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.\"
.IX Title "Math::Symbolic::AuxFunctions 3pm"
.TH Math::Symbolic::AuxFunctions 3pm "2021-01-07" "perl v5.32.0" "User Contributed Perl Documentation"
.\" For nroff, turn off justification.  Always turn off hyphenation; it makes
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.SH "NAME"
Math::Symbolic::AuxFunctions \- Auxiliary functions for Math::Symbolic hierarchy
.SH "SYNOPSIS"
.IX Header "SYNOPSIS"
.Vb 1
\&  use Math::Symbolic::AuxFunctions;
\&  
\&  Math::Symbolic::AuxFunctions::acos($x);
\&  # etc
.Ve
.SH "DESCRIPTION"
.IX Header "DESCRIPTION"
This module contains implementations of some auxiliary functions that are
used within the Math::Symbolic hierarchy of modules. In particular, this
module holds all trigonometric functions used for numeric evaluation of
trees by Math::Symbolic::Operator.
.SS "\s-1EXPORT\s0"
.IX Subsection "EXPORT"
None. On purpose. If I wished this module would pollute others' namespaces,
I'd have put the functions right where they're used.
.SH "TRIGONOMETRIC FUNCTIONS"
.IX Header "TRIGONOMETRIC FUNCTIONS"
.SS "tan"
.IX Subsection "tan"
Computes the tangent sin(x) / cos(x).
.SS "cot"
.IX Subsection "cot"
Computes the cotangent cos(x) / sin(x).
.SS "asin"
.IX Subsection "asin"
Computes the arc sine asin(z) = \-i log(iz + sqrt(1\-z*z)).
Above formula is for complex numbers.
.SS "acos"
.IX Subsection "acos"
Computes the arc cosine acos(z) = \-i log(z + sqrt(z*z\-1)).
Above formula is for complex numbers.
.SS "atan"
.IX Subsection "atan"
Computes the arc tangent atan(z) = i/2 log((i+z) / (i\-z)).
Above formula is for complex numbers.
.SS "acot"
.IX Subsection "acot"
Computes the arc cotangent ( atan( 1 / x ) ).
.SS "asinh"
.IX Subsection "asinh"
Computes the arc hyperbolic sine asinh(z) = log(z + sqrt(z*z+1))
.SS "acosh"
.IX Subsection "acosh"
Computes the arc hyperbolic cosine acosh(z) = log(z + sqrt(z*z\-1)).
.SH "OTHER FUNCTIONS"
.IX Header "OTHER FUNCTIONS"
.SS "binomial_coeff"
.IX Subsection "binomial_coeff"
Calculates the binomial coefficient n over k of its first two
arguments (n, k).
.PP
Code taken from Orwant et al, \*(L"Mastering Algorithms with Perl\*(R"
.SS "bell_number"
.IX Subsection "bell_number"
The Bell numbers are defined as follows:
.PP
.Vb 2
\&  B_0   = 1
\&  B_n+1 = sum_k=0_to_n( B_k * binomial_coeff(n, k) )
.Ve
.PP
This function uses memoization.
.SH "AUTHOR"
.IX Header "AUTHOR"
Please send feedback, bug reports, and support requests to the Math::Symbolic
support mailing list:
math-symbolic-support at lists dot sourceforge dot net. Please
consider letting us know how you use Math::Symbolic. Thank you.
.PP
If you're interested in helping with the development or extending the
module's functionality, please contact the developers' mailing list:
math-symbolic-develop at lists dot sourceforge dot net.
.PP
List of contributors:
.PP
.Vb 3
\&  Steffen MXller, symbolic\-module at steffen\-mueller dot net
\&  Stray Toaster, mwk at users dot sourceforge dot net
\&  Oliver EbenhXh
.Ve
.SH "SEE ALSO"
.IX Header "SEE ALSO"
New versions of this module can be found on
http://steffen\-mueller.net or \s-1CPAN.\s0 The module development takes place on
Sourceforge at http://sourceforge.net/projects/math\-symbolic/
.PP
Math::Symbolic