## Adding Functions to the Context: PG Code Snippet

This code snippet shows the essential PG code to add a named function to the Context in a problem. 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.

• Example 1: The newer and easier way to add a named function to the context using parserFunction.pl.
• Example 2: The rudimentary way to add a function to the context.

Example 1: The newer and easier way to add a named function to the context using parserFunction.pl.

PG problem file Explanation
```loadMacros(
"PGstandard.pl",
"MathObjects.pl",
"parserFunction.pl",
);

parserFunction("f(x,y)" => "sqrt(x*y)");

test_at => [[5,1],[6,2],[7,3]]
);
```

Initialization and Setup: We need to load the `parserFunction.pl` macro, and then use one of its routines to define a new function that students may type in their answers. For more information, see parserFunction.pl.html

```BEGIN_TEXT
Given a surface \(z=f(x,y)\), what is the equation
for the \(z\)-coordinate of the surface along a
line having \(y=3\), shifted four units to the
right?  \(z = \) \{ ans_rule(25) \}
END_TEXT
```

The text section of the file is the same as usual, though hopefully with a less strained problem formulation.

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

And we check the answer as we expect.

Example 2: The rudimentary way to add a function to the context.

(The information here is taken from this discussion thread and a sample problem in the doc/parser/extensions directory of the WeBWorK tree.)

PG problem file Explanation
```package NewFunc;
# this next line makes the function a
#   function from reals to reals
our @ISA = qw(Parser::Function::numeric);

sub log2 {
shift; my \$x = shift;
return CORE::log(\$x)/CORE::log(2);
}

package main;

# Make it work on formulas as well as numbers
sub log2 {Parser::Function->call('log2',@_)}

#  Add the new functions to the Context
log2 => {class => 'NewFunc',
TeX => '\log_2'}, );
```

To define our new function, we first create a class in which it can live, where the behavior of the function is articulated, and then we add the function to the Context for the problem. Here, we borrow from the extensions sample provided in the webwork2/doc directory of the distribution and define a log base 2 function. If we didn't have any fancy TeX formatting for the function we could omit that hash key in the functions->add() call from the Context.

We can define a multivariable function by changing the inheritance list: if we had `our ISA = qw(Parser::Function::numeric2);`, then our function would be a two-variable function, f(x,y), and the subroutine defining it would take two variable arguments:

```  sub f {
shift; my ( \$x, \$y ) = @_;
...
}
```
```  BEGIN_TEXT
Solve \( 2^{3x} = 5 \):
\( x = \) \{ ans_rule(25) \}
\$BR
function \(log_2(x)\), which you should
enter as \${BTT}log2(x)\$ETT.)\$EITALIC
END_TEXT
```

The problem text is as we would expect, except that we are allowed to use the function that we defined in the problem text.

```  ANS( Compute("(1/3)*log2(5)")->cmp() );
```

And then in the answer and solution section of the problem the function may also be used.