Commit | Line | Data |
89d0527d |
1 | #!./perl |
2 | |
89d0527d |
3 | # |
5aabfad6 |
4 | # Regression tests for the Math::Complex pacakge |
b42d0ec9 |
5 | # -- Raphael Manfredi since Sep 1996 |
6 | # -- Jarkko Hietaniemi since Mar 1997 |
7 | # -- Daniel S. Lewart since Sep 1997 |
5aabfad6 |
8 | |
89d0527d |
9 | BEGIN { |
bf5f1b4c |
10 | if ($ENV{PERL_CORE}) { |
11 | chdir 't' if -d 't'; |
12 | @INC = '../lib'; |
13 | } |
89d0527d |
14 | } |
5aabfad6 |
15 | |
57dd0abb |
16 | use Math::Complex 1.52; |
89d0527d |
17 | |
476757f7 |
18 | use vars qw($VERSION); |
19 | |
91cb744f |
20 | $VERSION = 1.92; |
b42d0ec9 |
21 | |
fb73857a |
22 | my ($args, $op, $target, $test, $test_set, $try, $val, $zvalue, @set, @val); |
23 | |
89d0527d |
24 | $test = 0; |
25 | $| = 1; |
fb73857a |
26 | my @script = ( |
bf5f1b4c |
27 | 'my ($res, $s0,$s1,$s2,$s3,$s4,$s5,$s6,$s7,$s8,$s9,$s10,$z0,$z1,$z2);' . |
fb73857a |
28 | "\n\n" |
29 | ); |
b42d0ec9 |
30 | my $eps = 1e-13; |
89d0527d |
31 | |
d09ae4e6 |
32 | if ($^O eq 'unicos') { # For some reason root() produces very inaccurate |
f3ff050f |
33 | $eps = 1e-10; # results in Cray UNICOS, and occasionally also |
d09ae4e6 |
34 | } # cos(), sin(), cosh(), sinh(). The division |
35 | # of doubles is the current suspect. |
36 | |
89d0527d |
37 | while (<DATA>) { |
0c721ce2 |
38 | s/^\s+//; |
39 | next if $_ eq '' || /^\#/; |
40 | chomp; |
41 | $test_set = 0; # Assume not a test over a set of values |
0e505df1 |
42 | if (/^&(.+)/) { |
89d0527d |
43 | $op = $1; |
44 | next; |
45 | } |
0e505df1 |
46 | elsif (/^\{(.+)\}/) { |
89d0527d |
47 | set($1, \@set, \@val); |
48 | next; |
49 | } |
50 | elsif (s/^\|//) { |
0c721ce2 |
51 | $test_set = 1; # Requests we loop over the set... |
89d0527d |
52 | } |
53 | my @args = split(/:/); |
0c721ce2 |
54 | if ($test_set == 1) { |
89d0527d |
55 | my $i; |
56 | for ($i = 0; $i < @set; $i++) { |
0c721ce2 |
57 | # complex number |
58 | $target = $set[$i]; |
59 | # textual value as found in set definition |
60 | $zvalue = $val[$i]; |
89d0527d |
61 | test($zvalue, $target, @args); |
62 | } |
63 | } else { |
64 | test($op, undef, @args); |
65 | } |
66 | } |
67 | |
b42d0ec9 |
68 | # |
69 | |
70 | sub test_mutators { |
71 | my $op; |
72 | |
73 | $test++; |
74 | push(@script, <<'EOT'); |
75 | { |
76 | my $z = cplx( 1, 1); |
77 | $z->Re(2); |
78 | $z->Im(3); |
16357284 |
79 | print "# $test Re(z) = ",$z->Re(), " Im(z) = ", $z->Im(), " z = $z\n"; |
b42d0ec9 |
80 | print 'not ' unless Re($z) == 2 and Im($z) == 3; |
81 | EOT |
82 | push(@script, qq(print "ok $test\\n"}\n)); |
83 | |
84 | $test++; |
85 | push(@script, <<'EOT'); |
86 | { |
87 | my $z = cplx( 1, 1); |
88 | $z->abs(3 * sqrt(2)); |
16357284 |
89 | print "# $test Re(z) = ",$z->Re(), " Im(z) = ", $z->Im(), " z = $z\n"; |
b42d0ec9 |
90 | print 'not ' unless (abs($z) - 3 * sqrt(2)) < $eps and |
91 | (arg($z) - pi / 4 ) < $eps and |
92 | (Re($z) - 3 ) < $eps and |
93 | (Im($z) - 3 ) < $eps; |
94 | EOT |
95 | push(@script, qq(print "ok $test\\n"}\n)); |
96 | |
97 | $test++; |
98 | push(@script, <<'EOT'); |
99 | { |
100 | my $z = cplx( 1, 1); |
101 | $z->arg(-3 / 4 * pi); |
16357284 |
102 | print "# $test Re(z) = ",$z->Re(), " Im(z) = ", $z->Im(), " z = $z\n"; |
b42d0ec9 |
