# Question:Physics package Determinant

## Question:Physics package Determinant

Maple 2018

Hello,

I have installed the Physics Package with:

PackageTools:-Install("5137472255164416", version = 329, overwrite)

I have a question about the calculation of the Tensor determinant:

I use two ways to calculate the determinant of the same matrix:

The first with Physics package and the second with LinearAlgebra Package:

It is easy to calculate analytically the result it is : -1

But Physics Package gives : +1 and LinearAlgebra gives: -1

My question is why I found +1 with Physics Package : What I doing wrong ?.

Please find my source hereafter:

**************************************************

restart

with(Physics)

Setup(coordinates = {X = [t, x, y, z]}, dimension = 4, metric = {(1, 1) = 1, (2, 2) = -1, (3, 3) = -1, (4, 4) = -1}, signature = `+---`, mathematicalnotation = true)

Define(H[mu, nu] = Matrix(4, {(1, 1) = 1+h, (1, 2) = h, (2, 2) = -1+h, (3, 3) = -1, (4, 4) = -1}, shape = symmetric))

H[]

H[determinant]

with(LinearAlgebra)

B := Matrix(4, {(1, 1) = 1+h, (1, 2) = h, (2, 2) = -1+h, (3, 3) = -1, (4, 4) = -1}, shape = symmetric)

Determinant(B)

***************************************

Thanks for your answer,

Sincerely yours

Xavier

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