NAME¶
Math::Symbolic::Operator - Operators in symbolic calculations
SYNOPSIS¶
use Math::Symbolic::Operator;
my $sum = Math::Symbolic::Operator->new('+', $term1, $term2);
# or:
my $division =
Math::Symbolic::Operator->new(
{
type => B_DIVISON,
operands => [$term1, $term2],
}
);
my $derivative =
Math::Symbolic::Operator->new(
{
type => U_P_DERIVATIVE,
operands => [$term],
}
);
DESCRIPTION¶
This module implements all Math::Symbolic::Operator objects. These objects are
overloaded in stringification-context to call the
to_string() method on
the object. In numeric and boolean context, they evaluate to their numerical
representation.
For a list of supported operators, please refer to the list found below, in the
documentation for the
new() constructor.
Math::Symbolic::Operator inherits from Math::Symbolic::Base.
EXPORT¶
None.
CLASS DATA¶
Math::Symbolic::Operator contains several class data structures. Usually, you
should not worry about dealing with any of them because they are mostly an
implementation detail, but for the sake of completeness, here's the gist, but
feel free to skip this section of the docs:
One of these is the %Op_Symbols hash that associates operator (and function)
symbols with the corresponding constant as exported by Math::Symbolic or
Math::Symbolic::ExportConstants. (For example, '+' => B_SUM which in turn
is 0, if I recall correctly. But I didn't tell you that. Because you're
supposed to use the supplied (inlined and hence fast) constants so I can
change their internal order if I deem it necessary.)
The array @Op_Types associates operator indices (recall those nifty constants?)
with anonymous hash datastructures that contain some info on the operator such
as its arity, the rule used to derive it, its infix string, its prefix string,
and information on how to actually apply it to numbers.
METHODS¶
Constructor new¶
Expects a hash reference as first argument. That hash's contents will be treated
as key-value pairs of object attributes. Important attributes are 'type' =>
OPERATORTYPE (use constants as exported by Math::Symbolic::ExportConstants!)
and 'operands=>[op1,op2,...]'. Where the operands themselves may either be
valid Math::Symbolic::* objects or strings that will be parsed as such.
Special case: if no hash reference was found, first argument is assumed to be
the operator's symbol and the operator is assumed to be binary. The following
2 arguments will be treated as operands. This special case will ignore
attempts to clone objects but if the operands are no valid Math::Symbolic::*
objects, they will be sent through a Math::Symbolic::Parser to construct
Math::Symbolic trees.
Returns a Math::Symbolic::Operator.
Supported operator symbols: (number of operands and their function in parens)
+ => sum (2)
- => difference (2)
* => product (2)
/ => division (2)
log => logarithm (2: base, function)
^ => exponentiation (2: base, exponent)
neg => unary minus (1)
partial_derivative => partial derivative (2: function, var)
total_derivative => total derivative (2: function, var)
sin => sine (1)
cos => cosine (1)
tan => tangent (1)
cot => cotangent (1)
asin => arc sine (1)
acos => arc cosine (1)
atan => arc tangent (1)
atan2 => arc tangent of y/x (2: y, x)
acot => arc cotangent (1)
sinh => hyperbolic sine (1)
cosh => hyperbolic cosine (1)
asinh => hyperbolic area sine (1)
acosh => hyperbolic area cosine (1)
Method arity¶
Returns the operator's arity as an integer.
Method type¶
Optional integer argument that sets the operator's type. Returns the operator's
type as an integer.
Method to_string¶
Returns a string representation of the operator and its operands. Optional
argument: 'prefix' or 'infix'. Defaults to 'infix'.
Method term_type¶
Returns the type of the term. ( T_OPERATOR )
Method simplify¶
Term simpilification. First argument: Boolean indicating that the tree does not
need to be cloned, but can be restructured instead. While this is faster, you
might not be able to use the old tree any more.
Example:
my $othertree = $tree->simplify();
# can use $othertree and $tree now.
my $yetanothertree = $tree->simplify(1);
# must not use $tree any more because its internal
# representation might have been destroyed.
If you want to optimize a routine and you're sure that you won't need the
unsimplified tree any more, go ahead and use the first parameter. In all other
cases, you should go the safe route.
Methods op1 and op2¶
Returns first/second operand of the operator if it exists or undef.
Method apply¶
Applies the operation to its operands'
value() and returns the result as
a constant (-object).
Without arguments, all variables in the tree are required to have a value. If
any don't, the call to
apply() returns undef.
To (temorarily, for this single method call) assign values to variables in the
tree, you may provide key/value pairs of variable names and values. Instead of
passing a list of key/value pairs, you may also pass a single hash reference
containing the variable mappings.
You usually want to call the
value() instead of this.
Method value¶
value() evaluates the Math::Symbolic tree to its numeric representation.
value() without arguments requires that every variable in the tree
contains a defined value attribute. Please note that this refers to every
variable
object, not just every named variable.
value() with one argument sets the object's value if you're dealing with
Variables or Constants. In case of operators, a call with one argument will
assume that the argument is a hash reference. (see next paragraph)
value() with named arguments (key/value pairs) associates variables in
the tree with the value-arguments if the corresponging key matches the
variable name. (Can one say this any more complicated?) Since version 0.132,
an equivalent and valid syntax is to pass a single hash reference instead of a
list.
Example: $tree->value(x => 1, y => 2, z => 3, t => 0) assigns the
value 1 to any occurrances of variables of the name "x", aso.
If a variable in the tree has no value set (and no argument of value sets it
temporarily), the call to
value() returns undef.
Method signature¶
signature() returns a tree's signature.
In the context of Math::Symbolic, signatures are the list of variables any given
tree depends on. That means the tree "v*t+x" depends on the
variables v, t, and x. Thus, applying
signature() on the tree that
would be parsed from above example yields the sorted list ('t', 'v', 'x').
Constants do not depend on any variables and therefore return the empty list.
Obviously, operators' dependencies vary.
Math::Symbolic::Variable objects, however, may have a slightly more involved
signature. By convention, Math::Symbolic variables depend on themselves. That
means their signature contains their own name. But they can also depend on
various other variables because variables themselves can be viewed as
placeholders for more compicated terms. For example in mechanics, the
acceleration of a particle depends on its mass and the sum of all forces
acting on it. So the variable 'acceleration' would have the signature
('acceleration', 'force1', 'force2',..., 'mass', 'time').
If you're just looking for a list of the names of all variables in the tree, you
should use the
explicit_signature() method instead.
Method explicit_signature¶
explicit_signature() returns a lexicographically sorted list of variable
names in the tree.
See also:
signature().
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
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