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NAME
Math::SymbolicX::Complex - Complex number support for the Math::Symbolic
parser
SYNOPSIS
use Math::Symbolic qw/parse_from_string/;
use Math::SymbolicX::Complex;
my $formula = parse_from_string('3 * complex(3,2)^2 + polar(1, pi/2)');
print $formula->value();
# prints '14.9999999997949+37i'
# (blame the inaccuracy on the floating point representation of "pi")
DESCRIPTION
This module adds complex number support to Math::Symbolic. It does so by
extending the parser of the Math::Symbolic module (that is, the one
stored in $Math::Symbolic::Parser) with certain special functions that
create complex constants. (Math::Symbolic::Variable objects have been
able to contain complex number objects since the very beginning.)
MOTIVATION
All constants in strings that are parsed by Math::Symbolic::Parser are
converted to Math::Symbolic::Constant objects holding the value
associated to the constant in an ordinary Perl Scalar by default.
Unfortunately, that means you are limited to real floating point
numbers.
On the other hand, there's the formidable Math::Complex module that
gives complex number support to Perl. Since the Math::Symbolic::Scalar
objects can hold any object, you can build your trees by hand using
Math::Complex objects instead of Perl Scalars for the value of the
constants. But since the Math::Symbolic::Parser is by far the most
convenient interface to Math::Symbolic, there had to be a reasonably
simple way of introducing Math::Complex support to the parser. So here
goes.
USAGE
In order to complex number constants in Math::Symbolic trees from the
parser, you just load this extension module and wrap any of the
functions listed hereafter around any constants that are complex in
nature.
The aforementioned functions are "complex()" and "polar()". "complex(RE,
IM)" takes a real portion and an imaginary portion of the complex number
as arguments. That means, it uses the "Math::Complex-"make(RE, IM)>
method to create the Math::Complex objects. Similarily, "polar()" uses
the "Math::Complex-"emake(R, ARG)> syntax provided by Math::Complex.
(Polar notation is r*e^(i*arg). It is equivalent to the "x+i*y" notation
because it also covers the whole complex plane.)
There are some usability extensions to the simple "complex(RE, IM)" and
"polar(R, ARG)" notations: You can use the basic operators ('+', '-',
'*', '/', and '**') and the symbolic constant 'pi' in the expressions
for RE, IM, R, and ARG. That means "polar(1, pi/2)" should be translated
to "polar(1, 1.5707963267949)" internally.
Note, however, that the floating point representation of pi used in this
module is far from exact. So, instead of yielding "0+i" as a result, the
above example will be "-3.49148336110938e-015+i". Of course,
-3.49148336110938e-015 is as close to a real zero as you'll get, but
testing for equality with the "==" operator will break.
AUTHOR
Copyright (C) 2004-2007 Steffen Mueller
This library is free software; you can redistribute it and/or modify it
under the same terms as Perl itself.
You may contact the author at symbolic-module at steffen-mueller dot net
Please send feedback, bug reports, and support requests to the
Math::Symbolic support mailing list: math-symbolic-support at lists dot
sourceforge dot net. Please consider letting us know how you use
Math::Symbolic. Thank you.
If you're interested in helping with the development or extending the
module's functionality, please contact the developers' mailing list:
math-symbolic-develop at lists dot sourceforge dot net.
SEE ALSO
New versions of this module can be found on http://steffen-mueller.net
or CPAN.
You should definately be familiar with Math::Complex before you start
using this module because the objects that are returned from
"$formula-"value()> calls are Math::Complex objects.
Also have a look at Math::Symbolic, and at Math::Symbolic::Parser
Refer to Math::SymbolicX::ParserExtensionFactory for the implementation
details.
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