NAME

Math::Symbolic::Parser - Parse strings into Math::Symbolic trees

SYNOPSIS

use Math::Symbolic::Parser;
my $parser = Math::Symbolic::Parser->new();
$string =~ s/\s+//g;
my $tree = $parser->parse($string);

# or better:
use Math::Symbolic;
my $tree = Math::Symbolic->parse_from_string($string);

DESCRIPTION

This module contains the parsing routines used by Math::Symbolic to parse strings into Math::Symbolic trees. Usually, you will want to simply use the Math::Symbolic->parse_from_string() class method instead of this module directly. If you do use this module directly, however, make sure to remove any whitespace from your input string.

NOTE

With version 0.501 of Math::Symbolic, an experimental, new parser is introduced, but it is not enabled by default. The new parser is based on Parse::Yapp instead of Parse::RecDescent and comes with an at least ten fold speed increase. However, it has not been availlable for a long time and is not as well tested. Furthermore, it currently does not play well with parser extensions such as Math::SymbolicX::ParserExtensionFactory. As soon as these problems have been addressed (which might be a long time away), the new parser will be enabled by default. Until then, you need to load it by hand as follows:

use Math::Symbolic::Parser::Yapp;
$Math::Symbolic::Parser = Math::Symbolic::Parser::Yapp->new();

This replaces the default Math::Symbolic parser with an instance of the new Yapp parser. Doing this voids the warranty, you've been warned.

STRING FORMAT

The parser has been designed to parse strings that are reminiscient of ordinary algebraic expressions including the standard arithmetic infix operators such as multiplication. Many functions such as a rather comprehensive set of trigonometric functions are parsed in prefix form like 'sin(expression)' or 'log(base, expression)'. Unknown identifiers starting with a letter and containing only letters, digits, and underscores are parsed as variables. If these identifiers are followed by parenthesis containing a list of identifiers, the list is parsed as the signature of the variable. Example: '5*x(t)' is parsed as the product of the constant five and the variable 'x' which depends on 't'. These dependencies are important for total derivatives.

The supported builtin-functions are listed in the documentation for Math::Symbolic::Operator in the section on the new() constructor.

EXTENSIONS

In version 0.503, a function named exp(...) is recognized and transformed into e^(...) internally.

EXAMPLES

# An example from analytical mechanics:
my $hamilton_function =
        Math::Symbolic->parse_from_string(
          'p_q(q, dq_dt, t) * dq_dt(q, t) - Lagrange(q, p_q, t)'
        );

This parses as "The product of the generalized impulse p_q (which is a function of the generalized coordinate q, its derivative, and the time) and the derivative of the generalized coordinate dq_dt (which depends on q itself and the time). This term minus the Lagrange Function (of q, the impulse, and the time) is the Hamilton Function."

Well, that's how it parses in my head anyway. The parser will generate a tree like this:

  Operator {
    type     => difference,
    operands => (
                  Operator {
                    type     => product,
	            operands => (
                                  Variable {
                                    name         => p_q,
                                    dependencies => q, dq_dt, t
                                  },
                                  Variable {
                                     name         => dq_dt,
                                     dependencies => q, t
                                  }
                    )
                  },
                  Variable {
                    name         => Lagrange,
                    dependencies => q, p_q, t
                  }
                )
  }

Possibly a simpler example would be 'amplitude * sin(phi(t))' which descibes an oscillation. sin(...) is assumed to be the sine function, amplitude is assumed to be a symbol / variable that doesn't depend on any others. phi is recognized as a variable that changes over time (t). So phi(t) is actually a function of t that hasn't yet been specified. phi(t) could look like 'omega*t + theta' where strictly speaking, omega, t, and theta are all symbols without dependencies. So omega and theta would be treated as constants if you derived them in respect to t. Figuratively speaking, omega would be a frequency and theta would be a initial value.

EXPORT

None by default.

CLASS DATA

While working with this module, you might get into the not-so-convient position of having to debug the parser and/or its grammar. In order to make this possible, there's the $DEBUG package variable which, when set to 1, makes the parser warn which grammar elements are being processed. Note, however, that their order is bottom-up, not top-down.

Constructor new

This constructor does not expect any arguments and returns a Parse::RecDescent parser to parse algebraic expressions from a string into Math::Symbolic trees.

The constructor takes key/value pairs of options. Currently, the only option is to regenerate the parser from the grammar in the scalar $Math::Symbolic::Parser::Grammar instead of using the (faster) precompiled grammar from Math::Symbolic::Parser::Precompiled. You can enable recompilation from the grammar with the option "recompile => 1".

AUTHOR

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.

List of contributors:

Steffen Müller, symbolic-module at steffen-mueller dot net
Stray Toaster, mwk at users dot sourceforge dot net
Oliver Ebenhöh

SEE ALSO

New versions of this module can be found on http://steffen-mueller.net or CPAN. The module development takes place on Sourceforge at http://sourceforge.net/projects/math-symbolic/

Math::Symbolic

Math::Symbolic::Parser::Precompiled

ADDITIONAL COPYRIGHT NOTICE

This package is distributed under the same license as the rest of the Math::Symbolic distribution (Artistic+GPL), but the author of Parse::Yapp has requested that his copyright and the licensing terms of Parse::Yapp derived works be reproduced. Note that the license is the same as Math::Symbolic's license. We're using the "standalone parser" option.

The Parse::Yapp module and its related modules and shell scripts
are copyright (c) 1998-2001 Francois Desarmenien, France. All
rights reserved.

You may use and distribute them under the terms of either the GNU
General Public License or the Artistic License, as specified in
the Perl README file.

If you use the "standalone parser" option so people don't need to
install Parse::Yapp on their systems in order to run you software,
this copyright notice should be included in your software
copyright too, and the copyright notice in the embedded driver
should be left untouched.

1 POD Error

The following errors were encountered while parsing the POD:

Around line 451:

Non-ASCII character seen before =encoding in 'Müller,'. Assuming CP1252