Important: The linalg package has been deprecated. Use the superseding packages, LinearAlgebra and VectorCalculus, instead.

- For information on migrating linalg code to the new packages, see examples/LinearAlgebraMigration.

The Smith normal form of a matrix with univariate polynomial entries in x over a field F is computed. Thus the polynomials are then regarded as elements of the Euclidean domain F[x].

This routine is only as powerful as Maple's normal function, since at present it only understands the field Q of rational numbers and rational functions over Q.

The Smith normal form of a matrix is a diagonal matrix S obtained by doing elementary row and column operations.  The diagonal entries satisfy the following property for all :  is equal to the (monic) greatest common divisor of all n by n minors of A.

In the case of four arguments, the third argument U and the fourth argument V will be assigned the transformation matrices on output, such that smith(A) = U &* A &* V.

The command with(linalg,smith) allows the use of the abbreviated form of this command.