Commit | Line | Data |
89d0527d |
1 | #!./perl |
2 | |
3 | # $RCSfile$ |
4 | # |
5aabfad6 |
5 | # Regression tests for the Math::Complex pacakge |
6 | # -- Raphael Manfredi, September 1996 |
5cd24f17 |
7 | # -- Jarkko Hietaniemi, March-April 1997 |
5aabfad6 |
8 | |
89d0527d |
9 | BEGIN { |
10 | chdir 't' if -d 't'; |
11 | @INC = '../lib'; |
12 | } |
5aabfad6 |
13 | |
89d0527d |
14 | use Math::Complex; |
15 | |
16 | $test = 0; |
17 | $| = 1; |
fe82cf6e |
18 | @script = (); |
5aabfad6 |
19 | my $eps = 1e-11; |
89d0527d |
20 | |
21 | while (<DATA>) { |
0c721ce2 |
22 | s/^\s+//; |
23 | next if $_ eq '' || /^\#/; |
24 | chomp; |
25 | $test_set = 0; # Assume not a test over a set of values |
0e505df1 |
26 | if (/^&(.+)/) { |
89d0527d |
27 | $op = $1; |
28 | next; |
29 | } |
0e505df1 |
30 | elsif (/^\{(.+)\}/) { |
89d0527d |
31 | set($1, \@set, \@val); |
32 | next; |
33 | } |
34 | elsif (s/^\|//) { |
0c721ce2 |
35 | $test_set = 1; # Requests we loop over the set... |
89d0527d |
36 | } |
37 | my @args = split(/:/); |
0c721ce2 |
38 | if ($test_set == 1) { |
89d0527d |
39 | my $i; |
40 | for ($i = 0; $i < @set; $i++) { |
0c721ce2 |
41 | # complex number |
42 | $target = $set[$i]; |
43 | # textual value as found in set definition |
44 | $zvalue = $val[$i]; |
89d0527d |
45 | test($zvalue, $target, @args); |
46 | } |
47 | } else { |
48 | test($op, undef, @args); |
49 | } |
50 | } |
51 | |
5cd24f17 |
52 | # test the divbyzeros |
53 | |
0e505df1 |
54 | sub test_dbz { |
55 | for my $op (@_) { |
56 | $test++; |
57 | |
58 | # push(@script, qq(print "# '$op'\n";)); |
59 | push(@script, qq(eval '$op';)); |
60 | push(@script, qq(print 'not ' unless (\$@ =~ /Division by zero/);)); |
61 | push(@script, qq(print "ok $test\n";)); |
62 | } |
63 | } |
64 | |
5cd24f17 |
65 | test_dbz( |
66 | 'i/0', |
67 | # 'tan(pi/2)', # may succeed thanks to floating point inaccuracies |
68 | # 'sec(pi/2)', # may succeed thanks to floating point inaccuracies |
69 | 'csc(0)', |
70 | 'cot(0)', |
71 | 'atan(i)', |
72 | 'asec(0)', |
73 | 'acsc(0)', |
74 | 'acot(i)', |
75 | # 'tanh(pi/2)', # may succeed thanks to floating point inaccuracies |
76 | # 'sech(pi/2)', # may succeed thanks to floating point inaccuracies |
77 | 'csch(0)', |
78 | 'coth(0)', |
79 | 'atanh(1)', |
80 | 'asech(0)', |
81 | 'acsch(0)', |
82 | 'acoth(1)' |
83 | ); |
84 | |
0e505df1 |
85 | # test the 0**0 |
86 | |
87 | sub test_ztz { |
88 | $test++; |
89 | |
90 | # push(@script, qq(print "# 0**0\n";)); |
