[Maxima] Improvement to nonintegerp (was: Improvement to askinteger for review/comment)
Billinghurst, David (RTATECH)
David.Billinghurst at riotinto.com
Wed Oct 14 22:26:24 CDT 2009
> From: dr dieter kaiser
>
> Am Sonntag, den 11.10.2009, 15:00 +1100 schrieb Billinghurst, David
> (RTATECH):
> > The askinteger function does not know that sqrt(3) is not
> an integer.
> >
> > For a rational numbers N, Maxima simplifies (most?) expressions
> > of form sqrt(N^2) to abs(N). The patch below assumes that this
> > simplification has occured and an expression of the form sqrt(x)
> > is not an integer if numberp(x)=true.
> > Are there cases when this is unsafe? One possibility I
> > considered is
> > for (very) large x.
> >
> > So some questions:
> > - is this patch correct?
> > - if not, what additional tests/constrains are needed?
> > - are there any simple generalizations?
>
> I do not like the functions $askinteger and $asksign. Very
> often these functions ask questions which are nonsense.
Agree, but I don't want to change the behaviour of the existing
ODE code
> It is a bit strange that a user has to call the function
> $featurep to get the functionality of maxima-integerp, e.g.
> featurep(sqrt(3),integer)
> -> false (Should we extend integerp, oddp and evenp to use
> maxima-integerp, mevenp and moddp?).
>
> When we extend the functionality of askinteger, we double
> functionality we already have in maxima-integerp.
maxima-integerp and nonintegerp both return false for "don't know".
featurep(sqrt(3),integer) -> false
featurep(sqrt(3),noninteger) -> false
I now believe the correct solution is to extend nonintegerp, which
is called by askinteger. With this change
featurep(sqrt(3),integer) -> false
featurep(sqrt(3),noninteger) -> true
I was unsure if this would work for sqrt(N^2) when N is a large
integer, after inspecting the code and some testing I now think it
is OK. I tested several cases near N^2 where N is a large Mersenne
prime.
OK to commit this?
Index: compar.lisp
===================================================================
RCS file: /cvsroot/maxima/maxima/src/compar.lisp,v
retrieving revision 1.58
diff -u -1 -1 -r1.58 compar.lisp
--- compar.lisp 8 Oct 2009 19:45:54 -0000 1.58
+++ compar.lisp 15 Oct 2009 02:43:35 -0000
@@ -1690,24 +1690,26 @@
(defmfun nonintegerp (e)
(let (num)
(cond ((integerp e) nil)
((mnump e) t)
((atom e) (kindp e '$noninteger))
((specrepp e) (nonintegerp (specdisrep e)))
((and (eq (caar e) 'mplus) (ratnump (cadr e)) (intp (cdr e)))
t)
((and (integerp (setq num ($num e)))
(prog2
(setq e ($denom e))
(or (eq (csign (sub e num)) '$pos)
- (eq (csign (add2 e num)) '$neg))))
- t))))
+ (eq (csign (add2 e num)) '$neg)))) t)
+ ;; Assumes a simplified sqrt of a number is not an integer.
+ ((and (mexptp e) (mnump (second e)) (alike1 (third e) 1//2))
t)
+ (t nil))))
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