Implicit Equations Evaluators

Setup

We specify that the Context should be ImplicitEquation, and define the answer to be an equation. It’s worth noting that there are a number of Context settings that may be specifying for equation answers. In particular, it’s often important to pay attention to the limits used by the answer checker.

By default, the ImplicitEquation context defines the variables x and y. To include other variables, it may be necessary to modify the context.

Two other notes: if it’s possible that a student’s solution may evaluate to true for the test points that are used in the answer checker, it may be a good idea to specify what (x,y) solution values are used to check the answer. This can be done in the ImplicitEquation initialization call, e.g.,

 $eqn = ImplicitEquation("y = (x-1)^2",
 solutions=>[[0,0],[1,1],[-1,1],[2,4],[-2,4]]);

And, for this type of answer checking it is more likely than for regular formulas that the student will represent the function in a form that exceeds the default problem checking tolerances, and so be marked as incorrect. To correct this, it may be necessary to specify a tolerance; an absolute tolerance can be set in the ImplicitEquation call, e.g.,

 $eqn = ImplicitEquation("y = (x-1)^2",
 tolerance=>0.0001);

It is possible to remove the error message “Can’t find any solutions to your equation” by remapping it to another error message. The message has to be non-empty, but it can be just a blank " ", as in

 Context()->{error}{msg}{"Can't find any solutions to your equation"} = " ";

This will eliminate the error message (though the “messages” column will be displayed in the answer table at the top of the problem, but no message will be there).

Another way to remove the error message “Can’t find any solutions to your equation” would be to use a post-filter to remove the message after the answer has been graded. The answerHints.pl file provides one way to do this, but it is probably just as easy to do it manually, as replacing the $ans line with the following:

 $ans = ImplicitEquation("y = (x-1)^2")->cmp->withPostFilter(sub {
    my $ans = shift;
    $ans->{ans_message} = " " if $ans->{ans_message} eq
    "Can't find any solutions to your equation";
    return $ans;
 }));