NAME

Math::Symbolic::MiscAlgebra - Miscellaneous algebra routines like det()

SYNOPSIS

  use Math::Symbolic qw/:all/;
  use Math::Symbolic::MiscAlgebra qw/:all/; # not loaded by Math::Symbolic
  
  @matrix = (['x*y', 'z*x', 'y*z'],['x', 'z', 'z'],['x', 'x', 'y']);
  $det = det @matrix;

DESCRIPTION

This module provides several subroutines related to algebra such as computing the determinant of nxn matrices and computation of Bell Polynomials.

Please note that the code herein may or may not be refactored into the OO-interface of the Math::Symbolic module in the future.

EXPORT

None by default.

You may choose to have any of the following routines exported to the calling namespace. ':all' tag exports all of the following:

  det

SUBROUTINES

det

det() computes the determinant of a matrix of Math::Symbolic trees (or strings that can be parsed as such). First argument must be a literal array: "det @matrix", where @matrix is an n x n matrix.

bell_polynomial

This functions returns the nth Bell Polynomial. It uses memoization for speed increase.

First argument is the n. Second (optional) argument is the variable or variable name to use in the polynomial. Defaults to 'x'.

The Bell Polynomial is defined as follows:

  phi_0  (x) = 1
  phi_n+1(x) = x * ( phi_n(x) + partial_derivative( phi_n(x), x ) )

Bell Polynomials are Exponential Polynimals with phi_n(1) = the nth bell number. Please refer to the bell_number() function in the Math::Symbolic::AuxFunctions module for a method of generating these numbers.

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 Müller, symbolic-module at steffen-mueller dot net
  Stray Toaster, mwk at users dot sourceforge dot net
  Oliver Ebenhöh

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