103 | print 'not ' unless (arg($z) + 3 / 4 * pi) < $eps and |
104 | (abs($z) - sqrt(2) ) < $eps and |
105 | (Re($z) + 1 ) < $eps and |
106 | (Im($z) + 1 ) < $eps; |
107 | EOT |
108 | push(@script, qq(print "ok $test\\n"}\n)); |
109 | } |
110 | |
111 | test_mutators(); |
112 | |
113 | my $constants = ' |
114 | my $i = cplx(0, 1); |
115 | my $pi = cplx(pi, 0); |
116 | my $pii = cplx(0, pi); |
117 | my $pip2 = cplx(pi/2, 0); |
bf5f1b4c |
118 | my $pip4 = cplx(pi/4, 0); |
b42d0ec9 |
119 | my $zero = cplx(0, 0); |
bf5f1b4c |
120 | my $inf = 9**9**9; |
b42d0ec9 |
121 | '; |
122 | |
123 | push(@script, $constants); |
124 | |
125 | |
5cd24f17 |
126 | # test the divbyzeros |
127 | |
0e505df1 |
128 | sub test_dbz { |
129 | for my $op (@_) { |
130 | $test++; |
b42d0ec9 |
131 | push(@script, <<EOT); |
16357284 |
132 | eval '$op'; |
133 | (\$bad) = (\$@ =~ /(.+)/); |
134 | print "# $test op = $op divbyzero? \$bad...\n"; |
135 | print 'not ' unless (\$@ =~ /Division by zero/); |
b42d0ec9 |
136 | EOT |
137 | push(@script, qq(print "ok $test\\n";\n)); |
0e505df1 |
138 | } |
139 | } |
140 | |
8c03c583 |
141 | # test the logofzeros |
142 | |
143 | sub test_loz { |
144 | for my $op (@_) { |
145 | $test++; |
b42d0ec9 |
146 | push(@script, <<EOT); |
16357284 |
147 | eval '$op'; |
148 | (\$bad) = (\$@ =~ /(.+)/); |
149 | print "# $test op = $op logofzero? \$bad...\n"; |
150 | print 'not ' unless (\$@ =~ /Logarithm of zero/); |
b42d0ec9 |
151 | EOT |
152 | push(@script, qq(print "ok $test\\n";\n)); |
8c03c583 |
153 | } |
154 | } |
155 | |
5cd24f17 |
156 | test_dbz( |
157 | 'i/0', |
b42d0ec9 |
158 | 'acot(0)', |
159 | 'acot(+$i)', |
160 | # 'acoth(-1)', # Log of zero. |
161 | 'acoth(0)', |
162 | 'acoth(+1)', |
5cd24f17 |
163 | 'acsc(0)', |
5cd24f17 |
164 | 'acsch(0)', |
b42d0ec9 |
165 | 'asec(0)', |
166 | 'asech(0)', |
b42d0ec9 |
167 | 'atan($i)', |
168 | # 'atanh(-1)', # Log of zero. |
169 | 'atanh(+1)', |
170 | 'cot(0)', |
171 | 'coth(0)', |
172 | 'csc(0)', |
b42d0ec9 |
173 | 'csch(0)', |
bf5f1b4c |
174 | 'atan(cplx(0, 1), cplx(1, 0))', |
8c03c583 |
175 | ); |
176 | |
177 | test_loz( |
fb73857a |
178 | 'log($zero)', |
1fa12f56 |
179 | 'atan(-$i)', |
b42d0ec9 |
180 | 'acot(-$i)', |
8c03c583 |
181 | 'atanh(-1)', |
182 | 'acoth(-1)', |
5cd24f17 |
183 | ); |
184 | |
0e505df1 |
185 | # test the bad roots |
186 | |
187 | sub test_broot { |
5cd24f17 |
188 | for my $op (@_) { |
189 | $test++; |
b42d0ec9 |
190 | push(@script, <<EOT); |
16357284 |
191 | eval 'root(2, $op)'; |
192 | (\$bad) = (\$@ =~ /(.+)/); |
193 | print "# $test op = $op badroot? \$bad...\n"; |
1fa12f56 |
194 | print 'not ' unless (\$@ =~ /root rank must be/); |
b42d0ec9 |
195 | EOT |
196 | push(@script, qq(print "ok $test\\n";\n)); |
5cd24f17 |
197 | } |
198 | } |
199 | |
0e505df1 |
200 | test_broot(qw(-3 -2.1 0 0.99)); |
201 | |
16357284 |
202 | sub test_display_format { |
476757f7 |
203 | $test++; |
204 | push @script, <<EOS; |
205 | print "# package display_format cartesian?\n"; |
206 | print "not " unless Math::Complex->display_format eq 'cartesian'; |
207 | print "ok $test\n"; |
208 | EOS |
209 | |
16357284 |
210 | push @script, <<EOS; |
211 | my \$j = (root(1,3))[1]; |
212 | |
213 | \$j->display_format('polar'); |
214 | EOS |
215 | |
