[GiNaC-list] series((x+x^2)^2,x,0) is broken

[Richard B. Kreckel]

On 6/23/23 12:28, Vitaly Magerya wrote:
>> For one thing, I suppose that the Order(x) function is missing a power
>> evaluation of the kind Order(x)^e -> Order(x^e). Does this sound right?
> 
> Thanks for looking into this.
> 
> The substitution above is not correct if e<0. For example:
> 
>      x = Order(1/A) => |x| <= Const * 1/A
> 
> but
> 
>      x = 1/Order(A) => |x| >= 1 / (Const * A)
> 
> so
> 
>      Order(1/A) =/= 1/Order(A)
> 
> It is correct for non-negative integer e though.

Right. Thanks for pointing this out!

>> The attached patch adds this. It solves some of your problems but not
>> all. It doesn't seem to introduce regressions. Can you test this, please?
> 
> I guess
> 
>      ginsh> series((x+x^2)^2,x,0);
>      Order(x^(-2))
> 
> is preferable to
> 
>      (Order(1)^2)*x^(-2)+Order(1)
> 
> but it is still incorrect and not that helpful: I'm asking for
> the expansion up to x^0, not x^-2.

That's right. The implementation in pseries::power_const(p, deg) does 
not pay proper attention to loop boundaries. That should be reworked.

This is also the cause why series((x+x^2)^2,x,42) returns an Order(x^42) 
term which it should not.

If you want to take a look, go ahead. I don't know if I'll find the time 
soon.

> On a bit of a tangential topic: I think the fact that Order(x^0)
> is simplified to Order(1) is a bad design choice, because the
> variable in which the expansion was made is lost. This leads to
> all kinds of special cases if one wants to work with series;
> e.g.
> 
>      Order(x^n)*x can be simplified to Order(x^(n+1)),
> 
> but
> 
>      Order(1)*x can no longer be Order(x).
> 
> Similarly,
> 
>      Order(x) + Order(x^2) = Order(x),
> 
> but
> 
>      Order(1) + Order(x) =/= Order(1),
> 
> because Order(1) could have been Order(othervar^0).
> 
> I'd much rather have Order() to have the variable and the exponent
> separately, i.e. Order(x, 0) instead of Order(1). This is a
> separate question though.

Hmmm.

   -richy.
-- 
Richard B. Kreckel
<https://in.terlu.de/~kreckel/>