Commit | Line | Data |
---|---|---|
89d0527d RM |
1 | #!./perl |
2 | ||
fb73857a | 3 | # $RCSfile: complex.t,v $ |
89d0527d | 4 | # |
5aabfad6 | 5 | # Regression tests for the Math::Complex pacakge |
b42d0ec9 JH |
6 | # -- Raphael Manfredi since Sep 1996 |
7 | # -- Jarkko Hietaniemi since Mar 1997 | |
8 | # -- Daniel S. Lewart since Sep 1997 | |
5aabfad6 | 9 | |
89d0527d RM |
10 | BEGIN { |
11 | chdir 't' if -d 't'; | |
20822f61 | 12 | @INC = '../lib'; |
89d0527d | 13 | } |
5aabfad6 | 14 | |
89d0527d RM |
15 | use Math::Complex; |
16 | ||
476757f7 YN |
17 | use vars qw($VERSION); |
18 | ||
19 | $VERSION = 1.91; | |
b42d0ec9 | 20 | |
fb73857a | 21 | my ($args, $op, $target, $test, $test_set, $try, $val, $zvalue, @set, @val); |
22 | ||
89d0527d RM |
23 | $test = 0; |
24 | $| = 1; | |
fb73857a | 25 | my @script = ( |
26 | 'my ($res, $s0,$s1,$s2,$s3,$s4,$s5,$s6,$s7,$s8,$s9,$s10, $z0,$z1,$z2);' . | |
27 | "\n\n" | |
28 | ); | |
b42d0ec9 | 29 | my $eps = 1e-13; |
89d0527d | 30 | |
d09ae4e6 | 31 | if ($^O eq 'unicos') { # For some reason root() produces very inaccurate |
f3ff050f | 32 | $eps = 1e-10; # results in Cray UNICOS, and occasionally also |
d09ae4e6 JH |
33 | } # cos(), sin(), cosh(), sinh(). The division |
34 | # of doubles is the current suspect. | |
35 | ||
89d0527d | 36 | while (<DATA>) { |
0c721ce2 JH |
37 | s/^\s+//; |
38 | next if $_ eq '' || /^\#/; | |
39 | chomp; | |
40 | $test_set = 0; # Assume not a test over a set of values | |
0e505df1 | 41 | if (/^&(.+)/) { |
89d0527d RM |
42 | $op = $1; |
43 | next; | |
44 | } | |
0e505df1 | 45 | elsif (/^\{(.+)\}/) { |
89d0527d RM |
46 | set($1, \@set, \@val); |
47 | next; | |
48 | } | |
49 | elsif (s/^\|//) { | |
0c721ce2 | 50 | $test_set = 1; # Requests we loop over the set... |
89d0527d RM |
51 | } |
52 | my @args = split(/:/); | |
0c721ce2 | 53 | if ($test_set == 1) { |
89d0527d RM |
54 | my $i; |
55 | for ($i = 0; $i < @set; $i++) { | |
0c721ce2 JH |
56 | # complex number |
57 | $target = $set[$i]; | |
58 | # textual value as found in set definition | |
59 | $zvalue = $val[$i]; | |
89d0527d RM |
60 | test($zvalue, $target, @args); |
61 | } | |
62 | } else { | |
63 | test($op, undef, @args); | |
64 | } | |
65 | } | |
66 | ||
b42d0ec9 JH |
67 | # |
68 | ||
69 | sub test_mutators { | |
70 | my $op; | |
71 | ||
72 | $test++; | |
73 | push(@script, <<'EOT'); | |
74 | { | |
75 | my $z = cplx( 1, 1); | |
76 | $z->Re(2); | |
77 | $z->Im(3); | |
16357284 | 78 | print "# $test Re(z) = ",$z->Re(), " Im(z) = ", $z->Im(), " z = $z\n"; |
b42d0ec9 JH |
79 | print 'not ' unless Re($z) == 2 and Im($z) == 3; |
80 | EOT | |
81 | push(@script, qq(print "ok $test\\n"}\n)); | |
82 | ||
83 | $test++; | |
84 | push(@script, <<'EOT'); | |
85 | { | |
86 | my $z = cplx( 1, 1); | |
87 | $z->abs(3 * sqrt(2)); | |
16357284 | 88 | print "# $test Re(z) = ",$z->Re(), " Im(z) = ", $z->Im(), " z = $z\n"; |
b42d0ec9 JH |
89 | print 'not ' unless (abs($z) - 3 * sqrt(2)) < $eps and |
90 | (arg($z) - pi / 4 ) < $eps and | |
91 | (Re($z) - 3 ) < $eps and | |
92 | (Im($z) - 3 ) < $eps; | |
93 | EOT | |
94 | push(@script, qq(print "ok $test\\n"}\n)); | |
95 | ||
96 | $test++; | |
97 | push(@script, <<'EOT'); | |
98 | { | |
99 | my $z = cplx( 1, 1); | |
100 | $z->arg(-3 / 4 * pi); | |
16357284 | 101 | print "# $test Re(z) = ",$z->Re(), " Im(z) = ", $z->Im(), " z = $z\n"; |
b42d0ec9 JH |
102 | print 'not ' unless (arg($z) + 3 / 4 * pi) < $eps and |
103 | (abs($z) - sqrt(2) ) < $eps and | |
104 | (Re($z) + 1 ) < $eps and | |
105 | (Im($z) + 1 ) < $eps; | |
106 | EOT | |
107 | push(@script, qq(print "ok $test\\n"}\n)); | |
108 | } | |
109 | ||
110 | test_mutators(); | |
111 | ||
112 | my $constants = ' | |
113 | my $i = cplx(0, 1); | |
114 | my $pi = cplx(pi, 0); | |
115 | my $pii = cplx(0, pi); | |
116 | my $pip2 = cplx(pi/2, 0); | |
117 | my $zero = cplx(0, 0); | |
118 | '; | |
119 | ||
120 | push(@script, $constants); | |
121 | ||
122 | ||
5cd24f17 | 123 | # test the divbyzeros |
124 | ||
0e505df1 JH |
125 | sub test_dbz { |
126 | for my $op (@_) { | |
127 | $test++; | |
b42d0ec9 | 128 | push(@script, <<EOT); |
16357284 JH |
129 | eval '$op'; |
130 | (\$bad) = (\$@ =~ /(.+)/); | |
131 | print "# $test op = $op divbyzero? \$bad...\n"; | |