216 | $test++; |
217 | push @script, <<EOS; |
476757f7 |
218 | print "# j display_format polar?\n"; |
16357284 |
219 | print "not " unless \$j->display_format eq 'polar'; |
220 | print "ok $test\n"; |
221 | EOS |
222 | |
223 | $test++; |
224 | push @script, <<EOS; |
225 | print "# j = \$j\n"; |
226 | print "not " unless "\$j" eq "[1,2pi/3]"; |
227 | print "ok $test\n"; |
228 | |
229 | my %display_format; |
230 | |
231 | %display_format = \$j->display_format; |
232 | EOS |
233 | |
234 | $test++; |
235 | push @script, <<EOS; |
236 | print "# display_format{style} polar?\n"; |
237 | print "not " unless \$display_format{style} eq 'polar'; |
238 | print "ok $test\n"; |
239 | EOS |
240 | |
241 | $test++; |
242 | push @script, <<EOS; |
243 | print "# keys %display_format == 2?\n"; |
244 | print "not " unless keys %display_format == 2; |
245 | print "ok $test\n"; |
246 | |
247 | \$j->display_format('style' => 'cartesian', 'format' => '%.5f'); |
248 | EOS |
249 | |
250 | $test++; |
251 | push @script, <<EOS; |
252 | print "# j = \$j\n"; |
253 | print "not " unless "\$j" eq "-0.50000+0.86603i"; |
254 | print "ok $test\n"; |
255 | |
256 | %display_format = \$j->display_format; |
257 | EOS |
258 | |
259 | $test++; |
260 | push @script, <<EOS; |
261 | print "# display_format{format} %.5f?\n"; |
262 | print "not " unless \$display_format{format} eq '%.5f'; |
263 | print "ok $test\n"; |
264 | EOS |
265 | |
266 | $test++; |
267 | push @script, <<EOS; |
268 | print "# keys %display_format == 3?\n"; |
269 | print "not " unless keys %display_format == 3; |
270 | print "ok $test\n"; |
271 | |
272 | \$j->display_format('format' => undef); |
273 | EOS |
274 | |
275 | $test++; |
276 | push @script, <<EOS; |
277 | print "# j = \$j\n"; |
057216a3 |
278 | print "not " unless "\$j" =~ /^-0(?:\\.5(?:0000\\d+)?|\\.49999\\d+)\\+0.86602540\\d+i\$/; |
16357284 |
279 | print "ok $test\n"; |
280 | |
281 | \$j->display_format('style' => 'polar', 'polar_pretty_print' => 0); |
282 | EOS |
283 | |
284 | $test++; |
285 | push @script, <<EOS; |
286 | print "# j = \$j\n"; |
1ab88a68 |
287 | print "not " unless "\$j" =~ /^\\[1,2\\.09439510\\d+\\]\$/; |
16357284 |
288 | print "ok $test\n"; |
289 | |
290 | \$j->display_format('style' => 'cartesian', 'format' => '(%.5g)'); |
291 | EOS |
476757f7 |
292 | |
16357284 |
293 | $test++; |
294 | push @script, <<EOS; |
295 | print "# j = \$j\n"; |
296 | print "not " unless "\$j" eq "(-0.5)+(0.86603)i"; |
297 | print "ok $test\n"; |
298 | EOS |
476757f7 |
299 | |
300 | $test++; |
301 | push @script, <<EOS; |
302 | print "# j display_format cartesian?\n"; |
303 | print "not " unless \$j->display_format eq 'cartesian'; |
304 | print "ok $test\n"; |
305 | EOS |
16357284 |
306 | } |
307 | |
308 | test_display_format(); |
309 | |
91cb744f |
310 | sub test_remake { |
311 | $test++; |
312 | push @script, <<EOS; |
313 | print "# remake 2+3i\n"; |
bf5f1b4c |
314 | \$z = cplx('2+3i'); |
91cb744f |
315 | print "not " unless \$z == Math::Complex->make(2,3); |
316 | print "ok $test\n"; |
317 | EOS |
318 | |
319 | $test++; |
320 | push @script, <<EOS; |
bf5f1b4c |
321 | print "# make 3i\n"; |
322 | \$z = Math::Complex->make('3i'); |
91cb744f |
323 | print "not " unless \$z == cplx(0,3); |
