Math::Symbolic::Base(3) 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.


Method to_string

Default method for stringification just returns the object's value.

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 (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.

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().

Method set_signature

set_signature expects any number of variable identifiers as arguments. It sets a variable's signature to this list of identifiers.

Method implement

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.

Method replace

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)"

Method simplify

Minimum method for term simpilification just clones.

Method descending_operands

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.

Method descend

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:

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:

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.
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.

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.

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.

This is a code reference which will be invoked as a callback after the descent into the operands.
Controls whether or not to modify the current tree node in-place. Defaults to false - cloning.
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.

Method term_type

Returns the type of the term. This is a stub to be overridden.

Method set_value

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 MXller, symbolic-module at steffen-mueller dot net
  Stray Toaster, mwk at users dot sourceforge dot net
  Oliver EbenhXh