akalin
Joined 19 years ago
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[ my public key: https://keybase.io/akalin; my proof: https://keybase.io/akalin/sigs/_BapYatproGRDzp2ygAPyhlpneyEYfx-wOj8t4dkBps ]
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Comment · 3 months ago
In this case, the same way I would -- calling out to SymPy.
Once you verify (with SymPy or another CAS, like Mathematica) that the given function has the claimed Jacobian determinant (which involves only taking partial derivatives and taking a determinant) and the given inputs map to the same output (which involves only evaluating polynomials with some inputs), you're done.
Comment · 1 year ago
I'm partial to Caratheodory's definition of the derivative, which avoid limits like the infinitesimal approach, but doesn't pull in all the extra baggage that come with infinitesimals (if you do it rigorously).
djb (yes, that one) has a pretty good primer on it: https://cr.yp.to/papers/calculus-19970403-retypeset20220326....