Re: [Axiom-math] Curious behavior of Taylor series

[Ralf Hemmecke]

> > Let's abbreviate U := UnivariateTaylorSeries(Expression Integer,x,0) and
> > E := Expression(Integer).
> >
> > That's what Axiom does. It tries to coerce to U, there is no such coerce
> > function. 
>
> But x::U works just fine.

Try the same thing in a .spad file and the compiler will complain. 
(Better use a .as file and compile with Aldor. I cannot say much about 
SPAD, since I don't know for sure.)

x::U on a command line is given to the interpreter. The interpreter 
tries to be smart and tries hard to find a way to achieve what it 
believes you meant.

> > Then maybe after checking some other coerce functions that
> > fail, it finds a coercion to Expression(Integer), furthermore there is
> > function *: (E, U) -> U. So Axiom does a minimal thing: it interprets

> > x*y as (x::E)*y

> > note that the coercion to U would go like

> > (x::E::U) * y

> So x::U is equivalent to x::E::U?

I cannot say for sure. Some other Axiom gurus know how to ask axiom what 
exact function call the interpreter actually finds. I don't. Keep 
waiting or write to the axiom-developer mailing list. I am sure someone 
is listening.

> > and would then be more costly. You surely also consider that
> > unreasonable to go the long way if there is a shorter path. No?

> I'm just wondering why it doesn't try x::U right off.

Maybe it does. But as I said. There is no function coerce: Symbol->U.
So it fails and has to look for something else.

> I'm getting the (probably wrong) impression that it looks at x::U,
> decides that that's too long, then goes for x::E.  I would think that
> deciding x::U is too long would be too long.

Try to write an interpreter then you (maybe) appreciate what it 
currently does and have some mercy with it. ;-)

Ralf