3 # $RCSfile: complex.t,v $
5 # Regression tests for the Math::Complex pacakge
6 # -- Raphael Manfredi since Sep 1996
7 # -- Jarkko Hietaniemi since Mar 1997
8 # -- Daniel S. Lewart since Sep 1997
12 unshift @INC, '../lib';
17 my $VERSION = sprintf("%s", q$Id: complex.t,v 1.9 1998/11/01 00:00:00 dsl Exp $ =~ /(\d+\.d+)/);
19 my ($args, $op, $target, $test, $test_set, $try, $val, $zvalue, @set, @val);
24 'my ($res, $s0,$s1,$s2,$s3,$s4,$s5,$s6,$s7,$s8,$s9,$s10, $z0,$z1,$z2);' .
29 if ($^O eq 'unicos') { # For some reason root() produces very inaccurate
30 $eps = 1e-10; # results in Cray UNICOS, and occasionally also
31 } # cos(), sin(), cosh(), sinh(). The division
32 # of doubles is the current suspect.
36 next if $_ eq '' || /^\#/;
38 $test_set = 0; # Assume not a test over a set of values
44 set($1, \@set, \@val);
48 $test_set = 1; # Requests we loop over the set...
50 my @args = split(/:/);
53 for ($i = 0; $i < @set; $i++) {
56 # textual value as found in set definition
58 test($zvalue, $target, @args);
61 test($op, undef, @args);
71 push(@script, <<'EOT');
76 print "# $test Re(z) = ",$z->Re(), " Im(z) = ", $z->Im(), " z = $z\n";
77 print 'not ' unless Re($z) == 2 and Im($z) == 3;
79 push(@script, qq(print "ok $test\\n"}\n));
82 push(@script, <<'EOT');
86 print "# $test Re(z) = ",$z->Re(), " Im(z) = ", $z->Im(), " z = $z\n";
87 print 'not ' unless (abs($z) - 3 * sqrt(2)) < $eps and
88 (arg($z) - pi / 4 ) < $eps and
89 (Re($z) - 3 ) < $eps and
92 push(@script, qq(print "ok $test\\n"}\n));
95 push(@script, <<'EOT');
99 print "# $test Re(z) = ",$z->Re(), " Im(z) = ", $z->Im(), " z = $z\n";
100 print 'not ' unless (arg($z) + 3 / 4 * pi) < $eps and
101 (abs($z) - sqrt(2) ) < $eps and
102 (Re($z) + 1 ) < $eps and
103 (Im($z) + 1 ) < $eps;
105 push(@script, qq(print "ok $test\\n"}\n));
112 my $pi = cplx(pi, 0);
113 my $pii = cplx(0, pi);
114 my $pip2 = cplx(pi/2, 0);
115 my $zero = cplx(0, 0);
118 push(@script, $constants);
121 # test the divbyzeros
126 push(@script, <<EOT);
128 (\$bad) = (\$@ =~ /(.+)/);
129 print "# $test op = $op divbyzero? \$bad...\n";
130 print 'not ' unless (\$@ =~ /Division by zero/);
132 push(@script, qq(print "ok $test\\n";\n));
136 # test the logofzeros
141 push(@script, <<EOT);
143 (\$bad) = (\$@ =~ /(.+)/);
144 print "# $test op = $op logofzero? \$bad...\n";
145 print 'not ' unless (\$@ =~ /Logarithm of zero/);
147 push(@script, qq(print "ok $test\\n";\n));
155 # 'acoth(-1)', # Log of zero.
163 # 'atanh(-1)', # Log of zero.
