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Question: Define A Vector as A Tensor

Question:Define A Vector as A Tensor

Kevin Wheelock 15 Maple
define physics
October 27 2013
2

I am trying to figure out how to enter tensors using the new Physics package in 17.02. For my first, presumably simple example, I am trying to reproduce the Lorentz transformation in Special Relativity:

 

Xμ' = Λνμ Xν

where

Λνμ = [{γ, -γβ, 0, 0}, {-γβ, γ, 0, 0}, {0, 0, 1, 0}, {0, 0, 0, 1}]

Xν = [x0, x1, x2, x3]T

My Λ tensor Defines just fine; I do

Lambda[nu, `~mu`] = (Matrix(4, 4, {(1, 1) = gamma, (1, 2) = -gamma*beta, (1, 3) = 0, (1, 4) = 0, (2, 1) = -gamma*beta, (2, 2) = gamma, (2, 3) = 0, (2, 4) = 0, (3, 1) = 0, (3, 2) = 0, (3, 3) = 1, (3, 4) = 0, (4, 1) = 0, (4, 2) = 0, (4, 3) = 0, (4, 4) = 1}))

(which, upon <Enter> is labeled (1)), and then

Define((1))

and this suceeds. However, when I do the X vector:

X[`~nu`] = (Vector(4, {(1) = x0, (2) = x1, (3) = x2, (4) = x3}))

which is labeled (2), then the Define((2)) function returns the following error:

Error, (in Physics:-Define) expected right-hand-side of tensor definition as an algebraic tensorial expression, or a Matrix or an Array, representing the evaluation rule for the tensor X[`~nu`]; received: Vector(4, {(1) = x0, (2) = x1, (3) = x2, (4) = x3})

So my question is, what is the correct syntax for Defining or declaring a vector to be a tensor?

(Also, incidentally, why is the covariant (superscript) index ~nu being displayed as a subscript when Maple echoes my entry?)

Thank you,

Kevin
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