On Thu, Aug 29, 2019 at 6:02 AM Chris Smith <[email protected]> wrote: > > Currently it returns NotImplemented. Were you thinking EmptySet returns (oo, > -oo) for (inf, sup)?
Yes, I noticed that it gives NotImplementedError, but the mathematically correct result for it is oo for inf and -oo for sup. See for instance https://en.wikipedia.org/wiki/Lattice_(order) (search for "emtpy set"). In a lattice, join is the supremum and meet is the infimum. The lattice in this case would be the real numbers union -oo and oo, which is a complete lattice. > > In any case, it is not only inf and sup that are problems for a symbolic > range. The problem of how to represent a slice or indexed element of the > range is also present, e.g. `Range(x,y,z)[0]` is not `x` unless the range is > not empty...and if it is empty then accessing `[0]` would generate an error. I'm not sure here. If we don't make any assumptions, then slicing cannot be allowed in any range with symbolic parameters, except in certain cases like Range(x, x + 10). Which means it wouldn't be very useful. But I'm not really sure if it's something that you'd want to use. Aaron Meurer > > On Tuesday, August 27, 2019 at 10:56:21 AM UTC-5, Aaron Meurer wrote: >> >> I think it's reasonable to return the result. I noticed that >> Interval.inf just returns the lower limit, even though Interval can >> also technically return an empty set. Actually, the infimum of the >> empty set is infinity, not nan, so if that's the concern, we can >> include that in the Piecewise result. >> >> Aaron Meurer >> >> On Mon, Aug 26, 2019 at 6:29 PM Chris Smith <[email protected]> wrote: >> > >> > Ok, that is a detail that can be changed. But the bigger question is >> > whether we want such an expression to be returned or if we just want to >> > forbid it and raise an error if a non-Piecewise result cannot be returned. >> > >> > On Monday, August 26, 2019 at 4:22:13 PM UTC-5, Aaron Meurer wrote: >> >> >> >> I would structure the Piecewise so that there is no True (otherwise) >> >> condition, and the empty set cases fall under that. I think Piecewise >> >> already gives nan in such cases. >> >> >> >> This is also somewhat related to >> >> https://github.com/sympy/sympy/issues/16362. >> >> >> >> Aaron Meurer >> >> >> >> On Mon, Aug 26, 2019 at 1:57 PM Chris Smith <[email protected]> wrote: >> >> > >> >> > In this PR `Range` has been modified to accept symbolic start, stop and >> >> > step values, e.g. `Range(x, y, z)`. One of the decisions that needs to >> >> > be made is whether such Ranges should return the symbolic logical >> >> > statement corresponding to a given attribute or not. >> >> > >> >> > e.g. the piecewise-folded version of `Range(x, y, z).inf` is >> >> > >> >> > Piecewise( >> >> > (nan, ceiling((-x + y)/z) <= 0), >> >> > (x, z > 0), >> >> > (x + z*ceiling((-x + y)/z) - z, Ne(x, x + 1)), >> >> > (y - z, True)) >> >> > >> >> > The problem is that the nan result is really not the inf...it is used >> >> > to indicate that inf is not defined under conditions that would lead to >> >> > an EmptySet, e.g. x=z=1,y=0. Is this of any value or should Range with >> >> > symbols just raise a ValueError if a property cannot be given as a >> >> > simple expression? >> >> > >> >> > /c >> >> > >> >> > -- >> >> > You received this message because you are subscribed to the Google >> >> > Groups "sympy" group. >> >> > To unsubscribe from this group and stop receiving emails from it, send >> >> > an email to [email protected]. >> >> > To view this discussion on the web visit >> >> > https://groups.google.com/d/msgid/sympy/6dc89b8f-cf15-4d9e-861c-1ad267df7955%40googlegroups.com. >> > >> > -- >> > You received this message because you are subscribed to the Google Groups >> > "sympy" group. >> > To unsubscribe from this group and stop receiving emails from it, send an >> > email to [email protected]. >> > To view this discussion on the web visit >> > https://groups.google.com/d/msgid/sympy/95f2dab1-446c-4196-9363-b51de7ed44e1%40googlegroups.com. > > -- > You received this message because you are subscribed to the Google Groups > "sympy" group. > To unsubscribe from this group and stop receiving emails from it, send an > email to [email protected]. > To view this discussion on the web visit > https://groups.google.com/d/msgid/sympy/dc79e5a0-a782-42f2-8220-e110191e2b5f%40googlegroups.com. -- You received this message because you are subscribed to the Google Groups "sympy" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To view this discussion on the web visit https://groups.google.com/d/msgid/sympy/CAKgW%3D6%2Bin6-n9kdavNLAU6OY%3DhwyBJAVz%2B0d6R1x-pyP9inYSQ%40mail.gmail.com.
