Math::Symbolic::AuxFunctions(3pm)

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 evalua‐
19       tion of trees by Math::Symbolic::Operator.
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21       EXPORT
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23       None. On purpose. If I wished this module would pollute others' names‐
24       paces, I'd have put the functions right where they're used.
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TRIGONOMETRIC FUNCTIONS

27       tan
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29       Computes the tangent sin(x) / cos(x).
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31       cot
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33       Computes the cotangent cos(x) / sin(x).
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35       asin
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37       Computes the arc sine asin(z) = -i log(iz + sqrt(1-z*z)).  Above for‐
38       mula is for complex numbers.
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40       acos
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42       Computes the arc cosine acos(z) = -i log(z + sqrt(z*z-1)).  Above for‐
43       mula is for complex numbers.
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45       atan
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47       Computes the arc tangent atan(z) = i/2 log((i+z) / (i-z)).  Above for‐
48       mula is for complex numbers.
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50       acot
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52       Computes the arc cotangent ( atan( 1 / x ) ).
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54       asinh
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56       Computes the arc hyperbolic sine asinh(z) = log(z + sqrt(z*z+1))
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58       acosh
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60       Computes the arc hyperbolic cosine acosh(z) = log(z + sqrt(z*z-1)).
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OTHER FUNCTIONS

63       binomial_coeff
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65       Calculates the binomial coefficient n over k of its first two arguments
66       (n, k).
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68       Code taken from Orwant et al, "Mastering Algorithms with Perl"
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70       bell_number
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72       The Bell numbers are defined as follows:
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74         B_0   = 1
75         B_n+1 = sum_k=0_to_n( B_k * binomial_coeff(n, k) )
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77       This function uses memoization.
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AUTHOR

80       Please send feedback, bug reports, and support requests to the
81       Math::Symbolic support mailing list: math-symbolic-support at lists dot
82       sourceforge dot net. Please consider letting us know how you use
83       Math::Symbolic. Thank you.
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85       If you're interested in helping with the development or extending the
86       module's functionality, please contact the developers' mailing list:
87       math-symbolic-develop at lists dot sourceforge dot net.
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89       List of contributors:
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91         Steffen Müller, symbolic-module at steffen-mueller dot net
92         Stray Toaster, mwk at users dot sourceforge dot net
93         Oliver Ebenhöh
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NAME

SYNOPSIS

DESCRIPTION

TRIGONOMETRIC FUNCTIONS

OTHER FUNCTIONS

AUTHOR

SEE ALSO