Manual Reference Pages  MATH::SYMBOLIC::BASE (3)
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NAME
Math::Symbolic::Base  Base class for symbols in symbolic calculations
CONTENTS
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 valuearguments 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 inplace!
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 inplace 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 keywords, 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 inplace 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 hardtodebug 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 inplace 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 inplace. 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 inplace 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 valuearguments 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:
mathsymbolicsupport 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:
mathsymbolicdevelop at lists dot sourceforge dot net.
List of contributors:
Steffen MXller, symbolicmodule at steffenmueller 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://steffenmueller.net or CPAN. The module development takes place on
Sourceforge at http://sourceforge.net/projects/mathsymbolic/
Math::Symbolic
perl v5.20.3  MATH::SYMBOLIC::BASE (3)  20130617 
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