Re: [Reduce-algebra-developers] taylor and sqrt of full squares

[Andrey I. <and...@ma...>]

Alan Barnes wrote:
> I note that using alternative power-series package tps, one gets:
> 
> 1: ps(sqrt((x-y)^2), z,0);
> 
> |x - y|
> 
> which is an improvement, but of course this is only correct if x-y is real. However, after
> 
> on precise_complex;
> 
> both power-series packages produce (sqrt(x^2-2x*y+y^2) as the first term which is correct, but somewhat messy if x-y is real .

I find that

1: on precise_complex;

sometimes works

2: taylor(sqrt((1-z)^2), s, 0, 1);
             2       2
sqrt((z - 1) ) + O(s )

and provide a desired workaround

3: taylor(sqrt((1-z)^2), s, 0, 1) where {sqrt((1-z)^2)=>1-z};
               2
  - z + 1 + O(s )

Strangely, however, it fails in a more realistic example

4: taylor(sqrt((1-z)*(1-s*z)), s, 1, 0);

z - 1 + O(s - 1)

ps, nevertheless, continues to work

5: pstruncate(ps(sqrt((1-z)*(1-s*z)), s, 1), 0) where {sqrt((1-z)^2)=>1-z};

  - z + 1

Best regards,
Andrey