132 | print 'not ' unless (\$@ =~ /Division by zero/); | |
b42d0ec9 JH |
133 | EOT |
134 | push(@script, qq(print "ok $test\\n";\n)); | |
0e505df1 JH |
135 | } |
136 | } | |
137 | ||
8c03c583 JH |
138 | # test the logofzeros |
139 | ||
140 | sub test_loz { | |
141 | for my $op (@_) { | |
142 | $test++; | |
b42d0ec9 | 143 | push(@script, <<EOT); |
16357284 JH |
144 | eval '$op'; |
145 | (\$bad) = (\$@ =~ /(.+)/); | |
146 | print "# $test op = $op logofzero? \$bad...\n"; | |
147 | print 'not ' unless (\$@ =~ /Logarithm of zero/); | |
b42d0ec9 JH |
148 | EOT |
149 | push(@script, qq(print "ok $test\\n";\n)); | |
8c03c583 JH |
150 | } |
151 | } | |
152 | ||
5cd24f17 | 153 | test_dbz( |
154 | 'i/0', | |
b42d0ec9 JH |
155 | 'acot(0)', |
156 | 'acot(+$i)', | |
157 | # 'acoth(-1)', # Log of zero. | |
158 | 'acoth(0)', | |
159 | 'acoth(+1)', | |
5cd24f17 | 160 | 'acsc(0)', |
5cd24f17 | 161 | 'acsch(0)', |
b42d0ec9 JH |
162 | 'asec(0)', |
163 | 'asech(0)', | |
b42d0ec9 JH |
164 | 'atan($i)', |
165 | # 'atanh(-1)', # Log of zero. | |
166 | 'atanh(+1)', | |
167 | 'cot(0)', | |
168 | 'coth(0)', | |
169 | 'csc(0)', | |
b42d0ec9 | 170 | 'csch(0)', |
8c03c583 JH |
171 | ); |
172 | ||
173 | test_loz( | |
fb73857a | 174 | 'log($zero)', |
1fa12f56 | 175 | 'atan(-$i)', |
b42d0ec9 | 176 | 'acot(-$i)', |
8c03c583 JH |
177 | 'atanh(-1)', |
178 | 'acoth(-1)', | |
5cd24f17 | 179 | ); |
180 | ||
0e505df1 JH |
181 | # test the bad roots |
182 | ||
183 | sub test_broot { | |
5cd24f17 | 184 | for my $op (@_) { |
185 | $test++; | |
b42d0ec9 | 186 | push(@script, <<EOT); |
16357284 JH |
187 | eval 'root(2, $op)'; |
188 | (\$bad) = (\$@ =~ /(.+)/); | |
189 | print "# $test op = $op badroot? \$bad...\n"; | |
1fa12f56 | 190 | print 'not ' unless (\$@ =~ /root rank must be/); |
b42d0ec9 JH |
191 | EOT |
192 | push(@script, qq(print "ok $test\\n";\n)); | |
5cd24f17 | 193 | } |
194 | } | |
195 | ||
0e505df1 JH |
196 | test_broot(qw(-3 -2.1 0 0.99)); |
197 | ||
16357284 | 198 | sub test_display_format { |
476757f7 YN |
199 | $test++; |
200 | push @script, <<EOS; | |
201 | print "# package display_format cartesian?\n"; | |
202 | print "not " unless Math::Complex->display_format eq 'cartesian'; | |
203 | print "ok $test\n"; | |
204 | EOS | |
205 | ||
16357284 JH |
206 | push @script, <<EOS; |
207 | my \$j = (root(1,3))[1]; | |
208 | ||
209 | \$j->display_format('polar'); | |
210 | EOS | |
211 | ||
212 | $test++; | |
213 | push @script, <<EOS; | |
476757f7 | 214 | print "# j display_format polar?\n"; |
16357284 JH |
215 | print "not " unless \$j->display_format eq 'polar'; |
216 | print "ok $test\n"; | |
217 | EOS | |
218 | ||
219 | $test++; | |
220 | push @script, <<EOS; | |
221 | print "# j = \$j\n"; | |
222 | print "not " unless "\$j" eq "[1,2pi/3]"; | |
223 | print "ok $test\n"; | |
224 | ||
225 | my %display_format; | |
226 | ||
227 | %display_format = \$j->display_format; | |
228 | EOS | |
229 | ||
230 | $test++; | |
231 | push @script, <<EOS; | |
232 | print "# display_format{style} polar?\n"; | |
233 | print "not " unless \$display_format{style} eq 'polar'; | |
234 | print "ok $test\n"; | |
235 | EOS | |
236 | ||
237 | $test++; | |
238 | push @script, <<EOS; | |
239 | print "# keys %display_format == 2?\n"; | |
240 | print "not " unless keys %display_format == 2; | |
241 | print "ok $test\n"; | |
242 | ||
243 | \$j->display_format('style' => 'cartesian', 'format' => '%.5f'); | |
244 | EOS | |
245 | ||
246 | $test++; | |
247 | push @script, <<EOS; | |
248 | print "# j = \$j\n"; | |
249 | print "not " unless "\$j" eq "-0.50000+0.86603i"; | |
250 | print "ok $test\n"; | |
251 | ||
252 | %display_format = \$j->display_format; | |
253 | EOS | |
254 | ||
255 | $test++; | |
256 | push @script, <<EOS; | |
257 | print "# display_format{format} %.5f?\n"; | |
258 | print "not " unless \$display_format{format} eq '%.5f'; | |
259 | print "ok $test\n"; | |
260 | EOS | |
261 | ||
262 | $test++; | |
263 | push @script, <<EOS; | |
264 | print "# keys %display_format == 3?\n"; | |
265 | print "not " unless keys %display_format == 3; | |
266 | print "ok $test\n"; | |
267 | ||
268 | \$j->display_format('format' => undef); | |
269 | EOS | |
270 | ||
271 | $test++; | |
