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/

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:

  $ calc 50*10 RET 500 $

• 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:

  $ calc 10%3 RET 1 $

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

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.

29.2 Outputting a Random Number

@sf{WWW}: http://dsl.org/comp/tinyutils/

• To output a random number from 0 to 9, type:

  $ random 10 RET

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:

  $ seq 7 RET

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

  $ seq -7 RET

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:

  $ seq 9 0 RET

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

  $ seq -1 -20 RET

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:

  $ seq -1 3 14 RET

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:

  $ seq -w 9 23 999 RET

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

  $ seq -s ' ' 1 23 RET

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

• 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'

• To output the English text equivalent of 100,000, type:

  $ number 100000 RET

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.