[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.

Wait.

Consider a series which terminates in Order(x^n). We don't make any 
statement about the magnitude or the sign of the constant in front of 
the Order(x^n) term. Likewise for Order(x)^n. Hence, I think the 
transformation Order(x)^n -> Order(x^n) is correct, even if n<0.

Comments or objections?

    -richard.