A workaround and general principle: if at all possible, avoid using the "symbolic ring", particularly if you're interested in numerical approximations anyway. Having all the overhead of SR involved will show down your computation considerably -- and, as you can see, can lead to unstable numerical schemes.
In your case, the symbolic ring gets involved by mentioning "pi". You could do instead RR = RealField(100) #by default this is 53, which is fine too (-12.0*RR.pii()).exp() #sage has "float literals" which deals with the precision ambiguity in this notation A little more mathematical-looking notation: exp(-12.0 * RR.pi() ) exp(-12.0 * RR(pi)) # this still involves SR, but only minimally Evaluating this expression should of course just work with pretty much any precision: exp is very well approximated. Rewriting it as a difference of hyperbolic functions is just obviously a bad idea. The reason why the SR takes such bad decisions may be deeper and more difficult to change. So I think it's a bug, but it may not be easily fixable. So: stick with the workaround (which will always be more efficient) On Sunday, 4 July 2021 at 23:04:44 UTC-7 Brian Lawrence wrote: > > Hi, > > I'm new to Sage, and I'm running across some unexpected behavior involving > numerical evaluation of exponentials involving pi. > > In my version (Sagemath 9.2), the following code > exp(-12.0*pi).n() > gives the output below. > 0.000000000000000 > > The true value of the exponential is something like 4e-17: very small, but > definitely not zero. The problem seems to be that Sage internally converts > the exponential to a difference (cosh-sinh) of two huge numbers, and then > precision problems kick in. > > This problem has been brought up before... > https://ask.sagemath.org/question/57182/numerical- > approximation-error-involving-cosh-and-sinh/ > ... but the folks over there seem to have concluded (for reasons I don't > understand) that the behavior is not a bug at all. > > Brian Lawrence > > 'SageMath version 9.2, Release Date: 2020-10-24' > > (P.S. I ran across this trying to do some computations with q-expansions > of modular forms, where these sorts of exponentials are quite common.) > > (P.P.S. Apologies if I'm posting this in the wrong place, I'm new here and > not familiar with local norms...) > -- 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 view this discussion on the web visit https://groups.google.com/d/msgid/sage-devel/aafa3344-60f6-4e0a-bfcd-59074ce15844n%40googlegroups.com.
