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1 : gage 102 #!/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 : gage 321
13 :    
14 :    
15 :    
16 :    
17 :    
18 :    
19 : gage 219 =head1 NAME
20 :    
21 :     Macros for complex numbers for the PG language
22 :    
23 :     =head1 SYNPOSIS
24 :    
25 :    
26 :    
27 :     =head1 DESCRIPTION
28 :    
29 :     =cut
30 :    
31 :    
32 : gage 45 BEGIN{
33 :     be_strict();
34 : gage 91
35 : gage 45 }
36 : gage 219 sub _PGcomplexmacros_init {
37 : gage 321
38 : gage 91 # export functions from Complex1.
39 : gage 45
40 : gage 321 foreach my $f (@Complex1::EXPORT) {
41 :     #PG_restricted_eval("\*$f = \*Complex1::$f"); # this is too clever --
42 :     # the original subroutines are destroyed
43 :     next if $f eq 'sqrt'; #exporting the square root caused conflicts with the standard version
44 :     # You can still use Complex1::sqrt to take square root of complex numbers
45 :     next if $f eq 'log'; #exporting loq caused conflicts with the standard version
46 :     # You can still use Complex1::log to take square root of complex numbers
47 :    
48 :     my $string = qq{
49 :     sub main::$f {
50 :     &Complex1::$f;
51 :     }
52 :     };
53 :     PG_restricted_eval($string);
54 :     }
55 : gage 45 }
56 :    
57 :     # You need to add
58 :     # sub i(); # to your problem or else to dangerousMacros.pl
59 :     # in order to use expressions such as 1 +3*i;
60 :     # Without this prototype you would have to write 1+3*i();
61 :     # The prototype has to be defined at compile time, but dangerousMacros.pl is complied first.
62 :     #Complex1::display_format('cartesian');
63 :    
64 : gage 219
65 : gage 293 =head4 polar
66 : gage 321
67 : gage 293 Usage polar($complex_number,r_format=>"%0.3f",theta_format=>"%0.3f")
68 :    
69 :     Output is text displaying the complex number in "e to the i theta" form. The
70 :     formats for the argument theta is determined by the option C<theta_format> and the
71 :     format for the modulus is determined by the C<r_format> option.
72 : gage 219
73 : gage 321 =cut
74 :    
75 :    
76 : gage 45 sub polar{
77 :     my $z = shift;
78 :     my %options = @_;
79 : gage 293 set_default_options(\%options, r_format => ':%0.3f',
80 : gage 321 theta_format => ':%0.3f',
81 : gage 293 );
82 :     my $r = rho($z);
83 :     my $theta = $z->theta;
84 : gage 321 my $r_format=":" . $options{r_format};
85 :     my $theta_format = ":" . $options{theta_format});
86 : gage 293 "{$r$r_format} e^{i {$theta$theta_format}}";
87 : gage 45
88 :     }
89 : gage 219
90 : gage 45 sub cplx_cmp {
91 :     my $correctAns = shift;
92 :     my %options = @_;
93 :     $correctAns = cplx($correctAns,0) unless ref($correctAns) =~/Complex/;
94 : gage 91 assign_option_aliases( \%options,
95 :     'reltol' => 'relTol',
96 :     );
97 : gage 45 set_default_options(\%options,
98 : gage 293 'tolType' => (defined($options{tol}) ) ? 'absolute' : 'relative',
99 :     # default mode should be relative, to obtain this tol must not be defined
100 :     'tol' => $main::numAbsTolDefault,
101 :     'relTol' => $main::numRelPercentTolDefault,
102 :     'zeroLevel' => $main::numZeroLevelDefault,
103 :     'zeroLevelTol' => $main::numZeroLevelTolDefault,
104 :     'format' => $main::numFormatDefault,
105 :     'debug' => 0,
106 : gage 91
107 : gage 45 );
108 : gage 91
109 :    
110 : gage 45 my $ans_eval = sub {
111 :     my $in = shift;
112 : gage 293 my $rh_ans = new AnswerHash;
113 : gage 91 $rh_ans->{correct_ans} = $correctAns;
114 :     unless (defined($in) and $in =~/\S/ ) { #bail on empty answer
115 :     $rh_ans->{student_ans} = "error: empty";
116 :     return $rh_ans;
117 :     }
118 : gage 45 my($PG_errors,$PG_errors_long);
119 : gage 91
120 : gage 45 $rh_ans->input($in);
121 : gage 91
122 :     $rh_ans->{student_ans}=math_constants($rh_ans->{student_ans});
123 :     $rh_ans->{student_ans} =~ s/e\^/exp /g; #try to handle exponents
124 : gage 45 $rh_ans=check_syntax($rh_ans);
125 : gage 91 $rh_ans->{student_ans} =~ s/\bi\b/(i)/g; #try to keep -i being recognized as a file reference
126 :     # and recognized as a function whose output is an imaginary number
127 :    
128 :    
129 :    
130 :     warn $rh_ans->pretty_print() if defined($options{debug}) and $options{debug}==1;
131 : gage 45 ($in,$PG_errors,$PG_errors_long) = PG_restricted_eval($rh_ans->{student_ans});
132 : gage 91 $in = $in +0*i; # force the input to be complex
133 : gage 45 if ($PG_errors_long) {
134 :     $rh_ans->{error}=1;
135 :     $rh_ans->{ans_message} = $PG_errors;
136 :     } else {
137 :     $in->display_format('cartesian') if ref($in) =~/Complex/;
138 :     $rh_ans->{student_ans}="$in";
139 : gage 91 my $permitted_error;
140 :     if (defined($options{tolType}) && $options{tolType} eq 'absolute') {
141 :     $permitted_error = $options{tol};
142 :     } elsif ( abs($correctAns) <= $options{zeroLevel}) {
143 :     $permitted_error = $options{zeroLevelTol}; ## want $tol to be non zero
144 :     } else {
145 :     $permitted_error = abs(.01*$options{relTol}*$correctAns); # relative tolerance is given in per cent
146 :     }
147 :     $rh_ans->{score} = (abs($in - $correctAns)<$permitted_error )? 1:0;
148 : gage 45
149 :     }
150 : gage 91
151 : gage 45 $rh_ans;
152 :     };
153 :     $ans_eval;
154 :     }
155 :    
156 :     1;

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