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

[Richard B. Kreckel]

On 6/24/23 18:15, Vitaly Magerya wrote:
>> If a series A starts with x^n, then the series 1/A *ends*, not starts,
>> with 1/x^n.
> 
> OK, sorry, that's not corect. Let me say it differently:
> 
>      series(sin(x)-x, x, 2) == Order(x^2)
> 
> This does not mean
> 
>      1/series(sin(x)-x, x, 2) == Order(x^-2),
> 
> because
> 
>      series(1/(sin(x)-x), x, -2) == -6/x^3 + Order(x^-2)

But sin(x)-x starts with (-1/6)*x^3 which is of Order(x^3).

   -richy.