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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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