184 push(@script, <<EOT);
186 (\$bad) = (\$@ =~ /(.+)/);
187 print "# $test op = $op badroot? \$bad...\n";
188 print 'not ' unless (\$@ =~ /root rank must be/);
190 push(@script, qq(print "ok $test\\n";\n));
194 test_broot(qw(-3 -2.1 0 0.99));
196 sub test_display_format {
198 my \$j = (root(1,3))[1];
200 \$j->display_format('polar');
205 print "# display_format polar?\n";
206 print "not " unless \$j->display_format eq 'polar';
213 print "not " unless "\$j" eq "[1,2pi/3]";
218 %display_format = \$j->display_format;
223 print "# display_format{style} polar?\n";
224 print "not " unless \$display_format{style} eq 'polar';
230 print "# keys %display_format == 2?\n";
231 print "not " unless keys %display_format == 2;
234 \$j->display_format('style' => 'cartesian', 'format' => '%.5f');
240 print "not " unless "\$j" eq "-0.50000+0.86603i";
243 %display_format = \$j->display_format;
248 print "# display_format{format} %.5f?\n";
249 print "not " unless \$display_format{format} eq '%.5f';
255 print "# keys %display_format == 3?\n";
256 print "not " unless keys %display_format == 3;
259 \$j->display_format('format' => undef);
265 print "not " unless "\$j" =~ /^-0(?:\\.5(?:0000\\d+)?|\\.49999\\d+)\\+0.86602540\\d+i\$/;
268 \$j->display_format('style' => 'polar', 'polar_pretty_print' => 0);
274 print "not " unless "\$j" =~ /^\\[1,2\\.09439510\\d+\\]\$/;
277 \$j->display_format('style' => 'cartesian', 'format' => '(%.5g)');
282 print "not " unless "\$j" eq "(-0.5)+(0.86603)i";
287 test_display_format();
290 eval join '', @script;
296 push(@script, qq(print "# $op=\n";));
300 my ($op, $z, @args) = @_;
304 $baop = 1 if ($op =~ s/;=$//);
305 for ($i = 0; $i < @args; $i++) {
306 $val = value($args[$i]);
307 push @script, "\$z$i = $val;\n";
310 $args = "'$op'"; # Really the value
311 $try = "abs(\$z0 - \$z1) <= $eps ? \$z1 : \$z0";
312 push @script, "\$res = $try; ";
313 push @script, "check($test, $args[0], \$res, \$z$#args, $args);\n";
318 $args = "'$args[0]'";
320 $try = ($op =~ /^\w/) ? "$op(\$z0, \$z1)" : "\$z0 $op \$z1";
321 $args = "'$args[0]', '$args[1]'";
323 push @script, "\$res = $try; ";
324 push @script, "check($test, '$try', \$res, \$z$#args, $args);\n";
325 if (@args > 2 and $baop) { # binary assignment ops
327 # check the op= works
330 my \$za = cplx(ref \$z0 ? \@{\$z0->cartesian} : (\$z0, 0));
332 my (\$z1r, \$z1i) = ref \$z1 ? \@{\$z1->cartesian} : (\$z1, 0);
334 my \$zb = cplx(\$z1r, \$z1i);
337 my (\$zbr, \$zbi) = \@{\$zb->cartesian};
339 check($test, '\$z0 $op= \$z1', \$za, \$z$#args, $args);
342 # check that the rhs has not changed
343 push @script, qq(print "not " unless (\$zbr == \$z1r and \$zbi == \$z1i););
344 push @script, qq(print "ok $test\\n";\n);