91 | push(@script, qq(eval 'cplx(0)**cplx(0)';)); |
92 | push(@script, qq(print 'not ' unless (\$@ =~ /zero raised to the/);)); |
93 | push(@script, qq(print "ok $test\n";)); |
94 | } |
95 | |
96 | test_ztz; |
97 | |
98 | # test the bad roots |
99 | |
100 | sub test_broot { |
5cd24f17 |
101 | for my $op (@_) { |
102 | $test++; |
103 | |
0e505df1 |
104 | # push(@script, qq(print "# root(2, $op)\n";)); |
105 | push(@script, qq(eval 'root(2, $op)';)); |
106 | push(@script, qq(print 'not ' unless (\$@ =~ /root must be/);)); |
5cd24f17 |
107 | push(@script, qq(print "ok $test\n";)); |
108 | } |
109 | } |
110 | |
0e505df1 |
111 | test_broot(qw(-3 -2.1 0 0.99)); |
112 | |
89d0527d |
113 | print "1..$test\n"; |
fe82cf6e |
114 | eval join '', @script; |
89d0527d |
115 | die $@ if $@; |
116 | |
0e505df1 |
117 | sub abop { |
118 | my ($op) = @_; |
119 | |
120 | push(@script, qq(print "# $op=\n";)); |
121 | } |
122 | |
89d0527d |
123 | sub test { |
124 | my ($op, $z, @args) = @_; |
0e505df1 |
125 | my ($baop) = 0; |
89d0527d |
126 | $test++; |
127 | my $i; |
0e505df1 |
128 | $baop = 1 if ($op =~ s/;=$//); |
89d0527d |
129 | for ($i = 0; $i < @args; $i++) { |
130 | $val = value($args[$i]); |
fe82cf6e |
131 | push @script, "\$z$i = $val;\n"; |
89d0527d |
132 | } |
133 | if (defined $z) { |
134 | $args = "'$op'"; # Really the value |
0c721ce2 |
135 | $try = "abs(\$z0 - \$z1) <= $eps ? \$z1 : \$z0"; |
fe82cf6e |
136 | push @script, "\$res = $try; "; |
137 | push @script, "check($test, $args[0], \$res, \$z$#args, $args);\n"; |
89d0527d |
138 | } else { |
139 | my ($try, $args); |
140 | if (@args == 2) { |
141 | $try = "$op \$z0"; |
142 | $args = "'$args[0]'"; |
143 | } else { |
144 | $try = ($op =~ /^\w/) ? "$op(\$z0, \$z1)" : "\$z0 $op \$z1"; |
145 | $args = "'$args[0]', '$args[1]'"; |
146 | } |
fe82cf6e |
147 | push @script, "\$res = $try; "; |
148 | push @script, "check($test, '$try', \$res, \$z$#args, $args);\n"; |
0e505df1 |
149 | if (@args > 2 and $baop) { # binary assignment ops |
150 | $test++; |
151 | # check the op= works |
152 | push @script, <<EOB; |
153 | { |
154 | my \$za = cplx(ref \$z0 ? \@{\$z0->cartesian} : (\$z0, 0)); |
155 | |
156 | my (\$z1r, \$z1i) = ref \$z1 ? \@{\$z1->cartesian} : (\$z1, 0); |
157 | |
158 | my \$zb = cplx(\$z1r, \$z1i); |
159 | |
160 | \$za $op= \$zb; |
161 | my (\$zbr, \$zbi) = \@{\$zb->cartesian}; |
162 | |
163 | check($test, '\$z0 $op= \$z1', \$za, \$z$#args, $args); |
164 | EOB |
165 | $test++; |
