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

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.