2024-01-03 10:32:56 +0200 | received badge | ● Popular Question (source) |
2019-09-28 20:21:05 +0200 | commented answer | Transformation of derivative under a change of chart Thanks, but this is not exactly what I want. From what I can understand, this option gives the same result, except that the notation is a bit more awkward. What I want is to transform the nabla that contain derivative wrt x y z to an expression for nabla with derivatives wrt lambda theta and r. I do not want derivative with respect to complicated expression like $\dfrac{\partial (...) }{\partial ( r \sin \theta)}$. In theory, this could be done using the standard transformation rule for partial derivative , i.e something of the form $$ \frac{\partial }{\partial \tilde{x}^i} = \frac{\partial x^j}{\partial \tilde{x}^i } \frac{\partial }{\partial x_j} $$ Is there something equivalent in sage for the transformation of connection coefficient ? |
2019-09-27 21:21:47 +0200 | received badge | ● Editor (source) |
2019-09-27 21:19:19 +0200 | asked a question | Transformation of derivative under a change of chart Consider the following code. When it display the connection coefficient in the Y frame at the end, we obtain derivative expressions that are quite complicated (for example derivative with respect to "r sin(\theta)". I would rather expect simpler expressions containing derivatives with respect to \lambda, \theta or r alone. Like what I would obtain by applying the "textbook" transformation rules for the partial derivatives. |
2019-09-27 21:05:26 +0200 | commented answer | Display connection coefficients under a change of chart Thanks a lot. I also applied your patch and the computation is much faster. I have a question on the results, but I will ask separately. |
2019-09-27 20:58:28 +0200 | received badge | ● Scholar (source) |
2019-09-27 17:04:08 +0200 | received badge | ● Student (source) |
2019-09-26 22:45:49 +0200 | asked a question | Display connection coefficients under a change of chart I want to define the connection components as the derivative of a scalar field in one frame and calculate their values in another frame. Then show that the coefficients are good in the X_U chart, but the change of coordinate fail What is wrong ? |