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I'm trying to calculate covariant derivatives of tensor fields in SageMath, I established the metric connection using g.connection(). But I cannot find any specific method to calculate the covariant derivatives unlike Lie derivative which is an inbuilt method. I looked up documentations and I found that I have to apply the connection (which is just the christoffel symbol) to the tensor field to calculate its covariant derivative. Is that the correct way or is there an inbuilt method that I'm missing? I tried diff() to calculate partial derivative of a tensor defined on a chart on a manifold but it is not working.

So ultimately I want to know the correct method to calculate partial and covariant derivatives of vector fields and tensors on a manifold. Please let me know. Thanks in advance for responding!

I'm trying to calculate covariant derivatives of tensor fields in SageMath, I established the metric connection using g.connection(). But I cannot find any specific method to calculate the covariant derivatives unlike Lie derivative which is an inbuilt method. I looked up documentations and I found that I have to apply the connection (which is just the christoffel symbol) to the tensor field to calculate its covariant derivative. Is that the correct way or is there an inbuilt method that I'm missing? I tried diff() to calculate partial derivative of a tensor defined on a chart on a manifold but it is not working.

So ultimately I want to know the correct method to calculate partial and covariant derivatives of vector fields and tensors on a manifold. Please let me know. Thanks in advance for responding!

I'm trying to calculate covariant derivatives of tensor fields in SageMath, I established the metric connection using g.connection(). But I cannot find any specific method to calculate the covariant derivatives unlike Lie derivative which is an inbuilt method. I looked up documentations and I found that I have to apply the connection (which is just the christoffel symbol) to the tensor field to calculate its covariant derivative. Is that the correct way or is there an inbuilt method that I'm missing? I tried diff() to calculate partial derivative of a tensor defined on a chart on a manifold but it is not working.

So ultimately I want to know the correct method to calculate partial and covariant derivatives of vector fields and tensors on a manifold.

On a related note, I want to know how to save a tensor quantity which I transformed from one coord to another using Tensor.display_comp(chart=differentOne). This method seems to take the original and just display the terms in a different coord system, how do I save the transformed one as a different tensor defined on the differentOnechart?

Please let me know. Thanks in advance for responding!