324 | print "ok $test\n"; |
325 | EOS |
326 | |
327 | $test++; |
328 | push @script, <<EOS; |
bf5f1b4c |
329 | print "# emake [2,3]\n"; |
330 | \$z = Math::Complex->emake('[2,3]'); |
331 | print "not " unless \$z == cplxe(2,3); |
332 | print "ok $test\n"; |
333 | EOS |
334 | |
335 | $test++; |
336 | push @script, <<EOS; |
337 | print "# make (2,3)\n"; |
338 | \$z = Math::Complex->make('(2,3)'); |
339 | print "not " unless \$z == cplx(2,3); |
340 | print "ok $test\n"; |
341 | EOS |
342 | |
343 | $test++; |
344 | push @script, <<EOS; |
345 | print "# emake [2,3pi/8]\n"; |
346 | \$z = Math::Complex->emake('[2,3pi/8]'); |
347 | print "not " unless \$z == cplxe(2,3*\$pi/8); |
91cb744f |
348 | print "ok $test\n"; |
349 | EOS |
350 | |
351 | $test++; |
352 | push @script, <<EOS; |
bf5f1b4c |
353 | print "# emake [2]\n"; |
354 | \$z = Math::Complex->emake('[2]'); |
91cb744f |
355 | print "not " unless \$z == cplxe(2); |
356 | print "ok $test\n"; |
357 | EOS |
358 | } |
359 | |
bf5f1b4c |
360 | sub test_no_args { |
361 | push @script, <<'EOS'; |
362 | { |
363 | print "# cplx, cplxe, make, emake without arguments\n"; |
364 | EOS |
365 | |
366 | $test++; |
367 | push @script, <<EOS; |
368 | my \$z0 = cplx(); |
369 | print ((\$z0->Re() == 0) ? "ok $test\n" : "not ok $test\n"); |
370 | EOS |
371 | |
372 | $test++; |
373 | push @script, <<EOS; |
374 | print ((\$z0->Im() == 0) ? "ok $test\n" : "not ok $test\n"); |
375 | EOS |
376 | |
377 | $test++; |
378 | push @script, <<EOS; |
379 | my \$z1 = cplxe(); |
380 | print ((\$z1->rho() == 0) ? "ok $test\n" : "not ok $test\n"); |
381 | EOS |
382 | |
383 | $test++; |
384 | push @script, <<EOS; |
385 | print ((\$z1->theta() == 0) ? "ok $test\n" : "not ok $test\n"); |
386 | EOS |
387 | |
388 | $test++; |
389 | push @script, <<EOS; |
390 | my \$z2 = Math::Complex->make(); |
391 | print ((\$z2->Re() == 0) ? "ok $test\n" : "not ok $test\n"); |
392 | EOS |
393 | |
394 | $test++; |
395 | push @script, <<EOS; |
396 | print ((\$z2->Im() == 0) ? "ok $test\n" : "not ok $test\n"); |
397 | EOS |
398 | |
399 | $test++; |
400 | push @script, <<EOS; |
401 | my \$z3 = Math::Complex->emake(); |
402 | print ((\$z3->rho() == 0) ? "ok $test\n" : "not ok $test\n"); |
403 | EOS |
404 | |
405 | $test++; |
406 | push @script, <<EOS; |
407 | print ((\$z3->theta() == 0) ? "ok $test\n" : "not ok $test\n"); |
408 | } |
409 | EOS |
410 | } |
411 | |
412 | sub test_atan2 { |
413 | push @script, <<'EOS'; |
414 | print "# atan2() with some real arguments\n"; |
415 | EOS |
416 | my @real = (-1, 0, 1); |
417 | for my $x (@real) { |
418 | for my $y (@real) { |
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 $test\n"); |
444 | EOS |
445 | } |
446 | |
447 | sub test_decplx { |
448 | } |
449 | |
91cb744f |
450 | test_remake(); |
451 | |
bf5f1b4c |
452 | test_no_args(); |
453 | |
454 | test_atan2(); |
455 | |
456 | test_decplx(); |
457 | |
89d0527d |
458 | print "1..$test\n"; |
bf5f1b4c |
459 | #print @script, "\n"; |
fe82cf6e |
460 | eval join '', @script; |
89d0527d |
461 | die $@ if $@; |
462 | |
0e505df1 |
463 | sub abop { |
464 | my ($op) = @_; |
465 | |
466 | push(@script, qq(print "# $op=\n";)); |
467 | } |
468 | |
89d0527d |
469 | sub test { |
470 | my ($op, $z, @args) = @_; |
