intervals.... more

Richard Fateman wrote:
> here's a sketch of a working (but incomplete) interval evaluator.
> More stuff is needed from my generic arithmetic package, on my web page..
>
>
> #| a Maxima interpreter for intervals |#
>
> (in-package :ri)                        ; real intervals
>
> (defun maxima::$IEVAL(expr)(ieval (meval expr)))
>
> (defun ieval(e)
>
>   (cond ((realp e) (widen-ri e e)) ;3.0 -> [3-eps,3+eps]
>
>         ((atom e)
>          (error "IEVAL cannot handle ~s" e))
>         (t (case
>                (caar e)
>
>            (maxima::MPLUS
>             (cond ((null (cdr e)) 0)
>                   ((null (cddr e))(ieval (cadr e)))
>                   (t  (+ (ieval (cadr e)) ;this + is a real-interval +
>                          (ieval (cons (car e) (cddr e)))))))
>            (maxima::MTIMES
>             (cond ((null (cdr e)) 0)
>                   ((null (cddr e))(ieval (cadr e)))
>                   (t  (* (ieval (cadr e)) ; this * is a real-interval *
>                          (ieval (cons (car e) (cddr e)))))))
>            (maxima:: MLIST
>                      ;; make a real interval, a structure of type ri
>                      ;; check it is a list of 2 items
>                      ;; both numbers, in order,
>                      (let ((a (second e))(b (third e)))
>                        (if (and (realp a)
>                                 (realp b)  ;; optional? (<= a b)
>                                 (null(cdddr e)))
>                            (widen-ri (cadr e)(caddr e))
>                          (error "can't convert ~s to interval")))
>            (otherwise
>             ;; look on property list of (car e)
>             ;; to see if it has an ieval property. eg.
>             (if (setf fn (get (caar e)
>                               'ieval))
>                 (apply fn (mapcar #'ieval (cdr e)))
>               (error "IEVAL cannot handle ~s" e)))))))
>
>
> (setf (get '$includes 'ieval) #'include-ri)
> (setf (get '$intersects 'ieval) #'intersect-ri)
> (setf (get '$min 'ieval) #'(lambda(x)(ri-lo x)))
> (setf (get '$max 'ieval) #'(lambda(x)(ri-hi x)))
>
> (setf (get '$sin 'ieval) #'intsin) ;; etc etc
>
> (defun maxima::$RealInterval(a b )(ri a b))
>
> ;; etc
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> .
>
>   
What is the link on your web page is the interval package?

TIA,
 -sen