On Wednesday, 8 September 2021 at 07:30:21 UTC-7 Simon King wrote:
>
> As I said, differentiation is not supposed to work. But I (as original
> author) don't fully understand *why* it sometimes works and how to fix
> that (by "fix", I mean "make it not work and, in the best case, suggest
> to convert to a symbolic expression").
>
> InfinitePolynomialRing was created for a very narrow purpose, namely
> computing symmetric Gröbner bases. In particular, calculus was not in
> the scope. If someone wants to extend its functionality, I wouldn't
> mind though.
>
> Hm, I wouldn't say derivatives of polynomials are "calculus".
Differentiation is perfectly valid formal algebraic operation with
well-studied properties and many applications in algebraic settings that
are not covered by "calculus". That doesn't change that the original
designer of InfinitePolynomialRing didn't put it in the scope, but I think
we can be a little more enthusiastic about potential attempts at remedying
that lack in functionality:
>From what Simon describes, differentiation in InfinitePolynomialRing only
works "by chance". The function "derivative" goes out of its way to make
sense of its arguments, mainly by putting them into SR (with variable
degree of success). This is its implementation:
try:
return f.derivative(*args, **kwds)
except AttributeError:
pass
if not isinstance(f, Expression):
f = SR(f)
return f.derivative(*args, **kwds)
so, if one would simply implement a derivative method on
infinitepolynomialring elements, then things would work.
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