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Gausselim - inert Gaussian elimination
Gaussjord - inert Gauss Jordan elimination
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Calling Sequence
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Gausselim(A) mod p
Gaussjord(A) mod p
Gausselim(A, 'r', 'd') mod p
Gaussjord(A, 'r', 'd') mod p
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Parameters
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A
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Matrix
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'r'
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(optional) for returning the rank of A
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'd'
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(optional) for returning the determinant of A
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'p'
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an integer, the modulus
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Description
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The Gausselim and Gaussjord functions are placeholders for representing row echelon forms of the rectangular matrix A.
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The commands Gausselim(A,...) mod p and Gassjord(A,...) mod p apply Gaussian elimination with row pivoting to A, a rectangular matrix over a finite ring of characteristic p. This includes finite fields, GF(p), the integers mod p, and GF(p^k) where elements of GF(p^k) are expressed as polynomials in RootOfs.
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The result of the Gausselim command is a an upper triangular matrix B in row echelon form. The result of the Gaussjord command is also an upper triangular matrix B but in reduced row echelon form.
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If an optional second parameter is specified, and it is a name, it is assigned the rank of the matrix A.
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Examples
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![A := Matrix([[1, 2, 3], [1, 3, 0], [1, 4, 3]])](/support/helpjp/helpview.aspx?si=6721/file00054/math152.png)
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)](/support/helpjp/helpview.aspx?si=6721/file00054/math166.png)
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![A := Matrix([[1, a, a^2], [a, a^2, a^3], [a^2, a^3, 1]])](/support/helpjp/helpview.aspx?si=6721/file00054/math191.png)
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