| 1 | #!./perl
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| 2 |
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| 3 | #
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| 4 | # Regression tests for the Math::Complex pacakge
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| 5 | # -- Raphael Manfredi since Sep 1996
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| 6 | # -- Jarkko Hietaniemi since Mar 1997
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| 7 | # -- Daniel S. Lewart since Sep 1997
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| 8 |
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| 9 | BEGIN {
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| 10 | if ($ENV{PERL_CORE}) {
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| 11 | chdir 't' if -d 't';
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| 12 | @INC = '../lib';
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| 13 | }
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| 14 | }
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| 15 |
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| 16 | use Math::Complex;
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| 17 |
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| 18 | use vars qw($VERSION);
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| 19 |
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| 20 | $VERSION = 1.92;
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| 21 |
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| 22 | my ($args, $op, $target, $test, $test_set, $try, $val, $zvalue, @set, @val);
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| 23 |
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| 24 | $test = 0;
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| 25 | $| = 1;
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| 26 | my @script = (
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| 27 | 'my ($res, $s0,$s1,$s2,$s3,$s4,$s5,$s6,$s7,$s8,$s9,$s10,$z0,$z1,$z2);' .
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| 28 | "\n\n"
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| 29 | );
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| 30 | my $eps = 1e-13;
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| 31 |
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| 32 | if ($^O eq 'unicos') { # For some reason root() produces very inaccurate
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| 33 | $eps = 1e-10; # results in Cray UNICOS, and occasionally also
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| 34 | } # cos(), sin(), cosh(), sinh(). The division
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| 35 | # of doubles is the current suspect.
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| 36 |
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| 37 | while (<DATA>) {
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| 38 | s/^\s+//;
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| 39 | next if $_ eq '' || /^\#/;
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| 40 | chomp;
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| 41 | $test_set = 0; # Assume not a test over a set of values
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| 42 | if (/^&(.+)/) {
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| 43 | $op = $1;
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| 44 | next;
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| 45 | }
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| 46 | elsif (/^\{(.+)\}/) {
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| 47 | set($1, \@set, \@val);
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| 48 | next;
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| 49 | }
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| 50 | elsif (s/^\|//) {
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| 51 | $test_set = 1; # Requests we loop over the set...
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| 52 | }
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| 53 | my @args = split(/:/);
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| 54 | if ($test_set == 1) {
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| 55 | my $i;
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| 56 | for ($i = 0; $i < @set; $i++) {
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| 57 | # complex number
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| 58 | $target = $set[$i];
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| 59 | # textual value as found in set definition
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| 60 | $zvalue = $val[$i];
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| 61 | test($zvalue, $target, @args);
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| 62 | }
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| 63 | } else {
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| 64 | test($op, undef, @args);
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| 65 | }
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| 66 | }
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| 67 |
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| 68 | #
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| 69 |
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| 70 | sub test_mutators {
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| 71 | my $op;
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| 72 |
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| 73 | $test++;
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| 74 | push(@script, <<'EOT');
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| 75 | {
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| 76 | my $z = cplx( 1, 1);
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| 77 | $z->Re(2);
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| 78 | $z->Im(3);
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| 79 | print "# $test Re(z) = ",$z->Re(), " Im(z) = ", $z->Im(), " z = $z\n";
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| 80 | print 'not ' unless Re($z) == 2 and Im($z) == 3;
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| 81 | EOT
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| 82 | push(@script, qq(print "ok $test\\n"}\n));
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| 83 |
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| 84 | $test++;
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| 85 | push(@script, <<'EOT');
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| 86 | {
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| 87 | my $z = cplx( 1, 1);
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| 88 | $z->abs(3 * sqrt(2));
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| 89 | print "# $test Re(z) = ",$z->Re(), " Im(z) = ", $z->Im(), " z = $z\n";
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| 90 | print 'not ' unless (abs($z) - 3 * sqrt(2)) < $eps and
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| 91 | (arg($z) - pi / 4 ) < $eps and
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| 92 | (Re($z) - 3 ) < $eps and
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| 93 | (Im($z) - 3 ) < $eps;
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| 94 | EOT
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| 95 | push(@script, qq(print "ok $test\\n"}\n));
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| 96 |
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| 97 | $test++;
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| 98 | push(@script, <<'EOT');
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| 99 | {
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| 100 | my $z = cplx( 1, 1);
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| 101 | $z->arg(-3 / 4 * pi);
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| 102 | print "# $test Re(z) = ",$z->Re(), " Im(z) = ", $z->Im(), " z = $z\n";
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| 103 | print 'not ' unless (arg($z) + 3 / 4 * pi) < $eps and
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| 104 | (abs($z) - sqrt(2) ) < $eps and
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| 105 | (Re($z) + 1 ) < $eps and
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| 106 | (Im($z) + 1 ) < $eps;
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| 107 | EOT
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| 108 | push(@script, qq(print "ok $test\\n"}\n));
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| 109 | }
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| 110 |
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| 111 | test_mutators();
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| 112 |
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| 113 | my $constants = '
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| 114 | my $i = cplx(0, 1);
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| 115 | my $pi = cplx(pi, 0);
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| 116 | my $pii = cplx(0, pi);
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| 117 | my $pip2 = cplx(pi/2, 0);
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| 118 | my $pip4 = cplx(pi/4, 0);
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| 119 | my $zero = cplx(0, 0);
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| 120 | my $inf = 9**9**9;
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| 121 | ';
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| 122 |
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| 123 | push(@script, $constants);
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| 124 |
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| 125 |
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| 126 | # test the divbyzeros
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| 127 |
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| 128 | sub test_dbz {
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| 129 | for my $op (@_) {
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| 130 | $test++;
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| 131 | push(@script, <<EOT);
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| 132 | eval '$op';
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| 133 | (\$bad) = (\$@ =~ /(.+)/);
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| 134 | print "# $test op = $op divbyzero? \$bad...\n";
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| 135 | print 'not ' unless (\$@ =~ /Division by zero/);
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| 136 | EOT
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| 137 | push(@script, qq(print "ok $test\\n";\n));
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| 138 | }
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| 139 | }
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| 140 |
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| 141 | # test the logofzeros
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| 142 |
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| 143 | sub test_loz {
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| 144 | for my $op (@_) {
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| 145 | $test++;
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| 146 | push(@script, <<EOT);
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| 147 | eval '$op';
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| 148 | (\$bad) = (\$@ =~ /(.+)/);
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| 149 | print "# $test op = $op logofzero? \$bad...\n";
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| 150 | print 'not ' unless (\$@ =~ /Logarithm of zero/);
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| 151 | EOT
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| 152 | push(@script, qq(print "ok $test\\n";\n));
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| 153 | }
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| 154 | }
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| 155 |
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| 156 | test_dbz(
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| 157 | 'i/0',
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| 158 | 'acot(0)',
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| 159 | 'acot(+$i)',
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| 160 | # 'acoth(-1)', # Log of zero.
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| 161 | 'acoth(0)',
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| 162 | 'acoth(+1)',
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| 163 | 'acsc(0)',
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| 164 | 'acsch(0)',
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| 165 | 'asec(0)',
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| 166 | 'asech(0)',
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| 167 | 'atan($i)',
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| 168 | # 'atanh(-1)', # Log of zero.
