linalg[hermite] - Hermite Normal Form (reduced row echelon form)
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Calling Sequence
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hermite(A, x)
hermite(A, x, U)
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Parameters
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A
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rectangular matrix of polynomials in x
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x
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name
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U
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name
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Description
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The function hermite computes the Hermite Normal Form (reduced row echelon form) of an m by n rectangular matrix of univariate polynomials in x over the field of rational numbers Q, or rational expressions over Q.
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In principle this should work for polynomials in x over any field F, i.e. the Euclidean domain F[x], but in practice the code is only as powerful as Maple's normal function.
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The Hermite normal form is obtained by doing elementary row operations on A. This includes interchanging rows, multiplying through a row by a unit, and subtracting a multiple of one row from another.
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One can use transposes to obtain the column form of the Hermite Normal Form of a matrix.
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In the case of three arguments, the third argument U will be assigned the transformation matrix on output, such that the following holds: hermite(A) = U &* A.
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The command with(linalg,hermite) allows the use of the abbreviated form of this command.
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Examples
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Important: The linalg package has been deprecated. Use the superseding packages, LinearAlgebra and VectorCalculus, instead.
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To obtain the column form of HNF for H do
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