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

Provided by: libmath-symbolic-perl_0.612-2_all

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 available for a long time and is not as well tested.
       Since version 2.00 of the Math::SymbolicX::ParserExtensionFactory module, it's possible to extend Yapp
       parsers.

       At some point in the future the Yapp-based parser will become the default! It is suggested you test your
       code against it before that.  Code that uses the RecDescent based parser's "Extend" method may fail!

       Until then, you need to load it by hand as follows:

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

       This replaces the default Math::Symbolic parser with an instance of the new Yapp parser.

   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. In
       version 0.506, a function named "sqrt(...)" was added which is transformed into "(...)^0.5".  Version
       0.511 added support for the typical "f'(x)" syntax for derivatives. For details, refer to the section on
       parsing derivatives below.

   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.

   PARSING DERIVATIVES
       The traditional way of specifying a derivative for parsing was "partial_derivative(EXPRESSION, VARIABLE)"
       where "EXPRESSION" can be any valid expression and "VARIABLE" is a variable name.  The syntax denotes a
       partial derivative of the expression with respect to the variable. The same syntax is available for total
       derivatives.

       With version 0.511, a new syntax for specifying partial derivatives was added to the parser(s). "f'(x)"
       denotes the first partial derivative of "f" with respect to "x". If "(x)" is omitted, "f'" defaults to
       using "x". "f''(a)" is the second order partial derivative with respect to "a". If there are multiple
       variables in the parenthesis, a la "f'(b, a)", the first variable is used for the derivatives.

   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.

You can regenerate the parser from the grammar in the scalar $Math::Symbolic::Parser::Grammar instead of
using the (slightly faster) precompiled grammar from Math::Symbolic::Parser::Precompiled. You can enable
recompilation from the grammar with the option "recompile => 1". This only has an effect if the
implementation is the Parse::RecDescent based parser (which is the default).

If you care about parsing speed more than about being able to extend the parser at run-time, you can
specify the "implementation" option. Currently recognized are "RecDescent" and "Yapp" implementations.
"RecDescent" is the default and "Yapp" is significantly faster. The Parse::Yapp based implementation may
not support all extension modules. It has been tested with Math::SymbolicX::ParserExtensionFactory and
Math::SymbolicX::Complex.

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 MXller, symbolic-module at steffen-mueller dot net
         Stray Toaster, mwk at users dot sourceforge dot net
         Oliver EbenhXh

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