1Math::Symbolic::Parser(U3s)er Contributed Perl DocumentatMiaotnh::Symbolic::Parser(3)
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NAME

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

9         use Math::Symbolic::Parser;
10         my $parser = Math::Symbolic::Parser->new();
11         $string =~ s/\s+//g;
12         my $tree = $parser->parse($string);
13
14         # or better:
15         use Math::Symbolic;
16         my $tree = Math::Symbolic->parse_from_string($string);
17

DESCRIPTION

19       This module contains the parsing routines used by Math::Symbolic to
20       parse strings into Math::Symbolic trees. Usually, you will want to
21       simply use the Math::Symbolic->parse_from_string() class method instead
22       of this module directly. If you do use this module directly, however,
23       make sure to remove any whitespace from your input string.
24
25   NOTE
26       With version 0.501 of Math::Symbolic, an experimental, new parser is
27       introduced, but it is not enabled by default. The new parser is based
28       on Parse::Yapp instead of Parse::RecDescent and comes with an at least
29       ten fold speed increase. However, it has not been available for a long
30       time and is not as well tested.  Since version 2.00 of the
31       Math::SymbolicX::ParserExtensionFactory module, it's possible to extend
32       Yapp parsers.
33
34       At some point in the future the Yapp-based parser will become the
35       default! It is suggested you test your code against it before that.
36       Code that uses the RecDescent based parser's "Extend" method may fail!
37
38       Until then, you need to load it by hand as follows:
39
40         $Math::Symbolic::Parser = Math::Symbolic::Parser->new(
41           implementation=>'Yapp'
42         );
43
44       This replaces the default Math::Symbolic parser with an instance of the
45       new Yapp parser.
46
47   STRING FORMAT
48       The parser has been designed to parse strings that are reminiscient of
49       ordinary algebraic expressions including the standard arithmetic infix
50       operators such as multiplication. Many functions such as a rather
51       comprehensive set of trigonometric functions are parsed in prefix form
52       like 'sin(expression)' or 'log(base, expression)'. Unknown identifiers
53       starting with a letter and containing only letters, digits, and
54       underscores are parsed as variables. If these identifiers are followed
55       by parenthesis containing a list of identifiers, the list is parsed as
56       the signature of the variable. Example: '5*x(t)' is parsed as the
57       product of the constant five and the variable 'x' which depends on 't'.
58       These dependencies are important for total derivatives.
59
60       The supported builtin-functions are listed in the documentation for
61       Math::Symbolic::Operator in the section on the new() constructor.
62
63   EXTENSIONS
64       In version 0.503, a function named "exp(...)" is recognized and
65       transformed into "e^(...)" internally. In version 0.506, a function
66       named "sqrt(...)" was added which is transformed into "(...)^0.5".
67       Version 0.511 added support for the typical "f'(x)" syntax for
68       derivatives. For details, refer to the section on parsing derivatives
69       below.
70
71   EXAMPLES
72         # An example from analytical mechanics:
73         my $hamilton_function =
74                 Math::Symbolic->parse_from_string(
75                   'p_q(q, dq_dt, t) * dq_dt(q, t) - Lagrange(q, p_q, t)'
76                 );
77
78       This parses as "The product of the generalized impulse p_q (which is a
79       function of the generalized coordinate q, its derivative, and the time)
80       and the derivative of the generalized coordinate dq_dt (which depends
81       on q itself and the time).  This term minus the Lagrange Function (of
82       q, the impulse, and the time) is the Hamilton Function."
83
84       Well, that's how it parses in my head anyway. The parser will generate
85       a tree like this:
86
87         Operator {
88           type     => difference,
89           operands => (
90                         Operator {
91                           type     => product,
92                           operands => (
93                                         Variable {
94                                           name         => p_q,
95                                           dependencies => q, dq_dt, t
96                                         },
97                                         Variable {
98                                            name         => dq_dt,
99                                            dependencies => q, t
100                                         }
101                           )
102                         },
103                         Variable {
104                           name         => Lagrange,
105                           dependencies => q, p_q, t
106                         }
107                       )
108         }
109
110       Possibly a simpler example would be 'amplitude * sin(phi(t))' which
111       descibes an oscillation. sin(...) is assumed to be the sine function,
112       amplitude is assumed to be a symbol / variable that doesn't depend on
113       any others. phi is recognized as a variable that changes over time (t).
114       So phi(t) is actually a function of t that hasn't yet been specified.
115       phi(t) could look like 'omega*t + theta' where strictly speaking,
116       omega, t, and theta are all symbols without dependencies. So omega and
117       theta would be treated as constants if you derived them in respect to
118       t.  Figuratively speaking, omega would be a frequency and theta would
119       be a initial value.
120
121   PARSING DERIVATIVES
122       The traditional way of specifying a derivative for parsing was
123       "partial_derivative(EXPRESSION, VARIABLE)" where "EXPRESSION" can be
124       any valid expression and "VARIABLE" is a variable name.  The syntax
125       denotes a partial derivative of the expression with respect to the
126       variable. The same syntax is available for total derivatives.
127
128       With version 0.511, a new syntax for specifying partial derivatives was
129       added to the parser(s). "f'(x)" denotes the first partial derivative of
130       "f" with respect to "x". If "(x)" is omitted, "f'" defaults to using
131       "x". "f''(a)" is the second order partial derivative with respect to
132       "a". If there are multiple variables in the parenthesis, a la "f'(b,
133       a)", the first variable is used for the derivatives.
134
135   EXPORT
136       None by default.
137

