NAME¶
Math::Symbolic::AuxFunctions - Auxiliary functions for Math::Symbolic hierarchy
SYNOPSIS¶
use Math::Symbolic::AuxFunctions;
Math::Symbolic::AuxFunctions::acos($x);
# etc
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.
EXPORT¶
None. On purpose. If I wished this module would pollute others' namespaces, I'd
have put the functions right where they're used.
TRIGONOMETRIC FUNCTIONS¶
tan¶
Computes the tangent sin(x) / cos(x).
cot¶
Computes the cotangent cos(x) / sin(x).
asin¶
Computes the arc sine asin(z) = -i log(iz + sqrt(1-z*z)). Above formula is for
complex numbers.
acos¶
Computes the arc cosine acos(z) = -i log(z + sqrt(z*z-1)). Above formula is for
complex numbers.
atan¶
Computes the arc tangent atan(z) = i/2 log((i+z) / (i-z)). Above formula is for
complex numbers.
acot¶
Computes the arc cotangent ( atan( 1 / x ) ).
asinh¶
Computes the arc hyperbolic sine asinh(z) = log(z + sqrt(z*z+1))
acosh¶
Computes the arc hyperbolic cosine acosh(z) = log(z + sqrt(z*z-1)).
OTHER FUNCTIONS¶
binomial_coeff¶
Calculates the binomial coefficient n over k of its first two arguments (n, k).
Code taken from Orwant et al, "Mastering Algorithms with Perl"
bell_number¶
The Bell numbers are defined as follows:
B_0 = 1
B_n+1 = sum_k=0_to_n( B_k * binomial_coeff(n, k) )
This function uses memoization.
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.
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.
List of contributors:
Steffen Mueller, symbolic-module at steffen-mueller dot net
Stray Toaster, mwk at users dot sourceforge dot net
Oliver Ebenhoeh
SEE ALSO¶
New versions of this module can be found on
http://steffen-mueller.net or CPAN.
The module development takes place on Sourceforge at
http://sourceforge.net/projects/math-symbolic/
Math::Symbolic