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Solving System of Equations that are made up of variables

I have a few questions as to how to write some parts of this code. Say I chose, n=1 Then it creates two vectors ...
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Linearised Einstein equations

I need to compute the linearised Einstein Equations around a fixed metric $g_{μν}=\text{Minkowski metric} + h_{μν}$, which is not the flat metric. Does anyone know a Mathematica package or a review ...
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step by step interactive indefinite integral

WolframAlpha can give step by step solution for indefinite integral. There seems to be similar question but for derivatives. Is there a way that I can generate my own step by step solution for ...