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Refine category of ScalarField #31883
Comments
comment:1
Unfortunately, trying to make
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Author: Matthias Koeppe |
Commit: |
comment:3
Anyway, here is a simple solution New commits:
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comment:4
Green bot => positive review. |
Reviewer: Travis Scrimshaw |
comment:5
The one in |
Branch pushed to git repo; I updated commit sha1. New commits:
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comment:7
The failing doctest in |
comment:8
Thanks. |
comment:9
Thank you! |
comment:10
I agree with the code added in this ticket, but let me seize the opportunity to point out some current inconsistency in the manifold set up, which is due to the lack of a proper real field in Sage (cf. #24456):
Of course, from a pure mathematical side, 1 and 2 should be identical. The basic reason for 1 is The basic reason for 2 is to naturally allow for algebra operations like If #24456 converges some day, both 1 and 2 should be set to the real field object that will emerge from it. Meanwhile, we have
With the
which is nice, but
Moreover, for images of scalar fields, we have
but this holds only because
Finally, it's worth to stress that in practice, the inconsistency 1 <-> 2 is a rather mild one: to my knowledge, it has never triggered any error nor yield any false result in actual computations on manifolds (apart from the trivial |
comment:11
Thanks a lot for sharing these insights! |
Changed branch from u/mkoeppe/refine_category_of_scalarfield to |
A
ScalarField
on a topological manifold is supposed to be a continuous map -- but this is not reflected by the category of its parent.CC: @egourgoulhon @tscrim @mjungmath
Component: manifolds
Author: Matthias Koeppe
Branch/Commit:
cd3ca79
Reviewer: Travis Scrimshaw
Issue created by migration from https://trac.sagemath.org/ticket/31883
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