complex.t

UNIX下perl实现代码

&Re
(3,4):3
(-3,4):-3
[1,pi/2]:0

&Im
(3,4):4
(3,-4):-4
[1,pi/2]:1

&abs
(3,4):5
(-3,4):5

&arg
[2,0]:0
[-2,0]:pi

&~
(4,5):(4,-5)
(-3,4):(-3,-4)
[2,pi/2]:[2,-(pi)/2]

&<
(3,4):(1,2):0
(3,4):(3,2):0
(3,4):(3,8):1
(4,4):(5,129):1

&==
(3,4):(4,5):0
(3,4):(3,5):0
(3,4):(2,4):0
(3,4):(3,4):1

&sqrt
-9:(0,3)
(-100,0):(0,10)
(16,-30):(5,-3)

&stringify_cartesian
(-100,0):"-100"
(0,1):"i"
(4,-3):"4-3i"
(4,0):"4"
(-4,0):"-4"
(-2,4):"-2+4i"
(-2,-1):"-2-i"

&stringify_polar
[-1, 0]:"[1,pi]"
[1, pi/3]:"[1,pi/3]"
[6, -2*pi/3]:"[6,-2pi/3]"
[0.5, -9*pi/11]:"[0.5,-9pi/11]"

{ (4,3); [3,2]; (-3,4); (0,2); [2,1] }

|'z + ~z':'2*Re(z)'
|'z - ~z':'2*i*Im(z)'
|'z * ~z':'abs(z) * abs(z)'

{ (0.5, 0); (-0.5, 0); (2,3); [3,2]; (-3,2); (0,2); 3; 1.2; (-3, 0); (-2, -1); [2,1] }

|'(root(z, 4))[1] ** 4':'z'
|'(root(z, 5))[3] ** 5':'z'
|'(root(z, 8))[7] ** 8':'z'
|'abs(z)':'r'
|'acot(z)':'acotan(z)'
|'acsc(z)':'acosec(z)'
|'acsc(z)':'asin(1 / z)'
|'asec(z)':'acos(1 / z)'
|'cbrt(z)':'cbrt(r) * exp(i * t/3)'
|'cos(acos(z))':'z'
|'addsq(cos(z), sin(z))':1
|'cos(z)':'cosh(i*z)'
|'subsq(cosh(z), sinh(z))':1
|'cot(acot(z))':'z'
|'cot(z)':'1 / tan(z)'
|'cot(z)':'cotan(z)'
|'csc(acsc(z))':'z'
|'csc(z)':'1 / sin(z)'
|'csc(z)':'cosec(z)'
|'exp(log(z))':'z'
|'exp(z)':'exp(a) * exp(i * b)'
|'ln(z)':'log(z)'
|'log(exp(z))':'z'
|'log(z)':'log(r) + i*t'
|'log10(z)':'log(z) / log(10)'
|'logn(z, 2)':'log(z) / log(2)'
|'logn(z, 3)':'log(z) / log(3)'
|'sec(asec(z))':'z'
|'sec(z)':'1 / cos(z)'
|'sin(asin(z))':'z'
|'sin(i * z)':'i * sinh(z)'
|'sqrt(z) * sqrt(z)':'z'
|'sqrt(z)':'sqrt(r) * exp(i * t/2)'
|'tan(atan(z))':'z'
|'z**z':'exp(z * log(z))'

{ (1,1); [1,0.5]; (-2, -1); 2; -3; (-1,0.5); (0,0.5); 0.5; (2, 0); (-1, -2) }

|'cosh(acosh(z))':'z'
|'coth(acoth(z))':'z'
|'coth(z)':'1 / tanh(z)'
|'coth(z)':'cotanh(z)'
|'csch(acsch(z))':'z'
|'csch(z)':'1 / sinh(z)'
|'csch(z)':'cosech(z)'
|'sech(asech(z))':'z'
|'sech(z)':'1 / cosh(z)'
|'sinh(asinh(z))':'z'
|'tanh(atanh(z))':'z'

