1Math::Symbolic::AuxFuncUtsieornsC(o3n)tributed Perl DocuMmaetnht:a:tSiyomnbolic::AuxFunctions(3)
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NAME

6       Math::Symbolic::AuxFunctions - Auxiliary functions for Math::Symbolic
7       hierarchy
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SYNOPSIS

10         use Math::Symbolic::AuxFunctions;
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12         Math::Symbolic::AuxFunctions::acos($x);
13         # etc
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DESCRIPTION

16       This module contains implementations of some auxiliary functions that
17       are used within the Math::Symbolic hierarchy of modules. In particular,
18       this module holds all trigonometric functions used for numeric
19       evaluation of trees by Math::Symbolic::Operator.
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21   EXPORT
22       None. On purpose. If I wished this module would pollute others'
23       namespaces, I'd have put the functions right where they're used.
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TRIGONOMETRIC FUNCTIONS

26   tan
27       Computes the tangent sin(x) / cos(x).
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29   cot
30       Computes the cotangent cos(x) / sin(x).
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32   asin
33       Computes the arc sine asin(z) = -i log(iz + sqrt(1-z*z)).  Above
34       formula is for complex numbers.
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36   acos
37       Computes the arc cosine acos(z) = -i log(z + sqrt(z*z-1)).  Above
38       formula is for complex numbers.
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40   atan
41       Computes the arc tangent atan(z) = i/2 log((i+z) / (i-z)).  Above
42       formula is for complex numbers.
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44   acot
45       Computes the arc cotangent ( atan( 1 / x ) ).
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47   asinh
48       Computes the arc hyperbolic sine asinh(z) = log(z + sqrt(z*z+1))
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50   acosh
51       Computes the arc hyperbolic cosine acosh(z) = log(z + sqrt(z*z-1)).
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OTHER FUNCTIONS

54   binomial_coeff
55       Calculates the binomial coefficient n over k of its first two arguments
56       (n, k).
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58       Code taken from Orwant et al, "Mastering Algorithms with Perl"
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60   bell_number
61       The Bell numbers are defined as follows:
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63         B_0   = 1
64         B_n+1 = sum_k=0_to_n( B_k * binomial_coeff(n, k) )
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66       This function uses memoization.
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AUTHOR

69       Please send feedback, bug reports, and support requests to the
70       Math::Symbolic support mailing list: math-symbolic-support at lists dot
71       sourceforge dot net. Please consider letting us know how you use
72       Math::Symbolic. Thank you.
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74       If you're interested in helping with the development or extending the
75       module's functionality, please contact the developers' mailing list:
76       math-symbolic-develop at lists dot sourceforge dot net.
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78       List of contributors:
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80         Steffen Mueller, symbolic-module at steffen-mueller dot net
81         Stray Toaster, mwk at users dot sourceforge dot net
82         Oliver Ebenhoeh
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SEE ALSO

85       New versions of this module can be found on http://steffen-mueller.net
86       or CPAN. The module development takes place on Sourceforge at
87       http://sourceforge.net/projects/math-symbolic/
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89       Math::Symbolic
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93perl v5.32.0                      2020-07-28   Math::Symbolic::AuxFunctions(3)
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