166 | # check that the rhs has not changed |
167 | push @script, qq(print "not " unless (\$zbr == \$z1r and \$zbi == \$z1i);); |
168 | push @script, qq(print "ok $test\n";); |
169 | push @script, "}\n"; |
170 | } |
89d0527d |
171 | } |
172 | } |
173 | |
174 | sub set { |
175 | my ($set, $setref, $valref) = @_; |
176 | @{$setref} = (); |
177 | @{$valref} = (); |
178 | my @set = split(/;\s*/, $set); |
179 | my @res; |
180 | my $i; |
181 | for ($i = 0; $i < @set; $i++) { |
182 | push(@{$valref}, $set[$i]); |
183 | my $val = value($set[$i]); |
fe82cf6e |
184 | push @script, "\$s$i = $val;\n"; |
185 | push @{$setref}, "\$s$i"; |
89d0527d |
186 | } |
187 | } |
188 | |
189 | sub value { |
190 | local ($_) = @_; |
191 | if (/^\s*\((.*),(.*)\)/) { |
192 | return "cplx($1,$2)"; |
193 | } |
194 | elsif (/^\s*\[(.*),(.*)\]/) { |
195 | return "cplxe($1,$2)"; |
196 | } |
197 | elsif (/^\s*'(.*)'/) { |
198 | my $ex = $1; |
199 | $ex =~ s/\bz\b/$target/g; |
200 | $ex =~ s/\br\b/abs($target)/g; |
201 | $ex =~ s/\bt\b/arg($target)/g; |
202 | $ex =~ s/\ba\b/Re($target)/g; |
203 | $ex =~ s/\bb\b/Im($target)/g; |
204 | return $ex; |
205 | } |
206 | elsif (/^\s*"(.*)"/) { |
207 | return "\"$1\""; |
208 | } |
209 | return $_; |
210 | } |
211 | |
212 | sub check { |
213 | my ($test, $try, $got, $expected, @z) = @_; |
0c721ce2 |
214 | |
215 | # print "# @_\n"; |
216 | |
217 | if ("$got" eq "$expected" |
218 | || |
219 | ($expected =~ /^-?\d/ && $got == $expected) |
220 | || |
221 | (abs($got - $expected) < $eps) |
222 | ) { |
89d0527d |
223 | print "ok $test\n"; |
224 | } else { |
225 | print "not ok $test\n"; |
226 | my $args = (@z == 1) ? "z = $z[0]" : "z0 = $z[0], z1 = $z[1]"; |
227 | print "# '$try' expected: '$expected' got: '$got' for $args\n"; |
228 | } |
229 | } |
230 | __END__ |
0e505df1 |
231 | &+;= |
89d0527d |
232 | (3,4):(3,4):(6,8) |
233 | (-3,4):(3,-4):(0,0) |
234 | (3,4):-3:(0,4) |
235 | 1:(4,2):(5,2) |
236 | [2,0]:[2,pi]:(0,0) |
237 | |
238 | &++ |
239 | (2,1):(3,1) |
240 | |
0e505df1 |
241 | &-;= |
89d0527d |
242 | (2,3):(-2,-3) |
243 | [2,pi/2]:[2,-(pi)/2] |
244 | 2:[2,0]:(0,0) |
245 | [3,0]:2:(1,0) |
246 | 3:(4,5):(-1,-5) |
247 | (4,5):3:(1,5) |
0e505df1 |
248 | (2,1):(3,5):(-1,-4) |
89d0527d |
249 | |
250 | &-- |
251 | (1,2):(0,2) |
252 | [2,pi]:[3,pi] |
253 | |
0e505df1 |
254 | &*;= |
89d0527d |
255 | (0,1):(0,1):(-1,0) |
256 | (4,5):(1,0):(4,5) |
257 | [2,2*pi/3]:(1,0):[2,2*pi/3] |
258 | 2:(0,1):(0,2) |
259 | (0,1):3:(0,3) |
260 | (0,1):(4,1):(-1,4) |
