---
name: "Math::Symbolic::AuxFunctions"
section: "3pm"
platform: "linux"
package: "libmath-symbolic-perl"
version: "0.613-1"
release: "Debian 13 (Trixie)"
platforms: ["linux"]
url: "https://new.carta.tech/Math::Symbolic::AuxFunctions"
---

# Math::Symbolic::AuxFunctions(3pm)

Auxiliary functions for Math::Symbolic hierarchy

## 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 M�ller, symbolic-module at steffen-mueller dot net
  Stray Toaster, mwk at users dot sourceforge dot net
  Oliver Ebenh�h
```

## 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