Fix bug 4686

Author: gajennings

OpenProblemLibrary/Rochester/setComplexNumbers3RationalFunctions/ss_3_1_11d.pg

@@ -37,60 +37,69 @@ Context("Complex");
 #
 #
 
-$a  = random(-1,10,1);
-$b  = random(-1,10,1);
+$a  = Complex(random(-3,8,1));
+$b  = Complex(random(-3,8,1));
 
+# create
+# f = 2z/((z-a)(z-b)) + 2/(z+1)  =  [2z(z+1) + 2(z-a)(z-b)]/[(z-a)(z-b)(z+1)]
 
-#create two complex roots
-$aa = Complex($a, $ai); # Formula("$a + i ($ai)");
-$bb = Complex($b, $bi); # Formula("$b + i ($bi)");
+$f = Compute("2z/(z^2 - ($a+$b)z + $a*$b) + 2/(z+1)")->reduce; 
 
-# calculate quadratic polynomial
-$cc =  $aa+$bb ;
-$dd =   $aa*$bb;
-$quad = Formula("z^2 - ${cc}z+$dd")->reduce;
+# initialize generic answer for use unless special conditions are met
 
-# enter rational function
-$f = Formula("2z/(".$quad->string.")+2/(z+1)");
-$f->reduce;
+$poles_deg1 = List(Complex(-1),Complex($a),Complex($b));
+$poles_deg2 = List("none");
+$poles_deg3 = List("none");
 
-#calculate pole locations factors
+# the special conditions are:
 
-if (($aa == -1)&&($bb == -1))
-# Repeated Root of -1
-{
-$poles_deg1 = List(Formula("none"));
-$poles_deg2 = List($bb);
-$poles_deg3 = List(Formula("none"));
+if ($a==0){                # then f = 2/(z-b) + 2/(z+1)
+   if ($b == -1) {
+      $poles_deg1 = List(Complex(-1));
+   }
+   else {
+      $poles_deg1 = List(Complex($b),Complex(-1));
+   }
 }
-elsif ($aa == -1)
-# Shared root of -1 amongst polynomial created and (z + 1)
-{
-$poles_deg1 = List($bb, $aa);
-$poles_deg2 = List(Formula("none"));
-$poles_deg3 = List(Formula("none"));
+elsif ($b==0) {             # then f = 2/(z-a) + 2/(z+1) 
+   if ($a == -1) {
+      $poles_deg1 = List(Complex(-1));
+   }
+   else {
+      $poles_deg1 = List(Complex($a),Complex(-1));
+   }
 }
-elsif ($bb == -1)
-{
-$poles_deg1 = List($bb, $aa);
-$poles_deg2 = List(Formula("none"));
-$poles_deg3 = List(Formula("none"));
+elsif ($a == -1) {         # then f = 2(2z-b)/((z+1)(z-b)) and b != 0
+   if ($b == -2) {
+      $poles_deg1 = List(Complex(-1));
+   }
+   elsif ($b == -1) {
+      $poles_deg1 = List("none");
+      $poles_deg2 = List(Complex(-1));
+   }
+   else {
+      $poles_deg1 = List(Complex(-1),Complex($b));
+   }
 }
-elsif($aa == $bb)
-# Repeated root (but not -1) with the -1 root
-{
-$poles_deg1 = List(Complex(-1,0));
-$poles_deg2 = List($aa);
-$poles_deg3 = List(Formula("none"));
+elsif ($b == -1) {         # then f = 2(2z-a)/((z+1)(z-a)) and a != 0
+   if ($a == -2) {
+      $poles_deg1 = List(Complex(-1));
+   }
+   elsif ($a == -1) {
+      $poles_deg1 = List("none");
+      $poles_deg2 = List(Complex(-1));
+   }
+   else {
+      $poles_deg1 = List(Complex(-1),Complex($a));
+   }
 }
-else
-# Two distinct roots (with neither = -1) and the -1 root
-{
-$poles_deg1 = List($aa, $bb, Complex(-1,0));
-$poles_deg2 = List(Formula("none"));
-$poles_deg3 = List(Formula("none"));
+elsif ($a == $b)  {        # then f = 2z/(z-a)^2 + 2/(z+1) and a != 0 and a != -1
+   $poles_deg1 = List(Complex(-1));
+   $poles_deg2 = List(Complex($a));
 }
 
+  
+
 ##############################################################
 #
 #  Text
@@ -99,7 +108,7 @@ $poles_deg3 = List(Formula("none"));
 Context()->texStrings;
 
 BEGIN_TEXT
-Find the poles  for the function:
+Find the poles  for the function: 
 
 \[ R(z) = $f \]