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[comment {-*- tcl -*- doctools manpage}]
[manpage_begin math::constants n 1.0.1]
[copyright {2004 Arjen Markus <arjenmarkus@users.sourceforge.net>}]
[moddesc {Tcl Math Library}]
[titledesc {Mathematical and numerical constants}]
[require Tcl [opt 8.3]]
[require math::constants [opt 1.0.1]]
[description]
[para]
This package defines some common mathematical and numerical constants.
By using the package you get consistent values for numbers like pi and
ln(10).
[para]
It defines two commands:
[list_begin itemized]
[item]
One for importing the constants
[item]
One for reporting which constants are defined and what values they
actually have.
[list_end]
[para]
The motivation for this package is that quite often, with
(mathematical) computations, you need a good approximation to, say,
the ratio of degrees to radians. You can, of course, define this
like:
[example {
variable radtodeg [expr {180.0/(4.0*atan(1.0))}]
}]
and use the variable radtodeg whenever you need the conversion.
[para]
This has two drawbacks:
[list_begin itemized]
[item]
You need to remember the proper formula or value and that is
error-prone.
[item]
Especially with the use of mathematical functions like [emph atan]
you assume that they have been accurately implemented. This is seldom or
never the case and for each platform you can get subtle differences.
[list_end]
Here is the way you can do it with the [emph math::constants] package:
[example {
package require math::constants
::math::constants::constants radtodeg degtorad
}]
which creates two variables, radtodeg and (its reciprocal) degtorad
in the calling namespace.
[para]
Constants that have been defined (their values are mostly taken
from mathematical tables with more precision than usually can be
handled) include:
[list_begin itemized]
[item]
basic constants like pi, e, gamma (Euler's constant)
[item]
derived values like ln(10) and sqrt(2)
[item]
purely numerical values such as 1/3 that are included for convenience
and for the fact that certain seemingly trivial computations like:
[example {
set value [expr {3.0*$onethird}]
}]
give [emph exactly] the value you expect (if IEEE arithmetic is
available).
[list_end]
[section "PROCEDURES"]
The package defines the following public procedures:
[list_begin definitions]
[call [cmd ::math::constants::constants] [arg args]]
Import the constants whose names are given as arguments
[para]
[call [cmd ::math::constants::print-constants] [arg args]]
Print the constants whose names are given as arguments on the screen
(name, value and description) or, if no arguments are given, print all
defined constants. This is mainly a convenience procedure.
[list_end]
[section {BUGS, IDEAS, FEEDBACK}]
This document, and the package it describes, will undoubtedly contain
bugs and other problems.
Please report such in the category [emph {math :: constants}] of the
[uri {http://sourceforge.net/tracker/?group_id=12883} {Tcllib SF Trackers}].
Please also report any ideas for enhancements you may have for either
package and/or documentation.
[keywords math constants pi e radians degrees]
[manpage_end]
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