Bill Page wrote:
>
> I would like to include:
>
> 2) my code for adding conjugate to special functions
> http://axiom-wiki.newsynthesis.org/SandBoxFunctionalSpecialFunction
Definitions you gave are debatable. In particular
'D(conjugate(x), x) = 0' may lead to troubles. For example,
'D(conjugate(conjugate(x)), x)' should be equal to 'D(x, x) = 1'
regardless how we compute it. Consider:
y := operator 'y
D(conjugate(y(x)), x)
substituting 'conjugate(x)' for 'y(x)' and derivative of
'conjugate(x)' for derivative of 'y(x)' should give derivative
of 'conjugate(conjugate(x))'.
If what I wrote looks like nitpicking let me note that FriCAS
blindly applies rather complex transformations. For example
during integration internal form is quite different than
user input and final result. Inconsistency in derivative
rule will bring all kinds of nasty bugs.
We probably can leave derivative of 'conjugate' unevaluated.
But even that needs some thought to make sure there are
no inconsistency. Signaling error would be safe from
correctness point of view, but would significantly limit
usefulness -- code handling expressions assumes that it
can freely compute derivatives, so when dealing with
'conjugate' we would routinely get errors deep inside
library code.
--
Waldek Hebisch
[email protected]
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