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Math::Symbolic::MiscAlUseraContributed Perl DocuMath::Symbolic::MiscAlgebra(3)

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;

	 @vector = ('x', 'y', 'z');
	 $solution = solve_linear(\@matrix, \@vector);

DESCRIPTION
       This module provides several subroutines	related	to algebra such	as
       computing the determinant of quadratic matrices,	solving	linear
       equation	systems	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
	 linear_solve
	 bell_polynomial

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.

       Please note that	calculating determinants of matrices using the
       straightforward Laplace algorithm is a slow (O(n!))  operation. This
       implementation cannot make use of the various optimizations resulting
       from the	determinant properties since we	are dealing with symbolic
       matrix elements.	If you have a matrix of	reals, it is strongly
       suggested that you use Math::MatrixReal or Math::Pari to	get the
       determinant which can be	calculated using LR decomposition much faster.

       On a related note: Calculating the determinant of a 20x20 matrix	would
       take over 77146 years if	your Perl could	do 1 million calculations per
       second.	Given that we're talking about several method calls per
       calculation, that's much	more than todays computers could do. On	the
       other hand, if you'd be using this straightforward algorithm with
       numbers only and	in C, you might	be done	in 26 years alright, so	please
       go for the smarter route	(better	algorithm) instead if you have numbers
       only.

   linear_solve
       Calculates the solutions	x (vector) of a	linear equation	system of the
       form "Ax	= b" with "A" being a matrix, "b" a vector and the solution
       "x" a vector. Due to implementation limitations,	"A" must be a
       quadratic matrix	and "b"	must have a dimension that is equivalent to
       that of "A". Furthermore, the determinant of "A"	must be	non-zero. The
       algorithm used is devised from Cramer's Rule and	thus inefficient. The
       preferred algorithm for this task is Gaussian Elimination. If you have
       a matrix	and a vector of	real numbers, please consider using either
       Math::MatrixReal	or Math::Pari instead.

       First argument must be a	reference to a matrix (array of	arrays)	of
       symbolic	terms, second argument must be a reference to a	vector (array)
       of symbolic terms. Strings will be automatically	converted to
       Math::Symbolic trees.  Returns a	reference to the solution vector.

   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 Mi?1/2ller, symbolic-module at	steffen-mueller	dot net
	 Stray Toaster,	mwk at users dot sourceforge dot net
	 Oliver	Ebenhi?1/2h

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

perl v5.32.1			  2013-06-17	Math::Symbolic::MiscAlgebra(3)

NAME | SYNOPSIS | DESCRIPTION | SUBROUTINES | AUTHOR | SEE ALSO

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