View of /trunk/webwork/system/courseScripts/PGcomplexmacros.pl

    1 #!/usr/local/bin/webwork-perl
    2 # This file     is PGcomplexmacros.pl
    3 # This includes the subroutines for the ANS macros, that
    4 # is, macros allowing a more flexible answer checking
    5 ####################################################################
    6 # Copyright @ 1995-2001 The WeBWorK Team
    7 # All Rights Reserved
    8 ####################################################################
    9 #$Id$
   10 
   11 
   12 =head1 NAME
   13 
   14   Macros for complex numbers for the PG language
   15 
   16 =head1 SYNPOSIS
   17 
   18 
   19 
   20 =head1 DESCRIPTION
   21 
   22 =cut
   23 
   24 
   25 BEGIN{
   26   be_strict();
   27 
   28 }
   29 sub _PGcomplexmacros_init {
   30 }
   31 # export functions from Complex1.
   32 
   33 foreach my $f (@Complex1::EXPORT) {
   34     #PG_restricted_eval("\*$f = \*Complex1::$f"); # this is too clever --
   35                                                   # the original subroutines are destroyed
   36         next if $f eq 'sqrt';  #exporting the square root caused conflicts with the standard version
   37                                # You can still use Complex1::sqrt to take square root of complex numbers
   38         next if $f eq 'log';  #exporting loq caused conflicts with the standard version
   39                                # You can still use Complex1::log to take square root of complex numbers
   40 
   41     my $string = qq{
   42        sub main::$f {
   43            &Complex1::$f;
   44        }
   45     };
   46     PG_restricted_eval($string);
   47 }
   48 
   49 # You need to add
   50 # sub i();  # to your problem or else to dangerousMacros.pl
   51 # in order to use expressions such as 1 +3*i;
   52 # Without this prototype you would have to write 1+3*i();
   53 # The prototype has to be defined at compile time, but dangerousMacros.pl is complied first.
   54 #Complex1::display_format('cartesian');
   55 
   56 
   57 =head4 polar
   58   Usage polar($complex_number,r_format=>"%0.3f",theta_format=>"%0.3f")
   59 
   60   Output is text displaying the complex number in "e to the i theta" form.  The
   61   formats for the argument theta is determined by the option C<theta_format> and the
   62   format for the modulus is determined by the C<r_format> option.
   63 
   64 
   65 
   66 sub polar{
   67   my $z = shift;
   68   my %options = @_;
   69   set_default_options(\%options,  r_format  => ':%0.3f',
   70           theta_format  => ':%0.3f',
   71   );
   72   my $r = rho($z);
   73   my $theta = $z->theta;
   74   $r_format=":" . $options{r_format};
   75   $theta_format = ":" . $options{theta_format});
   76   "{$r$r_format} e^{i {$theta$theta_format}}";
   77 
   78 }
   79 
   80 sub cplx_cmp {
   81   my $correctAns = shift;
   82   my %options = @_;
   83   $correctAns = cplx($correctAns,0) unless ref($correctAns) =~/Complex/;
   84   assign_option_aliases( \%options,
   85                 'reltol'    =>      'relTol',
   86     );
   87     set_default_options(\%options,
   88           'tolType'   =>  (defined($options{tol}) ) ? 'absolute' : 'relative',
   89           # default mode should be relative, to obtain this tol must not be defined
   90       'tol'     =>  $main::numAbsTolDefault,
   91                   'relTol'    =>  $main::numRelPercentTolDefault,
   92       'zeroLevel'   =>  $main::numZeroLevelDefault,
   93       'zeroLevelTol'    =>  $main::numZeroLevelTolDefault,
   94       'format'    =>  $main::numFormatDefault,
   95       'debug'     =>  0,
   96 
   97     );
   98 
   99 
  100   my $ans_eval = sub {
  101                my $in = shift;
  102       my $rh_ans = new AnswerHash;
  103          $rh_ans->{correct_ans} = $correctAns;
  104          unless (defined($in) and $in =~/\S/ ) { #bail on empty answer
  105             $rh_ans->{student_ans} = "error: empty";
  106           return $rh_ans;
  107          }
  108          my($PG_errors,$PG_errors_long);
  109 
  110                  $rh_ans->input($in);
  111 
  112                  $rh_ans->{student_ans}=math_constants($rh_ans->{student_ans});
  113                  $rh_ans->{student_ans} =~ s/e\^/exp /g;  #try to handle exponents
  114                  $rh_ans=check_syntax($rh_ans);
  115                  $rh_ans->{student_ans} =~ s/\bi\b/(i)/g;  #try to keep -i being recognized as a file reference
  116                                                            # and recognized as a function whose output is an imaginary number
  117 
  118 
  119 
  120          warn $rh_ans->pretty_print() if defined($options{debug}) and $options{debug}==1;
  121          ($in,$PG_errors,$PG_errors_long) = PG_restricted_eval($rh_ans->{student_ans});
  122                  $in = $in +0*i;   # force the input to be complex
  123          if ($PG_errors_long) {
  124           $rh_ans->{error}=1;
  125           $rh_ans->{ans_message} = $PG_errors;
  126          } else {
  127            $in->display_format('cartesian') if ref($in) =~/Complex/;
  128            $rh_ans->{student_ans}="$in";
  129            my $permitted_error;
  130           if (defined($options{tolType}) && $options{tolType} eq 'absolute')  {
  131             $permitted_error = $options{tol};
  132           } elsif ( abs($correctAns) <= $options{zeroLevel}) {
  133               $permitted_error = $options{zeroLevelTol};  ## want $tol  to be non zero
  134           } else {
  135               $permitted_error = abs(.01*$options{relTol}*$correctAns); # relative tolerance is given in per cent
  136           }
  137                   $rh_ans->{score} =  (abs($in - $correctAns)<$permitted_error )? 1:0;
  138 
  139                }
  140 
  141                  $rh_ans;
  142                  };
  143     $ans_eval;
  144 }
  145 
  146 1;