Math::Symbolic::ParserUser Contributed Perl DocumentaMath::Symbolic::Parser(3)NAMEMath::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 MA~Xller, symbolic-module at steffen-mueller dot net
Stray Toaster, mwk at users dot sourceforge dot net
Oliver EbenhA~Xh
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.
perl v5.14.1 2011-07-26 Math::Symbolic::Parser(3)
