###########################################################
#
#  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",
);

TEXT(beginproblem());

###########################################################
#
#   The setup
#
Context('Numeric')->variables->are(
  x=>'Real',y=>'Real',
  s=>'Real',t=>'Real'
);
$x = Formula('x'); $y = Formula('y');

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

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

$x = random(-5,5,1);
$y = random(-5,5,1);

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

Context()->texStrings;
BEGIN_TEXT

Suppose \(f(x) = $f\).
$PAR
Then \(f($x,$y)\) = \{ans_rule(20)\},$BR
and \(f(s+t,s-t)\) = \{ans_rule(30)\}.

END_TEXT
Context()->normalStrings;

###########################################################
#
#  The answers
#
ANS($f->eval(x=>$x,y=>$y)->cmp);
ANS($f->substitute(x=>'s+t',y=>'s-t')->cmp);
$showPartialCorrectAnswers = 1;

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

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