[LON-CAPA-users] Having an equation or a range as a response

[Gerd Kortemeyer]

Hi,

On Jan 22, 2012, at 8:38 AM, Gerd Kortemeyer wrote:
> 
>> Oh and I also tested:
>> 
>> x^3 = 125 and it failed on both which is good if you're looking for linear solutions.
>> 
> 
> That's apparently because MAXIMA wants to solve this in the complex plane:
> 
> (%i3) solve(x^3=125,x);
>                  5 sqrt(3) %i - 5        5 sqrt(3) %i + 5
> (%o3)        [x = ----------------, x = - ----------------, x = 5]
>                         2                       2
> 
> I guess I need to work in some way to tell MAXIMA if it should stay real.

MAXIMA does not respect declarations with doing "solve":

(%i4) declare(x,real);
(%o4)                                done
(%i5) solve(x^3=125,x);
                 5 sqrt(3) %i - 5        5 sqrt(3) %i + 5
(%o5)        [x = ----------------, x = - ----------------, x = 5]
                        2                       2
(%i6) facts();
(%o6)                           [kind(x, real)]

:-(

Thus, we need to do this in Perl:

<problem>
<script type="loncapa/perl">
$a=&random(3,8,1);
$b=$a+&random(2,5,1);
$sample="x=$b or y=$a*x would be correct";

sub compareequations {
    my ($var,$value,$equation,$real,$lenient)=@_;
# var is the variable given
# value is the expected value of $var, $var=$value
# equation is the equation to be tested
# real: if set, operate only in the real realm
# lenient: if set, give credit even if the correct answer is only one of the possible answers, e.g., x^2=9 is "correct" if x=3 is expected
    $correctanswer=&cas('maxima','trigsimp(trigreduce('.$var.'='.$value.'))');
    if ($correctanswer=~/^Error\:/) { return $correctanswer; }
    $solution=&cas('maxima','trigsimp(trigreduce(solve('.$equation.','.$var.')))');
    if ($solution=~/^Error\:/) { return $solution; }
    $solution=~s/^\[//;
    $solution=~s/\]$//;
    $total=0;
    $found=0;
    foreach my $thissolution (split(/\s*\,\s*/,$solution)) {
         if (($real) && ($thissolution=~/\%i/)) { next; }
         $total++;
         if ($thissolution eq $correctanswer) { $found=1; }
    }
    if ((!$lenient) && ($total>1)) { return 'false'; }
    if ($found) { return 'true'; }
    return 'false';
}
</script>

<startouttext />
Given an equation for an asymptote of <m eval="on">\[y=$a\cdot x+\frac{1}{x-$b}\]</m>
<endouttext />

<customresponse answerdisplay="$sample">

<answer type="loncapa/perl">$first=&compareequations('y',"$a*x",$submission,1);
if ($first=~/^Error/) { return 'BAD_FORMULA'; }
if ($first=~/true/) { return 'EXACT_ANS'; }

$second=&compareequations('x',$b,$submission,1);
if ($second=~/^Error/) { return 'BAD_FORMULA'; }
if ($second=~/true/) { return 'EXACT_ANS'; }

return 'INCORRECT';</answer>

    <textline readonly="no" />
</customresponse>

</problem>