{ (0.2,-0.4); [1,0.5]; -1.2; (-1,0.5); 0.5; (1.1, 0) }

|'acos(cos(z)) ** 2':'z * z'
|'acosh(cosh(z)) ** 2':'z * z'
|'acoth(z)':'acotanh(z)'
|'acoth(z)':'atanh(1 / z)'
|'acsch(z)':'acosech(z)'
|'acsch(z)':'asinh(1 / z)'
|'asech(z)':'acosh(1 / z)'
|'asin(sin(z))':'z'
|'asinh(sinh(z))':'z'
|'atan(tan(z))':'z'
|'atanh(tanh(z))':'z'

&log
(-2.0,0):(   0.69314718055995,  3.14159265358979)
(-1.0,0):(   0               ,  3.14159265358979)
(-0.5,0):(  -0.69314718055995,  3.14159265358979)
( 0.5,0):(  -0.69314718055995,  0               )
( 1.0,0):(   0               ,  0               )
( 2.0,0):(   0.69314718055995,  0               )

&log
( 2, 3):(    1.28247467873077,  0.98279372324733)
(-2, 3):(    1.28247467873077,  2.15879893034246)
(-2,-3):(    1.28247467873077, -2.15879893034246)
( 2,-3):(    1.28247467873077, -0.98279372324733)

&sin
(-2.0,0):(  -0.90929742682568,  0               )
(-1.0,0):(  -0.84147098480790,  0               )
(-0.5,0):(  -0.47942553860420,  0               )
( 0.0,0):(   0               ,  0               )
( 0.5,0):(   0.47942553860420,  0               )
( 1.0,0):(   0.84147098480790,  0               )
( 2.0,0):(   0.90929742682568,  0               )

&sin
( 2, 3):(  9.15449914691143, -4.16890695996656)
(-2, 3):( -9.15449914691143, -4.16890695996656)
(-2,-3):( -9.15449914691143,  4.16890695996656)
( 2,-3):(  9.15449914691143,  4.16890695996656)

&cos
(-2.0,0):(  -0.41614683654714,  0               )
(-1.0,0):(   0.54030230586814,  0               )
(-0.5,0):(   0.87758256189037,  0               )
( 0.0,0):(   1               ,  0               )
( 0.5,0):(   0.87758256189037,  0               )
( 1.0,0):(   0.54030230586814,  0               )
( 2.0,0):(  -0.41614683654714,  0               )

&cos
( 2, 3):( -4.18962569096881, -9.10922789375534)
(-2, 3):( -4.18962569096881,  9.10922789375534)
(-2,-3):( -4.18962569096881, -9.10922789375534)
( 2,-3):( -4.18962569096881,  9.10922789375534)

&tan
(-2.0,0):(   2.18503986326152,  0               )
(-1.0,0):(  -1.55740772465490,  0               )
(-0.5,0):(  -0.54630248984379,  0               )
( 0.0,0):(   0               ,  0               )
( 0.5,0):(   0.54630248984379,  0               )
( 1.0,0):(   1.55740772465490,  0               )
( 2.0,0):(  -2.18503986326152,  0               )

&tan
( 2, 3):( -0.00376402564150,  1.00323862735361)
(-2, 3):(  0.00376402564150,  1.00323862735361)
(-2,-3):(  0.00376402564150, -1.00323862735361)
( 2,-3):( -0.00376402564150, -1.00323862735361)

&sec
(-2.0,0):(  -2.40299796172238,  0               )
(-1.0,0):(   1.85081571768093,  0               )
(-0.5,0):(   1.13949392732455,  0               )
( 0.0,0):(   1               ,  0               )
( 0.5,0):(   1.13949392732455,  0               )
( 1.0,0):(   1.85081571768093,  0               )
( 2.0,0):(  -2.40299796172238,  0               )

