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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