# EquationEvaluators

## Equation Answer Evaluation

This code shows how to check student answers that are equations. Note that these are insertions, not a complete PG file. This code will have to be incorporated into the problem file on which you are working.
For equations that are lines or planes, use ImplicitPlane as it is more reliable.

PG problem file Explanation
```loadMacros("parserImplicitEquation.pl");
```

Initialization: To check equations given as answers, we don't have to change the tagging and documentation section of the problem file. In the initialization section, we need to include the macros file `parserImplicitEquation.pl`.

```Context("ImplicitEquation");
Context()->variables->set(
x=>{limits=>[-2,2]},
y=>{limits=>[0,4]}
);

\$eqn = ImplicitEquation("y = (x-1)^2");
```

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). For another way to remove this error message, see the `withPostFilter` option below in the Answer Evaluation section.

```BEGIN_TEXT
Give the equation of a shift of the
parabola \(y = x^2\) which is upward
opening and has its vertex at (1,0).
\$PAR
equation: \{ ans_rule(35) \}
END_TEXT
```

Main Text: The problem text section of the file is as we'd expect.

```ANS( \$eqn->cmp() );
```

Answer Evaluation: 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 in:

```ANS(\$eqn->cmp->withPostFilter(sub {
my \$ans = shift;
\$ans->{ans_message} = " " if \$ans->{ans_message} eq
"Can't find any solutions to your equation"; return \$ans;
}));
```