0e505df1 |
471 | my ($baop) = 0; |
89d0527d |
472 | $test++; |
473 | my $i; |
0e505df1 |
474 | $baop = 1 if ($op =~ s/;=$//); |
89d0527d |
475 | for ($i = 0; $i < @args; $i++) { |
476 | $val = value($args[$i]); |
fe82cf6e |
477 | push @script, "\$z$i = $val;\n"; |
89d0527d |
478 | } |
479 | if (defined $z) { |
480 | $args = "'$op'"; # Really the value |
0c721ce2 |
481 | $try = "abs(\$z0 - \$z1) <= $eps ? \$z1 : \$z0"; |
fe82cf6e |
482 | push @script, "\$res = $try; "; |
483 | push @script, "check($test, $args[0], \$res, \$z$#args, $args);\n"; |
89d0527d |
484 | } else { |
485 | my ($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 | } |
fe82cf6e |
493 | push @script, "\$res = $try; "; |
494 | push @script, "check($test, '$try', \$res, \$z$#args, $args);\n"; |
0e505df1 |
495 | if (@args > 2 and $baop) { # binary assignment ops |
496 | $test++; |
497 | # check the op= works |
498 | push @script, <<EOB; |
499 | { |
affad850 |
500 | my \$za = cplx(ref \$z0 ? \@{\$z0->_cartesian} : (\$z0, 0)); |
0e505df1 |
501 | |
affad850 |
502 | my (\$z1r, \$z1i) = ref \$z1 ? \@{\$z1->_cartesian} : (\$z1, 0); |
0e505df1 |
503 | |
fb73857a |
504 | my \$zb = cplx(\$z1r, \$z1i); |
0e505df1 |
505 | |
506 | \$za $op= \$zb; |
affad850 |
507 | my (\$zbr, \$zbi) = \@{\$zb->_cartesian}; |
0e505df1 |
508 | |
509 | check($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);); |
b42d0ec9 |
514 | push @script, qq(print "ok $test\\n";\n); |
0e505df1 |
515 | push @script, "}\n"; |
516 | } |
89d0527d |
517 | } |
518 | } |
519 | |
520 | sub set { |
521 | my ($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[$i]); |
fe82cf6e |
530 | push @script, "\$s$i = $val;\n"; |
531 | push @{$setref}, "\$s$i"; |
89d0527d |
532 | } |
533 | } |
534 | |
535 | sub value { |
536 | local ($_) = @_; |
537 | if (/^\s*\((.*),(.*)\)/) { |
538 | return "cplx($1,$2)"; |
539 | } |
b42d0ec9 |
540 | elsif (/^\s*([\-\+]?(?:\d+(\.\d+)?|\.\d+)(?:[e[\-\+]\d+])?)/) { |
541 | return "cplx($1,0)"; |
542 | } |
89d0527d |
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, $expected, @z) = @_; |
0c721ce2 |
563 | |
16357284 |
564 | print "# @_\n"; |
0c721ce2 |
565 | |
566 | if ("$got" eq "$expected" |
567 | || |
568 | ($expected =~ /^-?\d/ && $got == $expected) |
569 | || |
bf5f1b4c |
570 | (abs(Math::Complex->make($got) - Math::Complex->make($expected)) < $eps) |
571 | || |
0c721ce2 |
572 | (abs($got - $expected) < $eps) |
573 | ) { |
89d0527d |
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 $args\n"; |
579 | } |
580 | } |
fb73857a |
581 | |
582 | sub addsq { |
583 | my ($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 | |
89d0527d |
592 | __END__ |
0e505df1 |
593 | &+;= |
89d0527d |
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 | |
0e505df1 |
603 | &-;= |
89d0527d |
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) |
0e505df1 |
610 | (2,1):(3,5):(-1,-4) |
89d0527d |
611 | |
612 | &-- |
613 | (1,2):(0,2) |
614 | [2,pi]:[3,pi] |
615 | |
0e505df1 |
616 | &*;= |
89d0527d |
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 | |
0e505df1 |
625 | &/;= |
89d0527d |
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 | |
0e505df1 |
634 | &**;= |
635 | (2,0):(3,0):(8,0) |
636 | (3,0):(2,0):(9,0) |
