Gausselim
inert Gaussian elimination
Gaussjord
inert Gauss Jordan elimination
Calling Sequence
Parameters
Description
Examples
Gausselim(A) mod p
Gaussjord(A) mod p
Gausselim(A, 'r', 'd') mod p
Gaussjord(A, 'r', 'd') mod p
A
-
Matrix
'r'
(optional) for returning the rank of A
'd'
(optional) for returning the determinant of A
'p'
an integer, the modulus
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 m≤n 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].
A≔Matrix1,2,3,1,3,0,1,4,3
A≔123130143
GausselimAmod5
123012001
B≔ArrayToolsConcatenate2,A,LinearAlgebraIdentityMatrix3
B≔123100130010143001
GaussjordBmod5
100411010203001131
InverseAmod5
411203131
aliasa=RootOfx4+x+1mod2:
A≔Matrix1,a,a2,a,a2,a3,a2,a3,1
A≔1aa2aa2a3a2a31
GausselimA,r,dmod2
1aa200a000
r
2
d
0
See Also
Det
Inverse
LinearAlgebra[GaussianElimination]
LinearAlgebra[Modular]
mod
Modular[RowReduce]
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