I think this is the correct way of thinking about it. Basically, the expression is not well-defined to any one point, so we return nan. A rule of thumb is that any of the l'Hopital's rule "indeterminate forms" should return nan.
The one exception to this rule is that we follow Python's convention that 0**0 == 1 (see http://code.google.com/p/sympy/issues/detail?id=2260). Aaron Meurer On Apr 18, 2011, at 12:07 PM, Tom Bachmann wrote: > 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. > -- 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.
