Does SymPy have any builtin functionality for expressive derivatives w.r.t.
vectors and matrices as vector and matrix operations?
By "derivative w.r.t. a vector" I mean a vector of derivatives w.r.t. each
element. The reason for treating these derivatives differently that just a
vector of derivatives is that derivatives w.r.t. a vector often can be more
naturally and conveniently expressed as operations on vectors rather than
operations on individual elements. The same applies for matrices.
As a simple example of what I'm after:
|v| indicates the common Cartesian norm of a vector v
x1 and x2 are points in Cartesian space
I want the derivative of |x1 - x2| w.r.t. x1 to evaluate to (x1 -
x2)/|x1 - x2|.
If this functionality isn't builtin, is there a suggested way to
approximate or implement it?
>From searching the archives, it looks like this topic has been discussed
and is an area being developed but I can't find any posts from within the
last year.
I'm not a mathematician or physicist so I may be misusing terminology.
Please go ahead and ask for clarification if my intent is unclear. In
particular, I don't know if I should be using the word "gradient" here. In
the cases I'm familiar with, "gradient" is used in regards to functions of
a single vector. What I'm trying to describe here applies to functions of
multiple vectors.
Thanks.
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