I've been critical of Mathematica's use of Intervals for the result of
Limit, but perhaps we could come up with something similar.
Mathematica says this..
Limit[Sin[x],x->Infinity] is Interval[{-1,1}]
I object to the overloading of the "interval" arithmetic to represent
this, but I would not mind a notion of a limit set or constraint or
something like that.
e.g. limit(sin(x),x,inf) might be bounds(-1,1).
To some extent bounds(a,b) can be handled arithmetically like an
interval (which Maxima does not have now anyway!)
but it fails to satisfy the epsilon-delta kind of definition of limit,
or consequences that follow from that. But I have not
fully thought this through.
RJF
For people with access to Mathematica, try
Limit[Tan[x]^2+Sec[x]^2,x->Infinity]
Raymond Toy wrote:
> Barton Willis wrote:
>
>> I was playing with the idea of appending a simplim%function for the
>> hypergeometric
>> functions. To start, I wrote some 100% fake code:
>>
>>
>>
> [snip]
>
>> Limit assumes continuity?
>>
>> (%i14) limit(hypergeometric([a],[b],x),x,0);
>> (%o14) 1
>>
>> Limit doesn't even try limit-hg?
>>
>> (%i16) limit(hypergeometric([a],[b],x),a,0);
>> (%o16) limit(hypergeometric([a],[b],x),a,0)
>>
>>
>>
> This is caused by the following in simplimit:
>
> (defmfun simplimit (exp var val &aux op)
> (cond
> ((eq var exp) val)
> ((or (atom exp) (mnump exp)) exp)
> ((and (not (infinityp val))
> ;; *** HERE ***
> (not (amongl '(%sin %cos %atanh %cosh %sinh %tanh mfactorial %log)
> exp))
> (not (inf-typep exp))
> (simplimsubst val exp)))
>
> Since hypergeometric isn't among the list of "special" functions,
> simplimsubst is called.
>
> This looks like a bug in simplimit. The list of special functions needs
> to expanded. Or probably better, it should be removed and the rest of
> the code adjusted accordingly so that the special limit functions can
> decide what to do about continuity and such.
>
> Ray
>
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