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| 169 | 'atanh(+1)',
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| 170 | 'cot(0)',
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| 171 | 'coth(0)',
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| 172 | 'csc(0)',
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| 173 | 'csch(0)',
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| 174 | 'atan(cplx(0, 1), cplx(1, 0))',
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| 175 | );
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| 176 |
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| 177 | test_loz(
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| 178 | 'log($zero)',
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| 179 | 'atan(-$i)',
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| 180 | 'acot(-$i)',
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| 181 | 'atanh(-1)',
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| 182 | 'acoth(-1)',
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| 183 | );
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| 184 |
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| 185 | # test the bad roots
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| 186 |
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| 187 | sub test_broot {
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| 188 | for my $op (@_) {
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| 189 | $test++;
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| 190 | push(@script, <<EOT);
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| 191 | eval 'root(2, $op)';
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| 192 | (\$bad) = (\$@ =~ /(.+)/);
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| 193 | print "# $test op = $op badroot? \$bad...\n";
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| 194 | print 'not ' unless (\$@ =~ /root rank must be/);
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| 195 | EOT
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| 196 | push(@script, qq(print "ok $test\\n";\n));
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| 197 | }
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| 198 | }
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| 199 |
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| 200 | test_broot(qw(-3 -2.1 0 0.99));
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| 201 |
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| 202 | sub test_display_format {
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| 203 | $test++;
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| 204 | push @script, <<EOS;
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| 205 | print "# package display_format cartesian?\n";
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| 206 | print "not " unless Math::Complex->display_format eq 'cartesian';
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| 207 | print "ok $test\n";
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| 208 | EOS
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| 209 |
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| 210 | push @script, <<EOS;
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| 211 | my \$j = (root(1,3))[1];
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| 212 |
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| 213 | \$j->display_format('polar');
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| 214 | EOS
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| 215 |
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| 216 | $test++;
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| 217 | push @script, <<EOS;
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| 218 | print "# j display_format polar?\n";
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| 219 | print "not " unless \$j->display_format eq 'polar';
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| 220 | print "ok $test\n";
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| 221 | EOS
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| 222 |
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| 223 | $test++;
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| 224 | push @script, <<EOS;
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| 225 | print "# j = \$j\n";
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| 226 | print "not " unless "\$j" eq "[1,2pi/3]";
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| 227 | print "ok $test\n";
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| 228 |
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| 229 | my %display_format;
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| 230 |
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| 231 | %display_format = \$j->display_format;
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| 232 | EOS
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| 233 |
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| 234 | $test++;
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| 235 | push @script, <<EOS;
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| 236 | print "# display_format{style} polar?\n";
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| 237 | print "not " unless \$display_format{style} eq 'polar';
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| 238 | print "ok $test\n";
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| 239 | EOS
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| 240 |
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| 241 | $test++;
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| 242 | push @script, <<EOS;
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| 243 | print "# keys %display_format == 2?\n";
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| 244 | print "not " unless keys %display_format == 2;
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| 245 | print "ok $test\n";
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| 246 |
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| 247 | \$j->display_format('style' => 'cartesian', 'format' => '%.5f');
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| 248 | EOS
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| 249 |
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| 250 | $test++;
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| 251 | push @script, <<EOS;
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| 252 | print "# j = \$j\n";
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| 253 | print "not " unless "\$j" eq "-0.50000+0.86603i";
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| 254 | print "ok $test\n";
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| 255 |
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| 256 | %display_format = \$j->display_format;