351 my ($set, $setref, $valref) = @_;
354 my @set = split(/;\s*/, $set);
357 for ($i = 0; $i < @set; $i++) {
358 push(@{$valref}, $set[$i]);
359 my $val = value($set[$i]);
360 push @script, "\$s$i = $val;\n";
361 push @{$setref}, "\$s$i";
367 if (/^\s*\((.*),(.*)\)/) {
368 return "cplx($1,$2)";
370 elsif (/^\s*([\-\+]?(?:\d+(\.\d+)?|\.\d+)(?:[e[\-\+]\d+])?)/) {
373 elsif (/^\s*\[(.*),(.*)\]/) {
374 return "cplxe($1,$2)";
376 elsif (/^\s*'(.*)'/) {
378 $ex =~ s/\bz\b/$target/g;
379 $ex =~ s/\br\b/abs($target)/g;
380 $ex =~ s/\bt\b/arg($target)/g;
381 $ex =~ s/\ba\b/Re($target)/g;
382 $ex =~ s/\bb\b/Im($target)/g;
385 elsif (/^\s*"(.*)"/) {
392 my ($test, $try, $got, $expected, @z) = @_;
396 if ("$got" eq "$expected"
398 ($expected =~ /^-?\d/ && $got == $expected)
400 (abs($got - $expected) < $eps)
404 print "not ok $test\n";
405 my $args = (@z == 1) ? "z = $z[0]" : "z0 = $z[0], z1 = $z[1]";
406 print "# '$try' expected: '$expected' got: '$got' for $args\n";
412 return ($z1 + i*$z2) * ($z1 - i*$z2);
417 return ($z1 + $z2) * ($z1 - $z2);
447 [2,2*pi/3]:(1,0):[2,2*pi/3]
459 [4,pi]:[2,pi/2]:[2,pi/2]
460 [2,pi/2]:[4,pi]:[0.5,-(pi)/2]
465 (2,3):(4,0):(-119,-120)
527 [6, -2*pi/3]:"[6,-2pi/3]"
528 [0.5, -9*pi/11]:"[0.5,-9pi/11]"
530 { (4,3); [3,2]; (-3,4); (0,2); [2,1] }
533 |'z - ~z':'2*i*Im(z)'
534 |'z * ~z':'abs(z) * abs(z)'
536 { (0.5, 0); (-0.5, 0); (2,3); [3,2]; (-3,2); (0,2); 3; 1.2; (-3, 0); (-2, -1); [2,1] }
538 |'(root(z, 4))[1] ** 4':'z'
539 |'(root(z, 5))[3] ** 5':'z'
540 |'(root(z, 8))[7] ** 8':'z'
542 |'acot(z)':'acotan(z)'
543 |'acsc(z)':'acosec(z)'
544 |'acsc(z)':'asin(1 / z)'
545 |'asec(z)':'acos(1 / z)'
546 |'cbrt(z)':'cbrt(r) * exp(i * t/3)'
548 |'addsq(cos(z), sin(z))':1
549 |'cos(z)':'cosh(i*z)'
550 |'subsq(cosh(z), sinh(z))':1
552 |'cot(z)':'1 / tan(z)'
555 |'csc(z)':'1 / sin(z)'
558 |'exp(z)':'exp(a) * exp(i * b)'
561 |'log(z)':'log(r) + i*t'
562 |'log10(z)':'log(z) / log(10)'
563 |'logn(z, 2)':'log(z) / log(2)'
564 |'logn(z, 3)':'log(z) / log(3)'
566 |'sec(z)':'1 / cos(z)'
568 |'sin(i * z)':'i * sinh(z)'
569 |'sqrt(z) * sqrt(z)':'z'
570 |'sqrt(z)':'sqrt(r) * exp(i * t/2)'
572 |'z**z':'exp(z * log(z))'
574 { (1,1); [1,0.5]; (-2, -1); 2; -3; (-1,0.5); (0,0.5); 0.5; (2, 0); (-1, -2) }
576 |'cosh(acosh(z))':'z'
577 |'coth(acoth(z))':'z'
578 |'coth(z)':'1 / tanh(z)'
579 |'coth(z)':'cotanh(z)'
580 |'csch(acsch(z))':'z'
581 |'csch(z)':'1 / sinh(z)'
582 |'csch(z)':'cosech(z)'
583 |'sech(asech(z))':'z'
584 |'sech(z)':'1 / cosh(z)'
585 |'sinh(asinh(z))':'z'
586 |'tanh(atanh(z))':'z'
588 { (0.2,-0.4); [1,0.5]; -1.2; (-1,0.5); 0.5; (1.1, 0) }
590 |'acos(cos(z)) ** 2':'z * z'
591 |'acosh(cosh(z)) ** 2':'z * z'
592 |'acoth(z)':'acotanh(z)'
