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# Question:How to define and evaluate a function of two tensors in Maple?

## Question:How to define and evaluate a function of two tensors in Maple?

Maple

I am working with the de Sitter metric which takes the form

$$g=\tau^{-2}\left(-\left(\Lambda / 3-\tau^{2}\right)^{-1} d \tau^{2}+\left(\Lambda / 3-\tau^{2}\right) d t^{2}+g_{\mathbb{S}^{2}}\right)$$

or

g := evalDG((-d&tau; &t d&tau;/(Lambda/3 - tau^2) + (Lambda/3 - tau^2)*(dt &t dt) + (dtheta &t dtheta) + sin(theta)^2*(dphi &t dphi))/tau^2)

in the co-ordinates $\{\tau, t, \theta, \phi\}.$

or

DGsetup([tau, t, theta, phi], M1, verbose)

Define

F := evalDG(-Q*(d&tau; &t dt) + Q*(dt &t d&tau;))

Then I want to define the following function which takes a two tensor (metric) and returns a two tensor as well.

Here \dot(g) is the input tensor, F is the two tensor defined above and the g is the de Sitter metric.

I want to evaluate this expression of \dot{g} = d tau^2/tau^2 and other metrics. How can I do this in Maple?

Any help will be much appreciated.

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