Thank you all for your help with this problem. This does indeed seem to
work as expected:
<problem>
<startouttext />
<p>Give an example of an idempotent matrix that is neither a zero matrix
nor an identity matrix.</p>
<endouttext />
<customresponse>
<answer type="loncapa/perl">
# Get rid of white space
$submission=~s/\s+//gs;
# It's not a matrix if it does not at have parentheses
unless ($submission=~/^\(.+\)$/) { return 'BAD_FORMULA'; }
# Now evaluate something in MAXIMA
$idempotent=&cas('maxima','rank(matrix'.$submission.'^^2-matrix'.$submission.')');
$determinant=&cas('maxima','determinant(matrix'.$submission.')');
$rank=&cas('maxima','rank(matrix'.$submission.')');
# If $idempotent is not an integer, then the matrix is in the wrong format
unless ($idempotent=~/^\s*\d+\s*$/) { return 'BAD_FORMULA'; }
# Test the outcome of the MAXIMA expression
if ($idempotent == 0 && $determinant == 0 && $rank != 0) { return
'EXACT_ANS'; }
else {return 'INCORRECT';}
</answer>
<textline readonly="no" spellcheck="none" size="80" />
</customresponse>
</problem>
Justin
Justin Gray | Senior Lecturer
Department of Mathematics | Simon Fraser University
8888 University Drive, Burnaby | V5A 1S6 | Canada
Tel: +1 778.782.4237
On Wed, May 27, 2015 at 4:41 AM, Gerd Kortemeyer <korte...@msu.edu> wrote:
> Hi,
>
> > On May 26, 2015, at 10:36 PM, Damien Guillaume <dami...@msu.edu> wrote:
> >
> >> This seems to work as expected for square matrices. However, the example
> >> below accepts ([2,-2,-4],[-1,3,4]) as an answer, even though
> >> &cas('maxima','rank(matrix'.$submission.'^^2-matrix'.$submission.')')
> >> should generate an error in MAXIMA:
> >>
> >> (%i1) A:matrix([2,-2,-4],[-1,3,4]); [ 2
> >> - 2 - 4 ]
> >> (%o1) [ ]
> >> [ - 1 3 4 ]
> >> (%i2) rank(A^^2 - A);
> >> MULTIPLYMATRICES: attempt to multiply nonconformable matrices.
> >> -- an error. To debug this try: debugmode(true);
> >
> > It looks like maximareply() in lonmaxima.pm does not recognize this
> error message as an error message (it is only checking if there is
> "incorrect" in the reply). I guess the best solution would be to fix that,
> but maybe there is a way to tell if the result of the cas call makes sense
> or not (like testing if it is an integer), as a workaround.
>
> Argh! Yes, it’s really a problem that MAXIMA was designed throughout for
> interactive sessions. The replies are non-standardized.
>
> I am not sure if &maximareply() gives us back the whole message, since it
> is two lines (another problem), so I think we only get back
> “MULTIPLYMATRICES: attempt …” It is impossible to anticipate all the
> possible messages that MAXIMA returns, since there is no standard - each
> package spits out whatever the author imagined. In this case, probably the
> only remedies are to interpret the presence of “attempt” also as an error
>
> if ($determinant=~/(error|attempt)/i) { return ‘BAD_FORMULA’; }
>
> or to see if we only get back a number
>
> unless ($determinant=~/^\s*\d+\s*$) { return ‘BAD_FORMULA’; }
>
> - probably cleaner to do the latter, if we know that all ranks should just
> be numbers.
>
> - Gerd.
>
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