593 |'acoth(z)':'atanh(1 / z)'
594 |'acsch(z)':'acosech(z)'
595 |'acsch(z)':'asinh(1 / z)'
596 |'asech(z)':'acosh(1 / z)'
598 |'asinh(sinh(z))':'z'
600 |'atanh(tanh(z))':'z'
603 (-2.0,0):( 0.69314718055995, 3.14159265358979)
604 (-1.0,0):( 0 , 3.14159265358979)
605 (-0.5,0):( -0.69314718055995, 3.14159265358979)
606 ( 0.5,0):( -0.69314718055995, 0 )
608 ( 2.0,0):( 0.69314718055995, 0 )
611 ( 2, 3):( 1.28247467873077, 0.98279372324733)
612 (-2, 3):( 1.28247467873077, 2.15879893034246)
613 (-2,-3):( 1.28247467873077, -2.15879893034246)
614 ( 2,-3):( 1.28247467873077, -0.98279372324733)
617 (-2.0,0):( -0.90929742682568, 0 )
618 (-1.0,0):( -0.84147098480790, 0 )
619 (-0.5,0):( -0.47942553860420, 0 )
621 ( 0.5,0):( 0.47942553860420, 0 )
622 ( 1.0,0):( 0.84147098480790, 0 )
623 ( 2.0,0):( 0.90929742682568, 0 )
626 ( 2, 3):( 9.15449914691143, -4.16890695996656)
627 (-2, 3):( -9.15449914691143, -4.16890695996656)
628 (-2,-3):( -9.15449914691143, 4.16890695996656)
629 ( 2,-3):( 9.15449914691143, 4.16890695996656)
632 (-2.0,0):( -0.41614683654714, 0 )
633 (-1.0,0):( 0.54030230586814, 0 )
634 (-0.5,0):( 0.87758256189037, 0 )
636 ( 0.5,0):( 0.87758256189037, 0 )
637 ( 1.0,0):( 0.54030230586814, 0 )
638 ( 2.0,0):( -0.41614683654714, 0 )
641 ( 2, 3):( -4.18962569096881, -9.10922789375534)
642 (-2, 3):( -4.18962569096881, 9.10922789375534)
643 (-2,-3):( -4.18962569096881, -9.10922789375534)
644 ( 2,-3):( -4.18962569096881, 9.10922789375534)
647 (-2.0,0):( 2.18503986326152, 0 )
648 (-1.0,0):( -1.55740772465490, 0 )
649 (-0.5,0):( -0.54630248984379, 0 )
651 ( 0.5,0):( 0.54630248984379, 0 )
652 ( 1.0,0):( 1.55740772465490, 0 )
653 ( 2.0,0):( -2.18503986326152, 0 )
656 ( 2, 3):( -0.00376402564150, 1.00323862735361)
657 (-2, 3):( 0.00376402564150, 1.00323862735361)
658 (-2,-3):( 0.00376402564150, -1.00323862735361)
659 ( 2,-3):( -0.00376402564150, -1.00323862735361)
662 (-2.0,0):( -2.40299796172238, 0 )
663 (-1.0,0):( 1.85081571768093, 0 )
664 (-0.5,0):( 1.13949392732455, 0 )
666 ( 0.5,0):( 1.13949392732455, 0 )
667 ( 1.0,0):( 1.85081571768093, 0 )
668 ( 2.0,0):( -2.40299796172238, 0 )
671 ( 2, 3):( -0.04167496441114, 0.09061113719624)
672 (-2, 3):( -0.04167496441114, -0.09061113719624)
673 (-2,-3):( -0.04167496441114, 0.09061113719624)
674 ( 2,-3):( -0.04167496441114, -0.09061113719624)
677 (-2.0,0):( -1.09975017029462, 0 )
678 (-1.0,0):( -1.18839510577812, 0 )
679 (-0.5,0):( -2.08582964293349, 0 )
680 ( 0.5,0):( 2.08582964293349, 0 )
681 ( 1.0,0):( 1.18839510577812, 0 )
682 ( 2.0,0):( 1.09975017029462, 0 )
685 ( 2, 3):( 0.09047320975321, 0.04120098628857)
686 (-2, 3):( -0.09047320975321, 0.04120098628857)
687 (-2,-3):( -0.09047320975321, -0.04120098628857)