&sec
( 2, 3):( -0.04167496441114,  0.09061113719624)
(-2, 3):( -0.04167496441114, -0.09061113719624)
(-2,-3):( -0.04167496441114,  0.09061113719624)
( 2,-3):( -0.04167496441114, -0.09061113719624)

&csc
(-2.0,0):(  -1.09975017029462,  0               )
(-1.0,0):(  -1.18839510577812,  0               )
(-0.5,0):(  -2.08582964293349,  0               )
( 0.5,0):(   2.08582964293349,  0               )
( 1.0,0):(   1.18839510577812,  0               )
( 2.0,0):(   1.09975017029462,  0               )

&csc
( 2, 3):(  0.09047320975321,  0.04120098628857)
(-2, 3):( -0.09047320975321,  0.04120098628857)
(-2,-3):( -0.09047320975321, -0.04120098628857)
( 2,-3):(  0.09047320975321, -0.04120098628857)

&cot
(-2.0,0):(   0.45765755436029,  0               )
(-1.0,0):(  -0.64209261593433,  0               )
(-0.5,0):(  -1.83048772171245,  0               )
( 0.5,0):(   1.83048772171245,  0               )
( 1.0,0):(   0.64209261593433,  0               )
( 2.0,0):(  -0.45765755436029,  0               )

&cot
( 2, 3):( -0.00373971037634, -0.99675779656936)
(-2, 3):(  0.00373971037634, -0.99675779656936)
(-2,-3):(  0.00373971037634,  0.99675779656936)
( 2,-3):( -0.00373971037634,  0.99675779656936)

&asin
(-2.0,0):(  -1.57079632679490,  1.31695789692482)
(-1.0,0):(  -1.57079632679490,  0               )
(-0.5,0):(  -0.52359877559830,  0               )
( 0.0,0):(   0               ,  0               )
( 0.5,0):(   0.52359877559830,  0               )
( 1.0,0):(   1.57079632679490,  0               )
( 2.0,0):(   1.57079632679490, -1.31695789692482)

&asin
( 2, 3):(  0.57065278432110,  1.98338702991654)
(-2, 3):( -0.57065278432110,  1.98338702991654)
(-2,-3):( -0.57065278432110, -1.98338702991654)
( 2,-3):(  0.57065278432110, -1.98338702991654)

&acos
(-2.0,0):(   3.14159265358979, -1.31695789692482)
(-1.0,0):(   3.14159265358979,  0               )
(-0.5,0):(   2.09439510239320,  0               )
( 0.0,0):(   1.57079632679490,  0               )
( 0.5,0):(   1.04719755119660,  0               )
( 1.0,0):(   0               ,  0               )
( 2.0,0):(   0               ,  1.31695789692482)

&acos
( 2, 3):(  1.00014354247380, -1.98338702991654)
(-2, 3):(  2.14144911111600, -1.98338702991654)
(-2,-3):(  2.14144911111600,  1.98338702991654)
( 2,-3):(  1.00014354247380,  1.98338702991654)

&atan
(-2.0,0):(  -1.10714871779409,  0               )
(-1.0,0):(  -0.78539816339745,  0               )
(-0.5,0):(  -0.46364760900081,  0               )
( 0.0,0):(   0               ,  0               )
( 0.5,0):(   0.46364760900081,  0               )
( 1.0,0):(   0.78539816339745,  0               )
( 2.0,0):(   1.10714871779409,  0               )

&atan
( 2, 3):(  1.40992104959658,  0.22907268296854)
(-2, 3):( -1.40992104959658,  0.22907268296854)
(-2,-3):( -1.40992104959658, -0.22907268296854)
( 2,-3):(  1.40992104959658, -0.22907268296854)

&asec
(-2.0,0):(   2.09439510239320,  0               )
(-1.0,0):(   3.14159265358979,  0               )
(-0.5,0):(   3.14159265358979, -1.31695789692482)
( 0.5,0):(   0               ,  1.31695789692482)
( 1.0,0):(   0               ,  0               )
( 2.0,0):(   1.04719755119660,  0               )

