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

[Vitaly Magerya]

On 24/06/2023, Richard B. Kreckel <kreckel at in.terlu.de> wrote:
>> 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?

If a series A starts with x^n, then the series 1/A *ends*, not starts,
with 1/x^n.