Array answers not working for matrices outside of Matrix Context

[Alex-Jordan]

The attached problem has two answer array fields at the end, one for a matrix, one for a column vector (but really it's a MathObject matrix). The answers are defined in Fraction context, and the matrix entries are all Fraction objects. Clicking to display the correct answers shows them correctly. This all seems to be correct according to the documentation: https://webwork.pcc.edu/webwork2/pod/lib/Value/Matrix.pm#Fractions-in-Matrices

However if a user tries to enter the correct answers, they are told "Your answer isn't a matrix (it looks like a list of lists)

writeModel1.txt

[Alex-Jordan]

I wrote that both answer arrays are matrices, but I just saw that I was wrong and the second one really is a ColumnVector.

[Alex-Jordan]

OK, it seems this is not just about fractions, but matrix answer arrays in general. I changed the context to Numeric and made all of the entries Real, and I still get the "list of lists" feedback.

[Alex-Jordan]

Using Context("Matrix") makes it all work. But I'm confused about whether or not this should have been working with Context("Fraction") or Context("Numeric").

[dpvc]

Here's what's going on. When the MathObject answer checker processes an answer array like for your matrices, it first creates a Formula object for the $ans->{student_formula} from the entries in the array, and then evaluates that formula (if it is constant) to form $ans->{student_value}. The problem is that in Numeric and Fraction contexts, a formula can't generate a Matrix, since the delimiters in those contexts can only create lists, not matrices. That is why you are getting a list of lists, and why using the Matrix context allows it to work. From the viewpoint of contexts, that makes sense; but it does cause confusion in your case.

It would be possible to work it in reverse: create the $ans->{student_value} first, and if it is a constant, create a formula from it for $ans->{student_formula}. Here is a patch that does that:

diff --git a/lib/Value/AnswerChecker.pm b/lib/Value/AnswerChecker.pm
index fb4dacb0..3e3fea27 100644
--- a/lib/Value/AnswerChecker.pm
+++ b/lib/Value/AnswerChecker.pm
@@ -208,23 +208,21 @@ sub cmp_collect {
        }
        my $type = $self;
        $type = $self->Package($self->{tree}->type) if $self->isFormula;
-       $ans->{student_formula} = eval { $type->new($array)->with(ColumnVector => $self->{ColumnVector}) };
-       if (!defined($ans->{student_formula}) || $self->context->{error}{flag}) {
+       $ans->{student_value} = eval { $type->new($array)->with(ColumnVector => $self->{ColumnVector}) };
+       if (!defined($ans->{student_value}) || $self->context->{error}{flag}) {
                Parser::reportEvalError($@);
                $self->cmp_error($ans);
                return 0;
        }
-       $ans->{student_formula}{tree}{open}  = $self->{open}  if $self->{open};
-       $ans->{student_formula}{tree}{close} = $self->{close} if $self->{close};
-       $ans->{student_value}                = $ans->{student_formula};
+       $ans->{student_formula} =
+               Value::isFormula($ans->{student_value})
+               ? $ans->{student_value}
+               : $self->context->Package("Formula")->new($ans->{student_value});
+       $ans->{student_formula}{tree}{open}  = $self->{student_value}{open}  = $self->{open}  if $self->{open};
+       $ans->{student_formula}{tree}{close} = $self->{student_value}{close} = $self->{close} if $self->{close};
        $ans->{preview_text_string}          = $ans->{student_ans};
-       $ans->{preview_latex_string}         = $ans->{student_formula}->TeX;
-       return 0 if $ans->{typeError};
-       if (Value::isFormula($ans->{student_formula}) && $ans->{student_formula}->isConstant) {
-               $ans->{student_value} = Parser::Evaluate($ans->{student_formula});
-               return 0 unless $ans->{student_value};
-       }
-       return 1;
+       $ans->{preview_latex_string}         = $ans->{student_value}->TeX;
+       return !$ans->{typeError};
 }
 
 #
@@ -723,7 +721,7 @@ sub ans_collect {
                                $data->[$i][$j]->cmp(@ans_cmp_defaults, mathQuillOpts => $ans->{mathQuillOpts})->evaluate($entry);
                        $OK &= entryCheck($result, $blank);
                        $ans->{typeError} = 1 if $result->{typeError};
-                       push(@row, $result->{student_formula});
+                       push(@row, $result->{student_value} // $result->{student_formula});
                        entryMessage($result->{ans_message}, $errors, $i, $j, $rows, $cols);
                }
                push(@array, [@row]);

This is a significant change, so it might have unforeseen side-effects, so would need to be tested carefully.

The documentation you cite does show a way to produce a matrix of fractions, but as you found out, using a matrix array in a non-matrix context doesn't currently work, and I don't think it ever did.

The modern way of using fractions in a matrix context would be to use

Context(context::Fraction::extending("Matrix"));

to get both in the same context. See the POD for the contextFraction.pl file.

[dpvc]

PS, if you use this patch, you will want to stay in Context("Fraction") rather than switching to Context("Numeric") if you want the student answers to show as fractions rather than decimals. The student answers will be evaluated in the context where the Matrix was created, so you would want to use a fraction context for that in order to have student answers show as fractions.