272 | push @script, <<EOS; | |
273 | print "# j = \$j\n"; | |
057216a3 | 274 | print "not " unless "\$j" =~ /^-0(?:\\.5(?:0000\\d+)?|\\.49999\\d+)\\+0.86602540\\d+i\$/; |
16357284 JH |
275 | print "ok $test\n"; |
276 | ||
277 | \$j->display_format('style' => 'polar', 'polar_pretty_print' => 0); | |
278 | EOS | |
279 | ||
280 | $test++; | |
281 | push @script, <<EOS; | |
282 | print "# j = \$j\n"; | |
1ab88a68 | 283 | print "not " unless "\$j" =~ /^\\[1,2\\.09439510\\d+\\]\$/; |
16357284 JH |
284 | print "ok $test\n"; |
285 | ||
286 | \$j->display_format('style' => 'cartesian', 'format' => '(%.5g)'); | |
287 | EOS | |
476757f7 | 288 | |
16357284 JH |
289 | $test++; |
290 | push @script, <<EOS; | |
291 | print "# j = \$j\n"; | |
292 | print "not " unless "\$j" eq "(-0.5)+(0.86603)i"; | |
293 | print "ok $test\n"; | |
294 | EOS | |
476757f7 YN |
295 | |
296 | $test++; | |
297 | push @script, <<EOS; | |
298 | print "# j display_format cartesian?\n"; | |
299 | print "not " unless \$j->display_format eq 'cartesian'; | |
300 | print "ok $test\n"; | |
301 | EOS | |
16357284 JH |
302 | } |
303 | ||
304 | test_display_format(); | |
305 | ||
89d0527d | 306 | print "1..$test\n"; |
fe82cf6e | 307 | eval join '', @script; |
89d0527d RM |
308 | die $@ if $@; |
309 | ||
0e505df1 JH |
310 | sub abop { |
311 | my ($op) = @_; | |
312 | ||
313 | push(@script, qq(print "# $op=\n";)); | |
314 | } | |
315 | ||
89d0527d RM |
316 | sub test { |
317 | my ($op, $z, @args) = @_; | |
0e505df1 | 318 | my ($baop) = 0; |
89d0527d RM |
319 | $test++; |
320 | my $i; | |
0e505df1 | 321 | $baop = 1 if ($op =~ s/;=$//); |
89d0527d RM |
322 | for ($i = 0; $i < @args; $i++) { |
323 | $val = value($args[$i]); | |
fe82cf6e | 324 | push @script, "\$z$i = $val;\n"; |
89d0527d RM |
325 | } |
326 | if (defined $z) { | |
327 | $args = "'$op'"; # Really the value | |
0c721ce2 | 328 | $try = "abs(\$z0 - \$z1) <= $eps ? \$z1 : \$z0"; |
fe82cf6e CS |
329 | push @script, "\$res = $try; "; |
330 | push @script, "check($test, $args[0], \$res, \$z$#args, $args);\n"; | |
89d0527d RM |
331 | } else { |
332 | my ($try, $args); | |
333 | if (@args == 2) { | |
334 | $try = "$op \$z0"; | |
335 | $args = "'$args[0]'"; | |
336 | } else { | |
337 | $try = ($op =~ /^\w/) ? "$op(\$z0, \$z1)" : "\$z0 $op \$z1"; | |
338 | $args = "'$args[0]', '$args[1]'"; | |
339 | } | |
fe82cf6e CS |
340 | push @script, "\$res = $try; "; |
341 | push @script, "check($test, '$try', \$res, \$z$#args, $args);\n"; | |
0e505df1 JH |
342 | if (@args > 2 and $baop) { # binary assignment ops |
343 | $test++; | |
344 | # check the op= works | |
345 | push @script, <<EOB; | |
346 | { | |
fb73857a | 347 | my \$za = cplx(ref \$z0 ? \@{\$z0->cartesian} : (\$z0, 0)); |
0e505df1 JH |
348 | |
349 | my (\$z1r, \$z1i) = ref \$z1 ? \@{\$z1->cartesian} : (\$z1, 0); | |
350 | ||
fb73857a | 351 | my \$zb = cplx(\$z1r, \$z1i); |
0e505df1 JH |
352 | |
353 | \$za $op= \$zb; | |
354 | my (\$zbr, \$zbi) = \@{\$zb->cartesian}; | |
355 | ||
356 | check($test, '\$z0 $op= \$z1', \$za, \$z$#args, $args); | |
357 | EOB | |
358 | $test++; | |
359 | # check that the rhs has not changed | |
360 | push @script, qq(print "not " unless (\$zbr == \$z1r and \$zbi == \$z1i);); | |
b42d0ec9 | 361 | push @script, qq(print "ok $test\\n";\n); |
0e505df1 JH |
362 | push @script, "}\n"; |
363 | } | |
89d0527d RM |
364 | } |
365 | } | |
366 | ||
367 | sub set { | |
368 | my ($set, $setref, $valref) = @_; | |
369 | @{$setref} = (); | |
370 | @{$valref} = (); | |
371 | my @set = split(/;\s*/, $set); | |
372 | my @res; | |
373 | my $i; | |
374 | for ($i = 0; $i < @set; $i++) { | |
375 | push(@{$valref}, $set[$i]); | |
376 | my $val = value($set[$i]); | |
fe82cf6e CS |
377 | push @script, "\$s$i = $val;\n"; |
378 | push @{$setref}, "\$s$i"; | |
89d0527d RM |
379 | } |
380 | } | |
381 | ||
382 | sub value { | |
383 | local ($_) = @_; | |
384 | if (/^\s*\((.*),(.*)\)/) { | |
385 | return "cplx($1,$2)"; | |
386 | } | |
b42d0ec9 JH |
387 | elsif (/^\s*([\-\+]?(?:\d+(\.\d+)?|\.\d+)(?:[e[\-\+]\d+])?)/) { |
388 | return "cplx($1,0)"; | |
389 | } | |
89d0527d RM |
390 | elsif (/^\s*\[(.*),(.*)\]/) { |
391 | return "cplxe($1,$2)"; | |
392 | } | |
393 | elsif (/^\s*'(.*)'/) { | |
