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Det - inert determinant

Calling Sequence

Det(A)

Parameters

A

-

Matrix

Description

• 

The Det function is a placeholder for representing the determinant of the matrix A.  It is used in conjunction with mod and modp1 which define the coefficient domain as described below.

• 

The call DetAmodm computes the determinant of the matrix Amodm in characteristic m which may not not be prime.  The entries in A may be integers, rationals, polynomials, or in general, rational functions in parameters over a finite field.

• 

The call modp1DetA,p computes the determinant of the matrix Amodp where p is a prime integer and the entries of A are modp1 polynomials using fraction-free Gaussian elimination.

Examples

A:=Matrix2,3,1,3,2,3,0,3,2

A:=231323032

(1)

DetAmod3

2

(2)

DetAmod6

5

(3)

C:=Matrixx2,3,1,3,x2,3,0,3,x2

C:=x2313x2303x2

(4)

DetCmod3

x3+1

(5)

CharpolyA,xmod3

x3+1

(6)

aliasα=RootOfx4+x+1:

A:=Matrix1,α,α2,α,1,α,α2,α,1

A:=1αα2α1αα2α1

(7)

DetAmod2

α

(8)

A:=Matrix1α,αt,1αt,1+α,αt,1+αt,α,1αt,αt

A:=1ααtαt+11+ααtαt+1α1αtαt

(9)

collectDetAmod2,t

α2t2+α2t+α2+α2t

(10)

See Also

Charpoly, LinearAlgebra[Determinant], LinearAlgebra[Modular], mod, modp1, Modular[Determinant]


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