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1#!/usr/local/bin/webwork-perl 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
2BEGIN{ 24BEGIN{
3 be_strict(); 25 be_strict();
4 sub i(); 26
5} 27}
6 28
7foreach my $f (@Complex1::EXPORT) { 29 sub _PGcomplexmacros_init {
8 PG_restricted_eval("\*$f = \*Complex1::$f");
9} 30}
31
32# export functions from Complex1.
33
34 foreach my $f (@Complex1::EXPORT) {
35# #PG_restricted_eval("\*$f = \*Complex1::$f"); # this is too clever --
36 # the original subroutines are destroyed
37 next if $f eq 'sqrt'; #exporting the square root caused conflicts with the standard version
38 # You can still use Complex1::sqrt to take square root of complex numbers
39 next if $f eq 'log'; #exporting loq caused conflicts with the standard version
40 # You can still use Complex1::log to take square root of complex numbers
41
42 my $string = qq{
43 &Complex1::$f;
44 };
45
46 PG_restricted_eval($string);
47 };
48
49
50
51
10 52
11# You need to add 53# You need to add
12# sub i(); # to your problem or else to dangerousMacros.pl 54# sub i(); # to your problem or else to dangerousMacros.pl
13# in order to use expressions such as 1 +3*i; 55# in order to use expressions such as 1 +3*i;
14# Without this prototype you would have to write 1+3*i(); 56# Without this prototype you would have to write 1+3*i();
15# The prototype has to be defined at compile time, but dangerousMacros.pl is complied first. 57# The prototype has to be defined at compile time, but dangerousMacros.pl is complied first.
16#Complex1::display_format('cartesian'); 58#Complex1::display_format('cartesian');
17 59
60
61=head4 polar
62
63=pod
64
65 Usage polar($complex_number,r_format=>"%0.3f",theta_format=>"%0.3f")
66
67 Output is text displaying the complex number in "e to the i theta" form. The
68 formats for the argument theta is determined by the option C<theta_format> and the
69 format for the modulus is determined by the C<r_format> option.
70
71=cut
72
73
74
18sub polar{ 75sub polar{
19 my $z = shift; 76 my $z = shift;
20 my %options = @_; 77 my %options = @_;
78 set_default_options(\%options, r_format => ':%0.3f',
79 theta_format => ':%0.3f',
80 );
21 my $r = rho($z); 81 my $r = rho($z);
22 my $theta = $z->theta; 82 my $theta = $z->theta;
23 my $r_format = ':%0.3f'; 83 my $r_format=":" . $options{r_format};
24 my $theta_format = ':%0.3f'; 84 my $theta_format = ":" . $options{theta_format};
25 $r_format=":" . $options{r_format} if defined($options{r_format});
26 $theta_format = ":" . $options{theta_format} if defined($options{theta_format});
27 "{$r$r_format} e^{i {$theta$theta_format}}"; 85 "{$r$r_format} e^{i {$theta$theta_format}}";
86}
28 87
29}
30sub cplx_cmp { 88sub cplx_cmp {
31 my $correctAns = shift; 89 my $correctAns = shift;
32 my %options = @_; 90 my %options = @_;
33 $correctAns = cplx($correctAns,0) unless ref($correctAns) =~/Complex/; 91 $correctAns = cplx($correctAns,0) unless ref($correctAns) =~/Complex/;
92 assign_option_aliases( \%options,
93 'reltol' => 'relTol',
94 );
34 set_default_options(\%options, 95 set_default_options(\%options,
35 reltol => .01 96 'tolType' => (defined($options{tol}) ) ? 'absolute' : 'relative',
97 # default mode should be relative, to obtain this tol must not be defined
98 'tol' => $main::numAbsTolDefault,
99 'relTol' => $main::numRelPercentTolDefault,
100 'zeroLevel' => $main::numZeroLevelDefault,
101 'zeroLevelTol' => $main::numZeroLevelTolDefault,
102 'format' => $main::numFormatDefault,
103 'debug' => 0,
104
36 ); 105 );
37 my $tol = .01*$options{reltol}; 106
107
38 my $ans_eval = sub { 108 my $ans_eval = sub {
39 my $in = shift; 109 my $in = shift;
40 my $rh_ans = new AnswerHash; 110 my $rh_ans = new AnswerHash;
111 $rh_ans->{correct_ans} = $correctAns;
112 unless (defined($in) and $in =~/\S/ ) { #bail on empty answer
113 $rh_ans->{student_ans} = "error: empty";
114 return $rh_ans;
115 }
41 my($PG_errors,$PG_errors_long); 116 my($PG_errors,$PG_errors_long);
42 $rh_ans->{correct_ans} = $correctAns; 117
43 $rh_ans->input($in); 118 $rh_ans->input($in);
119
120 $rh_ans->{student_ans}=math_constants($rh_ans->{student_ans});
121 $rh_ans->{student_ans} =~ s/e\^/exp /g; #try to handle exponents
44 $rh_ans=check_syntax($rh_ans); 122 $rh_ans=check_syntax($rh_ans);
45 $rh_ans->{student_ans} =~ s/e\^/exp /g; #try to handle exponents
46 $rh_ans->{student_ans} =~ s/-\s*i/-1*i/g; #try to keep -i being recognized as a file reference 123 $rh_ans->{student_ans} =~ s/\bi\b/(i)/g; #try to keep -i being recognized as a file reference
124 # and recognized as a function whose output is an imaginary number
125
126
127 warn $rh_ans->pretty_print() if defined($options{debug}) and $options{debug}==1;
47 ($in,$PG_errors,$PG_errors_long) = PG_restricted_eval($rh_ans->{student_ans}); 128 ($in,$PG_errors,$PG_errors_long) = PG_restricted_eval($rh_ans->{student_ans});
129 $in = $in +0*i; # force the input to be complex
48 if ($PG_errors_long) { 130 if ($PG_errors_long) {
49 $rh_ans->{error}=1; 131 $rh_ans->{error}=1;
50 $rh_ans->{ans_message} = $PG_errors; 132 $rh_ans->{ans_message} = $PG_errors;
51 } else { 133 } else {
52 $in->display_format('cartesian') if ref($in) =~/Complex/; 134 $in->display_format('cartesian') if ref($in) =~/Complex/;
53 $rh_ans->{student_ans}="$in"; 135 $rh_ans->{student_ans}="$in";
136 my $permitted_error;
137 if (defined($options{tolType}) && $options{tolType} eq 'absolute') {
138 $permitted_error = $options{tol};
139 } elsif ( abs($correctAns) <= $options{zeroLevel}) {
140 $permitted_error = $options{zeroLevelTol}; ## want $tol to be non zero
141 } else {
142 $permitted_error = abs(.01*$options{relTol}*$correctAns); # relative tolerance is given in per cent
143 }
54 $rh_ans->{score} = (abs($in - $correctAns)<$tol*abs($correctAns) )? 1:0; 144 $rh_ans->{score} = (abs($in - $correctAns)<$permitted_error )? 1:0;
55 145
56 } 146 }
147
57 $rh_ans; 148 $rh_ans;
58 }; 149 };
59 $ans_eval; 150 $ans_eval;
60} 151}
61 152

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