[Maxima-bugs] [ maxima-Bugs-2802154 ] Problem with radcan simplifying an expression

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Bugs item #2802154, was opened at 2009-06-05 21:33
Message generated for change (Comment added) made by dvitanye
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Category: None
Group: None
Status: Open
Resolution: None
Priority: 5
Private: No
Submitted By: Dave Vitanye (dvitanye)
Assigned to: Nobody/Anonymous (nobody)
Summary: Problem with radcan simplifying an expression

Initial Comment:
I'm a new Maxima user, so I'm not sure this qualifies as a defect, but it just doesn't look right to me:

For some particular specific functions X and Q:

(%i4) radcan(X(Q(A/B),Q(A/B)));
                                                         A
(%o4)                                               -
                                                         B

and then I would expect also:

(%i5) radcan(X(Q(1/B),Q(1/B)));
                                                         1
(%o5)                                               -
                                                         B

However the next result seems peculiar to me:

(%i6) radcan(X(Q(A/1),Q(A/1)));
                                                       A + 1
(%o6)                                            -------
                                                      3 A - 1

where I would have expected the result to be either A or A/1, right?

Here are the two specific functions:

(%i2) X(S,T) := (S*T*(2*S*T+S+T)-2*S^(3/2)*T^(3/2)*(S+T+1)^(1/2)) / (S*T*(2*S*T-S-T)+(S-T)^2 + 2*S^(3/2)*T^(3/2)*(S+T+1)^(1/2));

                                                                                       3/2  3/2                 1/2
                                               S T (2 S T + S + T) - 2 S    T    (S + T + 1)
(%o2)                  X(S, T) := -----------------------------------------------------------
                                                                                            2         3/2  3/2               1/2
                                               S T (2 S T - S - T) + (S - T)  + 2 S    T    (S + T + 1)
 
(%i3) Q(x) := 4*x*(1+x)/(1-x)^2;

                                                                   4 x (1 + x)
(%o3)                                           Q(x) := -----------
                                                                               2
                                                                      (1 - x)

Here is the build information:
-------------------------------------------------------------

Maxima version: 5.18.1
Maxima build date: 20:57 4/19/2009
host type: i686-pc-mingw32
lisp-implementation-type: GNU Common Lisp (GCL)
lisp-implementation-version: GCL 2.6.8

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

Any comments or help are appreciated.

-Dave


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Comment By: Dave Vitanye (dvitanye)
Date: 2009-06-06 19:55

Message:
On further examination, I now believe the radcan result to be, in fact,
correct.
Surprising to me as a new user, but correct.

So please consider this artifact to be withdrawn by the original author. 
Details follow:

Since Q(x) blows up at x = 1 because of the term (1-x)^2 in the
denominator,
there are two distinct regions to examine:  x< 1 and x > 1.
It Turns Out that the domain of interest to me for the parameter of
function Q is x < 1. 
What I was attempting to confirm was the identity X(Q(x),Q(x)) = x.
And, it turns out, this really IS true IF x < 1. 

The surprise to me is that, without my indicating any explicit
assumptions, radcan
appears to be making some implicit assumptions about the range of variable
x.

So, X(Q(1/B),Q(1/B)) simplifies to 1/B, apparently based on the
determination
that 1/B will be < 1 (ie. B is > 1 and not something like .1).

And, X(Q(A),Q(A)) does NOT simplify to A, again based on the determination
that A will be > 1 (ie. A is not something like .1). 

The curious result is that X(Q(A/B),Q(A/B)) simplifies to A/B,
which is only true if A<B, but not true if A>B. How did radcan make the
choice?

If anyone more knowledgeable about how radcan is making these implicit
assumtions
about the range of variables being used could describe what's going on, I
would be
interested in understanding the details. Thanks.







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

Comment By: Dave Vitanye (dvitanye)
Date: 2009-06-05 21:45

Message:
Oops - original post format not very readable; I am attempting to re-post
the content using the attached file mechanism.

-Dave

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