Michael Xue wrote:
> Michel Talon <talon <at> lpthe.jussieu.fr> writes:
>
>>
>> It seems there is a problem here:
>>
>> niobe% maxima
>> (%i1) depends(f,[x,y])$
>>
>> (%i2) depends(y,x)$
>>
>> (%i3) diff(f);
>> df df dy df
>> (%o3) -- del(y) + (-- -- + --) del(x)
>> dy dy dx dx
>> (%i4)
>>
>
> try:
>
> depends(f, [x,y])$
> depends(y,x)$
> diff(f,x);
>
> - Michael Xue
Sorry but this is not the point. Answer should be either
df/dy del y + df/dx del x
according to maxima doc ( del x and del y are not further expanded) or
(df/dy dy/dx + df/dx) del x
according to sane mathematical rules. Both are correct since
the first reduces to the second when expanding del y.
On the contrary maxima result is hard to justify. If instead of
depends(y,x) there was
depends(y,[x,z]) then a correct rule looking a little bit like the above
would be:
(df/dy dy/dz) del z + (df/dy dy/dx + df/dx) del x
and with a lot of hand waving one could justify maxima result by replacing
(dy/dz) del z = del y.
--
Michel Talon