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5.1.2 bareiss

Syntax:
bareiss ( module_expression )
bareiss ( matrix_expression )
bareiss ( module_expression, int_expression, int_expression )
bareiss ( matrix_expression, int_expression, int_expression )
Type:
list of module and intvec
Purpose:
applies the sparse Gauss-Bareiss algorithm (see References, Lee and Saunders) to a module (or with type conversion to a matrix) with an 'optimal' pivot strategy. The vectors of the module are the columns of the matrix, hence elimination takes place w.r.t. rows.
With only one parameter a complete elimination is done. Result is a list: the first entry is a module with a minimal independent set of vectors (as a matrix lower triangular), the second entry an intvec with the permutation of the rows w.r.t. the original matrix, that is, a k at position l indicates that row k was carried over to the row l.
The further parameters control the algorithm. bareiss(M,i,j) does not attempt to diagonalize the last i rows in the elimination procedure and stops computing when the remaining number of vectors (columns) to reduce is at most j.
Example:
 
See det; matrix.

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