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.
AtsomepointinthefuturetheYapp-basedparserwillbecomethedefault! 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.
STRINGFORMAT
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.
PARSINGDERIVATIVES
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.
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