261 | (2,1):(4,-1):(9,2) |
262 | |
0e505df1 |
263 | &/;= |
89d0527d |
264 | (3,4):(3,4):(1,0) |
265 | (4,-5):1:(4,-5) |
266 | 1:(0,1):(0,-1) |
267 | (0,6):(0,2):(3,0) |
268 | (9,2):(4,-1):(2,1) |
269 | [4,pi]:[2,pi/2]:[2,pi/2] |
270 | [2,pi/2]:[4,pi]:[0.5,-(pi)/2] |
271 | |
0e505df1 |
272 | &**;= |
273 | (2,0):(3,0):(8,0) |
274 | (3,0):(2,0):(9,0) |
275 | (2,3):(4,0):(-119,-120) |
276 | |
0c721ce2 |
277 | &Re |
278 | (3,4):3 |
279 | (-3,4):-3 |
280 | [1,pi/2]:0 |
281 | |
282 | &Im |
283 | (3,4):4 |
284 | (3,-4):-4 |
285 | [1,pi/2]:1 |
286 | |
89d0527d |
287 | &abs |
288 | (3,4):5 |
289 | (-3,4):5 |
290 | |
0c721ce2 |
291 | &arg |
292 | [2,0]:0 |
293 | [-2,0]:pi |
294 | |
89d0527d |
295 | &~ |
296 | (4,5):(4,-5) |
297 | (-3,4):(-3,-4) |
298 | [2,pi/2]:[2,-(pi)/2] |
299 | |
300 | &< |
301 | (3,4):(1,2):0 |
302 | (3,4):(3,2):0 |
303 | (3,4):(3,8):1 |
304 | (4,4):(5,129):1 |
305 | |
306 | &== |
307 | (3,4):(4,5):0 |
308 | (3,4):(3,5):0 |
309 | (3,4):(2,4):0 |
310 | (3,4):(3,4):1 |
311 | |
312 | &sqrt |
0c721ce2 |
313 | -9:(0,3) |
89d0527d |
314 | (-100,0):(0,10) |
315 | (16,-30):(5,-3) |
316 | |
317 | &stringify_cartesian |
318 | (-100,0):"-100" |
319 | (0,1):"i" |
320 | (4,-3):"4-3i" |
321 | (4,0):"4" |
322 | (-4,0):"-4" |
323 | (-2,4):"-2+4i" |
324 | (-2,-1):"-2-i" |
325 | |
326 | &stringify_polar |
327 | [-1, 0]:"[1,pi]" |
328 | [1, pi/3]:"[1,pi/3]" |
329 | [6, -2*pi/3]:"[6,-2pi/3]" |
330 | [0.5, -9*pi/11]:"[0.5,-9pi/11]" |
331 | |
332 | { (4,3); [3,2]; (-3,4); (0,2); [2,1] } |
333 | |
334 | |'z + ~z':'2*Re(z)' |
335 | |'z - ~z':'2*i*Im(z)' |
336 | |'z * ~z':'abs(z) * abs(z)' |
337 | |
0c721ce2 |
338 | { (2,3); [3,2]; (-3,2); (0,2); 3; 1.2; -3; (-3, 0); (-2, -1); [2,1] } |
89d0527d |
339 | |
0c721ce2 |
340 | |'(root(z, 4))[1] ** 4':'z' |
341 | |'(root(z, 5))[3] ** 5':'z' |
342 | |'(root(z, 8))[7] ** 8':'z' |
89d0527d |
343 | |'abs(z)':'r' |
0c721ce2 |
344 | |'acot(z)':'acotan(z)' |
345 | |'acsc(z)':'acosec(z)' |
346 | |'acsc(z)':'asin(1 / z)' |
347 | |'asec(z)':'acos(1 / z)' |
89d0527d |
348 | |'cbrt(z)':'cbrt(r) * exp(i * t/3)' |
89d0527d |
349 | |'cos(acos(z))':'z' |
89d0527d |
350 | |'cos(z) ** 2 + sin(z) ** 2':1 |
89d0527d |
351 | |'cos(z)':'cosh(i*z)' |
0c721ce2 |
352 | |'cosh(z) ** 2 - sinh(z) ** 2':1 |
353 | |'cot(acot(z))':'z' |
354 | |'cot(z)':'1 / tan(z)' |
355 | |'cot(z)':'cotan(z)' |
356 | |'csc(acsc(z))':'z' |
357 | |'csc(z)':'1 / sin(z)' |
358 | |'csc(z)':'cosec(z)' |
89d0527d |
359 | |'exp(log(z))':'z' |
