## DESCRIPTION
##
##
## Randomization:
##
##
## ENDDESCRIPTION

## Author('Richard G. Lynch')

################################################################################
#  Initialization
################################################################################

DOCUMENT();

loadMacros(
    "PGstandard.pl",
    "MathObjects.pl",
    "PGML.pl",
    "contextFraction.pl",
    "PGchoicemacros.pl",
);

TEXT(beginproblem());

################################################################################
#  Problem Setup
################################################################################

Context("Fraction");
Context()->noreduce('(-x)-y');
Context()->noreduce('(-x)-y','(-x)+y');

do {
    $check = 1;
    do {
        @n = ((-9..-2),(2..9))[shuffle(16)];
        @b = (2,4,5,2,4,5,2,4,5,2,4,5,2,4,5,2,4,5)[shuffle(18)];
        $cntb = 0;
        for ($i = 0; $i < 4; $i++) {
            ($n[$i],$b[$i]) = reduce($n[$i],$b[$i]);
            $f[$i] = Fraction($n[$i],$b[$i])->reduce;
            $df[$i] = dfrac($f[$i]);
            for ($j = 0; $j < $i; $j++) {
                $check = 0 if $f[$i] == $f[$j];
                $cntb += 1 if $b[$i] == $b[$j];
            }
            $check = 0 if floor($f[$i]) == $f[$i];
        }
    } until ($f[2] != $f[0]); # prevent divide by zero
    $m1 = (($f[3]-$f[1])/($f[2]-$f[0]))->reduce;
} until ($check && $m1 != floor($m1) && $cntb <= 2);

sub dfrac {
    my ($n) = @_;
    my ($a,$b) = reduce($n->value);
    my ($pa,$pb) = (abs($a),abs($b));
    my $dfrac = ($n > 0) ? "" : "-";
    return $dfrac."\dfrac{$pa}{$pb}";
}

$case = random(0,1); # zero slope or DNE
@numsb = (1..10)[shuffle(10)];
if ($case) {
    @yb = (random(-1,1,2)*$numsb[0],random(-1,1,2)*$numsb[1]);
    $yb[1] = -sgn($yb[0])*$yb[1];
    @xb = (random(-1,1,2)*$numsb[2],$numsb[2]);
    $xb[1] = sgn($xb[0])*$xb[1];
} else {
    @xb = (random(-1,1,2)*$numsb[0],$numsb[1]);
    $xb[1] = -sgn($xb[0])*$xb[1];
    @yb = (random(-1,1,2)*$numsb[2],$numsb[2]);
    $yb[1] = sgn($yb[0])*$yb[1];
}


Context("LimitedFraction");
Context()->flags->set(tolerance => 0, tolType => "absolute");
Context()->flags->set(showMixedNumbers=>0);
Context()->parens->redefine('(');
$message = "Each answer should be a reduced integer or fraction, or DNE";
Context()->{error}{msg}{"Can't use '%s' in this context"} = $message;
Context()->{error}{msg}{"Can't use implied multiplication in this context"} = $message;
Context()->{error}{msg}{"Unexpected character '['"} = "Brackets are not allowed";

$m1 = Fraction($m1);
$m2 = ($case) ? String("DNE") : Fraction("0");

################################################################################
#  Text
################################################################################

BEGIN_PGML
>> *TAMU_QID:* BM_00033

[$HR]*
Determine the slope of the line passing through the given points.
Enter *DNE* in the blank if the slope does not exist.

Enter all answers in exact, reduced form. No decimals are allowed. 

a. [`\left([$df[0]],[$df[1]]\right)`] and [`\left([$df[2]],[$df[3]]\right)`]: [`\quad m = `] [__]{$m1}

b. [`\left([$xb[0]],[$yb[0]]\right)`] and [`\left([$xb[1]],[$yb[1]]\right)`]: [`\quad m = `] [__]{$m2->cmp(typeMatch => Fraction(1))}

END_PGML

################################################################################
#  Answers and Solutions
################################################################################

#BEGIN_HINT

#END_HINT

#BEGIN_PGML_SOLUTION

#END_PGML_SOLUTION

ENDDOCUMENT();