Math::Symbolic::Base - Base class for symbols in symbolic calculations
use Math::Symbolic::Base;
This is a base class for all Math::Symbolic::* terms such as
Math::Symbolic::Operator, Math::Symbolic::Variable and
Math::Symbolic::Constant objects.
None by default.
Default method for stringification just returns the object's 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 (in case of a variable
or constant).
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 alternative syntax is to pass a single hash reference.
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.
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.
explicit_signature() returns a lexicographically sorted list of variable
names in the tree.
See also:
signature().
set_signature expects any number of variable identifiers as arguments. It sets a
variable's signature to this list of identifiers.
implement() works in-place!
Takes key/value pairs as arguments. The keys are to be variable names and the
values must be valid Math::Symbolic trees. All occurrances of the variables
will be replaced with their implementation.
First argument must be a valid Math::Symbolic tree.
replace() modifies the object it is called on in-place in that it
replaces it with its first argument. Doing that, it retains the original
object reference. This destroys the object it is called on.
However, this also means that you can create recursive trees of objects if the
new tree is to contain the old tree. So make sure you clone the old tree using
the
new() method before using it in the replacement tree or you will
end up with a program that eats your memory fast.
This method returns a modified copy of the tree it was called on.
It walks the tree and replaces all variables whose value attribute is defined
(either done at the time of object creation or using
set_value()) with
the corresponding constant objects. Variables whose value is not defined are
unaffected. Take, for example, the following code:
$tree = parse_from_string('a*b+a*c');
$tree->set_value(a => 4, c => 10); # value of b still not defined.
print $tree->fill_in_vars();
# prints "(4 * b) + (4 * 10)"
Minimum method for term simpilification just clones.
When called on an operator, descending_operands tries hard to determine which
operands to descend into. (Which usually means all operands.) A list of these
is returned.
When called on a constant or a variable, it returns the empty list.
Of course, some routines may have to descend into different branches of the
Math::Symbolic tree, but this routine returns the default operands.
The first argument to this method may control its behaviour. If it is any of the
following key-words, behaviour is modified accordingly:
default -- obvious. Use default heuristics.
These are all supersets of 'default':
all -- returns ALL operands. Use with caution.
all_vars -- returns all operands that may contain vars.
The method takes named arguments (key/value pairs).
descend() descends
(Who would have guessed?) into the Math::Symbolic tree recursively and for
each node, it calls code references with a copy of the current node as
argument. The copy may be modified and will be used for construction of the
returned tree. The automatic copying behaviour may be turned off.
Returns a (modified) copy of the original tree. If in-place modification is
turned on, the returned tree will not be a copy.
Available parameters are:
- before
- A code reference to be used as a callback that will be invoked before
descent. Depending on whether or not the "in_place" option is
set, the callback will be passed a copy of the current node (default) or
the original node itself.
The callback may modify the tree node and the modified node will be used to
construct descend()'s return value.
The return value of this callback describes the way descend() handles
the descent into the current node's operands.
If it returns the empty list, the (possibly modified) copy of the current
that was passed to the callback is used as the return value of
descend(), but the recursive descent is continued for all of the
current node's operands which may or may not be modified by the callback.
The "after" callback will be called on the node after descent
into the operands. (This is the normal behavior.)
If the callback returns undef, the descent is stopped for the current branch
and an exact copy of the current branch's children will be used for
descend()'s return value. The "after" callback will be
called immediately.
If the callback returns a list of integers, these numbers are assumed to be
the indexes of the current node's operands that are to be descended into.
That means if the callback returns (1), descend will be called for the
second operand and only the second. All other children/operands will be
cloned. As usual, the "after" callback will be called after
descent.
Any other return lists will lead to hard-to-debug errors. Tough luck.
Returning a hash reference from the callback allows for complete control
over the descend() routine. The hash may contain the following
elements:
- operands
- This is a referenced array that will be put in place of the previous
operands. It is the callback's job to make sure the number of operands
stays correct. The "operands" entry is evaluated before
the "descend_into" entry.
- descend_into
- This is a referenced array of integers and references. The integers are
assumed to be indices of the array of operands. Returning (1) results in
descent into the second operand and only the second.
References are assumed to be operands to descend into. descend() will
be directly called on them.
If the array is empty, descend() will act just as if an empty list
had been returned.
- in_place
- Boolean indicating whether or not to modify the operands in-place or not.
If this is true, descend() will be called with the "in_place
=> 1" parameter. If false, it will be called with "in_place
=> 0" instead. Defaults to false. (Cloning)
This does not affect the call to the "after" callback but only the
descent into operands.
- skip_after
- If this option exists and is set to true, the "after" callback
will not be invoked. This only applies to the current node, not to its
children/operands.
The list of options may grow in future versions.
- after
- This is a code reference which will be invoked as a callback after the
descent into the operands.
- in_place
- Controls whether or not to modify the current tree node in-place. Defaults
to false - cloning.
- operand_finder
- This option controls how the descend routine chooses which operands to
recurse into by default. That means it controls which operands
descend() recurses into if the 'before' routine returned the empty
list or if no 'before' routine was specified.
The option may either be a code reference or a string. If it is a code
reference, this code reference will be called with the current node as
argument. If it is a string, the method with that name will be called on
the current node object.
By default, descend() calls the 'descending_operands()' method
on the current node to determine the operands to descend into.
Returns the type of the term. This is a stub to be overridden.
set_value() returns the tree it modifies, but acts in-place on the
Math::Symbolic tree it was called on.
set_value() requires named arguments (key/value pairs) that associate
variable names of 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 alternative syntax is to pass a single
hash reference to the method.
Example: $tree->set_value(x => 1, y => 2, z => 3, t => 0) assigns
the value 1 to any occurrances of variables of the name "x", aso.
As opposed to
value(),
set_value() assigns to the variables
permanently and does not evaluate the tree.
When called on constants,
set_value() sets their value to its first
argument, but only if there is only one argument.
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 M�ller, symbolic-module at steffen-mueller dot net
Stray Toaster, mwk at users dot sourceforge dot net
Oliver Ebenh�h
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