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, however, make sure to remove any whitespace from your input string.

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.

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

cpanm Math::Symbolic

perl -MCPAN -e shell
install Math::Symbolic