linalg[smith] - compute the Smith normal form of a matrix
|
Calling Sequence
|
|
smith(A, x)
smith(A, x, U, V)
|
|
Parameters
|
|
A
|
-
|
square matrix of univariate polynomials in x
|
x
|
-
|
the variable name
|
U
|
-
|
name
|
V
|
-
|
name
|
|
|
|
|
Description
|
|
•
|
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.
|
|
|
Download Help Document
Was this information helpful?