How Can I Use plot2d code for presence of singularities?

On 1/3/2013 11:11 AM, Raymond Toy wrote:
>>>>>> "Richard" == Richard Fateman <fateman at eecs.berkeley.edu> writes:
>      Richard> On 1/3/2013 9:41 AM, Henry Baker wrote:
>      >> This is why the interval code in my type inference package (section 7.3 in link below) has a union of disjoint intervals, rather than a single interval.
>      Richard> Using unions of disjoint intervals has some advantages --- Mathematica
>      Richard> and Maple both use this, I think.
>
> FWIW, cmucl's type-inference also uses unions of disjoint intervals
> when necessary.
>
> It also suffers from not rounding down the left limit and rounding up
> the right limit of intervals.  This has lead to a few rare cases where
> the compiler made bad assumptions.  This mostly happened with the
> 80-bit x87 float registers.
>
>      Richard> Disadvantages include:
>      Richard> Contrary to the needs of some platforms, intervals cannot be stored in
>      Richard> a fixed size (2 double-floats, e.g.) but
>      Richard> require memory allocation mechanisms.
>
>      Richard> Computing gets messier.
>
> There are some examples of lisp code that causes cmucl to take an
> inordinately long time to compile because the union of disjoint
> intervals becomes vary large.  As hack, if the union contains too many
> intervals (500?), they're all collapsed into one interval that is a
> superset of the union.
>
>      Richard> One alternative is to have exterior intervals.  That is 1/[-1,1]
>      Richard> becomes  [1, -1]  where the latter represents [-infinity,-1] U
>
> I assume you meant to write ]1, -1[ instead of [1,-1].
>
>      Richard> [1,infinity].
>      Richard> (or if you join the reals at +- inf, it is all of them except [0,1].
>
> To do more inference with these exterior intervals, don't you
> basically end up dealing with a union of intervals anyway?
>
> Ray
>
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You can write ][  if you want, but [ ]  works fine if you notice that 
the left value is larger than the right..

No, the exterior intervals re-connect if you divide by them.