[Axiom-developer] Re: Patches

[Manuel Bronstein]

> >   wrong. I have to remember the reasons for the design, but the current
> >   formula encoded in dvdsum is the following:
> > 
> >     D(sum(f(i),i=1..b)) = sum((Df)(i),i=a..b) + f(a) Da + f(b) Db
> 
> The Axiom version has:
> 
>       D(sum(f(i),i=a..b)) = sum((Df)(i),i=a..b) - f(a) Da + f(b) Db

You're right, my typo.

> I still do not know under what conditions dvdsum applies (correctly). Do you
> mean that it applies only when Da = - and Db = 0?

I hope not only those cases, but at least those (where it is trivial).
There must have been some examples with Da or Db nonzero and where that
formula worked.

> should return an evaluated (hopefully correct) answer.
> But when a closed form is
> not available (to the current version of Axiom), the original input should be
> returned. Mathematica uses many special functions to replace summations and
> perform differentiation afterwards. Axiom is not set up to do any such things
> yet, I believe. I tried, but just like Martin had, and found it impossible to
> "hold" the differentiation operator without getting into an infinite loop.
> (Holding the summation is ok). It seems this cannot be done in combfunc.spad
> alone.

I'll give it a try, but not before ISSAC.

Best,

-- mb