688 ( 2,-3):( 0.09047320975321, -0.04120098628857)
691 (-2.0,0):( 0.45765755436029, 0 )
692 (-1.0,0):( -0.64209261593433, 0 )
693 (-0.5,0):( -1.83048772171245, 0 )
694 ( 0.5,0):( 1.83048772171245, 0 )
695 ( 1.0,0):( 0.64209261593433, 0 )
696 ( 2.0,0):( -0.45765755436029, 0 )
699 ( 2, 3):( -0.00373971037634, -0.99675779656936)
700 (-2, 3):( 0.00373971037634, -0.99675779656936)
701 (-2,-3):( 0.00373971037634, 0.99675779656936)
702 ( 2,-3):( -0.00373971037634, 0.99675779656936)
705 (-2.0,0):( -1.57079632679490, 1.31695789692482)
706 (-1.0,0):( -1.57079632679490, 0 )
707 (-0.5,0):( -0.52359877559830, 0 )
709 ( 0.5,0):( 0.52359877559830, 0 )
710 ( 1.0,0):( 1.57079632679490, 0 )
711 ( 2.0,0):( 1.57079632679490, -1.31695789692482)
714 ( 2, 3):( 0.57065278432110, 1.98338702991654)
715 (-2, 3):( -0.57065278432110, 1.98338702991654)
716 (-2,-3):( -0.57065278432110, -1.98338702991654)
717 ( 2,-3):( 0.57065278432110, -1.98338702991654)
720 (-2.0,0):( 3.14159265358979, -1.31695789692482)
721 (-1.0,0):( 3.14159265358979, 0 )
722 (-0.5,0):( 2.09439510239320, 0 )
723 ( 0.0,0):( 1.57079632679490, 0 )
724 ( 0.5,0):( 1.04719755119660, 0 )
726 ( 2.0,0):( 0 , 1.31695789692482)
729 ( 2, 3):( 1.00014354247380, -1.98338702991654)
730 (-2, 3):( 2.14144911111600, -1.98338702991654)
731 (-2,-3):( 2.14144911111600, 1.98338702991654)
732 ( 2,-3):( 1.00014354247380, 1.98338702991654)
735 (-2.0,0):( -1.10714871779409, 0 )
736 (-1.0,0):( -0.78539816339745, 0 )
737 (-0.5,0):( -0.46364760900081, 0 )
739 ( 0.5,0):( 0.46364760900081, 0 )
740 ( 1.0,0):( 0.78539816339745, 0 )
741 ( 2.0,0):( 1.10714871779409, 0 )
744 ( 2, 3):( 1.40992104959658, 0.22907268296854)
745 (-2, 3):( -1.40992104959658, 0.22907268296854)
746 (-2,-3):( -1.40992104959658, -0.22907268296854)
747 ( 2,-3):( 1.40992104959658, -0.22907268296854)
750 (-2.0,0):( 2.09439510239320, 0 )
751 (-1.0,0):( 3.14159265358979, 0 )
752 (-0.5,0):( 3.14159265358979, -1.31695789692482)
753 ( 0.5,0):( 0 , 1.31695789692482)
755 ( 2.0,0):( 1.04719755119660, 0 )
758 ( 2, 3):( 1.42041072246703, 0.23133469857397)
759 (-2, 3):( 1.72118193112276, 0.23133469857397)
760 (-2,-3):( 1.72118193112276, -0.23133469857397)
761 ( 2,-3):( 1.42041072246703, -0.23133469857397)
764 (-2.0,0):( -0.52359877559830, 0 )
765 (-1.0,0):( -1.57079632679490, 0 )
766 (-0.5,0):( -1.57079632679490, 1.31695789692482)
767 ( 0.5,0):( 1.57079632679490, -1.31695789692482)
768 ( 1.0,0):( 1.57079632679490, 0 )
769 ( 2.0,0):( 0.52359877559830, 0 )
772 ( 2, 3):( 0.15038560432786, -0.23133469857397)
773 (-2, 3):( -0.15038560432786, -0.23133469857397)
774 (-2,-3):( -0.15038560432786, 0.23133469857397)
775 ( 2,-3):( 0.15038560432786, 0.23133469857397)
778 (-2.0,0):( -0.46364760900081, 0 )
