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Det

inert determinant

 

Calling Sequence

Parameters

Description

Examples

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 := Matrix([[2,3,1],[3,2,3],[0,3,2]]);

A231323032

(1)

Det(A) mod 3;

2

(2)

Det(A) mod 6;

5

(3)

C := Matrix([[x-2,3,1],[3,x-2,3],[0,3,x-2]]);

Cx2313x2303x2

(4)

Det(C) mod 3;

x3+1

(5)

Charpoly(A,x) mod 3;

x3+1

(6)

alias(alpha=RootOf(x^4+x+1)): # GF(16)

A := Matrix([[1,alpha,alpha^2],
             [alpha,1,alpha],
             [alpha^2,alpha,1]] );

A1αα2α1αα2α1

(7)

Det(A) mod 2;

α

(8)

A := Matrix([[1-alpha,alpha/t,1-alpha*t],
             [1+alpha,alpha*t,1+alpha*t],
             [alpha, 1-alpha/t, alpha*t]]) ;

A1ααtαt+11+ααtαt+1α1αtαt

(9)

collect( Det(A) mod 2, t );

α2t2+α2t+α2+α2t

(10)

See Also

Charpoly

LinearAlgebra[Determinant]

LinearAlgebra[Modular]

mod

modp1

Modular[Determinant]