0c721ce2 |
360 | |'exp(z)':'exp(a) * exp(i * b)' |
361 | |'ln(z)':'log(z)' |
362 | |'log(exp(z))':'z' |
363 | |'log(z)':'log(r) + i*t' |
89d0527d |
364 | |'log10(z)':'log(z) / log(10)' |
89d0527d |
365 | |'logn(z, 2)':'log(z) / log(2)' |
0c721ce2 |
366 | |'logn(z, 3)':'log(z) / log(3)' |
367 | |'sec(asec(z))':'z' |
368 | |'sec(z)':'1 / cos(z)' |
369 | |'sin(asin(z))':'z' |
370 | |'sin(i * z)':'i * sinh(z)' |
371 | |'sqrt(z) * sqrt(z)':'z' |
372 | |'sqrt(z)':'sqrt(r) * exp(i * t/2)' |
373 | |'tan(atan(z))':'z' |
374 | |'z**z':'exp(z * log(z))' |
89d0527d |
375 | |
0c721ce2 |
376 | { (1,1); [1,0.5]; (-2, -1); 2; -3; (-1,0.5); (0,0.5); 0.5; (2, 0); (-1, -2) } |
89d0527d |
377 | |
89d0527d |
378 | |'cosh(acosh(z))':'z' |
0c721ce2 |
379 | |'coth(acoth(z))':'z' |
380 | |'coth(z)':'1 / tanh(z)' |
381 | |'coth(z)':'cotanh(z)' |
382 | |'csch(acsch(z))':'z' |
383 | |'csch(z)':'1 / sinh(z)' |
384 | |'csch(z)':'cosech(z)' |
385 | |'sech(asech(z))':'z' |
386 | |'sech(z)':'1 / cosh(z)' |
387 | |'sinh(asinh(z))':'z' |
89d0527d |
388 | |'tanh(atanh(z))':'z' |
89d0527d |
389 | |
0c721ce2 |
390 | { (0.2,-0.4); [1,0.5]; -1.2; (-1,0.5); 0.5; (1.1, 0) } |
89d0527d |
391 | |
89d0527d |
392 | |'acos(cos(z)) ** 2':'z * z' |
89d0527d |
393 | |'acosh(cosh(z)) ** 2':'z * z' |
0c721ce2 |
394 | |'acoth(z)':'acotanh(z)' |
395 | |'acoth(z)':'atanh(1 / z)' |
396 | |'acsch(z)':'acosech(z)' |
397 | |'acsch(z)':'asinh(1 / z)' |
398 | |'asech(z)':'acosh(1 / z)' |
399 | |'asin(sin(z))':'z' |
400 | |'asinh(sinh(z))':'z' |
401 | |'atan(tan(z))':'z' |
89d0527d |
402 | |'atanh(tanh(z))':'z' |
403 | |
0c721ce2 |
404 | &sin |
405 | ( 2, 3):( 9.15449914691143, -4.16890695996656) |
406 | (-2, 3):( -9.15449914691143, -4.16890695996656) |
407 | (-2,-3):( -9.15449914691143, 4.16890695996656) |
408 | ( 2,-3):( 9.15449914691143, 4.16890695996656) |
409 | |
410 | &cos |
411 | ( 2, 3):( -4.18962569096881, -9.10922789375534) |
412 | (-2, 3):( -4.18962569096881, 9.10922789375534) |
413 | (-2,-3):( -4.18962569096881, -9.10922789375534) |
414 | ( 2,-3):( -4.18962569096881, 9.10922789375534) |
415 | |
416 | &tan |
417 | ( 2, 3):( -0.00376402564150, 1.00323862735361) |
418 | (-2, 3):( 0.00376402564150, 1.00323862735361) |
419 | (-2,-3):( 0.00376402564150, -1.00323862735361) |
420 | ( 2,-3):( -0.00376402564150, -1.00323862735361) |
421 | |
422 | &sec |
423 | ( 2, 3):( -0.04167496441114, 0.09061113719624) |
424 | (-2, 3):( -0.04167496441114, -0.09061113719624) |
425 | (-2,-3):( -0.04167496441114, 0.09061113719624) |