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| 257 | EOS
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| 258 |
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| 259 | $test++;
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| 260 | push @script, <<EOS;
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| 261 | print "# display_format{format} %.5f?\n";
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| 262 | print "not " unless \$display_format{format} eq '%.5f';
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| 263 | print "ok $test\n";
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| 264 | EOS
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| 265 |
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| 266 | $test++;
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| 267 | push @script, <<EOS;
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| 268 | print "# keys %display_format == 3?\n";
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| 269 | print "not " unless keys %display_format == 3;
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| 270 | print "ok $test\n";
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| 271 |
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| 272 | \$j->display_format('format' => undef);
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| 273 | EOS
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| 274 |
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| 275 | $test++;
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| 276 | push @script, <<EOS;
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| 277 | print "# j = \$j\n";
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| 278 | print "not " unless "\$j" =~ /^-0(?:\\.5(?:0000\\d+)?|\\.49999\\d+)\\+0.86602540\\d+i\$/;
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| 279 | print "ok $test\n";
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| 280 |
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| 281 | \$j->display_format('style' => 'polar', 'polar_pretty_print' => 0);
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| 282 | EOS
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| 283 |
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| 284 | $test++;
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| 285 | push @script, <<EOS;
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| 286 | print "# j = \$j\n";
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| 287 | print "not " unless "\$j" =~ /^\\[1,2\\.09439510\\d+\\]\$/;
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| 288 | print "ok $test\n";
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| 289 |
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| 290 | \$j->display_format('style' => 'cartesian', 'format' => '(%.5g)');
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| 291 | EOS
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| 292 |
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| 293 | $test++;
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| 294 | push @script, <<EOS;
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| 295 | print "# j = \$j\n";
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| 296 | print "not " unless "\$j" eq "(-0.5)+(0.86603)i";
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| 297 | print "ok $test\n";
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| 298 | EOS
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| 299 |
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| 300 | $test++;
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| 301 | push @script, <<EOS;
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| 302 | print "# j display_format cartesian?\n";
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| 303 | print "not " unless \$j->display_format eq 'cartesian';
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| 304 | print "ok $test\n";
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| 305 | EOS
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| 306 | }
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| 307 |
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| 308 | test_display_format();
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| 309 |
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| 310 | sub test_remake {
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| 311 | $test++;
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| 312 | push @script, <<EOS;
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| 313 | print "# remake 2+3i\n";
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| 314 | \$z = cplx('2+3i');
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| 315 | print "not " unless \$z == Math::Complex->make(2,3);
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| 316 | print "ok $test\n";
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| 317 | EOS
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| 318 |
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| 319 | $test++;
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| 320 | push @script, <<EOS;
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| 321 | print "# make 3i\n";
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| 322 | \$z = Math::Complex->make('3i');
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| 323 | print "not " unless \$z == cplx(0,3);
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| 324 | print "ok $test\n";
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| 325 | EOS
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| 326 |
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| 327 | $test++;
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| 328 | push @script, <<EOS;
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| 329 | print "# emake [2,3]\n";
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| 330 | \$z = Math::Complex->emake('[2,3]');
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| 331 | print "not " unless \$z == cplxe(2,3);
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| 332 | print "ok $test\n";
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| 333 | EOS
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| 334 |
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| 335 | $test++;
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| 336 | push @script, <<EOS;
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| 337 | print "# make (2,3)\n";
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| 338 | \$z = Math::Complex->make('(2,3)');
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| 339 | print "not " unless \$z == cplx(2,3);
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| 340 | print "ok $test\n";
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| 341 | EOS
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| 342 |
