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linalg[smith] - compute the Smith normal form of a matrix
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Calling Sequence
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smith(A, x)
smith(A, x, U, V)
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Parameters
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A
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square matrix of univariate polynomials in x
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x
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the variable name
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U
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name
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V
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name
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Description
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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].
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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.
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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  : ![product(S[i, i], i = 1 .. n)](/support/helpjp/helpview.aspx?si=6243/file07359/math111.png) is equal to the (monic) greatest common divisor of all n by n minors of A.
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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.
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The command with(linalg,smith) allows the use of the abbreviated form of this command.
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