On Tue, Nov 18, 2014 at 8:05 AM, Bill Page <bill.p...@newsynthesis.org> wrote:
> On 18 November 2014 09:02, David Roe <roed.m...@gmail.com> wrote:
>> On Tue, Nov 18, 2014 at 5:57 AM, Bill Page <bill.p...@newsynthesis.org>
>> wrote:
>>>
>>> > I think you are overly focused on trying to define a derivative that
>>> > reduces to the conventional derivative of non-analytic functions
>>> > over the reals.
>>>
>>> I've just been casually following this conversation, but I think it's
>>> important that the derivative of abs(x) be sign(x) not 2*sign(x) or
>>> 1/2*sign(x).
>>>
>
> What makes it important that "the" derivative of abs(x) be sign(x)?
> An important point here is that there is no one single unique
> derivative of non-analytic functions like abs, but rather than all of
> their derivatives can be expressed in terms of just two. I am
> seriously interested in reasons for retaining the status quo.
Because derivative is not just used in the context of functions of a
complex variable (whether they are analytic or not). Probably more
than 90% of Sage users don't know any complex analysis (as frequently
lamented by rtf). I will certainly acknowledge that people get things
wrong with regard to sqrt and log by not knowing about branch cuts.
But when it comes to the definition of derivative, we need to stay
consistent with the standard definition of lim_{h -> 0} (f(x + h) -
f(x))/h for functions of a real variable (or functions that many
people interpret as just functions of a real variable). Any other
decision will cause frustration for the vast majority of our users.
David
>
>>> If you use a different function, like f.wirtinger_derivative(), then
>>> it doesn't matter so much.
>>> David
>>>
>
> On 18 November 2014 10:11, kcrisman <kcris...@gmail.com> wrote:
>>
>> +1
>>
>
> Although I guess this would be consistent with the over all
> "assimilation philosophy" adopted by Sage, I am rather strongly
> against this in general. In my opinion it is in part what has lead to
> the rather confusing situation in most other computer algebra systems.
> I think rather that one should strive for the most general solution
> consistent with the mathematics. I suppose that to some extent this
> is conditioned by how the subject is taught. It came as a surprise to
> me that a solution of this problem (Wirtinger calculus or CR-calculus)
> was apparently "well-known" is some circles but considered only a
> marginal curiosity in others (if at all).
>
>> That notwithstanding, this conversation is really great to see and I hope
>> we get something that works for the usual cases in the original post
>> too!
>>
>
> Provided that one realizes its limitations I think the solution
> proposed by Vladimir V. Kisil for ginac and in more generality by
> Ondrej is quite good. I don't think a new name for this is desirable.
>
> Bill.
>
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