On May 31, 10:55 pm, Carl Witty <[EMAIL PROTECTED]> wrote: > Actually, there's no homomorphism either way; > RR(R2(2)+R2(3)) != RR(R2(2)) + RR(R2(3))
Hm, thats an argument. I somehow thought that it is closer to a homomorphism but perhaps this reasoning has no base. > IMHO, giving a+b the precision of the less-precise operand is better > than using the more-precise operand, because the latter has too much > chance of confusing people who don't understand floating point. For > instance, if 1.3+RealField(500)(pi) gave a 500-bit number, I'll bet a > lot of people would assume that this number matched 13/10+pi to almost > 500 bits. Hm, yes, but this binary decimal conversion is another topic, I mean nobody would assume that 0.3333333 coerced to 500 *decimal* digits matches 1/3 to 500 digits? I anyway wondered why one can not specify a base in RealField, or did I merely overlook the opportunity? > Of course, maybe there are other choices that are better than either > of these. We could throw away RealField and always use > RealIntervalField instead; but that's slower, has less special > functions implemented, and has counterintuitive semantics for > comparisons. We could do pseudo-interval arithmetic, and say that > 1e6+R2(3) should be a 20-bit number, because we know about 20 bits of > the answer; but to be consistent, we should do similar psuedo-interval > arithmetic even if both operands are the same precision, At least RR would then be a ring ;) > and then RR > becomes less useful for people who do understand how floating point > works and want to take advantage of it. Ya, I dont want to change floating point, it just seems somewhat arbitrary to me to coerce down precision, while coercing up precision with integers. Of course if you consider integer with precision infinity (as indeed there are no rounding errors and it is an exact ring) then this makes sense again. But if so then I want to have something like SymbolicNumber which is the subset of SymbolicRing that does not contain variables. And that this SymbolicNumber is coerced automatically down when used with RealField. --~--~---------~--~----~------------~-------~--~----~ To post to this group, send email to sage-devel@googlegroups.com To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/sage-devel URLs: http://www.sagemath.org -~----------~----~----~----~------~----~------~--~---
