I would like to formally prove the hairy ball theorem in Mathematica, initially just for $S^2$, and then see about generalizing. An approach I thought about to use the xAct package to define $S^2$ ...
I am new to xAct packages and I'm having some problems to compute tensor quantities with xCoba. I defined a manifold and a metric. I computed All quantities of ...
I am seeking a convenient and effective way to calculate such geometric quantities. I've used packages like TensoriaCalc, but they don't work at all time. ...