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| 343 | $test++;
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| 344 | push @script, <<EOS;
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| 345 | print "# emake [2,3pi/8]\n";
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| 346 | \$z = Math::Complex->emake('[2,3pi/8]');
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| 347 | print "not " unless \$z == cplxe(2,3*\$pi/8);
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| 348 | print "ok $test\n";
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| 349 | EOS
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| 350 |
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| 351 | $test++;
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| 352 | push @script, <<EOS;
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| 353 | print "# emake [2]\n";
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| 354 | \$z = Math::Complex->emake('[2]');
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| 355 | print "not " unless \$z == cplxe(2);
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| 356 | print "ok $test\n";
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| 357 | EOS
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| 358 | }
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| 359 |
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| 360 | sub test_no_args {
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| 361 | push @script, <<'EOS';
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| 362 | {
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| 363 | print "# cplx, cplxe, make, emake without arguments\n";
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| 364 | EOS
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| 365 |
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| 366 | $test++;
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| 367 | push @script, <<EOS;
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| 368 | my \$z0 = cplx();
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| 369 | print ((\$z0->Re() == 0) ? "ok $test\n" : "not ok $test\n");
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| 370 | EOS
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| 371 |
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| 372 | $test++;
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| 373 | push @script, <<EOS;
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| 374 | print ((\$z0->Im() == 0) ? "ok $test\n" : "not ok $test\n");
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| 375 | EOS
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| 376 |
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| 377 | $test++;
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| 378 | push @script, <<EOS;
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| 379 | my \$z1 = cplxe();
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| 380 | print ((\$z1->rho() == 0) ? "ok $test\n" : "not ok $test\n");
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| 381 | EOS
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| 382 |
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| 383 | $test++;
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| 384 | push @script, <<EOS;
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| 385 | print ((\$z1->theta() == 0) ? "ok $test\n" : "not ok $test\n");
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| 386 | EOS
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| 387 |
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| 388 | $test++;
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| 389 | push @script, <<EOS;
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| 390 | my \$z2 = Math::Complex->make();
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| 391 | print ((\$z2->Re() == 0) ? "ok $test\n" : "not ok $test\n");
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| 392 | EOS
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| 393 |
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| 394 | $test++;
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| 395 | push @script, <<EOS;
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| 396 | print ((\$z2->Im() == 0) ? "ok $test\n" : "not ok $test\n");
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| 397 | EOS
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| 398 |
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| 399 | $test++;
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| 400 | push @script, <<EOS;
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| 401 | my \$z3 = Math::Complex->emake();
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| 402 | print ((\$z3->rho() == 0) ? "ok $test\n" : "not ok $test\n");
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| 403 | EOS
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| 404 |
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| 405 | $test++;
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| 406 | push @script, <<EOS;
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| 407 | print ((\$z3->theta() == 0) ? "ok $test\n" : "not ok $test\n");
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| 408 | }
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| 409 | EOS
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| 410 | }
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| 411 |
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| 412 | sub test_atan2 {
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| 413 | push @script, <<'EOS';
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| 414 | print "# atan2() with some real arguments\n";
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| 415 | EOS
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| 416 | my @real = (-1, 0, 1);
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| 417 | for my $x (@real) {
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| 418 | for my $y (@real) {
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| 419 | next if $x == 0 && $y == 0;
|
|---|
| 420 | $test++;
|
|---|
| 421 | push @script, <<EOS;
|
|---|
| 422 | print ((Math::Complex::atan2($y, $x) == CORE::atan2($y, $x)) ? "ok $test\n" : "not ok $test\n");
|
|---|
| 423 | EOS
|
|---|
| 424 | }
|
|---|
| 425 | }
|
|---|
| 426 | push @script, <<'EOS';
|
|---|
| 427 | print "# atan2() with some complex arguments\n";
|
|---|
| 428 | EOS
|
|---|
| 429 | $test++;
|
|---|
| 430 | push @script, <<EOS;
|
|---|
| 431 | print (abs(atan2(0, cplx(0, 1))) < $eps ? "ok $test\n" : "not ok $test\n");
|
|---|
| 432 | EOS
|
|---|
| 433 | $test++;
|
|---|
| 434 | push @script, <<EOS;
|
|---|
| 435 | print (abs(atan2(cplx(0, 1), 0) - \$pip2) < $eps ? "ok $test\n" : "not ok $test\n");
|
|---|
| 436 | EOS
|
|---|
| 437 | $test++;
|
|---|
