###########################################################
#
#  Example showing how to use the Parser's function
#  answer checker.
#

DOCUMENT();        # This should be the first executable line in the problem.

loadMacros(
  "PGbasicmacros.pl",
  "PGanswermacros.pl",
  "Parser.pl",
  "parserUtils.pl",
);

TEXT(beginproblem());

###########################################################
#
#   The setup
#
Context('Vector')->variables->are(x=>'Real',y=>'Real');
$x = Formula('x'); $y = Formula('y');

$a = random(1,16,1);
$b = non_zero_random(-5,5,1);

$f = ($x**2 + $a*$y**2 + $b*$x**2*$y) -> reduce;

$x = sqrt(2*$a)/$b; $y = -1/$b;

###########################################################
#
#  The problem text
#

Context()->texStrings;
BEGIN_TEXT

Suppose \(f(x,y) = $f\).
$PAR
Then \(f\) has critical points at the following
points: \{ans_rule(30)\}.
$PAR
${BCENTER}
${BSMALL}
To enter more than one point, separate them by commas.$BR
Enter ${LQ}${BTT}NONE${ETT}${RQ} if there are none.
${ESMALL}
${ECENTER}

END_TEXT
Context()->normalStrings;

###########################################################
#
#  The answers
#
ANS(List(Point(0,0),Point($x,$y),Point(-$x,$y))->cmp);
$showPartialCorrectAnswers = 1;

###########################################################

ENDDOCUMENT();        # This should be the last executable line in the problem.