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7# All Rights Reserved 7# All Rights Reserved
8#################################################################### 8####################################################################
9#$Id$ 9#$Id$
10 10
11 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
12BEGIN{ 25BEGIN{
13 be_strict(); 26 be_strict();
14 27
28}
29sub _PGcomplexmacros_init {
15} 30}
16# export functions from Complex1. 31# export functions from Complex1.
17 32
18foreach my $f (@Complex1::EXPORT) { 33foreach my $f (@Complex1::EXPORT) {
19 #PG_restricted_eval("\*$f = \*Complex1::$f"); # this is too clever -- 34 #PG_restricted_eval("\*$f = \*Complex1::$f"); # this is too clever --
20 # the original subroutines are destroyed 35 # the original subroutines are destroyed
21 next if $f eq 'sqrt'; #exporting the square root caused conflicts with the standard version 36 next if $f eq 'sqrt'; #exporting the square root caused conflicts with the standard version
22 # You can still use Complex1::sqrt to take square root of complex numbers 37 # You can still use Complex1::sqrt to take square root of complex numbers
23 local($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 $string = qq{
24 sub main::$f { 42 sub main::$f {
25 &Complex1::$f; 43 &Complex1::$f;
26 } 44 }
27 }; 45 };
28 PG_restricted_eval($main::string); 46 PG_restricted_eval($string);
29} 47}
30 48
31# You need to add 49# You need to add
32# sub i(); # to your problem or else to dangerousMacros.pl 50# sub i(); # to your problem or else to dangerousMacros.pl
33# in order to use expressions such as 1 +3*i; 51# in order to use expressions such as 1 +3*i;
34# Without this prototype you would have to write 1+3*i(); 52# Without this prototype you would have to write 1+3*i();
35# The prototype has to be defined at compile time, but dangerousMacros.pl is complied first. 53# The prototype has to be defined at compile time, but dangerousMacros.pl is complied first.
36#Complex1::display_format('cartesian'); 54#Complex1::display_format('cartesian');
37 55
56
57=head4 polar
58 Usage polar($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
38sub polar{ 66sub polar{
39 my $z = shift; 67 my $z = shift;
40 my %options = @_; 68 my %options = @_;
69 set_default_options(\%options, r_format => ':%0.3f',
70 theta_format => ':%0.3f',
71 );
41 my $r = rho($z); 72 my $r = rho($z);
42 my $theta = $z->theta; 73 my $theta = $z->theta;
43 my $r_format = ':%0.3f'; 74 $r_format=":" . $options{r_format};
44 my $theta_format = ':%0.3f'; 75 $theta_format = ":" . $options{theta_format});
45 $r_format=":" . $options{r_format} if defined($options{r_format});
46 $theta_format = ":" . $options{theta_format} if defined($options{theta_format});
47 "{$r$r_format} e^{i {$theta$theta_format}}"; 76 "{$r$r_format} e^{i {$theta$theta_format}}";
48 77
49} 78}
79
50sub cplx_cmp { 80sub cplx_cmp {
51 my $correctAns = shift; 81 my $correctAns = shift;
52 my %options = @_; 82 my %options = @_;
53 $correctAns = cplx($correctAns,0) unless ref($correctAns) =~/Complex/; 83 $correctAns = cplx($correctAns,0) unless ref($correctAns) =~/Complex/;
54 assign_option_aliases( \%options, 84 assign_option_aliases( \%options,
55 'reltol' => 'relTol', 85 'reltol' => 'relTol',
56 ); 86 );
57 set_default_options(\%options, 87 set_default_options(\%options,
58 'tolType' => (defined($options{tol}) ) ? 'absolute' : 'relative', 88 'tolType' => (defined($options{tol}) ) ? 'absolute' : 'relative',
59 # 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
60 'tol' => $main::numAbsTolDefault, 90 'tol' => $main::numAbsTolDefault,
61 'relTol' => $main::numRelPercentTolDefault, 91 'relTol' => $main::numRelPercentTolDefault,
62 'zeroLevel' => $main::numZeroLevelDefault, 92 'zeroLevel' => $main::numZeroLevelDefault,
63 'zeroLevelTol' => $main::numZeroLevelTolDefault, 93 'zeroLevelTol' => $main::numZeroLevelTolDefault,
64 'format' => $main::numFormatDefault, 94 'format' => $main::numFormatDefault,
65 'debug' => 0, 95 'debug' => 0,
66 96
67 ); 97 );
68 98
69 99
70 my $ans_eval = sub { 100 my $ans_eval = sub {
71 my $in = shift; 101 my $in = shift;
72 my $rh_ans = new AnswerHash; 102 my $rh_ans = new AnswerHash;
73 $rh_ans->{correct_ans} = $correctAns; 103 $rh_ans->{correct_ans} = $correctAns;
74 unless (defined($in) and $in =~/\S/ ) { #bail on empty answer 104 unless (defined($in) and $in =~/\S/ ) { #bail on empty answer
75 $rh_ans->{student_ans} = "error: empty"; 105 $rh_ans->{student_ans} = "error: empty";
76 return $rh_ans; 106 return $rh_ans;
77 } 107 }

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