| 438 | push @script, <<EOS;
|
|---|
| 439 | print (abs(atan2(cplx(0, 1), cplx(0, 1)) - \$pip4) < $eps ? "ok $test\n" : "not ok $test\n");
|
|---|
| 440 | EOS
|
|---|
| 441 | $test++;
|
|---|
| 442 | push @script, <<EOS;
|
|---|
| 443 | print (abs(atan2(cplx(0, 1), cplx(1, 1)) - cplx(0.553574358897045, 0.402359478108525)) < $eps ? "ok $test\n" : "not ok $test\n");
|
|---|
| 444 | EOS
|
|---|
| 445 | }
|
|---|
| 446 |
|
|---|
| 447 | sub test_decplx {
|
|---|
| 448 | }
|
|---|
| 449 |
|
|---|
| 450 | test_remake();
|
|---|
| 451 |
|
|---|
| 452 | test_no_args();
|
|---|
| 453 |
|
|---|
| 454 | test_atan2();
|
|---|
| 455 |
|
|---|
| 456 | test_decplx();
|
|---|
| 457 |
|
|---|
| 458 | print "1..$test\n";
|
|---|
| 459 | #print @script, "\n";
|
|---|
| 460 | eval join '', @script;
|
|---|
| 461 | die $@ if $@;
|
|---|
| 462 |
|
|---|
| 463 | sub abop {
|
|---|
| 464 | my ($op) = @_;
|
|---|
| 465 |
|
|---|
| 466 | push(@script, qq(print "# $op=\n";));
|
|---|
| 467 | }
|
|---|
| 468 |
|
|---|
| 469 | sub test {
|
|---|
| 470 | my ($op, $z, @args) = @_;
|
|---|
| 471 | my ($baop) = 0;
|
|---|
| 472 | $test++;
|
|---|
| 473 | my $i;
|
|---|
| 474 | $baop = 1 if ($op =~ s/;=$//);
|
|---|
| 475 | for ($i = 0; $i < @args; $i++) {
|
|---|
| 476 | $val = value($args[$i]);
|
|---|
| 477 | push @script, "\$z$i = $val;\n";
|
|---|
| 478 | }
|
|---|
| 479 | if (defined $z) {
|
|---|
| 480 | $args = "'$op'"; # Really the value
|
|---|
| 481 | $try = "abs(\$z0 - \$z1) <= $eps ? \$z1 : \$z0";
|
|---|
| 482 | push @script, "\$res = $try; ";
|
|---|
| 483 | push @script, "check($test, $args[0], \$res, \$z$#args, $args);\n";
|
|---|
| 484 | } else {
|
|---|
| 485 | my ($try, $args);
|
|---|
| 486 | if (@args == 2) {
|
|---|
| 487 | $try = "$op \$z0";
|
|---|
| 488 | $args = "'$args[0]'";
|
|---|
| 489 | } else {
|
|---|
| 490 | $try = ($op =~ /^\w/) ? "$op(\$z0, \$z1)" : "\$z0 $op \$z1";
|
|---|
| 491 | $args = "'$args[0]', '$args[1]'";
|
|---|
| 492 | }
|
|---|
| 493 | push @script, "\$res = $try; ";
|
|---|
| 494 | push @script, "check($test, '$try', \$res, \$z$#args, $args);\n";
|
|---|
| 495 | if (@args > 2 and $baop) { # binary assignment ops
|
|---|
| 496 | $test++;
|
|---|
| 497 | # check the op= works
|
|---|
| 498 | push @script, <<EOB;
|
|---|
| 499 | {
|
|---|
| 500 | my \$za = cplx(ref \$z0 ? \@{\$z0->cartesian} : (\$z0, 0));
|
|---|
| 501 |
|
|---|
| 502 | my (\$z1r, \$z1i) = ref \$z1 ? \@{\$z1->cartesian} : (\$z1, 0);
|
|---|
| 503 |
|
|---|
| 504 | my \$zb = cplx(\$z1r, \$z1i);
|
|---|
| 505 |
|
|---|
| 506 | \$za $op= \$zb;
|
|---|
| 507 | my (\$zbr, \$zbi) = \@{\$zb->cartesian};
|
|---|
| 508 |
|
|---|
| 509 | check($test, '\$z0 $op= \$z1', \$za, \$z$#args, $args);
|
|---|
| 510 | EOB
|
|---|
| 511 | $test++;
|
|---|
| 512 | # check that the rhs has not changed
|
|---|
| 513 | push @script, qq(print "not " unless (\$zbr == \$z1r and \$zbi == \$z1i););
|
|---|
| 514 | push @script, qq(print "ok $test\\n";\n);
|
|---|
| 515 | push @script, "}\n";
|
|---|
| 516 | }
|
|---|
| 517 | }
|
|---|
| 518 | }
|
|---|
| 519 |
|
|---|
| 520 | sub set {
|
|---|
| 521 | my ($set, $setref, $valref) = @_;
|
|---|
| 522 | @{$setref} = ();
|
|---|
| 523 | @{$valref} = ();
|
|---|
| 524 | my @set = split(/;\s*/, $set);
|
|---|
| 525 | my @res;
|
|---|
| 526 | my $i;
|
|---|
| 527 | for ($i = 0; $i < @set; $i++) {
|
|---|
| 528 | push(@{$valref}, $set[$i]);
|
|---|
| 529 | my $val = value($set[$i]);
|
|---|
| 530 | push @script, "\$s$i = $val;\n";
|
|---|
| 531 | push @{$setref}, "\$s$i";
|
|---|
| 532 | }
|
|---|
| 533 | }
|
|---|
| 534 |
|
|---|
| 535 | sub value {
|
|---|
| 536 | local ($_) = @_;
|
|---|
| 537 | if (/^\s*\((.*),(.*)\)/) {
|
|---|
| 538 | return "cplx($1,$2)";
|
|---|
| 539 | }
|
|---|
| 540 | elsif (/^\s*([\-\+]?(?:\d+(\.\d+)?|\.\d+)(?:[e[\-\+]\d+])?)/) {
|
|---|
| 541 | return "cplx($1,0)";
|
|---|
| 542 | }
|
|---|
| 543 | elsif (/^\s*\[(.*),(.*)\]/) {
|
|---|
| 544 | return "cplxe($1,$2)";
|
|---|
| 545 | }
|
|---|
| 546 | elsif (/^\s*'(.*)'/) {
|
|---|
| 547 | my $ex = $1;
|
|---|
| 548 | $ex =~ s/\bz\b/$target/g;
|
|---|
| 549 | $ex =~ s/\br\b/abs($target)/g;
|
|---|
| 550 | $ex =~ s/\bt\b/arg($target)/g;
|
|---|
| 551 | $ex =~ s/\ba\b/Re($target)/g;
|
|---|
| 552 | $ex =~ s/\bb\b/Im($target)/g;
|
|---|
| 553 | return $ex;
|
|---|
| 554 | }
|
|---|
| 555 | elsif (/^\s*"(.*)"/) {
|
|---|
| 556 | return "\"$1\"";
|
|---|
| 557 | }
|
|---|
| 558 | return $_;
|
|---|
| 559 | }
|
|---|
| 560 |
|
|---|
| 561 | sub check {
|
|---|
| 562 | my ($test, $try, $got, $expected, @z) = @_;
|
|---|
| 563 |
|
|---|
| 564 | print "# @_\n";
|
|---|
| 565 |
|
|---|
| 566 | if ("$got" eq "$expected"
|
|---|
| 567 | ||
|
|---|
| 568 | ($expected =~ /^-?\d/ && $got == $expected)
|
|---|
| 569 | ||
|
|---|
| 570 | (abs(Math::Complex->make($got) - Math::Complex->make($expected)) < $eps)
|
|---|
| 571 | ||
|
|---|
| 572 | (abs($got - $expected) < $eps)
|
|---|
| 573 | ) {
|
|---|
| 574 | print "ok $test\n";
|
|---|
| 575 | } else {
|
|---|
| 576 | print "not ok $test\n";
|
|---|
| 577 | my $args = (@z == 1) ? "z = $z[0]" : "z0 = $z[0], z1 = $z[1]";
|
|---|
| 578 | print "# '$try' expected: '$expected' got: '$got' for $args\n";
|
|---|
| 579 | }
|
|---|
| 580 | }
|
|---|
| 581 |
|
|---|
| 582 | sub addsq {
|
|---|
| 583 | my ($z1, $z2) = @_;
|
|---|
| 584 | return ($z1 + i*$z2) * ($z1 - i*$z2);
|
|---|
| 585 | }
|
|---|
| 586 |
|
|---|
| 587 | sub subsq {
|
|---|
| 588 | my ($z1, $z2) = @_;
|
|---|
| 589 | return ($z1 + $z2) * ($z1 - $z2);
|
|---|
| 590 | }
|
|---|
| 591 |
|
|---|
| 592 | __END__
|
|---|
| 593 | &+;=
|
|---|
| 594 | (3,4):(3,4):(6,8)
|
|---|
| 595 | (-3,4):(3,-4):(0,0)
|
|---|
| 596 | (3,4):-3:(0,4)
|
|---|
| 597 | 1:(4,2):(5,2)
|
|---|
| 598 | [2,0]:[2,pi]:(0,0)
|
|---|
| 599 |
|
|---|
| 600 | &++
|
|---|
| 601 | (2,1):(3,1)
|
|---|
| 602 |
|
|---|
| 603 | &-;=
|
|---|
| 604 | (2,3):(-2,-3)
|
|---|
| 605 | [2,pi/2]:[2,-(pi)/2]
|
|---|
| 606 | 2:[2,0]:(0,0)
|
|---|
| 607 | [3,0]:2:(1,0)
|
|---|
| 608 | 3:(4,5):(-1,-5)
|
|---|
| 609 | (4,5):3:(1,5)
|
|---|
| 610 | (2,1):(3,5):(-1,-4)
|
|---|
| 611 |
|
|---|
| 612 | &--
|
|---|
| 613 | (1,2):(0,2)
|
|---|
| 614 | [2,pi]:[3,pi]
|
|---|
| 615 |
|
|---|
| 616 | &*;=
|
|---|
| 617 | (0,1):(0,1):(-1,0)
|
|---|
| 618 | (4,5):(1,0):(4,5)
|
|---|
| 619 | [2,2*pi/3]:(1,0):[2,2*pi/3]
|
|---|
| 620 | 2:(0,1):(0,2)
|
|---|
| 621 | (0,1):3:(0,3)
|
|---|
| 622 | (0,1):(4,1):(-1,4)
|
|---|
| 623 | (2,1):(4,-1):(9,2)
|
|---|
| 624 |
|
|---|
| 625 | &/;=
|
|---|
| 626 | (3,4):(3,4):(1,0)
|
|---|
| 627 | (4,-5):1:(4,-5)
|
|---|
| 628 | 1:(0,1):(0,-1)
|
|---|
| 629 | (0,6):(0,2):(3,0)
|
|---|
| 630 | (9,2):(4,-1):(2,1)
|
|---|
| 631 | [4,pi]:[2,pi/2]:[2,pi/2]
|
|---|
| 632 | [2,pi/2]:[4,pi]:[0.5,-(pi)/2]
|
|---|
| 633 |
|
|---|
| 634 | &**;=
|
|---|
| 635 | (2,0):(3,0):(8,0)
|
|---|
| 636 | (3,0):(2,0):(9,0)
|
|---|
| 637 | (2,3):(4,0):(-119,-120)
|
|---|
| 638 | (0,0):(1,0):(0,0)
|
|---|
| 639 | (0,0):(2,3):(0,0)