394 | my $ex = $1; | |
395 | $ex =~ s/\bz\b/$target/g; | |
396 | $ex =~ s/\br\b/abs($target)/g; | |
397 | $ex =~ s/\bt\b/arg($target)/g; | |
398 | $ex =~ s/\ba\b/Re($target)/g; | |
399 | $ex =~ s/\bb\b/Im($target)/g; | |
400 | return $ex; | |
401 | } | |
402 | elsif (/^\s*"(.*)"/) { | |
403 | return "\"$1\""; | |
404 | } | |
405 | return $_; | |
406 | } | |
407 | ||
408 | sub check { | |
409 | my ($test, $try, $got, $expected, @z) = @_; | |
0c721ce2 | 410 | |
16357284 | 411 | print "# @_\n"; |
0c721ce2 JH |
412 | |
413 | if ("$got" eq "$expected" | |
414 | || | |
415 | ($expected =~ /^-?\d/ && $got == $expected) | |
416 | || | |
417 | (abs($got - $expected) < $eps) | |
418 | ) { | |
89d0527d RM |
419 | print "ok $test\n"; |
420 | } else { | |
421 | print "not ok $test\n"; | |
422 | my $args = (@z == 1) ? "z = $z[0]" : "z0 = $z[0], z1 = $z[1]"; | |
423 | print "# '$try' expected: '$expected' got: '$got' for $args\n"; | |
424 | } | |
425 | } | |
fb73857a | 426 | |
427 | sub addsq { | |
428 | my ($z1, $z2) = @_; | |
429 | return ($z1 + i*$z2) * ($z1 - i*$z2); | |
430 | } | |
431 | ||
432 | sub subsq { | |
433 | my ($z1, $z2) = @_; | |
434 | return ($z1 + $z2) * ($z1 - $z2); | |
435 | } | |
436 | ||
89d0527d | 437 | __END__ |
0e505df1 | 438 | &+;= |
89d0527d RM |
439 | (3,4):(3,4):(6,8) |
440 | (-3,4):(3,-4):(0,0) | |
441 | (3,4):-3:(0,4) | |
442 | 1:(4,2):(5,2) | |
443 | [2,0]:[2,pi]:(0,0) | |
444 | ||
445 | &++ | |
446 | (2,1):(3,1) | |
447 | ||
0e505df1 | 448 | &-;= |
89d0527d RM |
449 | (2,3):(-2,-3) |
450 | [2,pi/2]:[2,-(pi)/2] | |
451 | 2:[2,0]:(0,0) | |
452 | [3,0]:2:(1,0) | |
453 | 3:(4,5):(-1,-5) | |
454 | (4,5):3:(1,5) | |
0e505df1 | 455 | (2,1):(3,5):(-1,-4) |
89d0527d RM |
456 | |
457 | &-- | |
458 | (1,2):(0,2) | |
459 | [2,pi]:[3,pi] | |
460 | ||
0e505df1 | 461 | &*;= |
89d0527d RM |
462 | (0,1):(0,1):(-1,0) |
463 | (4,5):(1,0):(4,5) | |
464 | [2,2*pi/3]:(1,0):[2,2*pi/3] | |
465 | 2:(0,1):(0,2) | |
466 | (0,1):3:(0,3) | |
467 | (0,1):(4,1):(-1,4) | |
468 | (2,1):(4,-1):(9,2) | |
469 | ||
0e505df1 | 470 | &/;= |
89d0527d RM |
471 | (3,4):(3,4):(1,0) |
472 | (4,-5):1:(4,-5) | |
473 | 1:(0,1):(0,-1) | |
474 | (0,6):(0,2):(3,0) | |
475 | (9,2):(4,-1):(2,1) | |
476 | [4,pi]:[2,pi/2]:[2,pi/2] | |
477 | [2,pi/2]:[4,pi]:[0.5,-(pi)/2] | |
478 | ||
0e505df1 JH |
479 | &**;= |
480 | (2,0):(3,0):(8,0) | |
481 | (3,0):(2,0):(9,0) | |
482 | (2,3):(4,0):(-119,-120) | |
ace5de91 GS |
483 | (0,0):(1,0):(0,0) |
484 | (0,0):(2,3):(0,0) | |
485 | (1,0):(0,0):(1,0) | |
486 | (1,0):(1,0):(1,0) | |
487 | (1,0):(2,3):(1,0) | |
488 | (2,3):(0,0):(1,0) | |
489 | (2,3):(1,0):(2,3) | |
2820d885 | 490 | (0,0):(0,0):(1,0) |
0e505df1 | 491 | |
0c721ce2 JH |
492 | &Re |
493 | (3,4):3 | |
494 | (-3,4):-3 | |
495 | [1,pi/2]:0 | |
496 | ||
497 | &Im | |
498 | (3,4):4 | |
499 | (3,-4):-4 | |
500 | [1,pi/2]:1 | |
501 | ||
89d0527d RM |
502 | &abs |
503 | (3,4):5 | |
504 | (-3,4):5 | |
505 | ||
0c721ce2 JH |
506 | &arg |
507 | [2,0]:0 | |
508 | [-2,0]:pi | |
509 | ||
89d0527d RM |
510 | &~ |
511 | (4,5):(4,-5) | |
512 | (-3,4):(-3,-4) | |
513 | [2,pi/2]:[2,-(pi)/2] | |
514 | ||
515 | &< | |
516 | (3,4):(1,2):0 | |
517 | (3,4):(3,2):0 | |
518 | (3,4):(3,8):1 | |
519 | (4,4):(5,129):1 | |
520 | ||
521 | &== | |
522 | (3,4):(4,5):0 | |
523 | (3,4):(3,5):0 | |
524 | (3,4):(2,4):0 | |
525 | (3,4):(3,4):1 | |
526 | ||
527 | &sqrt | |
0c721ce2 | 528 | -9:(0,3) |
89d0527d RM |
529 | (-100,0):(0,10) |
530 | (16,-30):(5,-3) | |
531 | ||
532 | &stringify_cartesian | |
533 | (-100,0):"-100" | |
534 | (0,1):"i" | |
535 | (4,-3):"4-3i" | |
536 | (4,0):"4" | |
537 | (-4,0):"-4" | |
538 | (-2,4):"-2+4i" | |
539 | (-2,-1):"-2-i" | |
540 | ||
541 | &stringify_polar | |
542 | [-1, 0]:"[1,pi]" | |
543 | [1, pi/3]:"[1,pi/3]" | |
544 | [6, -2*pi/3]:"[6,-2pi/3]" | |
545 | [0.5, -9*pi/11]:"[0.5,-9pi/11]" | |
546 | ||
547 | { (4,3); [3,2]; (-3,4); (0,2); [2,1] } | |
548 | ||
549 | |'z + ~z':'2*Re(z)' | |
550 | |'z - ~z':'2*i*Im(z)' | |
551 | |'z * ~z':'abs(z) * abs(z)' | |
552 | ||
8c03c583 | 553 | { (0.5, 0); (-0.5, 0); (2,3); [3,2]; (-3,2); (0,2); 3; 1.2; (-3, 0); (-2, -1); [2,1] } |
89d0527d | 554 | |
0c721ce2 JH |
555 | |'(root(z, 4))[1] ** 4':'z' |
556 | |'(root(z, 5))[3] ** 5':'z' | |