779 (-1.0,0):( -0.78539816339745, 0 )
780 (-0.5,0):( -1.10714871779409, 0 )
781 ( 0.5,0):( 1.10714871779409, 0 )
782 ( 1.0,0):( 0.78539816339745, 0 )
783 ( 2.0,0):( 0.46364760900081, 0 )
786 ( 2, 3):( 0.16087527719832, -0.22907268296854)
787 (-2, 3):( -0.16087527719832, -0.22907268296854)
788 (-2,-3):( -0.16087527719832, 0.22907268296854)
789 ( 2,-3):( 0.16087527719832, 0.22907268296854)
792 (-2.0,0):( -3.62686040784702, 0 )
793 (-1.0,0):( -1.17520119364380, 0 )
794 (-0.5,0):( -0.52109530549375, 0 )
796 ( 0.5,0):( 0.52109530549375, 0 )
797 ( 1.0,0):( 1.17520119364380, 0 )
798 ( 2.0,0):( 3.62686040784702, 0 )
801 ( 2, 3):( -3.59056458998578, 0.53092108624852)
802 (-2, 3):( 3.59056458998578, 0.53092108624852)
803 (-2,-3):( 3.59056458998578, -0.53092108624852)
804 ( 2,-3):( -3.59056458998578, -0.53092108624852)
807 (-2.0,0):( 3.76219569108363, 0 )
808 (-1.0,0):( 1.54308063481524, 0 )
809 (-0.5,0):( 1.12762596520638, 0 )
811 ( 0.5,0):( 1.12762596520638, 0 )
812 ( 1.0,0):( 1.54308063481524, 0 )
813 ( 2.0,0):( 3.76219569108363, 0 )
816 ( 2, 3):( -3.72454550491532, 0.51182256998738)
817 (-2, 3):( -3.72454550491532, -0.51182256998738)
818 (-2,-3):( -3.72454550491532, 0.51182256998738)
819 ( 2,-3):( -3.72454550491532, -0.51182256998738)
822 (-2.0,0):( -0.96402758007582, 0 )
823 (-1.0,0):( -0.76159415595576, 0 )
824 (-0.5,0):( -0.46211715726001, 0 )
826 ( 0.5,0):( 0.46211715726001, 0 )
827 ( 1.0,0):( 0.76159415595576, 0 )
828 ( 2.0,0):( 0.96402758007582, 0 )
831 ( 2, 3):( 0.96538587902213, -0.00988437503832)
832 (-2, 3):( -0.96538587902213, -0.00988437503832)
833 (-2,-3):( -0.96538587902213, 0.00988437503832)
834 ( 2,-3):( 0.96538587902213, 0.00988437503832)
837 (-2.0,0):( 0.26580222883408, 0 )
838 (-1.0,0):( 0.64805427366389, 0 )
839 (-0.5,0):( 0.88681888397007, 0 )
841 ( 0.5,0):( 0.88681888397007, 0 )
842 ( 1.0,0):( 0.64805427366389, 0 )
843 ( 2.0,0):( 0.26580222883408, 0 )
846 ( 2, 3):( -0.26351297515839, -0.03621163655877)
847 (-2, 3):( -0.26351297515839, 0.03621163655877)
848 (-2,-3):( -0.26351297515839, -0.03621163655877)
849 ( 2,-3):( -0.26351297515839, 0.03621163655877)
852 (-2.0,0):( -0.27572056477178, 0 )
853 (-1.0,0):( -0.85091812823932, 0 )
854 (-0.5,0):( -1.91903475133494, 0 )
855 ( 0.5,0):( 1.91903475133494, 0 )
856 ( 1.0,0):( 0.85091812823932, 0 )
857 ( 2.0,0):( 0.27572056477178, 0 )
860 ( 2, 3):( -0.27254866146294, -0.04030057885689)
861 (-2, 3):( 0.27254866146294, -0.04030057885689)
862 (-2,-3):( 0.27254866146294, 0.04030057885689)
863 ( 2,-3):( -0.27254866146294, 0.04030057885689)
866 (-2.0,0):( -1.03731472072755, 0 )
867 (-1.0,0):( -1.31303528549933, 0 )
868 (-0.5,0):( -2.16395341373865, 0 )
869 ( 0.5,0):( 2.16395341373865, 0 )
870 ( 1.0,0):( 1.31303528549933, 0 )
