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1#!/usr/local/bin/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
24
2BEGIN{ 25BEGIN{
3 be_strict(); 26 be_strict();
4 27
28}
29sub _PGcomplexmacros_init {
5} 30}
6# export functions from Complex1. 31# export functions from Complex1.
7 32
8foreach my $f (@Complex1::EXPORT) { 33foreach my $f (@Complex1::EXPORT) {
9 #PG_restricted_eval("\*$f = \*Complex1::$f"); # this is too clever -- 34 #PG_restricted_eval("\*$f = \*Complex1::$f"); # this is too clever --
10 # the original subroutines are destroyed 35 # the original subroutines are destroyed
11 next if $f eq 'sqrt'; #exporting the square root caused conflicts with the standard version 36 next if $f eq 'sqrt'; #exporting the square root caused conflicts with the standard version
12 # You can still use Complex1::sqrt to take square root of complex numbers 37 # You can still use Complex1::sqrt to take square root of complex numbers
13 local($main::string) = qq{ 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 $string = qq{
14 sub main::$f { 42 sub main::$f {
15 &Complex1::$f; 43 &Complex1::$f;
16 } 44 }
17 }; 45 };
18 PG_restricted_eval($main::string); 46 PG_restricted_eval($string);
19} 47}
20 48
21# You need to add 49# You need to add
22# sub i(); # to your problem or else to dangerousMacros.pl 50# sub i(); # to your problem or else to dangerousMacros.pl
23# in order to use expressions such as 1 +3*i; 51# in order to use expressions such as 1 +3*i;
24# Without this prototype you would have to write 1+3*i(); 52# Without this prototype you would have to write 1+3*i();
25# The prototype has to be defined at compile time, but dangerousMacros.pl is complied first. 53# The prototype has to be defined at compile time, but dangerousMacros.pl is complied first.
26#Complex1::display_format('cartesian'); 54#Complex1::display_format('cartesian');
27 55
56
57=head4 polar
58 Usage polar($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
28sub polar{ 66sub polar{
29 my $z = shift; 67 my $z = shift;
30 my %options = @_; 68 my %options = @_;
69 set_default_options(\%options, r_format => ':%0.3f',
70 theta_format => ':%0.3f',
71 );
31 my $r = rho($z); 72 my $r = rho($z);
32 my $theta = $z->theta; 73 my $theta = $z->theta;
33 my $r_format = ':%0.3f'; 74 $r_format=":" . $options{r_format};
34 my $theta_format = ':%0.3f'; 75 $theta_format = ":" . $options{theta_format});
35 $r_format=":" . $options{r_format} if defined($options{r_format});
36 $theta_format = ":" . $options{theta_format} if defined($options{theta_format});
37 "{$r$r_format} e^{i {$theta$theta_format}}"; 76 "{$r$r_format} e^{i {$theta$theta_format}}";
38 77
39} 78}
79
40sub cplx_cmp { 80sub cplx_cmp {
41 my $correctAns = shift; 81 my $correctAns = shift;
42 my %options = @_; 82 my %options = @_;
43 $correctAns = cplx($correctAns,0) unless ref($correctAns) =~/Complex/; 83 $correctAns = cplx($correctAns,0) unless ref($correctAns) =~/Complex/;
44 assign_option_aliases( \%options, 84 assign_option_aliases( \%options,
45 'reltol' => 'relTol', 85 'reltol' => 'relTol',
46 ); 86 );
47 set_default_options(\%options, 87 set_default_options(\%options,
48 'tolType' => (defined($options{tol}) ) ? 'absolute' : 'relative', 88 'tolType' => (defined($options{tol}) ) ? 'absolute' : 'relative',
49 # default mode should be relative, to obtain this tol must not be defined 89 # default mode should be relative, to obtain this tol must not be defined
50 'tol' => $main::numAbsTolDefault, 90 'tol' => $main::numAbsTolDefault,
51 'relTol' => $main::numRelPercentTolDefault, 91 'relTol' => $main::numRelPercentTolDefault,
52 'zeroLevel' => $main::numZeroLevelDefault, 92 'zeroLevel' => $main::numZeroLevelDefault,
53 'zeroLevelTol' => $main::numZeroLevelTolDefault, 93 'zeroLevelTol' => $main::numZeroLevelTolDefault,
54 'format' => $main::numFormatDefault, 94 'format' => $main::numFormatDefault,
55 'debug' => 0, 95 'debug' => 0,
56 96
57 ); 97 );
58 98
59 99
60 my $ans_eval = sub { 100 my $ans_eval = sub {
61 my $in = shift; 101 my $in = shift;
62 my $rh_ans = new AnswerHash; 102 my $rh_ans = new AnswerHash;
63 $rh_ans->{correct_ans} = $correctAns; 103 $rh_ans->{correct_ans} = $correctAns;
64 unless (defined($in) and $in =~/\S/ ) { #bail on empty answer 104 unless (defined($in) and $in =~/\S/ ) { #bail on empty answer
65 $rh_ans->{student_ans} = "error: empty"; 105 $rh_ans->{student_ans} = "error: empty";
66 return $rh_ans; 106 return $rh_ans;
67 } 107 }

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