
{@sf{Debian}}: `gnuplot'
{@sf{WWW}}: ftp://ftp.gnu.org/pub/gnu/gnuplot/
|
oleo |
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.
{@sf{Debian}}: `oleo'
{@sf{WWW}}: http://www.gnu.org/software/oleo/oleo.html
|
sc |
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.
|
xcalc |
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.
|
xspread |
xspread is the X client front-end to sc.
{@sf{Debian}}: `xspread'
|
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