426 | ( 2,-3):( -0.04167496441114, -0.09061113719624) |
427 | |
428 | &csc |
429 | ( 2, 3):( 0.09047320975321, 0.04120098628857) |
430 | (-2, 3):( -0.09047320975321, 0.04120098628857) |
431 | (-2,-3):( -0.09047320975321, -0.04120098628857) |
432 | ( 2,-3):( 0.09047320975321, -0.04120098628857) |
433 | |
434 | &cot |
435 | ( 2, 3):( -0.00373971037634, -0.99675779656936) |
436 | (-2, 3):( 0.00373971037634, -0.99675779656936) |
437 | (-2,-3):( 0.00373971037634, 0.99675779656936) |
438 | ( 2,-3):( -0.00373971037634, 0.99675779656936) |
439 | |
440 | &asin |
441 | ( 2, 3):( 0.57065278432110, 1.98338702991654) |
442 | (-2, 3):( -0.57065278432110, 1.98338702991654) |
443 | (-2,-3):( -0.57065278432110, -1.98338702991654) |
444 | ( 2,-3):( 0.57065278432110, -1.98338702991654) |
445 | |
446 | &acos |
447 | ( 2, 3):( 1.00014354247380, -1.98338702991654) |
448 | (-2, 3):( 2.14144911111600, -1.98338702991654) |
449 | (-2,-3):( 2.14144911111600, 1.98338702991654) |
450 | ( 2,-3):( 1.00014354247380, 1.98338702991654) |
451 | |
452 | &atan |
453 | ( 2, 3):( 1.40992104959658, 0.22907268296854) |
454 | (-2, 3):( -1.40992104959658, 0.22907268296854) |
455 | (-2,-3):( -1.40992104959658, -0.22907268296854) |
456 | ( 2,-3):( 1.40992104959658, -0.22907268296854) |
457 | |
458 | &asec |
459 | ( 2, 3):( 1.42041072246703, 0.23133469857397) |
460 | (-2, 3):( 1.72118193112276, 0.23133469857397) |
461 | (-2,-3):( 1.72118193112276, -0.23133469857397) |
462 | ( 2,-3):( 1.42041072246703, -0.23133469857397) |
463 | |
464 | &acsc |
465 | ( 2, 3):( 0.15038560432786, -0.23133469857397) |
466 | (-2, 3):( -0.15038560432786, -0.23133469857397) |
467 | (-2,-3):( -0.15038560432786, 0.23133469857397) |
468 | ( 2,-3):( 0.15038560432786, 0.23133469857397) |
469 | |
470 | &acot |
471 | ( 2, 3):( 0.16087527719832, -0.22907268296854) |
472 | (-2, 3):( -0.16087527719832, -0.22907268296854) |
473 | (-2,-3):( -0.16087527719832, 0.22907268296854) |
474 | ( 2,-3):( 0.16087527719832, 0.22907268296854) |
475 | |
476 | &sinh |
477 | ( 2, 3):( -3.59056458998578, 0.53092108624852) |
478 | (-2, 3):( 3.59056458998578, 0.53092108624852) |
479 | (-2,-3):( 3.59056458998578, -0.53092108624852) |
480 | ( 2,-3):( -3.59056458998578, -0.53092108624852) |
481 | |
482 | &cosh |
483 | ( 2, 3):( -3.72454550491532, 0.51182256998738) |
484 | (-2, 3):( -3.72454550491532, -0.51182256998738) |
485 | (-2,-3):( -3.72454550491532, 0.51182256998738) |
486 | ( 2,-3):( -3.72454550491532, -0.51182256998738) |
