Math::Symbolic::Custom::DefaultTests(3pm)

1Math::Symbolic::Custom:U:sDeerfaCuolnttTreisbtust(e3d)PMeartlh:D:oScyummbeonltiact:i:oCnustom::DefaultTests(3)
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NAME

6       Math::Symbolic::Custom::DefaultTests - Default Math::Symbolic tree
7       tests
8

SYNOPSIS

10         use Math::Symbolic;
11

DESCRIPTION

13       This is a class of default tests for Math::Symbolic trees. Likewise,
14       Math::Symbolic::Custom::DefaultMods defines default tree transformation
15       routines.  For details on how the custom method delegation model works,
16       please have a look at the Math::Symbolic::Custom and Math::Sym‐
17       bolic::Custom::Base classes.
18
19       EXPORT
20
21       Please see the docs for Math::Symbolic::Custom::Base for details, but
22       you should not try to use the standard Exporter semantics with this
23       class.
24

SUBROUTINES

26       is_zero()
27
28       Returns true (1) of the tree is a constant and '0'. Returns false (0)
29       otherwise.
30
31       is_one()
32
33       Returns true (1) of the tree is a constant and '1'. Returns false (0)
34       otherwise.
35
36       is_zero_or_one()
37
38       Returns true ('1' for 1, '0E0' for 0) of the tree is a constant and '1'
39       or '0'.  Returns false (0) otherwise.
40
41       is_integer()
42
43       is_integer() returns a boolean.
44
45       It returns true (1) if the tree is a constant object representing an
46       integer value. It does not compute the value of the tree.  (eg. '5*10'
47       is not considered an integer, but '50' is.)
48
49       It returns false (0) otherwise.
50
51       is_simple_constant()
52
53       is_simple_constant() returns a boolean.
54
55       It returns true if the tree consists of only constants and operators.
56       As opposed to is_constant(), is_simple_constant() does not apply deriv‐
57       atives if necessary.
58
59       It returns false (0) otherwise.
60
61       is_constant()
62
63       is_constant() returns a boolean.
64
65       It returns true (1) if the tree consists of only constants and opera‐
66       tors or if it becomes a tree of only constants and operators after
67       application of derivatives.
68
69       It returns false (0) otherwise.
70
71       If you need not pay the price of applying derivatives, you should use
72       the is_simple_constant() method instead.
73
74       is_identical()
75
76       is_identical() returns a boolean.
77
78       It compares the tree it is called on to its first argument. If the
79       first argument is not a Math::Symbolic tree, it is sent through the
80       parser.
81
82       is_identical() returns true (1) if the trees are completely identical.
83       That includes operands of commutating operators having the same order,
84       etc. This does not test of mathematical equivalence! (Which is much,
85       much harder to test for. If you know how to, please let me know!)
86
87       It returns false (0) otherwise.
88
89       is_identical_base
90
91       is_identical_base() returns a boolean.
92
93       It compares the tree it is called on to its first argument. If the
94       first argument is not a Math::Symbolic tree, it is sent through the
95       parser.
96
97       is_identical_base() returns true (1) if the trees are identical or if
98       they are exponentiations with the same base. The same gotchas that
99       apply to is_identical apply here, too.
100
101       For example, 'x*y' and '(x*y)^e' result in a true return value because
102       'x*y' is equal to '(x*y)^1' and this has the same base as '(x*y)^e'.
103
104       It returns false (0) otherwise.
105
106       is_sum()
107
108       (beta)
109
110       is_constant() returns a boolean.
111
112       It returns true (1) if the tree contains no variables (because it can
113       then be evaluated to a single constant which is a sum). It also returns
114       true if it is a sum or difference of constants and variables. Further‐
115       more, it is true for products of integers and constants because those
116       products are really sums of variables.  If none of the above cases
117       match, it applies all derivatives and tries again.
118
119       It returns false (0) otherwise.
120
121       Please contact the author in case you encounter bugs in the specs or
122       implementation. The heuristics aren't all that great.
123
124       test_num_equiv()
125
126       Takes another Math::Symbolic tree or a code ref as first argument.
127       Tests the tree it is called on and the one passed in as first argument
128       for equivalence by sampling random numbers for their parameters and
129       evaluating them.
130
131       This is no guarantee that the functions are actually similar. The com‐
132       putation required for this test may be very high for large numbers of
133       tests.
134
135       In case of a subroutine reference passed in, the values of the parame‐
136       ters of the Math::Symbolic tree are passed to the sub ref sorted by the
137       parameter names.
138
139       Following the test-tree, there may be various options as key/value
140       pairs:
141
142         limits: A hash reference with parameter names as keys and code refs
143                 as arguments. A code ref for parameter 'x', will be executed
144                 for every number of 'x' that is generated. If the code
145                 returns false, the number is discarded and regenerated.
146         tests:  The number of tests to carry out. Default: 20
147         epsilon: The accuracy of the numeric comparison. Default: 1e-7
148         retries: The number of attempts to make if a function evaluation
149                  throws an error.
150         upper:   Upper limit of the random numbers. Default: 10
151         lower:   Lower limit of the random numbers. Default: -10
152

AUTHOR

154       Please send feedback, bug reports, and support requests to the
155       Math::Symbolic support mailing list: math-symbolic-support at lists dot
156       sourceforge dot net. Please consider letting us know how you use
157       Math::Symbolic. Thank you.
158
159       If you're interested in helping with the development or extending the
160       module's functionality, please contact the developers' mailing list:
161       math-symbolic-develop at lists dot sourceforge dot net.
162
163       List of contributors:
164
165         Steffen Müller, symbolic-module at steffen-mueller dot net
166         Stray Toaster, mwk at users dot sourceforge dot net
167         Oliver Ebenhöh
168

NAME

SYNOPSIS

DESCRIPTION

SUBROUTINES

AUTHOR

SEE ALSO