557 | |'(root(z, 8))[7] ** 8':'z' | |
89d0527d | 558 | |'abs(z)':'r' |
0c721ce2 JH |
559 | |'acot(z)':'acotan(z)' |
560 | |'acsc(z)':'acosec(z)' | |
fb73857a | 561 | |'acsc(z)':'asin(1 / z)' |
562 | |'asec(z)':'acos(1 / z)' | |
89d0527d | 563 | |'cbrt(z)':'cbrt(r) * exp(i * t/3)' |
89d0527d | 564 | |'cos(acos(z))':'z' |
fb73857a | 565 | |'addsq(cos(z), sin(z))':1 |
89d0527d | 566 | |'cos(z)':'cosh(i*z)' |
fb73857a | 567 | |'subsq(cosh(z), sinh(z))':1 |
0c721ce2 JH |
568 | |'cot(acot(z))':'z' |
569 | |'cot(z)':'1 / tan(z)' | |
570 | |'cot(z)':'cotan(z)' | |
571 | |'csc(acsc(z))':'z' | |
572 | |'csc(z)':'1 / sin(z)' | |
573 | |'csc(z)':'cosec(z)' | |
89d0527d | 574 | |'exp(log(z))':'z' |
0c721ce2 JH |
575 | |'exp(z)':'exp(a) * exp(i * b)' |
576 | |'ln(z)':'log(z)' | |
577 | |'log(exp(z))':'z' | |
578 | |'log(z)':'log(r) + i*t' | |
89d0527d | 579 | |'log10(z)':'log(z) / log(10)' |
89d0527d | 580 | |'logn(z, 2)':'log(z) / log(2)' |
0c721ce2 JH |
581 | |'logn(z, 3)':'log(z) / log(3)' |
582 | |'sec(asec(z))':'z' | |
583 | |'sec(z)':'1 / cos(z)' | |
584 | |'sin(asin(z))':'z' | |
585 | |'sin(i * z)':'i * sinh(z)' | |
586 | |'sqrt(z) * sqrt(z)':'z' | |
587 | |'sqrt(z)':'sqrt(r) * exp(i * t/2)' | |
588 | |'tan(atan(z))':'z' | |
589 | |'z**z':'exp(z * log(z))' | |
89d0527d | 590 | |
0c721ce2 | 591 | { (1,1); [1,0.5]; (-2, -1); 2; -3; (-1,0.5); (0,0.5); 0.5; (2, 0); (-1, -2) } |
89d0527d | 592 | |
89d0527d | 593 | |'cosh(acosh(z))':'z' |
0c721ce2 JH |
594 | |'coth(acoth(z))':'z' |
595 | |'coth(z)':'1 / tanh(z)' | |
596 | |'coth(z)':'cotanh(z)' | |
597 | |'csch(acsch(z))':'z' | |
598 | |'csch(z)':'1 / sinh(z)' | |
599 | |'csch(z)':'cosech(z)' | |
600 | |'sech(asech(z))':'z' | |
601 | |'sech(z)':'1 / cosh(z)' | |
602 | |'sinh(asinh(z))':'z' | |
89d0527d | 603 | |'tanh(atanh(z))':'z' |
89d0527d | 604 | |
0c721ce2 | 605 | { (0.2,-0.4); [1,0.5]; -1.2; (-1,0.5); 0.5; (1.1, 0) } |
89d0527d | 606 | |
89d0527d | 607 | |'acos(cos(z)) ** 2':'z * z' |
89d0527d | 608 | |'acosh(cosh(z)) ** 2':'z * z' |
0c721ce2 JH |
609 | |'acoth(z)':'acotanh(z)' |
610 | |'acoth(z)':'atanh(1 / z)' | |
611 | |'acsch(z)':'acosech(z)' | |
612 | |'acsch(z)':'asinh(1 / z)' | |
613 | |'asech(z)':'acosh(1 / z)' | |
614 | |'asin(sin(z))':'z' | |
615 | |'asinh(sinh(z))':'z' | |
616 | |'atan(tan(z))':'z' | |
89d0527d RM |
617 | |'atanh(tanh(z))':'z' |
618 | ||
fb73857a | 619 | &log |
620 | (-2.0,0):( 0.69314718055995, 3.14159265358979) | |
621 | (-1.0,0):( 0 , 3.14159265358979) | |
622 | (-0.5,0):( -0.69314718055995, 3.14159265358979) | |
623 | ( 0.5,0):( -0.69314718055995, 0 ) | |
624 | ( 1.0,0):( 0 , 0 ) | |
625 | ( 2.0,0):( 0.69314718055995, 0 ) | |
626 | ||
627 | &log | |
628 | ( 2, 3):( 1.28247467873077, 0.98279372324733) | |
629 | (-2, 3):( 1.28247467873077, 2.15879893034246) | |
630 | (-2,-3):( 1.28247467873077, -2.15879893034246) | |
631 | ( 2,-3):( 1.28247467873077, -0.98279372324733) | |
632 | ||
0c721ce2 | 633 | &sin |
8c03c583 JH |
634 | (-2.0,0):( -0.90929742682568, 0 ) |
635 | (-1.0,0):( -0.84147098480790, 0 ) | |
636 | (-0.5,0):( -0.47942553860420, 0 ) | |
637 | ( 0.0,0):( 0 , 0 ) | |
638 | ( 0.5,0):( 0.47942553860420, 0 ) | |
639 | ( 1.0,0):( 0.84147098480790, 0 ) | |
640 | ( 2.0,0):( 0.90929742682568, 0 ) | |
641 | ||
642 | &sin | |
0c721ce2 JH |
643 | ( 2, 3):( 9.15449914691143, -4.16890695996656) |
644 | (-2, 3):( -9.15449914691143, -4.16890695996656) | |
645 | (-2,-3):( -9.15449914691143, 4.16890695996656) | |
646 | ( 2,-3):( 9.15449914691143, 4.16890695996656) | |
647 | ||
648 | &cos | |
8c03c583 JH |
649 | (-2.0,0):( -0.41614683654714, 0 ) |
650 | (-1.0,0):( 0.54030230586814, 0 ) | |
651 | (-0.5,0):( 0.87758256189037, 0 ) | |
652 | ( 0.0,0):( 1 , 0 ) | |
653 | ( 0.5,0):( 0.87758256189037, 0 ) | |
654 | ( 1.0,0):( 0.54030230586814, 0 ) | |
655 | ( 2.0,0):( -0.41614683654714, 0 ) | |
656 | ||
657 | &cos | |
0c721ce2 JH |
658 | ( 2, 3):( -4.18962569096881, -9.10922789375534) |
659 | (-2, 3):( -4.18962569096881, 9.10922789375534) | |
660 | (-2,-3):( -4.18962569096881, -9.10922789375534) | |
661 | ( 2,-3):( -4.18962569096881, 9.10922789375534) | |
662 | ||
663 | &tan | |
8c03c583 JH |
664 | (-2.0,0):( 2.18503986326152, 0 ) |
665 | (-1.0,0):( -1.55740772465490, 0 ) | |
