Fix bug 4674

Author: gajennings

OpenProblemLibrary/274/Exact/prob5.pg

@@ -20,17 +20,14 @@ loadMacros(
   "PGcourse.pl"
 );
 
+Context("Numeric");
 Context()->variables->add(y=>"Real");
 
 TEXT(beginproblem()) ;
 $showPartialCorrectAnswers = 1;
 
-$a= non_zero_random(-4,4,1);
 do {$b= non_zero_random(-4,4,1);} until ($b!=-1);
-$z = random (1,3);
-$k = non_zero_random(-4,4,1);
-$c = non_zero_random(-4,4,1);
-$d = non_zero_random(-4,4,1);  
+
 $n = random(1,6,1);
 $n1=$n+1;
 do {$m = random(2,6,1);} until ($m!=$n);
@@ -39,81 +36,63 @@ $p = $m1-$n1;
 $p1 = $p + 1;
 if  ($n1-$m1==1) {
   $Fxy = Compute("-ln(y)+x/y^$n+$b x");
-  $r1 = [0,1];
-  $r2 = [2,5];
 } else {
   $Fxy = Compute("-y^$p1/$p1+x/y^$n+$b x");
-  $r1 = [1/$p1/($b+1),1];
-  $r2 = [20, 3.141592653589793238];
 }
 
-$M=Compute("y + $b y^$n1");
-$N=Compute("-y^{$m1}-$n x");
+$M=Compute("y + $b y^$n1")->reduce;
+$minusN = Compute("y^{$m1}+$n x");
+$N=-$minusN;
 
-$multians = MultiAnswer($M, $N)->with(
+$multians = MultiAnswer($M, $N, $Fxy)->with(
   singleResult => 0,
+  allowBlankAnswers=>1,
+  checkTypes=>0,
   checker => sub {
       my ( $correct, $student, $self ) = @_;
-      my ( $Mstu, $Nstu ) = @{$student};
-      my ( $M, $N) = @{$correct};
-      if ( ($M == $Mstu && $N == $Nstu) ||
-           ($M == -$Mstu && $N == -$Nstu) ) {
-          return [1,1];
-      } else {
-          if ($M == $Mstu || $M == -$Mstu) {
-              return [1,0];
-          } elsif ($N == $Nstu || $N == -$Nstu) {
-              return [0,1];
-          } else {
-              return [0,0];
-          }
+      my ( $Mstu, $Nstu, $Fxystu ) = @{$student};
+      my ( $M, $N, $Fxycorrect) = @{$correct};
+      my @score = (0,0,0);
+      my $mult = Compute("y^$n1");
+      # check types and values of first two inputs
+      if ( $M->typeMatch($Mstu) && $N->typeMatch($Nstu) ){
+         # check values of first two inputs
+         if ( ($Mstu != Formula(0) || $Nstu != Formula(0)) && $Mstu*$N - $Nstu*$M == Formula(0) ) { 
+            $score[0] = $score[1] = 1;
+         }
+      }
+      else { return [0,0,0]; }
+      # check type and value of third input
+      if ( $score[0]==1 && $score[1]==1 && $Fxycorrect->typeMatch($Fxystu) ) {
+         my $DFx = $Fxystu->D('x');
+         my $DFy = $Fxystu->D('y');
+         if ( ($DFx != Formula(0) || $DFy != Formula(0)) && $DFx*$N - $DFy*$M == Formula(0) ){
+            $score[2]=1; 
+         }
       }
+      return [@score];
   }
 );
 
-$lpol = nicestring([$b], ["y^${n1}"]);
-$rpol = nicestring([$n], ["x"]);
-
+Context()->texStrings;
 BEGIN_TEXT
 
 The differential equation 
-\[ y + $lpol = \left(y^${m1} + $rpol\right)y' \]
+\[ $M = \left($minusN \right)y' \]
 can be written in differential form:
 \[ M(x,y) \, dx + N(x,y) \, dy  = 0 \]
 where $BR
-\(M(x,y)= \) \{$multians->ans_rule(30)\} , and 
-\(N(x,y)= \) \{$multians->ans_rule(30)\}.
+\(M(x,y)= \) \{$multians->ans_rule(30)\} , and $BR
+\(N(x,y)= \) \{$multians->ans_rule(30)\}.  (To receive credit both answers must be correct.)
 $PAR
-The term \(M(x,y) \, dx + N(x,y) \, dy\) becomes an exact differential if the left hand side above is divided by \( y^${n1}\). Integrating that new equation, the solution of the differential equation is 
- \{ ans_rule(45) \} \(= C \).
+The term \(M(x,y) \, dx + N(x,y) \, dy\) becomes an exact differential if the left hand side above is divided by \( y^${n1}\). Integrating that new equation we obtain a solution of the differential equation: 
+ \{ $multians->ans_rule(45) \} \(= C \).
 
 END_TEXT
-
-# Can input a root, which defaults to [0,0], and another point
-#  which defaults to [2,1]
-sub lcc {
-  my ( $correct, $student, $anshash) = @_;
-  my %ah = %{ $anshash };
-  my $root = $ah{root};
-  $root = [0,0] unless defined($root);
-  my $other = $ah{other};
-  $other = [2,1] unless defined($other);
-  my $const = $student->eval(x=>$root->[0], y=>$root->[1]);
-  $student = $student-$const;
-  if($student== 0) {
-    Value::Error("The function cannot be constant");
-    return 0;
-  }
-  my $c1 = $student->eval(x=>$other->[0], y=>$other->[1])/
-    $correct->eval(x=>$other->[0], y=>$other->[1]);
-  return 0 if $c1 == 0;
-  $student = $student/$c1;
-  return $correct == $student;
-}
+Context()->normalStrings;
 
 
-ANS( $multians->cmp() );
-ANS( $Fxy->cmp(checker =>~~&lcc, root=> $r1, other=>$r2));
+ANS( $multians->cmp(limits => [[-2,2],[.1,10]]) ); 
 
 
 ENDDOCUMENT() ;        # This should be the last executable line in the problem.