Math::Symbolic::Base(3User Contributed Perl DocumentatiMath::Symbolic::Base(3)NAMEMath::Symbolic::Base - Base class for symbols in symbolic calculations
SYNOPSIS
use Math::Symbolic::Base;
DESCRIPTION
This is a base class for all Math::Symbolic::* terms such as
Math::Symbolic::Operator, Math::Symbolic::Variable and
Math::Symbolic::Constant objects.
EXPORT
None by default.
METHODS
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.
fill_in_vars
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:
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.
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.
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 MA~Xller, symbolic-module at steffen-mueller dot net
Stray Toaster, mwk at users dot sourceforge dot net
Oliver EbenhA~Xh
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
perl v5.14.1 2011-07-26 Math::Symbolic::Base(3)
