On Wed, Nov 19, 2014 at 9:42 AM, Ondřej Čertík <ondrej.cer...@gmail.com> wrote:
> On Wed, Nov 19, 2014 at 9:32 AM, Bill Page <bill.p...@newsynthesis.org> wrote:
>> OK, this looks better!
>>
>> (1) -> D(abs(x),x)
>>
>>          _
>>          x + x
>>    (1)  -------
>>         2abs(x)
>>                                                     Type:
>> Expression(Integer)
>> (2) -> D(conjugate(x),y)
>>
>>    (2)  0
>>                                                     Type:
>> Expression(Integer)
>> (3) -> D(conjugate(x),x)
>>
>>    (3)  1
>>                                                     Type:
>> Expression(Integer)
>> (4) -> f:=operator 'f
>>
>>    (4)  f
>>                                                           Type:
>> BasicOperator
>> (5) -> D(abs(f(x)),x)
>>
>>              , _      _  ,
>>         f(x)f (x) + f(x)f (x)
>>
>>    (5)  ---------------------
>>               2abs(f(x))
>>                                                     Type:
>> Expression(Integer)
>> (6) -> D(abs(log(x)),x)
>>
>>         _    _
>>         xlog(x) + x log(x)
>>    (6)  ------------------
>>             _
>>           2xxabs(log(x))
>>                                                     Type:
>> Expression(Integer)
>
> That looks good, right? What about arg(z). What are the Wirtinger
> derivatives of arg(z)? Do you have other examples of non-analytic
> functions?
>
> Would you mind posting your patch to FriCAS somewhere? I would be
> interested in how you implemented it.

I'll try to compile FriCAS myself and apply your patch, so that I can
play with it. Can you also try:

abs(I*x)

1/abs(x)
1/abs(x)^2
x/abs(x)^3
abs(x)^2

The x/abs(x)^3 is a Coulomb's law in 1D.

Ondrej

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