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D.11.3.1 smith

Procedure from library jacobson.lib (see jacobson_lib).

Usage:
smith(M[, eng1, eng2]); M matrix, eng1 and eng2 are optional integers

Return:
matrix or list of matrices, depending on arguments

Assume:
Basering is a commutative polynomial ring in one variable

Purpose:
compute the Smith Normal Form of M with (optionally) transformation matrices

Theory:
Groebner bases are used for the Smith form like in [2] and [3].

Note:
By default, just the Smith normal form of M is returned.
If the optional integer eng1 is non-zero, the list {U,D,V} is returned
where U*M*V = D and the diagonal field entries of D are not normalized.
The normalization of the latter can be done with the 'divideUnits' procedure.
U and V above are square unimodular (invertible) matrices.
Note, that the procedure works for a rectangular matrix M.

The optional integer eng2 determines the Groebner basis engine:
0 (default) ensures the use of 'slimgb' , otherwise 'std' is used.

Display:
If printlevel=1, progress debug messages will be printed,
if printlevel>=2, all the debug messages will be printed.

Example:
 
See also: divideUnits; jacobson.


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