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parserAssignment.pl - Implements assignments to variables

This file implements an assignment operator that allows only a single variable reference on the left and any value on the right. You can use this to require students to enter things like

` y = 3x + 1`

rather than making the "y = " part of the text of the question. This also allows you to ask for lists of assignments more easily.

To use it, load the macro file, select the Context you want to use, add any variables you may need, and enable the assignment operator as in the following example:

```
loadMacros(
"PGstandard.pl",
"MathObjects.pl",
"parserAssignment.pl",
);
Context("Numeric")->variables->add(y=>'Real');
parser::Assignment->Allow;
```

Now you can use the equal sign in Formula() objects to create assignments.

```
$f = Formula("y = 3x + 1");
...
ANS($f->cmp);
```

The student will have to make an assignment to the same variable in order to get credit. For example, he or she could enter y = 1+3x to get credit for the answer above.

The left-hand side of an assignment must be a single variable, so

` $f = Formula("3y = 2x");`

will produce an error. The right-hand side can not include the variable being assigned on the left, so

` $f = Formula("x = 2x+1");`

also is not allowed.

You can produce lists of assignments just as easily:

` $f = Formula("y = 3x, y = 2x-1");`

and the assignment can be of any type of MathObject. For example:

```
Context("Vector")->variables->add(p=>'Vector3D');
parser::Assignment->Allow;
$f = Formula("p = <1,2x,1-x>");
```

To produce a constant assignment, use Compute(), as in:

` $p = Compute("p = <1,2,3>");`

(in fact, Compute() could be used for in place of Formula() in the examples above as well, since it returns a Formula when the value is one).

The left-hand side of an assignment can also be a function declaration, as in

` f(x) = 3x + 1`

To allow this, use

` parser::Assignment->Function("f");`

You can supply more than one function name if you want. E.g.,

` parser::Assignment->Function("f","g");`

The number of variables for these functions is determined by the assignment itself, so after declaring f to be a function, you can use either

```
f(x) = x+1
or
f(x,y) = x^2 + y^2
```

provided the variables are defined in the current context.

Type-checking between the student and correct answers is performed using the right-hand values of the assignment, and a warning message will be issued if the types are not compatible. The type of the variable on the left-hand side, however, is not checked.

For function declarations, the name of the function and the order of the variables must match the professor's answer; however, the names of the variables don't have to match, as long as the function returns the same results for the same inputs. So

```
f(x) = x + 1
and
f(y) = y + 1
```

will be marked as equal.