On 21 November 2014 at 20:18, Ondřej Čertík <ondrej.cer...@gmail.com> wrote: > On Fri, Nov 21, 2014 at 9:37 AM, Bill Page <bill.p...@newsynthesis.org> wrote: >> >> You are right about the derivative. But my limited understanding >> is that the strategy is not to avoid 'abs(x)' but rather to avoid 'sin'. >> We cannot similarly avoid 'conjugate' and in general the effect >> of including 'conjugate' is apparently unknown. But one effect >> of including 'conjugate' is that we can have expressions like >> >> x+conjugate(x) >> >> which is necessarily real-valued, rather like 'abs(x)' for x >> real-valued is non-negative. > ...
On reconsidering "my limited understanding" I see that contrary to what I said, rewriting sin(x) = 2*tan(x/2)/(tan(x/2)^2+1) does not avoid Richardson's theorem. Rather I think what is really going on in FriCAS is rewriting abs(x) = sqrt(x^2) or in my case abs(x) = sqrt(x*conjugate(x)) taking 'sqrt' as "algebraic", i.e. the solution to y^2 = x, without selecting a specific branch. Bill. -- You received this message because you are subscribed to the Google Groups "sage-devel" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To post to this group, send email to sage-devel@googlegroups.com. Visit this group at http://groups.google.com/group/sage-devel. For more options, visit https://groups.google.com/d/optout.
