Math::Symbolic::Base is a case class for symbols in symbolic calculations.
This is a base class for all Math::Symbolic::* terms such as Math::Symbolic::Operator, Math::Symbolic::Variable and Math::Symbolic::Constant objects.
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.
# 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.