Imho there are (at least) two ways of thinking about this. One consistent way is the following:
Let c, d be "extended numbers" (reals, complexes, oo, zoo, etc). Let f(x,y) be any function of two "ordinary numbers". We define f(c,d) = e if for all expressions e1, e2 such that limit(e1) = c, limit(e2) = d we have limit(f(e1, e2)) = e. We define f(c,d) = nan if there exist expressions e1, e2, e3, e4 with limit(e1) = c, limit(e2) = c, limit(e3) = d, limit(e4) = d and limit(f(e1, e3)) != limit(f(e2, e4)). [It is understood here that all limits are of the same kind, e.g. all as x->0 in C or all es x->oo in R, or whatever.] In particular then for f(x,y) = x - y, it follows that zoo-zoo = nan, since e1=z, e2=z, e3=z+1, e4=z have the desired properties. A slightly less ad-hoc way of thinking about this is using filters, c.f. the wiki [1]. Actually I think that no matter what the "high-powered" definition is going to be, the first property I described should be whenever the result is not nan. Obviously not more involved in sympy than you are, I'm just reporting what I have caught up, hence take my words with a (big) grain of salt :-). [1] https://github.com/sympy/sympy/wiki/Infinities-and-Singularities On 18 Apr., 17:33, Saptarshi Mandal <[email protected]> wrote: > I am just having difficulty wrapping my head around zoo - zoo. Complex > infinity should be unsigned. And even if you did write something like > this should this be nan or zoo? > > Otoh, since zoo - zoo doesnt make sense, S.NaN should actually be the > correct answer. Can someone more knowledgeable about this enlighten > me? > > On Apr 18, 4:36 pm, "Alexey U. Gudchenko" <[email protected]> wrote: > > > 18.04.2011 08:20, smichr пишет: > > > > Does zoo absorb everything in an addition or multiplication (except > > > maybe oo or another zoo)? > > > It is related with this old > > issue:http://code.google.com/p/sympy/issues/detail?id=360 > > > And with this open pull > > request:https://github.com/sympy/sympy/pull/173/files > > > E.g. Those assertions have quit right behavior: > > > assert zoo == zoo > > assert zoo != oo > > assert 1*zoo == zoo > > assert 2*zoo == zoo > > assert 1 != zoo > > assert zoo != 1 > > assert zoo != Symbol("x")**3 > > assert zoo + 1 == zoo + 1 > > assert zoo + 1 == zoo > > assert 2 + zoo == zoo > > assert 3*zoo + 2 == zoo > > assert 1/zoo == 0 > > > x = Symbol('x') > > > assert zoo + zoo == nan > > assert zoo - zoo == nan > > assert zoo + oo == nan > > assert zoo - oo == nan > > > assert zoo + I == zoo > > assert zoo * I == zoo > > assert zoo + x + 2 + 3*I == zoo + x > > assert zoo * x * 2 * 3*I * -oo == zoo * x > > > assert zoo * (1+I) == zoo > > assert zoo * (4+I+x) != zoo > > > assert zoo * 0 == nan > > assert zoo * nan == nan > > assert 0 * zoo == nan > > assert nan * zoo == nan > > assert zoo + nan == nan > > > assert zoo**zoo == nan > > assert zoo**0 == nan > > assert zoo**2 == zoo > > assert zoo**(-1) == 0 > > > assert abs(zoo) == oo > > > If anyone disagree with those assertions please let us know. > > > -- > > Alexey U. > > -- You received this message because you are subscribed to the Google Groups "sympy" group. To post to this group, send email to [email protected]. To unsubscribe from this group, send email to [email protected]. For more options, visit this group at http://groups.google.com/group/sympy?hl=en.
