On 20 November 2014 22:08, Ondřej Čertík <ondrej.cer...@gmail.com> wrote: > On Thu, Nov 20, 2014 at 7:53 PM, Bill Page <bill.p...@newsynthesis.org> wrote: > ... >> This problem can be reduced to finding an algorithm to determine >> if f(x) is everywhere non-negative. Richardson proves that no such >> algorithm exists. > > I see. But what does this have to do with the derivative of |f(x)| that > we are trying to figure out? >
This has to do with 'conjugate' in general, not just derivatives of expressions containing 'conjugate'. The problem is that 'conjugate' is transcendental but it cannot be written in terms of log and exp. > As you pointed out, the challenge is that if you include conjugate(x), > then you might be out of luck. But aren't you out of luck already if > you have abs(x) in the expression in the first place? I.e. taking a > derivative is not going to change anything, you are still out of luck. > 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. So it would be nice to know, for example for any expression composed of x, integers, +, *, sin, and conjugate, if there is an algorithm to determine if this expression is everywhere real-valued. -- 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.
