Improvement to nonintegerp (was: Improvement to askinteger for review/comment)

> 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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