Without thinking about this too much, it seems that there is a
possibility of using a
(relatively strong) interval arithmetic package to do what sign is
supposed to do,
(or vice versa).
That is, given an expression f(x) and an interval for x, e.g. [0,inf],
it is an interval
arithmetic problem to see if f([0,inf]) is bounded away from 0 or not.
Interval arithmetic may be too sloppy to do this sufficiently
accurately, but it
addresses the same kind of problems and could use the same kinds of
solutions,
like finding the extrema of f.
Does it makes sense to do both at at the same time? There are a number
of lisp-language
interval arithmetic package; I've written at least 3 myself. (one in my
generic arithmetic
package)
RJF
On 7/10/2011 7:16 AM, Dieter Kaiser wrote:
> Am Sonntag, den 10.07.2011, 07:59 -0500 schrieb Barton Willis:
>> When I wrote conjugate.lisp, there was a rudimentary csign (not
>> $csign) function. Given the limitations of $sign and the (extreme)
>> difficultly in working with code in compar.lisp, your work on $csign
>> improved Maxima a great deal--I didn't mean to imply anything negative
>> about the function $csign.
> Thank you very much for your comment.
>
>> The other day when I gave the sign function object-oriented dispatch,
>> I thought (not long) about appending code that would do a better job
>> of determining the sign of a single variable polynomial. For a
>> polynomial defined on the entire reals, a few lines of code with
>> nroots might work, but for a polynomial defined on a subset of the
>> reals, it's not easy to determine from the fact database lower and
>> upper bounds for a variable (suppose x+y<2 and x-y>5, deduce y<-3/2).
>> It would be great if the fact database would maintain bunch of
>> derived facts--re-deriving them each time sign is called is too spendy, I
>> think.
> I like the object-oriented dispatch very much, which gives the
> possibility to extend the functionality for functions very easy. At the
> moment I am working almost exclusively on the the German translation and
> the Maxima manual. But this way, I have collected a lot of ideas to
> improve the implemented functions .
>
> Dieter Kaiser
>
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