** Using WeBWorK **

There are several issues that are affecting your results. I will respond to each in a separate message.

The most important one is that when Vector() has an argument that is a Formula, it returns a Vector-valued formula, and those do not support the coordinate hints. The reason is that the student answer may not be a simple list of coordinates, but rather some more complicated vector equation, where the "coordinates" are not so obvious.

When the student provides an answer for a constant-valued answer, the reduced numeric result is shown in the answer preview area, and so the coordinates of a constant vector would show up and make sense. But for Formula answers (vector or otherwise) the student's preview is the formula, and coordinates may not be apparent, so it could be confusing to discuss coordinates in that case.

On the other hand, you can achieve the result you want by using a custom answer checker. Here is one approach that is very general:

  $ans = Vector("<t,1-t,3t^2>");

  ANS($ans->cmp(checker => sub {
    my ($correct,$student,$ans) = @_;
    return 1 if $correct == $student;
    if (!$ans->{isPreview}) {
      my $m = $correct->length;
      my $I = Value::Matrix->I($m);
      my @errors = ();
      foreach my $i (1..$m) {
        my $e = Vector($I->row($i));
        push (@errors,"Your ".$correct->NameForNumber($i)." coordinate is incorrect")
           unless $correct.$e == $student.$e;
      }
      Value->Error(join("<BR>",@errors)) if @errors;
    }
    return 0;
  }));

The rows of that matrix will be the unit coordinate vectors of the correct dimension, and dotting a vector with one of those will extract one of the coordinates of the answer. We can use that fact to check the individual coordinates of the student's answer.

To do so, we loop through the indices of the vector (1..$m) and extract a row of the matrix (the vector that has a 1 in position $i and zeros elsewhere), and dot that with the correct and student answers. If they aren't the same, we store an error message indicating that fact. The message uses the NameForNumber() call to turn "1" into "first", "2" into "second" and so on.

Once all the coordinates are checked, we join all the errors together (with BR tags to force them to be on separate lines) and report the errors. If there were no errors (shouldn't happen), or the student is previewing, simply return 0 to indicate the answer is incorrect.

That should have the effect you want. You could even package this checker in a macro file of your own and use loadMacros() to load it. For example, make a file containing

  sub VectorCoordinateHints {
    my ($correct,$student,$ans) = @_;
    ...
    return 0;
  }
  $VectorCoordinateHints = \&VectorCoordinateHints;

  ANS($ans->cmp(checker=>$VectorCoordianteHints));

Davide

  Context("Vector");
  Context("Vector")->variables->are(x=>'Real',y=>'Real',theta=>'Real',phi=>'Real');
  Context("Vector")->flags->set(showCoordinateHints=>1);
  $r = Vector("$x","$y","$z");
  $ru = $r->D('theta')->reduce;
  $rv = $r->D('phi')->reduce;
  $prod = Vector("$ru >< $rv");

The way to do this is to use Context() with no name in order to get the current context without changing it. So

  Context("Vector");
  Context()->variables->are(x=>'Real',y=>'Real',theta=>'Real',phi=>'Real');
  Context()->flags->set(showCoordinateHints=>1);

Of course, this still won't solve the problem, since vector-valued formulas don't show coordinate hints, but it is the correct way to add variables to and set flags in the same context.

Davide

   $r = Vector("$x","$y","$z");

  $r = Vector($x,$y,$z);

The only reason to go through the extra parsing is if the variables were defined in a different context originally. In that case, you might use

  $r = Vector("<$x,$y,$z>");

  $r = Compute("<$x,$y,$z>");

I'm trying to promote the use of Compute() when the input is a string, since it works just like parsing the student's answer and returns a value of the correct type, whatever that may be.

Davide

I love math objects!

Davide