637 | (2,3):(4,0):(-119,-120) |
ace5de91 |
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) |
2820d885 |
645 | (0,0):(0,0):(1,0) |
0e505df1 |
646 | |
0c721ce2 |
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 | |
89d0527d |
657 | &abs |
658 | (3,4):5 |
659 | (-3,4):5 |
660 | |
0c721ce2 |
661 | &arg |
662 | [2,0]:0 |
663 | [-2,0]:pi |
664 | |
89d0527d |
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 |
0c721ce2 |
683 | -9:(0,3) |
89d0527d |
684 | (-100,0):(0,10) |
685 | (16,-30):(5,-3) |
686 | |
affad850 |
687 | &_stringify_cartesian |
89d0527d |
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 | |
affad850 |
696 | &_stringify_polar |
89d0527d |
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 | |
8c03c583 |
708 | { (0.5, 0); (-0.5, 0); (2,3); [3,2]; (-3,2); (0,2); 3; 1.2; (-3, 0); (-2, -1); [2,1] } |
89d0527d |
709 | |
0c721ce2 |
710 | |'(root(z, 4))[1] ** 4':'z' |
711 | |'(root(z, 5))[3] ** 5':'z' |
712 | |'(root(z, 8))[7] ** 8':'z' |
bf5f1b4c |
713 | |'(root(z, 8, 0)) ** 8':'z' |
714 | |'(root(z, 8, 7)) ** 8':'z' |
89d0527d |
715 | |'abs(z)':'r' |
0c721ce2 |
716 | |'acot(z)':'acotan(z)' |
717 | |'acsc(z)':'acosec(z)' |
fb73857a |
718 | |'acsc(z)':'asin(1 / z)' |
719 | |'asec(z)':'acos(1 / z)' |
89d0527d |
720 | |'cbrt(z)':'cbrt(r) * exp(i * t/3)' |
89d0527d |
721 | |'cos(acos(z))':'z' |
fb73857a |
722 | |'addsq(cos(z), sin(z))':1 |
89d0527d |
723 | |'cos(z)':'cosh(i*z)' |
fb73857a |
724 | |'subsq(cosh(z), sinh(z))':1 |
0c721ce2 |
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)' |
89d0527d |
731 | |'exp(log(z))':'z' |
0c721ce2 |
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' |
89d0527d |
736 | |'log10(z)':'log(z) / log(10)' |
89d0527d |
737 | |'logn(z, 2)':'log(z) / log(2)' |
0c721ce2 |
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))' |
89d0527d |
747 | |
0c721ce2 |
748 | { (1,1); [1,0.5]; (-2, -1); 2; -3; (-1,0.5); (0,0.5); 0.5; (2, 0); (-1, -2) } |
89d0527d |
749 | |
89d0527d |
750 | |'cosh(acosh(z))':'z' |
0c721ce2 |
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' |
89d0527d |
760 | |'tanh(atanh(z))':'z' |
89d0527d |
761 | |
0c721ce2 |
762 | { (0.2,-0.4); [1,0.5]; -1.2; (-1,0.5); 0.5; (1.1, 0) } |
89d0527d |
763 | |
89d0527d |
764 | |'acos(cos(z)) ** 2':'z * z' |
89d0527d |
765 | |'acosh(cosh(z)) ** 2':'z * z' |
0c721ce2 |
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' |
89d0527d |
774 | |'atanh(tanh(z))':'z' |
775 | |
fb73857a |
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 | |
0c721ce2 |
790 | &sin |
8c03c583 |
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 |
0c721ce2 |
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 |
8c03c583 |
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 |
0c721ce2 |
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 |
8c03c583 |
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 |
0c721ce2 |
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 |
8c03c583 |
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 |
0c721ce2 |
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 |
8c03c583 |
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 |
0c721ce2 |
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 |
8c03c583 |
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 |