&asec
( 2, 3):(  1.42041072246703,  0.23133469857397)
(-2, 3):(  1.72118193112276,  0.23133469857397)
(-2,-3):(  1.72118193112276, -0.23133469857397)
( 2,-3):(  1.42041072246703, -0.23133469857397)

&acsc
(-2.0,0):(  -0.52359877559830,  0               )
(-1.0,0):(  -1.57079632679490,  0               )
(-0.5,0):(  -1.57079632679490,  1.31695789692482)
( 0.5,0):(   1.57079632679490, -1.31695789692482)
( 1.0,0):(   1.57079632679490,  0               )
( 2.0,0):(   0.52359877559830,  0               )

&acsc
( 2, 3):(  0.15038560432786, -0.23133469857397)
(-2, 3):( -0.15038560432786, -0.23133469857397)
(-2,-3):( -0.15038560432786,  0.23133469857397)
( 2,-3):(  0.15038560432786,  0.23133469857397)

&acot
(-2.0,0):(  -0.46364760900081,  0               )
(-1.0,0):(  -0.78539816339745,  0               )
(-0.5,0):(  -1.10714871779409,  0               )
( 0.5,0):(   1.10714871779409,  0               )
( 1.0,0):(   0.78539816339745,  0               )
( 2.0,0):(   0.46364760900081,  0               )

&acot
( 2, 3):(  0.16087527719832, -0.22907268296854)
(-2, 3):( -0.16087527719832, -0.22907268296854)
(-2,-3):( -0.16087527719832,  0.22907268296854)
( 2,-3):(  0.16087527719832,  0.22907268296854)

&sinh
(-2.0,0):(  -3.62686040784702,  0               )
(-1.0,0):(  -1.17520119364380,  0               )
(-0.5,0):(  -0.52109530549375,  0               )
( 0.0,0):(   0               ,  0               )
( 0.5,0):(   0.52109530549375,  0               )
( 1.0,0):(   1.17520119364380,  0               )
( 2.0,0):(   3.62686040784702,  0               )

&sinh
( 2, 3):( -3.59056458998578,  0.53092108624852)
(-2, 3):(  3.59056458998578,  0.53092108624852)
(-2,-3):(  3.59056458998578, -0.53092108624852)
( 2,-3):( -3.59056458998578, -0.53092108624852)

&cosh
(-2.0,0):(   3.76219569108363,  0               )
(-1.0,0):(   1.54308063481524,  0               )
(-0.5,0):(   1.12762596520638,  0               )
( 0.0,0):(   1               ,  0               )
( 0.5,0):(   1.12762596520638,  0               )
( 1.0,0):(   1.54308063481524,  0               )
( 2.0,0):(   3.76219569108363,  0               )

&cosh
( 2, 3):( -3.72454550491532,  0.51182256998738)
(-2, 3):( -3.72454550491532, -0.51182256998738)
(-2,-3):( -3.72454550491532,  0.51182256998738)
( 2,-3):( -3.72454550491532, -0.51182256998738)

&tanh
(-2.0,0):(  -0.96402758007582,  0               )
(-1.0,0):(  -0.76159415595576,  0               )
(-0.5,0):(  -0.46211715726001,  0               )
( 0.0,0):(   0               ,  0               )
( 0.5,0):(   0.46211715726001,  0               )
( 1.0,0):(   0.76159415595576,  0               )
( 2.0,0):(   0.96402758007582,  0               )

&tanh
( 2, 3):(  0.96538587902213, -0.00988437503832)
(-2, 3):( -0.96538587902213, -0.00988437503832)
(-2,-3):( -0.96538587902213,  0.00988437503832)
( 2,-3):(  0.96538587902213,  0.00988437503832)