666 | (-0.5,0):( -0.54630248984379, 0 ) | |
667 | ( 0.0,0):( 0 , 0 ) | |
668 | ( 0.5,0):( 0.54630248984379, 0 ) | |
669 | ( 1.0,0):( 1.55740772465490, 0 ) | |
670 | ( 2.0,0):( -2.18503986326152, 0 ) | |
671 | ||
672 | &tan | |
0c721ce2 JH |
673 | ( 2, 3):( -0.00376402564150, 1.00323862735361) |
674 | (-2, 3):( 0.00376402564150, 1.00323862735361) | |
675 | (-2,-3):( 0.00376402564150, -1.00323862735361) | |
676 | ( 2,-3):( -0.00376402564150, -1.00323862735361) | |
677 | ||
678 | &sec | |
8c03c583 JH |
679 | (-2.0,0):( -2.40299796172238, 0 ) |
680 | (-1.0,0):( 1.85081571768093, 0 ) | |
681 | (-0.5,0):( 1.13949392732455, 0 ) | |
682 | ( 0.0,0):( 1 , 0 ) | |
683 | ( 0.5,0):( 1.13949392732455, 0 ) | |
684 | ( 1.0,0):( 1.85081571768093, 0 ) | |
685 | ( 2.0,0):( -2.40299796172238, 0 ) | |
686 | ||
687 | &sec | |
0c721ce2 JH |
688 | ( 2, 3):( -0.04167496441114, 0.09061113719624) |
689 | (-2, 3):( -0.04167496441114, -0.09061113719624) | |
690 | (-2,-3):( -0.04167496441114, 0.09061113719624) | |
691 | ( 2,-3):( -0.04167496441114, -0.09061113719624) | |
692 | ||
693 | &csc | |
8c03c583 JH |
694 | (-2.0,0):( -1.09975017029462, 0 ) |
695 | (-1.0,0):( -1.18839510577812, 0 ) | |
696 | (-0.5,0):( -2.08582964293349, 0 ) | |
697 | ( 0.5,0):( 2.08582964293349, 0 ) | |
698 | ( 1.0,0):( 1.18839510577812, 0 ) | |
699 | ( 2.0,0):( 1.09975017029462, 0 ) | |
700 | ||
701 | &csc | |
0c721ce2 JH |
702 | ( 2, 3):( 0.09047320975321, 0.04120098628857) |
703 | (-2, 3):( -0.09047320975321, 0.04120098628857) | |
704 | (-2,-3):( -0.09047320975321, -0.04120098628857) | |
705 | ( 2,-3):( 0.09047320975321, -0.04120098628857) | |
706 | ||
707 | &cot | |
8c03c583 JH |
708 | (-2.0,0):( 0.45765755436029, 0 ) |
709 | (-1.0,0):( -0.64209261593433, 0 ) | |
710 | (-0.5,0):( -1.83048772171245, 0 ) | |
711 | ( 0.5,0):( 1.83048772171245, 0 ) | |
712 | ( 1.0,0):( 0.64209261593433, 0 ) | |
713 | ( 2.0,0):( -0.45765755436029, 0 ) | |
714 | ||
715 | &cot | |
0c721ce2 JH |
716 | ( 2, 3):( -0.00373971037634, -0.99675779656936) |
717 | (-2, 3):( 0.00373971037634, -0.99675779656936) | |
718 | (-2,-3):( 0.00373971037634, 0.99675779656936) | |
719 | ( 2,-3):( -0.00373971037634, 0.99675779656936) | |
720 | ||
721 | &asin | |
8c03c583 JH |
722 | (-2.0,0):( -1.57079632679490, 1.31695789692482) |
723 | (-1.0,0):( -1.57079632679490, 0 ) | |
724 | (-0.5,0):( -0.52359877559830, 0 ) | |
725 | ( 0.0,0):( 0 , 0 ) | |
726 | ( 0.5,0):( 0.52359877559830, 0 ) | |
727 | ( 1.0,0):( 1.57079632679490, 0 ) | |
728 | ( 2.0,0):( 1.57079632679490, -1.31695789692482) | |
729 | ||
730 | &asin | |
0c721ce2 JH |
731 | ( 2, 3):( 0.57065278432110, 1.98338702991654) |
732 | (-2, 3):( -0.57065278432110, 1.98338702991654) | |
733 | (-2,-3):( -0.57065278432110, -1.98338702991654) | |
734 | ( 2,-3):( 0.57065278432110, -1.98338702991654) | |
735 | ||
736 | &acos | |
8c03c583 JH |
737 | (-2.0,0):( 3.14159265358979, -1.31695789692482) |
738 | (-1.0,0):( 3.14159265358979, 0 ) | |
739 | (-0.5,0):( 2.09439510239320, 0 ) | |
740 | ( 0.0,0):( 1.57079632679490, 0 ) | |
741 | ( 0.5,0):( 1.04719755119660, 0 ) | |
742 | ( 1.0,0):( 0 , 0 ) | |
743 | ( 2.0,0):( 0 , 1.31695789692482) | |
744 | ||
745 | &acos | |
0c721ce2 JH |
746 | ( 2, 3):( 1.00014354247380, -1.98338702991654) |
747 | (-2, 3):( 2.14144911111600, -1.98338702991654) | |
748 | (-2,-3):( 2.14144911111600, 1.98338702991654) | |
749 | ( 2,-3):( 1.00014354247380, 1.98338702991654) | |
750 | ||
751 | &atan | |
8c03c583 JH |
752 | (-2.0,0):( -1.10714871779409, 0 ) |
753 | (-1.0,0):( -0.78539816339745, 0 ) | |
754 | (-0.5,0):( -0.46364760900081, 0 ) | |
755 | ( 0.0,0):( 0 , 0 ) | |
756 | ( 0.5,0):( 0.46364760900081, 0 ) | |
757 | ( 1.0,0):( 0.78539816339745, 0 ) | |
758 | ( 2.0,0):( 1.10714871779409, 0 ) | |
759 | ||
760 | &atan | |
0c721ce2 JH |
761 | ( 2, 3):( 1.40992104959658, 0.22907268296854) |
762 | (-2, 3):( -1.40992104959658, 0.22907268296854) | |
763 | (-2,-3):( -1.40992104959658, -0.22907268296854) | |
764 | ( 2,-3):( 1.40992104959658, -0.22907268296854) | |
765 | ||
766 | &asec | |
8c03c583 JH |
767 | (-2.0,0):( 2.09439510239320, 0 ) |
768 | (-1.0,0):( 3.14159265358979, 0 ) | |
769 | (-0.5,0):( 3.14159265358979, -1.31695789692482) | |
770 | ( 0.5,0):( 0 , 1.31695789692482) | |
