Implicit Function as an Equation

An equation implicitly defining a function

Return to the PG docs home

Complete Code

Download file: EquationImplicitFunction.pg

POD for Macro Files

PG problem file

Explanation

DOCUMENT();

loadMacros(
    'PGstandard.pl',             'PGML.pl',
    'parserImplicitEquation.pl', 'PGcourse.pl'
);

Preamble

The macro parserImplicitEquation.pl allows the entry of equations.

Context('ImplicitEquation');
Context()->{error}{msg}{"Can't find any solutions to your equation"} = ' ';
Context()->{error}{msg}{"Can't generate enough valid points for comparison"} =
    ' ';

Context()->variables->set(
    x => { limits => [ -6, 11 ] },
    y => { limits => [ -6, 11 ] },
);

$a = random(1, 5);
$b = random(1, 5);
$r = random(2, 5);
$p = Compute("($a,$b)");

$answer = ImplicitEquation(
    "(x-$a)^2 + (y-$b)^2 = $r^2",
    solutions => [
        [ $a,                    $b + $r ],
        [ $a,                    $b - $r ],
        [ $a + $r,               $b ],
        [ $a - $r,               $b ],
        [ $a + $r * sqrt(2) / 2, $b + $r * sqrt(2) / 2 ],
    ]
);

Setup

We quash some error messages by redefining them to be a blank string ’ ’ (notice the space). Since the circle will always be contained in a rectangle with two opposite corners at (-4, -4) and (10, 10), we set the limits for the variables x and y to be outside of this rectangle. The ImplicitEquation object allows us to specify as many solutions as we like, and doing so should improve the accuracy of the answer evaluator.

If your equation is linear of the form x = 3, 4x + 3y = 12, or 4x + 3y + 5z = 21 for example, you should use the parserImplicitPlane.pl context and answer evaluator instead.

BEGIN_PGML
Enter an equation for a circle in the [`xy`]-plane
of radius [`[$r]`] centered at [`[$p]`].

[_]{$answer}{25}
END_PGML

Statement

This is the problem statement in PGML. 
BEGIN_PGML_SOLUTION
Solution explanation goes here.
END_PGML_SOLUTION

ENDDOCUMENT();

Solution

A solution should be provided here.