|
|---|
| 640 | (1,0):(0,0):(1,0)
|
|---|
| 641 | (1,0):(1,0):(1,0)
|
|---|
| 642 | (1,0):(2,3):(1,0)
|
|---|
| 643 | (2,3):(0,0):(1,0)
|
|---|
| 644 | (2,3):(1,0):(2,3)
|
|---|
| 645 | (0,0):(0,0):(1,0)
|
|---|
| 646 |
|
|---|
| 647 | &Re
|
|---|
| 648 | (3,4):3
|
|---|
| 649 | (-3,4):-3
|
|---|
| 650 | [1,pi/2]:0
|
|---|
| 651 |
|
|---|
| 652 | &Im
|
|---|
| 653 | (3,4):4
|
|---|
| 654 | (3,-4):-4
|
|---|
| 655 | [1,pi/2]:1
|
|---|
| 656 |
|
|---|
| 657 | &abs
|
|---|
| 658 | (3,4):5
|
|---|
| 659 | (-3,4):5
|
|---|
| 660 |
|
|---|
| 661 | &arg
|
|---|
| 662 | [2,0]:0
|
|---|
| 663 | [-2,0]:pi
|
|---|
| 664 |
|
|---|
| 665 | &~
|
|---|
| 666 | (4,5):(4,-5)
|
|---|
| 667 | (-3,4):(-3,-4)
|
|---|
| 668 | [2,pi/2]:[2,-(pi)/2]
|
|---|
| 669 |
|
|---|
| 670 | &<
|
|---|
| 671 | (3,4):(1,2):0
|
|---|
| 672 | (3,4):(3,2):0
|
|---|
| 673 | (3,4):(3,8):1
|
|---|
| 674 | (4,4):(5,129):1
|
|---|
| 675 |
|
|---|
| 676 | &==
|
|---|
| 677 | (3,4):(4,5):0
|
|---|
| 678 | (3,4):(3,5):0
|
|---|
| 679 | (3,4):(2,4):0
|
|---|
| 680 | (3,4):(3,4):1
|
|---|
| 681 |
|
|---|
| 682 | &sqrt
|
|---|
| 683 | -9:(0,3)
|
|---|
| 684 | (-100,0):(0,10)
|
|---|
| 685 | (16,-30):(5,-3)
|
|---|
| 686 |
|
|---|
| 687 | &stringify_cartesian
|
|---|
| 688 | (-100,0):"-100"
|
|---|
| 689 | (0,1):"i"
|
|---|
| 690 | (4,-3):"4-3i"
|
|---|
| 691 | (4,0):"4"
|
|---|
| 692 | (-4,0):"-4"
|
|---|
| 693 | (-2,4):"-2+4i"
|
|---|
| 694 | (-2,-1):"-2-i"
|
|---|
| 695 |
|
|---|
| 696 | &stringify_polar
|
|---|
| 697 | [-1, 0]:"[1,pi]"
|
|---|
| 698 | [1, pi/3]:"[1,pi/3]"
|
|---|
| 699 | [6, -2*pi/3]:"[6,-2pi/3]"
|
|---|
| 700 | [0.5, -9*pi/11]:"[0.5,-9pi/11]"
|
|---|
| 701 |
|
|---|
| 702 | { (4,3); [3,2]; (-3,4); (0,2); [2,1] }
|
|---|
| 703 |
|
|---|
| 704 | |'z + ~z':'2*Re(z)'
|
|---|
| 705 | |'z - ~z':'2*i*Im(z)'
|
|---|
| 706 | |'z * ~z':'abs(z) * abs(z)'
|
|---|
| 707 |
|
|---|
| 708 | { (0.5, 0); (-0.5, 0); (2,3); [3,2]; (-3,2); (0,2); 3; 1.2; (-3, 0); (-2, -1); [2,1] }
|
|---|
| 709 |
|
|---|
| 710 | |'(root(z, 4))[1] ** 4':'z'
|
|---|
| 711 | |'(root(z, 5))[3] ** 5':'z'
|
|---|
| 712 | |'(root(z, 8))[7] ** 8':'z'
|
|---|
| 713 | |'(root(z, 8, 0)) ** 8':'z'
|
|---|
| 714 | |'(root(z, 8, 7)) ** 8':'z'
|
|---|
| 715 | |'abs(z)':'r'
|
|---|
| 716 | |'acot(z)':'acotan(z)'
|
|---|
| 717 | |'acsc(z)':'acosec(z)'
|
|---|
| 718 | |'acsc(z)':'asin(1 / z)'
|
|---|
| 719 | |'asec(z)':'acos(1 / z)'
|
|---|
| 720 | |'cbrt(z)':'cbrt(r) * exp(i * t/3)'
|
|---|
| 721 | |'cos(acos(z))':'z'
|
|---|
| 722 | |'addsq(cos(z), sin(z))':1
|
|---|
| 723 | |'cos(z)':'cosh(i*z)'
|
|---|
| 724 | |'subsq(cosh(z), sinh(z))':1
|
|---|
| 725 | |'cot(acot(z))':'z'
|
|---|
| 726 | |'cot(z)':'1 / tan(z)'
|
|---|
| 727 | |'cot(z)':'cotan(z)'
|
|---|
| 728 | |'csc(acsc(z))':'z'
|
|---|
| 729 | |'csc(z)':'1 / sin(z)'
|
|---|
| 730 | |'csc(z)':'cosec(z)'
|
|---|
| 731 | |'exp(log(z))':'z'
|
|---|
| 732 | |'exp(z)':'exp(a) * exp(i * b)'
|
|---|
| 733 | |'ln(z)':'log(z)'
|
|---|
| 734 | |'log(exp(z))':'z'
|
|---|
| 735 | |'log(z)':'log(r) + i*t'
|
|---|
| 736 | |'log10(z)':'log(z) / log(10)'
|
|---|
| 737 | |'logn(z, 2)':'log(z) / log(2)'
|
|---|
| 738 | |'logn(z, 3)':'log(z) / log(3)'
|
|---|
| 739 | |'sec(asec(z))':'z'
|
|---|
| 740 | |'sec(z)':'1 / cos(z)'
|
|---|
| 741 | |'sin(asin(z))':'z'
|
|---|
| 742 | |'sin(i * z)':'i * sinh(z)'
|
|---|
| 743 | |'sqrt(z) * sqrt(z)':'z'
|
|---|
| 744 | |'sqrt(z)':'sqrt(r) * exp(i * t/2)'
|
|---|
| 745 | |'tan(atan(z))':'z'
|
|---|
| 746 | |'z**z':'exp(z * log(z))'
|
|---|
| 747 |
|
|---|
| 748 | { (1,1); [1,0.5]; (-2, -1); 2; -3; (-1,0.5); (0,0.5); 0.5; (2, 0); (-1, -2) }
|
|---|
| 749 |
|
|---|
| 750 | |'cosh(acosh(z))':'z'
|
|---|
| 751 | |'coth(acoth(z))':'z'
|
|---|
| 752 | |'coth(z)':'1 / tanh(z)'
|
|---|
| 753 | |'coth(z)':'cotanh(z)'
|
|---|
| 754 | |'csch(acsch(z))':'z'
|
|---|
| 755 | |'csch(z)':'1 / sinh(z)'
|
|---|
| 756 | |'csch(z)':'cosech(z)'
|
|---|
| 757 | |'sech(asech(z))':'z'
|
|---|
| 758 | |'sech(z)':'1 / cosh(z)'
|
|---|
| 759 | |'sinh(asinh(z))':'z'
|
|---|
| 760 | |'tanh(atanh(z))':'z'
|
|---|
| 761 |
|
|---|
| 762 | { (0.2,-0.4); [1,0.5]; -1.2; (-1,0.5); 0.5; (1.1, 0) }
|
|---|
| 763 |
|
|---|
| 764 | |'acos(cos(z)) ** 2':'z * z'
|
|---|
| 765 | |'acosh(cosh(z)) ** 2':'z * z'
|
|---|
| 766 | |'acoth(z)':'acotanh(z)'
|
|---|
| 767 | |'acoth(z)':'atanh(1 / z)'
|
|---|
| 768 | |'acsch(z)':'acosech(z)'
|
|---|
| 769 | |'acsch(z)':'asinh(1 / z)'
|
|---|
| 770 | |'asech(z)':'acosh(1 / z)'
|
|---|
| 771 | |'asin(sin(z))':'z'
|
|---|
| 772 | |'asinh(sinh(z))':'z'
|
|---|
| 773 | |'atan(tan(z))':'z'
|
|---|
| 774 | |'atanh(tanh(z))':'z'
|
|---|
| 775 |
|
|---|
| 776 | &log
|
|---|
| 777 | (-2.0,0):( 0.69314718055995, 3.14159265358979)
|
|---|
| 778 | (-1.0,0):( 0 , 3.14159265358979)
|
|---|
| 779 | (-0.5,0):( -0.69314718055995, 3.14159265358979)
|
|---|
| 780 | ( 0.5,0):( -0.69314718055995, 0 )
|
|---|
| 781 | ( 1.0,0):( 0 , 0 )
|
|---|
| 782 | ( 2.0,0):( 0.69314718055995, 0 )
|
|---|
| 783 |
|
|---|
| 784 | &log
|
|---|
| 785 | ( 2, 3):( 1.28247467873077, 0.98279372324733)
|
|---|
| 786 | (-2, 3):( 1.28247467873077, 2.15879893034246)
|
|---|
| 787 | (-2,-3):( 1.28247467873077, -2.15879893034246)
|
|---|
| 788 | ( 2,-3):( 1.28247467873077, -0.98279372324733)
|
|---|
| 789 |
|
|---|
| 790 | &sin
|
|---|
| 791 | (-2.0,0):( -0.90929742682568, 0 )
|
|---|
| 792 | (-1.0,0):( -0.84147098480790, 0 )
|
|---|
| 793 | (-0.5,0):( -0.47942553860420, 0 )
|
|---|
| 794 | ( 0.0,0):( 0 , 0 )
|
|---|
| 795 | ( 0.5,0):( 0.47942553860420, 0 )
|
|---|
| 796 | ( 1.0,0):( 0.84147098480790, 0 )
|
|---|
| 797 | ( 2.0,0):( 0.90929742682568, 0 )
|
|---|
| 798 |
|
|---|
| 799 | &sin
|
|---|
| 800 | ( 2, 3):( 9.15449914691143, -4.16890695996656)
|
|---|
| 801 | (-2, 3):( -9.15449914691143, -4.16890695996656)
|
|---|
| 802 | (-2,-3):( -9.15449914691143, 4.16890695996656)
|
|---|
| 803 | ( 2,-3):( 9.15449914691143, 4.16890695996656)
|
|---|
| 804 |
|
|---|
| 805 | &cos
|
|---|
| 806 | (-2.0,0):( -0.41614683654714, 0 )
|
|---|
| 807 | (-1.0,0):( 0.54030230586814, 0 )
|
|---|
| 808 | (-0.5,0):( 0.87758256189037, 0 )
|
|---|
| 809 | ( 0.0,0):( 1 , 0 )
|
|---|
| 810 | ( 0.5,0):( 0.87758256189037, 0 )
|
|---|
| 811 | ( 1.0,0):( 0.54030230586814, 0 )
|
|---|
| 812 | ( 2.0,0):( -0.41614683654714, 0 )
|
|---|
| 813 |
|
|---|
| 814 | &cos
|
|---|
| 815 | ( 2, 3):( -4.18962569096881, -9.10922789375534)
|
|---|
| 816 | (-2, 3):( -4.18962569096881, 9.10922789375534)
|
|---|
| 817 | (-2,-3):( -4.18962569096881, -9.10922789375534)
|
|---|
| 818 | ( 2,-3):( -4.18962569096881, 9.10922789375534)
|
|---|
| 819 |
|
|---|
| 820 | &tan
|
|---|
| 821 | (-2.0,0):( 2.18503986326152, 0 )
|
|---|
| 822 | (-1.0,0):( -1.55740772465490, 0 )
|
|---|
| 823 | (-0.5,0):( -0.54630248984379, 0 )
|
|---|
| 824 | ( 0.0,0):( 0 , 0 )
|
|---|
| 825 | ( 0.5,0):( 0.54630248984379, 0 )
|
|---|
| 826 | ( 1.0,0):( 1.55740772465490, 0 )
|
|---|
| 827 | ( 2.0,0):( -2.18503986326152, 0 )
|
|---|
| 828 |
