sage.tensor.modules: Add backends using TensorFlow Core, PyTorch, SymPy

[mkoeppe]

Tensors from sage.tensor are stored as sage.tensor.modules.Components, which is a dictionary with index tuples as keys.

We propose to create additional backends for numerical coordinate rings:

• https://www.tensorflow.org/guide/tensor
• https://pytorch.org/docs/stable/tensors.html

They provide efficient storage and GPU-accelerated computations for numerical tensors.

For SymPy, see #31946

CC: @egourgoulhon

Component: linear algebra

Issue created by migration from https://trac.sagemath.org/ticket/30096

[mkoeppe]

comment:2

Setting new milestone based on a cursory review of ticket status, priority, and last modification date.

[mkoeppe]

Description changed:

--- 
+++ 
@@ -1,9 +1,10 @@
 Tensors from `sage.tensor` are stored as `sage.tensor.modules.Components`, which is a dictionary with index tuples as keys.

-We propose to create additional backends.
+We propose to create additional backends for numerical coordinate rings:
 - https://www.tensorflow.org/guide/tensor
 - https://pytorch.org/docs/stable/tensors.html

-They provide efficient storage and GPU-accelerated computations.
+They provide efficient storage and GPU-accelerated computations for numerical tensors.

+For SymPy, see #31946

[hyperactivecoder]

@mkoeppe, can you please let us know more about this? Do we just have to implement all the function in Component class in Pytorch / Tensorflow? What i am understanding is we have to impliment symbolic expressions in tensors, am i mistaken?

[mkoeppe]

The tensors in Sage can be defined with different element types (this is what is called a "base ring" in Sage).

When talking about using Pytorch or Tensorflow as the backend, the most natural thing to consider is the element type being a floating-point number of some precision / format.

When talking about SymPy as the backend, the most natural thing to consider is symbolic expressions.