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Inverse - inert matrix inverse

Calling Sequence

Inverse(A) mod n

Parameters

A

-

Matrix

n

-

integer, the modulus

Description

• 

The Inverse function is a placeholder for representing the inverse of a square matrix A.

• 

The call Inverse(A) mod n computes the inverse of the square matrix A over a finite ring of characteristic n. 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 RootOf's.

Examples

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

A:=123130143

(1)

B:=InverseAmod5

B:=411203131

(2)

`~`ExpandA.Bmod5

100010001

(3)

The matrix A is singular mod 2:

InverseAmod2

Error, (in mod/Inverse) singular matrix

aliasa=RootOfx4+x+1mod2:

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

A:=1aa21a211a3a2

(4)

B:=InverseAmod2

B:=a2+aa3+aa3+a2+1a3+a20a3+a2a+1a3+a+1a3

(5)

`~`ExpandA.Bmod2

100010001

(6)

See Also

Det, Gaussjord, LinearAlgebra[MatrixInverse], LinearAlgebra[Modular], LinearAlgebra[Modular][Inverse], Linsolve, mod


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