0c721ce2 |
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 |
8c03c583 |
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 |
0c721ce2 |
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 |
8c03c583 |
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 |
0c721ce2 |
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 |
8c03c583 |
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 |
0c721ce2 |
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 |
8c03c583 |
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 |
0c721ce2 |
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 |
8c03c583 |
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 |
0c721ce2 |
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 |
8c03c583 |
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 |
0c721ce2 |
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 |
8c03c583 |
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 |
0c721ce2 |
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 |
8c03c583 |
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 |
0c721ce2 |
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 |
8c03c583 |
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 |
0c721ce2 |
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 |
8c03c583 |
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 |
0c721ce2 |
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 |
8c03c583 |
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 |
0c721ce2 |
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 |
8c03c583 |
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 |
0c721ce2 |
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 |
8c03c583 |
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 |
0c721ce2 |
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 |
9bc5fa8d |
1069 | (-2.0,0):( 1.31695789692482, 3.14159265358979) |
8c03c583 |
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 |
0c721ce2 |
1078 | ( 2, 3):( 1.98338702991654, 1.00014354247380) |
9bc5fa8d |
1079 | (-2, 3):( 1.98338702991653, 2.14144911111600) |
1080 | (-2,-3):( 1.98338702991653, -2.14144911111600) |
0c721ce2 |
1081 | ( 2,-3):( 1.98338702991654, -1.00014354247380) |
1082 | |
1083 | &atanh |
8c03c583 |
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 |
0c721ce2 |
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 |
8c03c583 |
1097 | (-2.0,0):( 0 , 2.09439510239320) |
1098 | (-1.0,0):( 0 , 3.14159265358979) |
9bc5fa8d |
1099 | (-0.5,0):( 1.31695789692482, 3.14159265358979) |
8c03c583 |
1100 | ( 0.5,0):( 1.31695789692482, 0 ) |
1101 | ( 1.0,0):( 0 , 0 ) |
1102 | ( 2.0,0):( 0 , 1.04719755119660) |
1103 | |
1104 | &asech |
0c721ce2 |
1105 | ( 2, 3):( 0.23133469857397, -1.42041072246703) |
9bc5fa8d |
1106 | (-2, 3):( 0.23133469857397, -1.72118193112276) |
1107 | (-2,-3):( 0.23133469857397, 1.72118193112276) |
0c721ce2 |
1108 | ( 2,-3):( 0.23133469857397, 1.42041072246703) |
1109 | |
1110 | &acsch |
8c03c583 |
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 |
0c721ce2 |
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 |
8c03c583 |
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 |
0c721ce2 |
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 |