inert Gaussian elimination - Maple Help

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Gausselim - inert Gaussian elimination

Gaussjord - inert Gauss Jordan elimination

Calling Sequence

Gausselim(A) mod p

Gaussjord(A) mod p

Gausselim(A, 'r', 'd') mod p

Gaussjord(A, 'r', 'd') mod p

Parameters

A

-

Matrix

'r'

-

(optional) for returning the rank of A

'd'

-

(optional) for returning the determinant of A

'p'

-

an integer, the modulus

Description

• 

The Gausselim and Gaussjord functions are placeholders for representing row echelon forms of the rectangular matrix A.

• 

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.

• 

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.

• 

If an optional second parameter is specified, and it is a name, it is assigned the rank of the matrix A.

• 

If A is an m by n matrix with mn and if an optional third parameter is also specified, and it is a name, it is assigned the determinant of the matrix A[1..m,1..m].

Examples

A:=Matrix1,2,3,1,3,0,1,4,3

A:=123130143

(1)

GausselimAmod5

123012001

(2)

B:=ArrayTools[Concatenate]2,A,LinearAlgebra[IdentityMatrix]3

B:=123100130010143001

(3)

GaussjordBmod5

100411010203001131

(4)

InverseAmod5

411203131

(5)

aliasa=RootOfx4+x+1mod2:

A:=Matrix1,a,a2,a,a2,a3,a2,a3,1

A:=1aa2aa2a3a2a31

(6)

GausselimA,'r','d'mod2

1aa200a000

(7)

r

2

(8)

d

0

(9)

See Also

Det, Inverse, LinearAlgebra[GaussianElimination], LinearAlgebra[Modular], mod, Modular[RowReduce]


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