[Maxima-bugs] [ maxima-Bugs-2937182 ] Assume does not always affect ratsimp/fullratsimp result

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Bugs item #2937182, was opened at 2010-01-22 16:05
Message generated for change (Comment added) made by kirzhanov
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Category: None
Group: None
>Status: Open
Resolution: Invalid
Priority: 5
Private: No
Submitted By: Dmitry Kirzhanov (kirzhanov)
Assigned to: Nobody/Anonymous (nobody)
Summary: Assume does not always affect ratsimp/fullratsimp result

Initial Comment:
First, assume that x>=0:

assume(x>=0);
facts(); // returns x>=0
is(fullratsimp(sqrt(x^2))=x); // returns TRUE

Now, forget about x>=0 and assume x<0:

forget(x>=0);
assume(x<0);
facts(); // returns 0>x
is(fullratsimp(sqrt(x^2))=-x); // returns FALSE

Is the expected result here TRUE instead of FALSE?

For me this result is unexpected. It was achieved using the SAGE 4.3 system which is shipped with Maxima 5.20. I'm not sure this bug is related to Maxima, but it seems so. The behavior of this Maxima 5.20 built into the SAGE system differs from behavior of Maxima 5.17.1 which was used by me previously. Because of such difference I receive not exactly incorrect, but slightly different results in the newer version of Maxima. Thus it seems to me that the results given by the latest version can be simplified at higher degree.

Cheers,
Dima

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>Comment By: Dmitry Kirzhanov (kirzhanov)
Date: 2010-01-23 16:07

Message:
On my compilation command sequence 

assume(x<0);
sqrt(x^2);

gives output sqrt(x^2), and *not* -x. Command ratsimp also does not affect
this expression.

Version information: Maxima 5.19.1, Using Lisp ECL 9.10.2.
I could not get any output from function bug_report() or build_info().
Command run_testsuite() retuns 'done'.


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Comment By: Dieter Kaiser (crategus)
Date: 2010-01-22 21:55

Message:
For a negative symbol x Maxima simplifies the sqrt function the following
way:

(%i1) assume(x<0)$

(%i2) sqrt(x^2);
(%o2) -x

The function fullratsimp is not needed and does not change anything for
this example. We always get for this example:

(%i3) is(sqrt(x^2)=-x);
(%o3) true

The only way I have found to get the reported oberservation is to give the
variable x a positive value. (Maxima does not give an error if we assign a
positive value to a symbol which is assumed to be negative).

(%i6) x:10;
(%o6) 10

Now the sqrt function simplifies to a positive value:

(%i7) sqrt(x^2);
(%o7) 10

We get false for the example from above:

(%i9) is(sqrt(x^2)=-x);
(%o9) false

I think there is no real problem. Setting the status to pending and the
resoltution to invalid.

Dieter Kaiser

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