Fix bug 4825, simplify the code

OpenProblemLibrary/AlfredUniv/anton8e/chapter10/review/prob2.pg

@@ -32,83 +32,52 @@ DOCUMENT();
 loadMacros(
   "PGstandard.pl",
   "MathObjects.pl",
-  "PGgraphmacros.pl",
-  "PGchoicemacros.pl",
+  "PGML.pl", 
+  "parserCheckboxList.pl", 
+  "parserPopUp.pl",
   "PGcourse.pl"
 );
-TEXT(beginproblem());
-$showPartialCorrectAnswers = 1;
 
+$showPartialCorrectAnswers = 0;
 
-my @all,@correct,%difference;
-
-###############################################################################
-##
-## The list of series tests
-##
-Context()->strings->are("Converges"=>{},"Converges Absolutely"=>{},"Converges Conditionally"=>{},"Diverges"=>{},"Divergence Test"=>{},"Geometric Series"=>{},"Integral Test"=>{},"P-Series"=>{},"Comparison Test"=>{},"Limit Comparison Test"=>{},"Ratio Test"=>{},"Alternating Series Test"=>{});
-
-$blank = String("");
-$converges = String("Converges");
-$convergesabs = String("Converges Absolutely");
-$convergescond = String("Converges Conditionally");
-$diverges = String("Diverges");
-
-$divergence = String("Divergence Test");
-$geometric = String("Geometric Series");
-$integral = String("Integral Test");
-$pseries = String("P-Series");
-$comparison = String("Comparison Test");
-$limitcomparison = String("Limit Comparison Test");
-$ratio = String("Ratio Test");
-$alternating = String("Alternating Series Test");
-
-
-##############################################################################
-##############################################################################
-##
-##  Set up the infinite series
-##    
-##  To change the problem change $n the start value for the series, $an the 
-## terms of the series, $correct which is the list of test that can be used 
-## for the series, $ans which is whether the series converges or not.
-
-Context()->variables->are(n=>"Real",k=>"Real");
-
-$n = 1; # starting value for the series
-$an = Formula("1/(n^2)")->TeX;
-$ans = $converges;
-
-my @all = ($divergence->string,$geometric->string,$integral->string,$pseries->string,$comparison->string,$limitcomparison->string,$ratio->string,$alternating->string);
-
-my @correct = ($pseries->string,$integral->string); 
-
-my %all=map{$_ =>1} @all;
-my %correct=map{$_=>1} @correct;
-my @difference=grep(!defined $correct{$_}, @all);
-
-## The multiple choice question.
-$mc =  new_checkbox_multiple_choice();
-## the correct answers.
-$mc->qa("", @correct);
-## the list of other answers.
-$mc->extra(@difference);
-
-Context()->texStrings;
-BEGIN_TEXT
-Which of the following series convergence tests could be applied to the infinite series  \(\sum\limits_{n=$n}^\infty $an\)? Check all that apply.
-\{ $mc->print_q() \}
-\{ $mc->print_a() \}
-$BR
-The series \{ pop_up_list([$blank->string,$converges->string,$convergesabs->string,$convergescond->string,$diverges->string]) \}
-END_TEXT
-Context()->normalStrings;
-
-install_problem_grader(~~&std_problem_grader);
+$test = CheckboxList(
+  [ "Divergence Test",
+    "Geometric Series Test",
+    "Integral Test",
+    "P-Series Test",
+    "Comparison Test",
+    "Limit Comparison Test",
+    "Ratio Test",
+    "Alternating Series Test"
+  ],
+  [2,3]
+);
 
-$showPartialCorrectAnswers = 0;
-ANS( checkbox_cmp( $mc->correct_ans() ) );
-ANS($ans->cmp);
+$convergeQ = PopUp(
+  ["??", "Yes, it converges.","No, it diverges.", "The test(s) fail to decide this."],
+  "Yes, it converges."
+);
 
+BEGIN_PGML
+Consider the infinite series     
+    [`` \sum_{n=1}^{\infty} \frac{1}{n^2} ``]    
+Which of the following convergence tests is a good way to decide whether or not this series converges?  Check all that apply.    
+    [_]{$test}
+
+Does the series converge?    
+    [_]{$convergeQ}
+END_PGML 
+
+BEGIN_PGML_SOLUTION
+* [``0=\lim_{n\to\infty} 1/n^2 \ ``] so the "divergence test" does not apply.
+* Our series is not a geometric series.
+* Our series is a series of positive terms and [``\int_1^\infty 1/x^2\; dx < \infty ``] so the integral test says that the series converges. 
+* Our series is a "p-series" with [`p=2`] which is larger than 1, so the "P-series test" says that the series converges.
+* To use the "comparison test" we'd need another series [``\ \sum_{n=1}^{\infty} b_n \ ``] that satisfies the criteria for the comparison test, and where it's easier to decide the convergence or divergence of this series than it is for 
+our series.  I can't think of any good candidates for the series [``\ \sum_{n=1}^{\infty} b_n``], can you?
+* The "limit comparison test" has the same issue as the "comparison test".
+* [``\lim_{n\to\infty} \frac{1/(n+1)^2}{1/n^2} = 1 ``] so the "ratio test" does not yield any useful information.
+* Our series is not an alternating series.
+END_PGML_SOLUTION
 
 ENDDOCUMENT();