[Maxima-bugs] [ maxima-Bugs-826623 ] simplifer returns %i*%i

[SourceForge.net <no...@so...>]

Bugs item #826623, was opened at 2003-10-20 06:25
Message generated for change (Comment added) made by crategus
You can respond by visiting: 
https://sourceforge.net/tracker/?func=detail&atid=104933&aid=826623&group_id=4933

Please note that this message will contain a full copy of the comment thread,
including the initial issue submission, for this request,
not just the latest update.
Category: Lisp Core - Simplification
Group: Includes proposed fix
>Status: Closed
>Resolution: Fixed
Priority: 5
Private: No
Submitted By: Stavros Macrakis (macrakis)
Assigned to: Nobody/Anonymous (nobody)
Summary: simplifer returns %i*%i

Initial Comment:
((-%i)^(1/2)*%i)*((-%i)^(1/2)) => -%i*%i

Resimplifying -- expand(%,0,0) -- correctly returns 1.

Maxima 5.9.0 gcl 2.5.0 mingw32 W2k Athlon


----------------------------------------------------------------------

>Comment By: Dieter Kaiser (crategus)
Date: 2009-05-29 01:13

Message:
Suggested test for a base which is a mtimes expressions in expressions like
(a*b)^q*(a*b)^q, where q+r=1 has been checked out.

The example of this bug report now simplifies:

(%i6) sqrt(-%i)*sqrt(-%i)*%i;
(%o6) 1

Other examples are:

(%i7) sqrt(a*b)*sqrt(a*b)*a*b;
(%o7) a^2*b^2

(%i8) (a*b*x)^(1/5)*(a*b*x)^(4/5)*x;
(%o8) a*b*x^2

The initial example simplifies correctly. Closing this bug report as
fixed.

Dieter Kaiser

----------------------------------------------------------------------

Comment By: Dieter Kaiser (crategus)
Date: 2009-05-25 18:54

Message:
I had a look at this bug. Here are some more general examples related to
this report:

(%i3) a*sqrt(a*b)*sqrt(a*b);
(%o3) a*(a*b)

(%i4) a*b*sqrt(a*b)*sqrt(a*b);
(%o4) a*b*(a*b)

Now with another exponent:

(%i5) a*b*(a*b)^(1/4)*(a*b)^(3/4);
(%o5) a*b*(a*b)

Here is the example from this bug report:

(%i6) %i*sqrt(-%i)*sqrt(-%i);
(%o6) -%i*%i

This simplification error can be located to occur in the routine timesin
in simp.lisp. This is the small piece of code which is responsible:

((onep1 w)
 (return (rplaca (cdr fm) (car x))))

When two factors are equal and the exonentents of the factors sum to 1, e.
g. for sqrt(a*b)*sqrt(a*b) the factor is replaced by the base, that is for
this example (a*b). Unfortunately, this is a mtimes expression. The
simplifier generates a result with an unsimplified and nested mtimes
expression in it.

I have tried to find a better implementation and I have found the
following code which works:

((onep1 w)
 (cond ((mtimesp (car x))
        ;; A base which is a mtimes expression.
        ;; Remove the factor from the lists of products.
        (rplacd fm (cddr fm))
        ;; We multiply the complete base with the list
        ;; of all remaining factors.
        (setq rulesw t)
        (return (muln (nconc y (cdar x)) t)))
       ;; The old code for the other cases.
       (t (return (rplaca (cdr fm) (car x))))))

Again the above examples with the modified code:

(%i3) a*b*sqrt(a*b)*sqrt(a*b);
(%o3) a^2*b^2

(%i4) a*sqrt(a*b)*sqrt(a*b);
(%o4) a^2*b

(%i5) a*b*sqrt(a*b)*sqrt(a*b);
(%o5) a^2*b^2

(%i6) a*b*(a*b)^(1/4)*(a*b)^(3/4);
(%o6) a^2*b^2

That is the example of this bug report:

(%i7) %i*sqrt(-%i)*sqrt(-%i);
(%o7) 1

The testsuite has no problems with the new code. Because this is a
fundamental simplification error I supposed to get more problems with the
testsuite. Perhaps a lot of examples do some extra expansions to get the
desired simple result.

The other inconsistencies reported in the bug report are not caused by
this problem. I am not sure if the code above is the best way to remove
this problem, but it works.

Any comments?

Dieter Kaiser

----------------------------------------------------------------------

Comment By: Robert Dodier (robert_dodier)
Date: 2006-07-11 06:40

Message:
Logged In: YES 
user_id=501686

Observed in 5.9.3cvs.


----------------------------------------------------------------------

Comment By: Stavros Macrakis (macrakis)
Date: 2003-10-20 07:55

Message:
Logged In: YES 
user_id=588346

This may be related to the inconsistent simplification of simple 
expressions involving %i:

Mathematically, %i^(1/4) = (-%i)^(-1/4), but the first 
simplifies to (-1)^(1/8) and the second to (-%i)^(1/4) .

Mathematically, (-1)^(-1/4) = %i^(-1/2) = (-%i)^(1/2), but 
the first two simplify to 1/(-1)^(1/4), while the third simplifies 
to sqrt(-%i).

There are other similar cases.  This is also reminiscent of the 
the non-normalization of 1/sqrt(2) -- bug # 721575.

----------------------------------------------------------------------

You can respond by visiting: 
https://sourceforge.net/tracker/?func=detail&atid=104933&aid=826623&group_id=4933