771 | ( 1.0,0):( 0 , 0 ) | |
772 | ( 2.0,0):( 1.04719755119660, 0 ) | |
773 | ||
774 | &asec | |
0c721ce2 JH |
775 | ( 2, 3):( 1.42041072246703, 0.23133469857397) |
776 | (-2, 3):( 1.72118193112276, 0.23133469857397) | |
777 | (-2,-3):( 1.72118193112276, -0.23133469857397) | |
778 | ( 2,-3):( 1.42041072246703, -0.23133469857397) | |
779 | ||
780 | &acsc | |
8c03c583 JH |
781 | (-2.0,0):( -0.52359877559830, 0 ) |
782 | (-1.0,0):( -1.57079632679490, 0 ) | |
783 | (-0.5,0):( -1.57079632679490, 1.31695789692482) | |
784 | ( 0.5,0):( 1.57079632679490, -1.31695789692482) | |
785 | ( 1.0,0):( 1.57079632679490, 0 ) | |
786 | ( 2.0,0):( 0.52359877559830, 0 ) | |
787 | ||
788 | &acsc | |
0c721ce2 JH |
789 | ( 2, 3):( 0.15038560432786, -0.23133469857397) |
790 | (-2, 3):( -0.15038560432786, -0.23133469857397) | |
791 | (-2,-3):( -0.15038560432786, 0.23133469857397) | |
792 | ( 2,-3):( 0.15038560432786, 0.23133469857397) | |
793 | ||
794 | &acot | |
8c03c583 JH |
795 | (-2.0,0):( -0.46364760900081, 0 ) |
796 | (-1.0,0):( -0.78539816339745, 0 ) | |
797 | (-0.5,0):( -1.10714871779409, 0 ) | |
798 | ( 0.5,0):( 1.10714871779409, 0 ) | |
799 | ( 1.0,0):( 0.78539816339745, 0 ) | |
800 | ( 2.0,0):( 0.46364760900081, 0 ) | |
801 | ||
802 | &acot | |
0c721ce2 JH |
803 | ( 2, 3):( 0.16087527719832, -0.22907268296854) |
804 | (-2, 3):( -0.16087527719832, -0.22907268296854) | |
805 | (-2,-3):( -0.16087527719832, 0.22907268296854) | |
806 | ( 2,-3):( 0.16087527719832, 0.22907268296854) | |
807 | ||
808 | &sinh | |
8c03c583 JH |
809 | (-2.0,0):( -3.62686040784702, 0 ) |
810 | (-1.0,0):( -1.17520119364380, 0 ) | |
811 | (-0.5,0):( -0.52109530549375, 0 ) | |
812 | ( 0.0,0):( 0 , 0 ) | |
813 | ( 0.5,0):( 0.52109530549375, 0 ) | |
814 | ( 1.0,0):( 1.17520119364380, 0 ) | |
815 | ( 2.0,0):( 3.62686040784702, 0 ) | |
816 | ||
817 | &sinh | |
0c721ce2 JH |
818 | ( 2, 3):( -3.59056458998578, 0.53092108624852) |
819 | (-2, 3):( 3.59056458998578, 0.53092108624852) | |
820 | (-2,-3):( 3.59056458998578, -0.53092108624852) | |
821 | ( 2,-3):( -3.59056458998578, -0.53092108624852) | |
822 | ||
823 | &cosh | |
8c03c583 JH |
824 | (-2.0,0):( 3.76219569108363, 0 ) |
825 | (-1.0,0):( 1.54308063481524, 0 ) | |
826 | (-0.5,0):( 1.12762596520638, 0 ) | |
827 | ( 0.0,0):( 1 , 0 ) | |
828 | ( 0.5,0):( 1.12762596520638, 0 ) | |
829 | ( 1.0,0):( 1.54308063481524, 0 ) | |
830 | ( 2.0,0):( 3.76219569108363, 0 ) | |
831 | ||
832 | &cosh | |
0c721ce2 JH |
833 | ( 2, 3):( -3.72454550491532, 0.51182256998738) |
834 | (-2, 3):( -3.72454550491532, -0.51182256998738) | |
835 | (-2,-3):( -3.72454550491532, 0.51182256998738) | |
836 | ( 2,-3):( -3.72454550491532, -0.51182256998738) | |
837 | ||
838 | &tanh | |
8c03c583 JH |
839 | (-2.0,0):( -0.96402758007582, 0 ) |
840 | (-1.0,0):( -0.76159415595576, 0 ) | |
841 | (-0.5,0):( -0.46211715726001, 0 ) | |
842 | ( 0.0,0):( 0 , 0 ) | |
843 | ( 0.5,0):( 0.46211715726001, 0 ) | |
844 | ( 1.0,0):( 0.76159415595576, 0 ) | |
845 | ( 2.0,0):( 0.96402758007582, 0 ) | |
846 | ||
847 | &tanh | |
0c721ce2 JH |
848 | ( 2, 3):( 0.96538587902213, -0.00988437503832) |
849 | (-2, 3):( -0.96538587902213, -0.00988437503832) | |
850 | (-2,-3):( -0.96538587902213, 0.00988437503832) | |
851 | ( 2,-3):( 0.96538587902213, 0.00988437503832) | |
852 | ||
853 | &sech | |
8c03c583 JH |
854 | (-2.0,0):( 0.26580222883408, 0 ) |
855 | (-1.0,0):( 0.64805427366389, 0 ) | |
856 | (-0.5,0):( 0.88681888397007, 0 ) | |
857 | ( 0.0,0):( 1 , 0 ) | |
858 | ( 0.5,0):( 0.88681888397007, 0 ) | |
859 | ( 1.0,0):( 0.64805427366389, 0 ) | |
860 | ( 2.0,0):( 0.26580222883408, 0 ) | |
861 | ||
862 | &sech | |
0c721ce2 JH |
863 | ( 2, 3):( -0.26351297515839, -0.03621163655877) |
864 | (-2, 3):( -0.26351297515839, 0.03621163655877) | |
865 | (-2,-3):( -0.26351297515839, -0.03621163655877) | |
866 | ( 2,-3):( -0.26351297515839, 0.03621163655877) | |
867 | ||
868 | &csch | |
8c03c583 JH |
869 | (-2.0,0):( -0.27572056477178, 0 ) |
870 | (-1.0,0):( -0.85091812823932, 0 ) | |
871 | (-0.5,0):( -1.91903475133494, 0 ) | |
872 | ( 0.5,0):( 1.91903475133494, 0 ) | |
873 | ( 1.0,0):( 0.85091812823932, 0 ) | |
874 | ( 2.0,0):( 0.27572056477178, 0 ) | |
875 | ||
876 | &csch | |
0c721ce2 JH |
