Waldek, Do you mean that 'sqrt(x^2)' is generated internally in transformation Kurt's (1), resulting in incorrect sign?
I suppose that you must have meant to write the transformation using 'sqrt(x^2)/x', i.e. 'f(sqrt(x^2))' into (1 + sqrt(x^2)/x)/2*f(x) + (1 - sqrt(x^2)/x)/2*f(-x) It looks interesting but I guess this is for real-valued x only? For complex z sqrt(z*conjugate(z))/z = exp(argument(z)) is the "complex sign". Transforming 'f(sqrt(z*conjugate(z)))' into (1 + sqrt(z*conjugate(z))/z)/2*f(z) + (1 - sqrt(z*conjugate(z))/z)/2*f(-z) (assuming conjugate existed), looks funny to me. Bill. On 26 September 2014 14:06, Waldek Hebisch <[email protected]> wrote: > > Bill Page wrote: > > > > It seems to me that algebraically any transformation that eliminates or > > adds an extra sqrt is likely incorrect. So I would say that (1) in your > > example is very suspicious. > > > > On 25 September 2014 20:04, kfp <[email protected]> wrote: > > > > > > > > Indeed. Since we get > > > > > > (1) -> normalize sqrt(1-sin(z)^2) > > > > > > z 2 > > > tan(-) - 1 > > > 2 > > > (1) ----------- > > > z 2 > > > tan(-) + 1 > > > 2 > > We have problem when roots exist in base field. That is > lone 'sqrt(x)' does not cause correctness problems. > So, as long as there are no roots in base field we can > add them. OTOH 'sqrt(x^2)' is problematic. In principle > we could transform 'f(sqrt(x^2))' into > > (1 + sqrt(x^2))/2*f(x) + (1 - sqrt(x^2))/2*f(-x) > > and then handle 'f(x)' and 'f(-x)' separately. However, > there are many places where we would need to implement > such transformation. Also this leads to ugly results. > > > -- > Waldek Hebisch > [email protected] > > -- > You received this message because you are subscribed to the Google Groups > "FriCAS - computer algebra system" group. > To unsubscribe from this group and stop receiving emails from it, send an > email to [email protected]. > To post to this group, send email to [email protected]. > Visit this group at http://groups.google.com/group/fricas-devel. > For more options, visit https://groups.google.com/d/optout. -- You received this message because you are subscribed to the Google Groups "FriCAS - computer algebra system" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To post to this group, send email to [email protected]. Visit this group at http://groups.google.com/group/fricas-devel. For more options, visit https://groups.google.com/d/optout.