|
|---|
| 829 | &tan
|
|---|
| 830 | ( 2, 3):( -0.00376402564150, 1.00323862735361)
|
|---|
| 831 | (-2, 3):( 0.00376402564150, 1.00323862735361)
|
|---|
| 832 | (-2,-3):( 0.00376402564150, -1.00323862735361)
|
|---|
| 833 | ( 2,-3):( -0.00376402564150, -1.00323862735361)
|
|---|
| 834 |
|
|---|
| 835 | &sec
|
|---|
| 836 | (-2.0,0):( -2.40299796172238, 0 )
|
|---|
| 837 | (-1.0,0):( 1.85081571768093, 0 )
|
|---|
| 838 | (-0.5,0):( 1.13949392732455, 0 )
|
|---|
| 839 | ( 0.0,0):( 1 , 0 )
|
|---|
| 840 | ( 0.5,0):( 1.13949392732455, 0 )
|
|---|
| 841 | ( 1.0,0):( 1.85081571768093, 0 )
|
|---|
| 842 | ( 2.0,0):( -2.40299796172238, 0 )
|
|---|
| 843 |
|
|---|
| 844 | &sec
|
|---|
| 845 | ( 2, 3):( -0.04167496441114, 0.09061113719624)
|
|---|
| 846 | (-2, 3):( -0.04167496441114, -0.09061113719624)
|
|---|
| 847 | (-2,-3):( -0.04167496441114, 0.09061113719624)
|
|---|
| 848 | ( 2,-3):( -0.04167496441114, -0.09061113719624)
|
|---|
| 849 |
|
|---|
| 850 | &csc
|
|---|
| 851 | (-2.0,0):( -1.09975017029462, 0 )
|
|---|
| 852 | (-1.0,0):( -1.18839510577812, 0 )
|
|---|
| 853 | (-0.5,0):( -2.08582964293349, 0 )
|
|---|
| 854 | ( 0.5,0):( 2.08582964293349, 0 )
|
|---|
| 855 | ( 1.0,0):( 1.18839510577812, 0 )
|
|---|
| 856 | ( 2.0,0):( 1.09975017029462, 0 )
|
|---|
| 857 |
|
|---|
| 858 | &csc
|
|---|
| 859 | ( 2, 3):( 0.09047320975321, 0.04120098628857)
|
|---|
| 860 | (-2, 3):( -0.09047320975321, 0.04120098628857)
|
|---|
| 861 | (-2,-3):( -0.09047320975321, -0.04120098628857)
|
|---|
| 862 | ( 2,-3):( 0.09047320975321, -0.04120098628857)
|
|---|
| 863 |
|
|---|
| 864 | &cot
|
|---|
| 865 | (-2.0,0):( 0.45765755436029, 0 )
|
|---|
| 866 | (-1.0,0):( -0.64209261593433, 0 )
|
|---|
| 867 | (-0.5,0):( -1.83048772171245, 0 )
|
|---|
| 868 | ( 0.5,0):( 1.83048772171245, 0 )
|
|---|
| 869 | ( 1.0,0):( 0.64209261593433, 0 )
|
|---|
| 870 | ( 2.0,0):( -0.45765755436029, 0 )
|
|---|
| 871 |
|
|---|
| 872 | &cot
|
|---|
| 873 | ( 2, 3):( -0.00373971037634, -0.99675779656936)
|
|---|
| 874 | (-2, 3):( 0.00373971037634, -0.99675779656936)
|
|---|
| 875 | (-2,-3):( 0.00373971037634, 0.99675779656936)
|
|---|
| 876 | ( 2,-3):( -0.00373971037634, 0.99675779656936)
|
|---|
| 877 |
|
|---|
| 878 | &asin
|
|---|
| 879 | (-2.0,0):( -1.57079632679490, 1.31695789692482)
|
|---|
| 880 | (-1.0,0):( -1.57079632679490, 0 )
|
|---|
| 881 | (-0.5,0):( -0.52359877559830, 0 )
|
|---|
| 882 | ( 0.0,0):( 0 , 0 )
|
|---|
| 883 | ( 0.5,0):( 0.52359877559830, 0 )
|
|---|
| 884 | ( 1.0,0):( 1.57079632679490, 0 )
|
|---|
| 885 | ( 2.0,0):( 1.57079632679490, -1.31695789692482)
|
|---|
| 886 |
|
|---|
| 887 | &asin
|
|---|
| 888 | ( 2, 3):( 0.57065278432110, 1.98338702991654)
|
|---|
| 889 | (-2, 3):( -0.57065278432110, 1.98338702991654)
|
|---|
| 890 | (-2,-3):( -0.57065278432110, -1.98338702991654)
|
|---|
| 891 | ( 2,-3):( 0.57065278432110, -1.98338702991654)
|
|---|
| 892 |
|
|---|
| 893 | &acos
|
|---|
| 894 | (-2.0,0):( 3.14159265358979, -1.31695789692482)
|
|---|
| 895 | (-1.0,0):( 3.14159265358979, 0 )
|
|---|
| 896 | (-0.5,0):( 2.09439510239320, 0 )
|
|---|
| 897 | ( 0.0,0):( 1.57079632679490, 0 )
|
|---|
| 898 | ( 0.5,0):( 1.04719755119660, 0 )
|
|---|
| 899 | ( 1.0,0):( 0 , 0 )
|
|---|
| 900 | ( 2.0,0):( 0 , 1.31695789692482)
|
|---|
| 901 |
|
|---|
| 902 | &acos
|
|---|
| 903 | ( 2, 3):( 1.00014354247380, -1.98338702991654)
|
|---|
| 904 | (-2, 3):( 2.14144911111600, -1.98338702991654)
|
|---|
| 905 | (-2,-3):( 2.14144911111600, 1.98338702991654)
|
|---|
| 906 | ( 2,-3):( 1.00014354247380, 1.98338702991654)
|
|---|
| 907 |
|
|---|
| 908 | &atan
|
|---|
| 909 | (-2.0,0):( -1.10714871779409, 0 )
|
|---|
| 910 | (-1.0,0):( -0.78539816339745, 0 )
|
|---|
| 911 | (-0.5,0):( -0.46364760900081, 0 )
|
|---|
| 912 | ( 0.0,0):( 0 , 0 )
|
|---|
| 913 | ( 0.5,0):( 0.46364760900081, 0 )
|
|---|
| 914 | ( 1.0,0):( 0.78539816339745, 0 )
|
|---|
| 915 | ( 2.0,0):( 1.10714871779409, 0 )
|
|---|
| 916 |
|
|---|
| 917 | &atan
|
|---|
| 918 | ( 2, 3):( 1.40992104959658, 0.22907268296854)
|
|---|
| 919 | (-2, 3):( -1.40992104959658, 0.22907268296854)
|
|---|
| 920 | (-2,-3):( -1.40992104959658, -0.22907268296854)
|
|---|
| 921 | ( 2,-3):( 1.40992104959658, -0.22907268296854)
|
|---|
| 922 |
|
|---|
| 923 | &asec
|
|---|
| 924 | (-2.0,0):( 2.09439510239320, 0 )
|
|---|
| 925 | (-1.0,0):( 3.14159265358979, 0 )
|
|---|
| 926 | (-0.5,0):( 3.14159265358979, -1.31695789692482)
|
|---|
| 927 | ( 0.5,0):( 0 , 1.31695789692482)
|
|---|
| 928 | ( 1.0,0):( 0 , 0 )
|
|---|
| 929 | ( 2.0,0):( 1.04719755119660, 0 )
|
|---|
| 930 |
|
|---|
| 931 | &asec
|
|---|
| 932 | ( 2, 3):( 1.42041072246703, 0.23133469857397)
|
|---|
| 933 | (-2, 3):( 1.72118193112276, 0.23133469857397)
|
|---|
| 934 | (-2,-3):( 1.72118193112276, -0.23133469857397)
|
|---|
| 935 | ( 2,-3):( 1.42041072246703, -0.23133469857397)
|
|---|
| 936 |
|
|---|
| 937 | &acsc
|
|---|
| 938 | (-2.0,0):( -0.52359877559830, 0 )
|
|---|
| 939 | (-1.0,0):( -1.57079632679490, 0 )
|
|---|
| 940 | (-0.5,0):( -1.57079632679490, 1.31695789692482)
|
|---|
| 941 | ( 0.5,0):( 1.57079632679490, -1.31695789692482)
|
|---|
| 942 | ( 1.0,0):( 1.57079632679490, 0 )
|
|---|
| 943 | ( 2.0,0):( 0.52359877559830, 0 )
|
|---|
| 944 |
|
|---|
| 945 | &acsc
|
|---|
| 946 | ( 2, 3):( 0.15038560432786, -0.23133469857397)
|
|---|
| 947 | (-2, 3):( -0.15038560432786, -0.23133469857397)
|
|---|
| 948 | (-2,-3):( -0.15038560432786, 0.23133469857397)
|
|---|
| 949 | ( 2,-3):( 0.15038560432786, 0.23133469857397)
|
|---|
| 950 |
|
|---|
| 951 | &acot
|
|---|
| 952 | (-2.0,0):( -0.46364760900081, 0 )
|
|---|
| 953 | (-1.0,0):( -0.78539816339745, 0 )
|
|---|
| 954 | (-0.5,0):( -1.10714871779409, 0 )
|
|---|
| 955 | ( 0.5,0):( 1.10714871779409, 0 )
|
|---|
| 956 | ( 1.0,0):( 0.78539816339745, 0 )
|
|---|
| 957 | ( 2.0,0):( 0.46364760900081, 0 )
|
|---|
| 958 |
|
|---|
| 959 | &acot
|
|---|
| 960 | ( 2, 3):( 0.16087527719832, -0.22907268296854)
|
|---|
| 961 | (-2, 3):( -0.16087527719832, -0.22907268296854)
|
|---|
| 962 | (-2,-3):( -0.16087527719832, 0.22907268296854)
|
|---|
| 963 | ( 2,-3):( 0.16087527719832, 0.22907268296854)
|
|---|
| 964 |
|
|---|
| 965 | &sinh
|
|---|
| 966 | (-2.0,0):( -3.62686040784702, 0 )
|
|---|
| 967 | (-1.0,0):( -1.17520119364380, 0 )
|
|---|
| 968 | (-0.5,0):( -0.52109530549375, 0 )
|
|---|
| 969 | ( 0.0,0):( 0 , 0 )
|
|---|
| 970 | ( 0.5,0):( 0.52109530549375, 0 )
|
|---|
| 971 | ( 1.0,0):( 1.17520119364380, 0 )
|
|---|
| 972 | ( 2.0,0):( 3.62686040784702, 0 )
|
|---|
| 973 |
|
|---|
| 974 | &sinh
|
|---|
| 975 | ( 2, 3):( -3.59056458998578, 0.53092108624852)
|
|---|
| 976 | (-2, 3):( 3.59056458998578, 0.53092108624852)
|
|---|
| 977 | (-2,-3):( 3.59056458998578, -0.53092108624852)
|
|---|
| 978 | ( 2,-3):( -3.59056458998578, -0.53092108624852)
|
|---|
| 979 |
|
|---|
| 980 | &cosh
|
|---|
| 981 | (-2.0,0):( 3.76219569108363, 0 )
|
|---|
| 982 | (-1.0,0):( 1.54308063481524, 0 )
|
|---|
| 983 | (-0.5,0):( 1.12762596520638, 0 )
|