877 | ( 2, 3):( -0.27254866146294, -0.04030057885689) |
878 | (-2, 3):( 0.27254866146294, -0.04030057885689) | |
879 | (-2,-3):( 0.27254866146294, 0.04030057885689) | |
880 | ( 2,-3):( -0.27254866146294, 0.04030057885689) | |
881 | ||
882 | &coth | |
8c03c583 JH |
883 | (-2.0,0):( -1.03731472072755, 0 ) |
884 | (-1.0,0):( -1.31303528549933, 0 ) | |
885 | (-0.5,0):( -2.16395341373865, 0 ) | |
886 | ( 0.5,0):( 2.16395341373865, 0 ) | |
887 | ( 1.0,0):( 1.31303528549933, 0 ) | |
888 | ( 2.0,0):( 1.03731472072755, 0 ) | |
889 | ||
890 | &coth | |
0c721ce2 JH |
891 | ( 2, 3):( 1.03574663776500, 0.01060478347034) |
892 | (-2, 3):( -1.03574663776500, 0.01060478347034) | |
893 | (-2,-3):( -1.03574663776500, -0.01060478347034) | |
894 | ( 2,-3):( 1.03574663776500, -0.01060478347034) | |
895 | ||
896 | &asinh | |
8c03c583 JH |
897 | (-2.0,0):( -1.44363547517881, 0 ) |
898 | (-1.0,0):( -0.88137358701954, 0 ) | |
899 | (-0.5,0):( -0.48121182505960, 0 ) | |
900 | ( 0.0,0):( 0 , 0 ) | |
901 | ( 0.5,0):( 0.48121182505960, 0 ) | |
902 | ( 1.0,0):( 0.88137358701954, 0 ) | |
903 | ( 2.0,0):( 1.44363547517881, 0 ) | |
904 | ||
905 | &asinh | |
0c721ce2 JH |
906 | ( 2, 3):( 1.96863792579310, 0.96465850440760) |
907 | (-2, 3):( -1.96863792579310, 0.96465850440761) | |
908 | (-2,-3):( -1.96863792579310, -0.96465850440761) | |
909 | ( 2,-3):( 1.96863792579310, -0.96465850440760) | |
910 | ||
911 | &acosh | |
9bc5fa8d | 912 | (-2.0,0):( 1.31695789692482, 3.14159265358979) |
8c03c583 JH |
913 | (-1.0,0):( 0, 3.14159265358979) |
914 | (-0.5,0):( 0, 2.09439510239320) | |
915 | ( 0.0,0):( 0, 1.57079632679490) | |
916 | ( 0.5,0):( 0, 1.04719755119660) | |
917 | ( 1.0,0):( 0 , 0 ) | |
918 | ( 2.0,0):( 1.31695789692482, 0 ) | |
919 | ||
920 | &acosh | |
0c721ce2 | 921 | ( 2, 3):( 1.98338702991654, 1.00014354247380) |
9bc5fa8d JH |
922 | (-2, 3):( 1.98338702991653, 2.14144911111600) |
923 | (-2,-3):( 1.98338702991653, -2.14144911111600) | |
0c721ce2 JH |
924 | ( 2,-3):( 1.98338702991654, -1.00014354247380) |
925 | ||
926 | &atanh | |
8c03c583 JH |
927 | (-2.0,0):( -0.54930614433405, 1.57079632679490) |
928 | (-0.5,0):( -0.54930614433405, 0 ) | |
929 | ( 0.0,0):( 0 , 0 ) | |
930 | ( 0.5,0):( 0.54930614433405, 0 ) | |
931 | ( 2.0,0):( 0.54930614433405, 1.57079632679490) | |
932 | ||
933 | &atanh | |
0c721ce2 JH |
934 | ( 2, 3):( 0.14694666622553, 1.33897252229449) |
935 | (-2, 3):( -0.14694666622553, 1.33897252229449) | |
936 | (-2,-3):( -0.14694666622553, -1.33897252229449) | |
937 | ( 2,-3):( 0.14694666622553, -1.33897252229449) | |
938 | ||
939 | &asech | |
8c03c583 JH |
940 | (-2.0,0):( 0 , 2.09439510239320) |
941 | (-1.0,0):( 0 , 3.14159265358979) | |
9bc5fa8d | 942 | (-0.5,0):( 1.31695789692482, 3.14159265358979) |
8c03c583 JH |
943 | ( 0.5,0):( 1.31695789692482, 0 ) |
944 | ( 1.0,0):( 0 , 0 ) | |
945 | ( 2.0,0):( 0 , 1.04719755119660) | |
946 | ||
947 | &asech | |
0c721ce2 | 948 | ( 2, 3):( 0.23133469857397, -1.42041072246703) |
9bc5fa8d JH |
949 | (-2, 3):( 0.23133469857397, -1.72118193112276) |
950 | (-2,-3):( 0.23133469857397, 1.72118193112276) | |
0c721ce2 JH |
951 | ( 2,-3):( 0.23133469857397, 1.42041072246703) |
952 | ||
953 | &acsch | |
8c03c583 JH |
954 | (-2.0,0):( -0.48121182505960, 0 ) |
955 | (-1.0,0):( -0.88137358701954, 0 ) | |
956 | (-0.5,0):( -1.44363547517881, 0 ) | |
957 | ( 0.5,0):( 1.44363547517881, 0 ) | |
958 | ( 1.0,0):( 0.88137358701954, 0 ) | |
959 | ( 2.0,0):( 0.48121182505960, 0 ) | |
960 | ||
961 | &acsch | |
0c721ce2 JH |
962 | ( 2, 3):( 0.15735549884499, -0.22996290237721) |
963 | (-2, 3):( -0.15735549884499, -0.22996290237721) | |
964 | (-2,-3):( -0.15735549884499, 0.22996290237721) | |
965 | ( 2,-3):( 0.15735549884499, 0.22996290237721) | |
966 | ||
967 | &acoth | |
8c03c583 JH |
968 | (-2.0,0):( -0.54930614433405, 0 ) |
969 | (-0.5,0):( -0.54930614433405, 1.57079632679490) | |
970 | ( 0.5,0):( 0.54930614433405, 1.57079632679490) | |
971 | ( 2.0,0):( 0.54930614433405, 0 ) | |
972 | ||
973 | &acoth | |
0c721ce2 JH |
974 | ( 2, 3):( 0.14694666622553, -0.23182380450040) |
975 | (-2, 3):( -0.14694666622553, -0.23182380450040) | |
976 | (-2,-3):( -0.14694666622553, 0.23182380450040) | |
977 | ( 2,-3):( 0.14694666622553, 0.23182380450040) | |
978 | ||
979 | # eof |