Det
inert determinant
Calling Sequence
Parameters
Description
Examples
Det(A)
A
-
Matrix
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.
A≔Matrix2,3,1,3,2,3,0,3,2
A≔231323032
DetAmod3
2
DetAmod6
5
C≔Matrixx−2,3,1,3,x−2,3,0,3,x−2
C≔x−2313x−2303x−2
DetCmod3
x3+1
CharpolyA,xmod3
aliasα=RootOfx4+x+1:
A≔Matrix1,α,α2,α,1,α,α2,α,1
A≔1αα2α1αα2α1
DetAmod2
α
A≔Matrix1−α,αt,1−αt,1+α,αt,1+αt,α,1−αt,αt
A≔1−ααt−αt+11+ααtαt+1α1−αtαt
collectDetAmod2,t
α2t2+α2t+α2+α2t
See Also
Charpoly
LinearAlgebra[Determinant]
LinearAlgebra[Modular]
mod
modp1
Modular[Determinant]
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