Math::Symbolic::Base(3pm)

1Math::Symbolic::Base(3)User Contributed Perl DocumentatioMnath::Symbolic::Base(3)
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NAME

6       Math::Symbolic::Base - Base class for symbols in symbolic calculations
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SYNOPSIS

9         use Math::Symbolic::Base;
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DESCRIPTION

12       This is a base class for all Math::Symbolic::* terms such as
13       Math::Symbolic::Operator, Math::Symbolic::Variable and
14       Math::Symbolic::Constant objects.
15
16   EXPORT
17       None by default.
18

METHODS

20   Method to_string
21       Default method for stringification just returns the object's value.
22
23   Method value
24       value() evaluates the Math::Symbolic tree to its numeric
25       representation.
26
27       value() without arguments requires that every variable in the tree
28       contains a defined value attribute. Please note that this refers to
29       every variable object, not just every named variable.
30
31       value() with one argument sets the object's value (in case of a
32       variable or constant).
33
34       value() with named arguments (key/value pairs) associates variables in
35       the tree with the value-arguments if the corresponging key matches the
36       variable name.  (Can one say this any more complicated?) Since version
37       0.132, an alternative syntax is to pass a single hash reference.
38
39       Example: $tree->value(x => 1, y => 2, z => 3, t => 0) assigns the value
40       1 to any occurrances of variables of the name "x", aso.
41
42       If a variable in the tree has no value set (and no argument of value
43       sets it temporarily), the call to value() returns undef.
44
45   Method signature
46       signature() returns a tree's signature.
47
48       In the context of Math::Symbolic, signatures are the list of variables
49       any given tree depends on. That means the tree "v*t+x" depends on the
50       variables v, t, and x. Thus, applying signature() on the tree that
51       would be parsed from above example yields the sorted list ('t', 'v',
52       'x').
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54       Constants do not depend on any variables and therefore return the empty
55       list.  Obviously, operators' dependencies vary.
56
57       Math::Symbolic::Variable objects, however, may have a slightly more
58       involved signature. By convention, Math::Symbolic variables depend on
59       themselves. That means their signature contains their own name. But
60       they can also depend on various other variables because variables
61       themselves can be viewed as placeholders for more compicated terms. For
62       example in mechanics, the acceleration of a particle depends on its
63       mass and the sum of all forces acting on it. So the variable
64       'acceleration' would have the signature ('acceleration', 'force1',
65       'force2',..., 'mass', 'time').
66
67       If you're just looking for a list of the names of all variables in the
68       tree, you should use the explicit_signature() method instead.
69
70   Method explicit_signature
71       explicit_signature() returns a lexicographically sorted list of
72       variable names in the tree.
73
74       See also: signature().
75
76   Method set_signature
77       set_signature expects any number of variable identifiers as arguments.
78       It sets a variable's signature to this list of identifiers.
79
80   Method implement
81       implement() works in-place!
82
83       Takes key/value pairs as arguments. The keys are to be variable names
84       and the values must be valid Math::Symbolic trees. All occurrances of
85       the variables will be replaced with their implementation.
86
87   Method replace
88       First argument must be a valid Math::Symbolic tree.
89
90       replace() modifies the object it is called on in-place in that it
91       replaces it with its first argument. Doing that, it retains the
92       original object reference. This destroys the object it is called on.
93
94       However, this also means that you can create recursive trees of objects
95       if the new tree is to contain the old tree. So make sure you clone the
96       old tree using the new() method before using it in the replacement tree
97       or you will end up with a program that eats your memory fast.
98
99   fill_in_vars
100       This method returns a modified copy of the tree it was called on.
101
102       It walks the tree and replaces all variables whose value attribute is
103       defined (either done at the time of object creation or using
104       set_value()) with the corresponding constant objects. Variables whose
105       value is not defined are unaffected. Take, for example, the following
106       code:
107
108         $tree = parse_from_string('a*b+a*c');
109         $tree->set_value(a => 4, c => 10); # value of b still not defined.
110         print $tree->fill_in_vars();
111         # prints "(4 * b) + (4 * 10)"
112
113   Method simplify
114       Minimum method for term simpilification just clones.
115
116   Method descending_operands
117       When called on an operator, descending_operands tries hard to determine
118       which operands to descend into. (Which usually means all operands.)  A
119       list of these is returned.
120
121       When called on a constant or a variable, it returns the empty list.
122
123       Of course, some routines may have to descend into different branches of
124       the Math::Symbolic tree, but this routine returns the default operands.
125
126       The first argument to this method may control its behaviour. If it is
127       any of the following key-words, behaviour is modified accordingly:
128
129         default   -- obvious. Use default heuristics.
130
131         These are all supersets of 'default':
132         all       -- returns ALL operands. Use with caution.
133         all_vars  -- returns all operands that may contain vars.
134
135   Method descend
136       The method takes named arguments (key/value pairs).  descend() descends
137       (Who would have guessed?) into the Math::Symbolic tree recursively and
138       for each node, it calls code references with a copy of the current node
139       as argument. The copy may be modified and will be used for construction
140       of the returned tree. The automatic copying behaviour may be turned
141       off.
142
143       Returns a (modified) copy of the original tree. If in-place