871 ( 2.0,0):( 1.03731472072755, 0 )
874 ( 2, 3):( 1.03574663776500, 0.01060478347034)
875 (-2, 3):( -1.03574663776500, 0.01060478347034)
876 (-2,-3):( -1.03574663776500, -0.01060478347034)
877 ( 2,-3):( 1.03574663776500, -0.01060478347034)
880 (-2.0,0):( -1.44363547517881, 0 )
881 (-1.0,0):( -0.88137358701954, 0 )
882 (-0.5,0):( -0.48121182505960, 0 )
884 ( 0.5,0):( 0.48121182505960, 0 )
885 ( 1.0,0):( 0.88137358701954, 0 )
886 ( 2.0,0):( 1.44363547517881, 0 )
889 ( 2, 3):( 1.96863792579310, 0.96465850440760)
890 (-2, 3):( -1.96863792579310, 0.96465850440761)
891 (-2,-3):( -1.96863792579310, -0.96465850440761)
892 ( 2,-3):( 1.96863792579310, -0.96465850440760)
895 (-2.0,0):( 1.31695789692482, 3.14159265358979)
896 (-1.0,0):( 0, 3.14159265358979)
897 (-0.5,0):( 0, 2.09439510239320)
898 ( 0.0,0):( 0, 1.57079632679490)
899 ( 0.5,0):( 0, 1.04719755119660)
901 ( 2.0,0):( 1.31695789692482, 0 )
904 ( 2, 3):( 1.98338702991654, 1.00014354247380)
905 (-2, 3):( 1.98338702991653, 2.14144911111600)
906 (-2,-3):( 1.98338702991653, -2.14144911111600)
907 ( 2,-3):( 1.98338702991654, -1.00014354247380)
910 (-2.0,0):( -0.54930614433405, 1.57079632679490)
911 (-0.5,0):( -0.54930614433405, 0 )
913 ( 0.5,0):( 0.54930614433405, 0 )
914 ( 2.0,0):( 0.54930614433405, 1.57079632679490)
917 ( 2, 3):( 0.14694666622553, 1.33897252229449)
918 (-2, 3):( -0.14694666622553, 1.33897252229449)
919 (-2,-3):( -0.14694666622553, -1.33897252229449)
920 ( 2,-3):( 0.14694666622553, -1.33897252229449)
923 (-2.0,0):( 0 , 2.09439510239320)
924 (-1.0,0):( 0 , 3.14159265358979)
925 (-0.5,0):( 1.31695789692482, 3.14159265358979)
926 ( 0.5,0):( 1.31695789692482, 0 )
928 ( 2.0,0):( 0 , 1.04719755119660)
931 ( 2, 3):( 0.23133469857397, -1.42041072246703)
932 (-2, 3):( 0.23133469857397, -1.72118193112276)
933 (-2,-3):( 0.23133469857397, 1.72118193112276)
934 ( 2,-3):( 0.23133469857397, 1.42041072246703)
937 (-2.0,0):( -0.48121182505960, 0 )
938 (-1.0,0):( -0.88137358701954, 0 )
939 (-0.5,0):( -1.44363547517881, 0 )
940 ( 0.5,0):( 1.44363547517881, 0 )
941 ( 1.0,0):( 0.88137358701954, 0 )
942 ( 2.0,0):( 0.48121182505960, 0 )
945 ( 2, 3):( 0.15735549884499, -0.22996290237721)
946 (-2, 3):( -0.15735549884499, -0.22996290237721)
947 (-2,-3):( -0.15735549884499, 0.22996290237721)
948 ( 2,-3):( 0.15735549884499, 0.22996290237721)
951 (-2.0,0):( -0.54930614433405, 0 )
952 (-0.5,0):( -0.54930614433405, 1.57079632679490)
953 ( 0.5,0):( 0.54930614433405, 1.57079632679490)
954 ( 2.0,0):( 0.54930614433405, 0 )
957 ( 2, 3):( 0.14694666622553, -0.23182380450040)
958 (-2, 3):( -0.14694666622553, -0.23182380450040)
959 (-2,-3):( -0.14694666622553, 0.23182380450040)
960 ( 2,-3):( 0.14694666622553, 0.23182380450040)