|---|
| 984 | ( 0.0,0):( 1 , 0 )
|
|---|
| 985 | ( 0.5,0):( 1.12762596520638, 0 )
|
|---|
| 986 | ( 1.0,0):( 1.54308063481524, 0 )
|
|---|
| 987 | ( 2.0,0):( 3.76219569108363, 0 )
|
|---|
| 988 |
|
|---|
| 989 | &cosh
|
|---|
| 990 | ( 2, 3):( -3.72454550491532, 0.51182256998738)
|
|---|
| 991 | (-2, 3):( -3.72454550491532, -0.51182256998738)
|
|---|
| 992 | (-2,-3):( -3.72454550491532, 0.51182256998738)
|
|---|
| 993 | ( 2,-3):( -3.72454550491532, -0.51182256998738)
|
|---|
| 994 |
|
|---|
| 995 | &tanh
|
|---|
| 996 | (-2.0,0):( -0.96402758007582, 0 )
|
|---|
| 997 | (-1.0,0):( -0.76159415595576, 0 )
|
|---|
| 998 | (-0.5,0):( -0.46211715726001, 0 )
|
|---|
| 999 | ( 0.0,0):( 0 , 0 )
|
|---|
| 1000 | ( 0.5,0):( 0.46211715726001, 0 )
|
|---|
| 1001 | ( 1.0,0):( 0.76159415595576, 0 )
|
|---|
| 1002 | ( 2.0,0):( 0.96402758007582, 0 )
|
|---|
| 1003 |
|
|---|
| 1004 | &tanh
|
|---|
| 1005 | ( 2, 3):( 0.96538587902213, -0.00988437503832)
|
|---|
| 1006 | (-2, 3):( -0.96538587902213, -0.00988437503832)
|
|---|
| 1007 | (-2,-3):( -0.96538587902213, 0.00988437503832)
|
|---|
| 1008 | ( 2,-3):( 0.96538587902213, 0.00988437503832)
|
|---|
| 1009 |
|
|---|
| 1010 | &sech
|
|---|
| 1011 | (-2.0,0):( 0.26580222883408, 0 )
|
|---|
| 1012 | (-1.0,0):( 0.64805427366389, 0 )
|
|---|
| 1013 | (-0.5,0):( 0.88681888397007, 0 )
|
|---|
| 1014 | ( 0.0,0):( 1 , 0 )
|
|---|
| 1015 | ( 0.5,0):( 0.88681888397007, 0 )
|
|---|
| 1016 | ( 1.0,0):( 0.64805427366389, 0 )
|
|---|
| 1017 | ( 2.0,0):( 0.26580222883408, 0 )
|
|---|
| 1018 |
|
|---|
| 1019 | &sech
|
|---|
| 1020 | ( 2, 3):( -0.26351297515839, -0.03621163655877)
|
|---|
| 1021 | (-2, 3):( -0.26351297515839, 0.03621163655877)
|
|---|
| 1022 | (-2,-3):( -0.26351297515839, -0.03621163655877)
|
|---|
| 1023 | ( 2,-3):( -0.26351297515839, 0.03621163655877)
|
|---|
| 1024 |
|
|---|
| 1025 | &csch
|
|---|
| 1026 | (-2.0,0):( -0.27572056477178, 0 )
|
|---|
| 1027 | (-1.0,0):( -0.85091812823932, 0 )
|
|---|
| 1028 | (-0.5,0):( -1.91903475133494, 0 )
|
|---|
| 1029 | ( 0.5,0):( 1.91903475133494, 0 )
|
|---|
| 1030 | ( 1.0,0):( 0.85091812823932, 0 )
|
|---|
| 1031 | ( 2.0,0):( 0.27572056477178, 0 )
|
|---|
| 1032 |
|
|---|
| 1033 | &csch
|
|---|
| 1034 | ( 2, 3):( -0.27254866146294, -0.04030057885689)
|
|---|
| 1035 | (-2, 3):( 0.27254866146294, -0.04030057885689)
|
|---|
| 1036 | (-2,-3):( 0.27254866146294, 0.04030057885689)
|
|---|
| 1037 | ( 2,-3):( -0.27254866146294, 0.04030057885689)
|
|---|
| 1038 |
|
|---|
| 1039 | &coth
|
|---|
| 1040 | (-2.0,0):( -1.03731472072755, 0 )
|
|---|
| 1041 | (-1.0,0):( -1.31303528549933, 0 )
|
|---|
| 1042 | (-0.5,0):( -2.16395341373865, 0 )
|
|---|
| 1043 | ( 0.5,0):( 2.16395341373865, 0 )
|
|---|
| 1044 | ( 1.0,0):( 1.31303528549933, 0 )
|
|---|
| 1045 | ( 2.0,0):( 1.03731472072755, 0 )
|
|---|
| 1046 |
|
|---|
| 1047 | &coth
|
|---|
| 1048 | ( 2, 3):( 1.03574663776500, 0.01060478347034)
|
|---|
| 1049 | (-2, 3):( -1.03574663776500, 0.01060478347034)
|
|---|
| 1050 | (-2,-3):( -1.03574663776500, -0.01060478347034)
|
|---|
| 1051 | ( 2,-3):( 1.03574663776500, -0.01060478347034)
|
|---|
| 1052 |
|
|---|
| 1053 | &asinh
|
|---|
| 1054 | (-2.0,0):( -1.44363547517881, 0 )
|
|---|
| 1055 | (-1.0,0):( -0.88137358701954, 0 )
|
|---|
| 1056 | (-0.5,0):( -0.48121182505960, 0 )
|
|---|
| 1057 | ( 0.0,0):( 0 , 0 )
|
|---|
| 1058 | ( 0.5,0):( 0.48121182505960, 0 )
|
|---|
| 1059 | ( 1.0,0):( 0.88137358701954, 0 )
|
|---|
| 1060 | ( 2.0,0):( 1.44363547517881, 0 )
|
|---|
| 1061 |
|
|---|
| 1062 | &asinh
|
|---|
| 1063 | ( 2, 3):( 1.96863792579310, 0.96465850440760)
|
|---|
| 1064 | (-2, 3):( -1.96863792579310, 0.96465850440761)
|
|---|
| 1065 | (-2,-3):( -1.96863792579310, -0.96465850440761)
|
|---|
| 1066 | ( 2,-3):( 1.96863792579310, -0.96465850440760)
|
|---|
| 1067 |
|
|---|
| 1068 | &acosh
|
|---|
| 1069 | (-2.0,0):( 1.31695789692482, 3.14159265358979)
|
|---|
| 1070 | (-1.0,0):( 0, 3.14159265358979)
|
|---|
| 1071 | (-0.5,0):( 0, 2.09439510239320)
|
|---|
| 1072 | ( 0.0,0):( 0, 1.57079632679490)
|
|---|
| 1073 | ( 0.5,0):( 0, 1.04719755119660)
|
|---|
| 1074 | ( 1.0,0):( 0 , 0 )
|
|---|
| 1075 | ( 2.0,0):( 1.31695789692482, 0 )
|
|---|
| 1076 |
|
|---|
| 1077 | &acosh
|
|---|
| 1078 | ( 2, 3):( 1.98338702991654, 1.00014354247380)
|
|---|
| 1079 | (-2, 3):( 1.98338702991653, 2.14144911111600)
|
|---|
| 1080 | (-2,-3):( 1.98338702991653, -2.14144911111600)
|
|---|
| 1081 | ( 2,-3):( 1.98338702991654, -1.00014354247380)
|
|---|
| 1082 |
|
|---|
| 1083 | &atanh
|
|---|
| 1084 | (-2.0,0):( -0.54930614433405, 1.57079632679490)
|
|---|
| 1085 | (-0.5,0):( -0.54930614433405, 0 )
|
|---|
| 1086 | ( 0.0,0):( 0 , 0 )
|
|---|
| 1087 | ( 0.5,0):( 0.54930614433405, 0 )
|
|---|
| 1088 | ( 2.0,0):( 0.54930614433405, 1.57079632679490)
|
|---|
| 1089 |
|
|---|
| 1090 | &atanh
|
|---|
| 1091 | ( 2, 3):( 0.14694666622553, 1.33897252229449)
|
|---|
| 1092 | (-2, 3):( -0.14694666622553, 1.33897252229449)
|
|---|
| 1093 | (-2,-3):( -0.14694666622553, -1.33897252229449)
|
|---|
| 1094 | ( 2,-3):( 0.14694666622553, -1.33897252229449)
|
|---|
| 1095 |
|
|---|
| 1096 | &asech
|
|---|
| 1097 | (-2.0,0):( 0 , 2.09439510239320)
|
|---|
| 1098 | (-1.0,0):( 0 , 3.14159265358979)
|
|---|
| 1099 | (-0.5,0):( 1.31695789692482, 3.14159265358979)
|
|---|
| 1100 | ( 0.5,0):( 1.31695789692482, 0 )
|
|---|
| 1101 | ( 1.0,0):( 0 , 0 )
|
|---|
| 1102 | ( 2.0,0):( 0 , 1.04719755119660)
|
|---|
| 1103 |
|
|---|
| 1104 | &asech
|
|---|
| 1105 | ( 2, 3):( 0.23133469857397, -1.42041072246703)
|
|---|
| 1106 | (-2, 3):( 0.23133469857397, -1.72118193112276)
|
|---|
| 1107 | (-2,-3):( 0.23133469857397, 1.72118193112276)
|
|---|
| 1108 | ( 2,-3):( 0.23133469857397, 1.42041072246703)
|
|---|
| 1109 |
|
|---|
| 1110 | &acsch
|
|---|
| 1111 | (-2.0,0):( -0.48121182505960, 0 )
|
|---|
| 1112 | (-1.0,0):( -0.88137358701954, 0 )
|
|---|
| 1113 | (-0.5,0):( -1.44363547517881, 0 )
|
|---|
| 1114 | ( 0.5,0):( 1.44363547517881, 0 )
|
|---|
| 1115 | ( 1.0,0):( 0.88137358701954, 0 )
|
|---|
| 1116 | ( 2.0,0):( 0.48121182505960, 0 )
|
|---|
| 1117 |
|
|---|
| 1118 | &acsch
|
|---|
| 1119 | ( 2, 3):( 0.15735549884499, -0.22996290237721)
|
|---|
| 1120 | (-2, 3):( -0.15735549884499, -0.22996290237721)
|
|---|
| 1121 | (-2,-3):( -0.15735549884499, 0.22996290237721)
|
|---|
| 1122 | ( 2,-3):( 0.15735549884499, 0.22996290237721)
|
|---|
| 1123 |
|
|---|
| 1124 | &acoth
|
|---|
| 1125 | (-2.0,0):( -0.54930614433405, 0 )
|
|---|
| 1126 | (-0.5,0):( -0.54930614433405, 1.57079632679490)
|
|---|
| 1127 | ( 0.5,0):( 0.54930614433405, 1.57079632679490)
|
|---|
| 1128 | ( 2.0,0):( 0.54930614433405, 0 )
|
|---|
| 1129 |
|
|---|
| 1130 | &acoth
|
|---|
| 1131 | ( 2, 3):( 0.14694666622553, -0.23182380450040)
|
|---|
| 1132 | (-2, 3):( -0.14694666622553, -0.23182380450040)
|
|---|
| 1133 | (-2,-3):( -0.14694666622553, 0.23182380450040)
|
|---|
| 1134 | ( 2,-3):( 0.14694666622553, 0.23182380450040)
|
|---|
| 1135 |
|
|---|
| 1136 | # eof
|
|---|