144       modification is turned on, the returned tree will not be a copy.
145
146       Availlable parameters are:
147
148       before
149         A code reference to be used as a callback that will be invoked before
150         descent.  Depending on whether or not the "in_place" option is set,
151         the callback will be passed a copy of the current node (default) or
152         the original node itself.
153
154         The callback may modify the tree node and the modified node will be
155         used to construct descend()'s return value.
156
157         The return value of this callback describes the way descend() handles
158         the descent into the current node's operands.
159
160         If it returns the empty list, the (possibly modified) copy of the
161         current that was passed to the callback is used as the return value
162         of descend(), but the recursive descent is continued for all of the
163         current node's operands which may or may not be modified by the
164         callback. The "after" callback will be called on the node after
165         descent into the operands. (This is the normal behavior.)
166
167         If the callback returns undef, the descent is stopped for the current
168         branch and an exact copy of the current branch's children will be
169         used for descend()'s return value. The "after" callback will be
170         called immediately.
171
172         If the callback returns a list of integers, these numbers are assumed
173         to be the indexes of the current node's operands that are to be
174         descended into.  That means if the callback returns (1), descend will
175         be called for the second operand and only the second. All other
176         children/operands will be cloned.  As usual, the "after" callback
177         will be called after descent.
178
179         Any other return lists will lead to hard-to-debug errors. Tough luck.
180
181         Returning a hash reference from the callback allows for complete
182         control over the descend() routine. The hash may contain the
183         following elements:
184
185         operands
186           This is a referenced array that will be put in place of the
187           previous operands. It is the callback's job to make sure the number
188           of operands stays correct. The "operands" entry is evaluated before
189           the "descend_into" entry.
190
191         descend_into
192           This is a referenced array of integers and references. The integers
193           are assumed to be indices of the array of operands. Returning (1)
194           results in descent into the second operand and only the second.
195
196           References are assumed to be operands to descend into. descend()
197           will be directly called on them.
198
199           If the array is empty, descend() will act just as if an empty list
200           had been returned.
201
202         in_place
203           Boolean indicating whether or not to modify the operands in-place
204           or not.  If this is true, descend() will be called with the
205           "in_place => 1" parameter.  If false, it will be called with
206           "in_place => 0" instead.  Defaults to false. (Cloning)
207
208           This does not affect the call to the "after" callback but only the
209           descent into operands.
210
211         skip_after
212           If this option exists and is set to true, the "after" callback will
213           not be invoked. This only applies to the current node, not to its
214           children/operands.
215
216         The list of options may grow in future versions.
217
218       after
219         This is a code reference which will be invoked as a callback after
220         the descent into the operands.
221
222       in_place
223         Controls whether or not to modify the current tree node in-place.
224         Defaults to false - cloning.
225
226       operand_finder
227         This option controls how the descend routine chooses which operands
228         to recurse into by default. That means it controls which operands
229         descend() recurses into if the 'before' routine returned the empty
230         list or if no 'before' routine was specified.
231
232         The option may either be a code reference or a string. If it is a
233         code reference, this code reference will be called with the current
234         node as argument. If it is a string, the method with that name will
235         be called on the current node object.
236
237         By default, descend() calls the 'descending_operands()' method on the
238         current node to determine the operands to descend into.
239
240   Method term_type
241       Returns the type of the term. This is a stub to be overridden.
242
243   Method set_value
244       set_value() returns the tree it modifies, but acts in-place on the
245       Math::Symbolic tree it was called on.
246
247       set_value() requires named arguments (key/value pairs) that associate
248       variable names of variables in the tree with the value-arguments if the
249       corresponging key matches the variable name.  (Can one say this any
250       more complicated?) Since version 0.132, an alternative syntax is to
251       pass a single hash reference to the method.
252
253       Example: $tree->set_value(x => 1, y => 2, z => 3, t => 0) assigns the
254       value 1 to any occurrances of variables of the name "x", aso.
255
256       As opposed to value(), set_value() assigns to the variables permanently
257       and does not evaluate the tree.
258
259       When called on constants, set_value() sets their value to its first
260       argument, but only if there is only one argument.
261

AUTHOR

263       Please send feedback, bug reports, and support requests to the
264       Math::Symbolic support mailing list: math-symbolic-support at lists dot
265       sourceforge dot net. Please consider letting us know how you use
266       Math::Symbolic. Thank you.
267
268       If you're interested in helping with the development or extending the
269       module's functionality, please contact the developers' mailing list:
270       math-symbolic-develop at lists dot sourceforge dot net.
271
272       List of contributors:
273
274         Steffen MA~Xller, symbolic-module at steffen-mueller dot net
275         Stray Toaster, mwk at users dot sourceforge dot net
276         Oliver EbenhA~Xh
277

NAME

SYNOPSIS

DESCRIPTION

METHODS

AUTHOR

SEE ALSO