###########################################################
#
#  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",
  "Differentiation.pl",
);

TEXT(beginproblem());

###########################################################
#
#   The setup
#
Context('Numeric')->variables->add(y=>'Real');
$x = Formula('x');  # used to construct formulas below.
$y = Formula('y');

#
#   Define a function and its derivative and make them pretty
#
$a = random(1,8,1);
$b = random(-8,8,1);
$c = random(-8,8,1);

$f = ($a*$x**2 + $b*$x*$y + $c*$y**2) -> reduce;
$fx = $f->D('x');
$fy = $f->D('y');

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

Context()->texStrings;
BEGIN_TEXT

Suppose \(f(x,y) = $f\).
$PAR
Then \(f_x(x,y) =\) \{ans_rule(30)\},$BR
and \(f_y(x,y) =\) \{ans_rule(30)\}.


END_TEXT
Context()->normalStrings;

###########################################################
#
#  The answers
#
ANS($fx->cmp);
ANS($fy->cmp);
$showPartialCorrectAnswers = 1;

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

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