487 | |
488 | &tanh |
489 | ( 2, 3):( 0.96538587902213, -0.00988437503832) |
490 | (-2, 3):( -0.96538587902213, -0.00988437503832) |
491 | (-2,-3):( -0.96538587902213, 0.00988437503832) |
492 | ( 2,-3):( 0.96538587902213, 0.00988437503832) |
493 | |
494 | &sech |
495 | ( 2, 3):( -0.26351297515839, -0.03621163655877) |
496 | (-2, 3):( -0.26351297515839, 0.03621163655877) |
497 | (-2,-3):( -0.26351297515839, -0.03621163655877) |
498 | ( 2,-3):( -0.26351297515839, 0.03621163655877) |
499 | |
500 | &csch |
501 | ( 2, 3):( -0.27254866146294, -0.04030057885689) |
502 | (-2, 3):( 0.27254866146294, -0.04030057885689) |
503 | (-2,-3):( 0.27254866146294, 0.04030057885689) |
504 | ( 2,-3):( -0.27254866146294, 0.04030057885689) |
505 | |
506 | &coth |
507 | ( 2, 3):( 1.03574663776500, 0.01060478347034) |
508 | (-2, 3):( -1.03574663776500, 0.01060478347034) |
509 | (-2,-3):( -1.03574663776500, -0.01060478347034) |
510 | ( 2,-3):( 1.03574663776500, -0.01060478347034) |
511 | |
512 | &asinh |
513 | ( 2, 3):( 1.96863792579310, 0.96465850440760) |
514 | (-2, 3):( -1.96863792579310, 0.96465850440761) |
515 | (-2,-3):( -1.96863792579310, -0.96465850440761) |
516 | ( 2,-3):( 1.96863792579310, -0.96465850440760) |
517 | |
518 | &acosh |
519 | ( 2, 3):( 1.98338702991654, 1.00014354247380) |
520 | (-2, 3):( -1.98338702991653, -2.14144911111600) |
521 | (-2,-3):( -1.98338702991653, 2.14144911111600) |
522 | ( 2,-3):( 1.98338702991654, -1.00014354247380) |
523 | |
524 | &atanh |
525 | ( 2, 3):( 0.14694666622553, 1.33897252229449) |
526 | (-2, 3):( -0.14694666622553, 1.33897252229449) |
527 | (-2,-3):( -0.14694666622553, -1.33897252229449) |
528 | ( 2,-3):( 0.14694666622553, -1.33897252229449) |
529 | |
530 | &asech |
531 | ( 2, 3):( 0.23133469857397, -1.42041072246703) |
532 | (-2, 3):( -0.23133469857397, 1.72118193112276) |
533 | (-2,-3):( -0.23133469857397, -1.72118193112276) |
534 | ( 2,-3):( 0.23133469857397, 1.42041072246703) |
535 | |
536 | &acsch |
537 | ( 2, 3):( 0.15735549884499, -0.22996290237721) |
538 | (-2, 3):( -0.15735549884499, -0.22996290237721) |
539 | (-2,-3):( -0.15735549884499, 0.22996290237721) |
540 | ( 2,-3):( 0.15735549884499, 0.22996290237721) |
541 | |
542 | &acoth |
543 | ( 2, 3):( 0.14694666622553, -0.23182380450040) |
544 | (-2, 3):( -0.14694666622553, -0.23182380450040) |
545 | (-2,-3):( -0.14694666622553, 0.23182380450040) |
546 | ( 2,-3):( 0.14694666622553, 0.23182380450040) |
547 | |
548 | # eof |