CLASS DATA

139       While working with this module, you might get into the not-so-convient
140       position of having to debug the parser and/or its grammar. In order to
141       make this possible, there's the $DEBUG package variable which, when set
142       to 1, makes the parser warn which grammar elements are being processed.
143       Note, however, that their order is bottom-up, not top-down.
144
145   Constructor new
146       This constructor does not expect any arguments and returns a
147       Parse::RecDescent parser to parse algebraic expressions from a string
148       into Math::Symbolic trees.
149
150       The constructor takes key/value pairs of options.
151
152       You can regenerate the parser from the grammar in the scalar
153       $Math::Symbolic::Parser::Grammar instead of using the (slightly faster)
154       precompiled grammar from Math::Symbolic::Parser::Precompiled.  You can
155       enable recompilation from the grammar with the option "recompile => 1".
156       This only has an effect if the implementation is the Parse::RecDescent
157       based parser (which is the default).
158
159       If you care about parsing speed more than about being able to extend
160       the parser at run-time, you can specify the "implementation" option.
161       Currently recognized are "RecDescent" and "Yapp" implementations.
162       "RecDescent" is the default and "Yapp" is significantly faster. The
163       Parse::Yapp based implementation may not support all extension modules.
164       It has been tested with Math::SymbolicX::ParserExtensionFactory and
165       Math::SymbolicX::Complex.
166

AUTHOR

168       Please send feedback, bug reports, and support requests to the
169       Math::Symbolic support mailing list: math-symbolic-support at lists dot
170       sourceforge dot net. Please consider letting us know how you use
171       Math::Symbolic. Thank you.
172
173       If you're interested in helping with the development or extending the
174       module's functionality, please contact the developers' mailing list:
175       math-symbolic-develop at lists dot sourceforge dot net.
176
177       List of contributors:
178
179         Steffen Mueller, symbolic-module at steffen-mueller dot net
180         Stray Toaster, mwk at users dot sourceforge dot net
181         Oliver Ebenhoeh
182

SEE ALSO

184       New versions of this module can be found on http://steffen-mueller.net
185       or CPAN. The module development takes place on Sourceforge at
186       http://sourceforge.net/projects/math-symbolic/
187
188       Math::Symbolic
189
190       Math::Symbolic::Parser::Precompiled
191
193       This package is distributed under the same license as the rest of the
194       Math::Symbolic distribution (Artistic+GPL), but the author of
195       Parse::Yapp has requested that his copyright and the licensing terms of
196       Parse::Yapp derived works be reproduced. Note that the license is the
197       same as Math::Symbolic's license. We're using the "standalone parser"
198       option.
199
200         The Parse::Yapp module and its related modules and shell scripts
201         are copyright (c) 1998-2001 Francois Desarmenien, France. All
202         rights reserved.
203
204         You may use and distribute them under the terms of either the GNU
205         General Public License or the Artistic License, as specified in
206         the Perl README file.
207
208         If you use the "standalone parser" option so people don't need to
209         install Parse::Yapp on their systems in order to run you software,
210         this copyright notice should be included in your software
211         copyright too, and the copyright notice in the embedded driver
212         should be left untouched.
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216perl v5.32.0                      2020-07-28         Math::Symbolic::Parser(3)
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