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;
10

DESCRIPTION

12       This is a base class for all Math::Symbolic::* terms such as Math::Sym‐
13       bolic::Operator, Math::Symbolic::Variable and Math::Symbolic::Constant
14       objects.
15
16       EXPORT
17
18       None by default.
19

METHODS

21       Method to_string
22
23       Default method for stringification just returns the object's value.
24
25       Method value
26
27       value() evaluates the Math::Symbolic tree to its numeric representa‐
28       tion.
29
30       value() without arguments requires that every variable in the tree con‐
31       tains a defined value attribute. Please note that this refers to every
32       variable object, not just every named variable.
33
34       value() with one argument sets the object's value (in case of a vari‐
35       able or constant).
36
37       value() with named arguments (key/value pairs) associates variables in
38       the tree with the value-arguments if the corresponging key matches the
39       variable name.  (Can one say this any more complicated?) Since version
40       0.132, an alternative syntax is to pass a single hash reference.
41
42       Example: $tree->value(x => 1, y => 2, z => 3, t => 0) assigns the value
43       1 to any occurrances of variables of the name "x", aso.
44
45       If a variable in the tree has no value set (and no argument of value
46       sets it temporarily), the call to value() returns undef.
47
48       Method signature
49
50       signature() returns a tree's signature.
51
52       In the context of Math::Symbolic, signatures are the list of variables
53       any given tree depends on. That means the tree "v*t+x" depends on the
54       variables v, t, and x. Thus, applying signature() on the tree that
55       would be parsed from above example yields the sorted list ('t', 'v',
56       'x').
57
58       Constants do not depend on any variables and therefore return the empty
59       list.  Obviously, operators' dependencies vary.
60
61       Math::Symbolic::Variable objects, however, may have a slightly more
62       involved signature. By convention, Math::Symbolic variables depend on
63       themselves. That means their signature contains their own name. But
64       they can also depend on various other variables because variables them‐
65       selves can be viewed as placeholders for more compicated terms. For
66       example in mechanics, the acceleration of a particle depends on its
67       mass and the sum of all forces acting on it. So the variable 'accelera‐
68       tion' would have the signature ('acceleration', 'force1', 'force2',...,
69       'mass', 'time').
70
71       If you're just looking for a list of the names of all variables in the
72       tree, you should use the explicit_signature() method instead.
73
74       Method explicit_signature
75
76       explicit_signature() returns a lexicographically sorted list of vari‐
77       able names in the tree.
78
79       See also: signature().
80
81       Method set_signature
82
83       set_signature expects any number of variable identifiers as arguments.
84       It sets a variable's signature to this list of identifiers.
85
86       Method implement
87
88       implement() works in-place!
89
90       Takes key/value pairs as arguments. The keys are to be variable names
91       and the values must be valid Math::Symbolic trees. All occurrances of
92       the variables will be replaced with their implementation.
93
94       Method replace
95
96       First argument must be a valid Math::Symbolic tree.
97
98       replace() modifies the object it is called on in-place in that it
99       replaces it with its first argument. Doing that, it retains the origi‐
100       nal object reference. This destroys the object it is called on.
101
102       However, this also means that you can create recursive trees of objects
103       if the new tree is to contain the old tree. So make sure you clone the
104       old tree using the new() method before using it in the replacement tree
105       or you will end up with a program that eats your memory fast.
106
107       fill_in_vars
108
109       This method returns a modified copy of the tree it was called on.
110
111       It walks the tree and replaces all variables whose value attribute is
112       defined (either done at the time of object creation or using
113       set_value()) with the corresponding constant objects. Variables whose
114       value is not defined are unaffected. Take, for example, the following
115       code:
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117         $tree = parse_from_string('a*b+a*c');
118         $tree->set_value(a => 4, c => 10); # value of b still not defined.
119         print $tree->fill_in_vars();
120         # prints "(4 * b) + (4 * 10)"
121
122       Method simplify
123
124       Minimum method for term simpilification just clones.
125
126       Method descending_operands
127
128       When called on an operator, descending_operands tries hard to determine
129       which operands to descend into. (Which usually means all operands.)  A
130       list of these is returned.
131
132       When called on a constant or a variable, it returns the empty list.
133
134       Of course, some routines may have to descend into different branches of
135       the Math::Symbolic tree, but this routine returns the default operands.
136
137       The first argument to this method may control its behaviour. If it is
138       any of the following key-words, behaviour is modified accordingly:
139
140         default   -- obvious. Use default heuristics.
141
142         These are all supersets of 'default':
143         all       -- returns ALL operands. Use with caution.
144         all_vars  -- returns all operands that may contain vars.
145
146       Method descend
147
148       The method takes named arguments (key/value pairs).  descend() descends
149       (Who would have guessed?) into the Math::Symbolic tree recursively and
150       for each node, it calls code references with a copy of the current node
151       as argument. The copy may be modified and will be used for construction
152       of the returned tree. The automatic copying behaviour may be turned
153       off.
154
155       Returns a (modified) copy of the original tree. If in-place modifica‐
156       tion is turned on, the returned tree will not be a copy.
157
158       Availlable parameters are:
159
160       before
161         A code reference to be used as a callback that will be invoked before
162         descent.  Depending on whether or not the "in_place" option is set,
163         the callback will be passed a copy of the current node (default) or
164         the original node itself.
165
166         The callback may modify the tree node and the modified node will be
167         used to construct descend()'s return value.
168
169         The return value of this callback describes the way descend() handles
170         the descent into the current node's operands.
171
172         If it returns the empty list, the (possibly modified) copy of the
173         current that was passed to the callback is used as the return value
174         of descend(), but the recursive descent is continued for all of the
175         current node's operands which may or may not be modified by the call‐
176         back. The "after" callback will be called on the node after descent
177         into the operands. (This is the normal behavior.)
178
179         If the callback returns undef, the descent is stopped for the current
180         branch and an exact copy of the current branch's children will be
181         used for descend()'s return value. The "after" callback will be
182         called immediately.
183
184         If the callback returns a list of integers, these numbers are assumed
185         to be the indexes of the current node's operands that are to be
186         descended into.  That means if the callback returns (1), descend will
187         be called for the second operand and only the second. All other chil‐
188         dren/operands will be cloned.  As usual, the "after" callback will be
189         called after descent.
190
191         Any other return lists will lead to hard-to-debug errors. Tough luck.
192
193         Returning a hash reference from the callback allows for complete con‐
194         trol over the descend() routine. The hash may contain the following
195         elements:
196
197         operands
198           This is a referenced array that will be put in place of the previ‐
199           ous operands. It is the callback's job to make sure the number of
200           operands stays correct. The "operands" entry is evaluated before
201           the "descend_into" entry.
202
203         descend_into
204           This is a referenced array of integers and references. The integers
205           are assumed to be indices of the array of operands. Returning (1)
206           results in descent into the second operand and only the second.
207
208           References are assumed to be operands to descend into. descend()
209           will be directly called on them.
210
211           If the array is empty, descend() will act just as if an empty list
212           had been returned.
213
214         in_place
215           Boolean indicating whether or not to modify the operands in-place
216           or not.  If this is true, descend() will be called with the
217           "in_place => 1" parameter.  If false, it will be called with
218           "in_place => 0" instead.  Defaults to false. (Cloning)
219
220           This does not affect the call to the "after" callback but only the
221           descent into operands.
222
223         skip_after
224           If this option exists and is set to true, the "after" callback will
225           not be invoked. This only applies to the current node, not to its
226           children/operands.
227
228         The list of options may grow in future versions.
229
230       after
231         This is a code reference which will be invoked as a callback after
232         the descent into the operands.
233
234       in_place
235         Controls whether or not to modify the current tree node in-place.
236         Defaults to false - cloning.
237
238       operand_finder
239         This option controls how the descend routine chooses which operands
240         to recurse into by default. That means it controls which operands
241         descend() recurses into if the 'before' routine returned the empty
242         list or if no 'before' routine was specified.
243
244         The option may either be a code reference or a string. If it is a
245         code reference, this code reference will be called with the current
246         node as argument. If it is a string, the method with that name will
247         be called on the current node object.
248
249         By default, descend() calls the 'descending_operands()' method on the
250         current node to determine the operands to descend into.
251
252       Method term_type
253
254       Returns the type of the term. This is a stub to be overridden.
255
256       Method set_value
257
258       set_value() returns the tree it modifies, but acts in-place on the
259       Math::Symbolic tree it was called on.
260
261       set_value() requires named arguments (key/value pairs) that associate
262       variable names of variables in the tree with the value-arguments if the
263       corresponging key matches the variable name.  (Can one say this any
264       more complicated?) Since version 0.132, an alternative syntax is to
265       pass a single hash reference to the method.
266
267       Example: $tree->set_value(x => 1, y => 2, z => 3, t => 0) assigns the
268       value 1 to any occurrances of variables of the name "x", aso.
269
270       As opposed to value(), set_value() assigns to the variables permanently
271       and does not evaluate the tree.
272
273       When called on constants, set_value() sets their value to its first
274       argument, but only if there is only one argument.
275

AUTHOR

277       Please send feedback, bug reports, and support requests to the
278       Math::Symbolic support mailing list: math-symbolic-support at lists dot
279       sourceforge dot net. Please consider letting us know how you use
280       Math::Symbolic. Thank you.
281
282       If you're interested in helping with the development or extending the
283       module's functionality, please contact the developers' mailing list:
284       math-symbolic-develop at lists dot sourceforge dot net.
285
286       List of contributors:
287
288         Steffen Müller, symbolic-module at steffen-mueller dot net
289         Stray Toaster, mwk at users dot sourceforge dot net
290         Oliver Ebenhöh
291

NAME

SYNOPSIS

DESCRIPTION

METHODS

AUTHOR

SEE ALSO