&sech
(-2.0,0):(   0.26580222883408,  0               )
(-1.0,0):(   0.64805427366389,  0               )
(-0.5,0):(   0.88681888397007,  0               )
( 0.0,0):(   1               ,  0               )
( 0.5,0):(   0.88681888397007,  0               )
( 1.0,0):(   0.64805427366389,  0               )
( 2.0,0):(   0.26580222883408,  0               )

&sech
( 2, 3):( -0.26351297515839, -0.03621163655877)
(-2, 3):( -0.26351297515839,  0.03621163655877)
(-2,-3):( -0.26351297515839, -0.03621163655877)
( 2,-3):( -0.26351297515839,  0.03621163655877)

&csch
(-2.0,0):(  -0.27572056477178,  0               )
(-1.0,0):(  -0.85091812823932,  0               )
(-0.5,0):(  -1.91903475133494,  0               )
( 0.5,0):(   1.91903475133494,  0               )
( 1.0,0):(   0.85091812823932,  0               )
( 2.0,0):(   0.27572056477178,  0               )

&csch
( 2, 3):( -0.27254866146294, -0.04030057885689)
(-2, 3):(  0.27254866146294, -0.04030057885689)
(-2,-3):(  0.27254866146294,  0.04030057885689)
( 2,-3):( -0.27254866146294,  0.04030057885689)

&coth
(-2.0,0):(  -1.03731472072755,  0               )
(-1.0,0):(  -1.31303528549933,  0               )
(-0.5,0):(  -2.16395341373865,  0               )
( 0.5,0):(   2.16395341373865,  0               )
( 1.0,0):(   1.31303528549933,  0               )
( 2.0,0):(   1.03731472072755,  0               )

&coth
( 2, 3):(  1.03574663776500,  0.01060478347034)
(-2, 3):( -1.03574663776500,  0.01060478347034)
(-2,-3):( -1.03574663776500, -0.01060478347034)
( 2,-3):(  1.03574663776500, -0.01060478347034)

&asinh
(-2.0,0):(  -1.44363547517881,  0               )
(-1.0,0):(  -0.88137358701954,  0               )
(-0.5,0):(  -0.48121182505960,  0               )
( 0.0,0):(   0               ,  0               )
( 0.5,0):(   0.48121182505960,  0               )
( 1.0,0):(   0.88137358701954,  0               )
( 2.0,0):(   1.44363547517881,  0               )

&asinh
( 2, 3):(  1.96863792579310,  0.96465850440760)
(-2, 3):( -1.96863792579310,  0.96465850440761)
(-2,-3):( -1.96863792579310, -0.96465850440761)
( 2,-3):(  1.96863792579310, -0.96465850440760)

&acosh
(-2.0,0):(   1.31695789692482,  3.14159265358979)
(-1.0,0):(   0,                 3.14159265358979)
(-0.5,0):(   0,                 2.09439510239320)
( 0.0,0):(   0,                 1.57079632679490)
( 0.5,0):(   0,                 1.04719755119660)
( 1.0,0):(   0               ,  0               )
( 2.0,0):(   1.31695789692482,  0               )

&acosh
( 2, 3):(  1.98338702991654,  1.00014354247380)
(-2, 3):(  1.98338702991653,  2.14144911111600)
(-2,-3):(  1.98338702991653, -2.14144911111600)
( 2,-3):(  1.98338702991654, -1.00014354247380)

&atanh
(-2.0,0):(  -0.54930614433405,  1.57079632679490)
(-0.5,0):(  -0.54930614433405,  0               )
( 0.0,0):(   0               ,  0               )
( 0.5,0):(   0.54930614433405,  0               )
( 2.0,0):(   0.54930614433405,  1.57079632679490)

&atanh
( 2, 3):(  0.14694666622553,  1.33897252229449)
(-2, 3):( -0.14694666622553,  1.33897252229449)
(-2,-3):( -0.14694666622553, -1.33897252229449)
( 2,-3):(  0.14694666622553, -1.33897252229449)

&asech
(-2.0,0):(   0               , 2.09439510239320)
(-1.0,0):(   0               , 3.14159265358979)
(-0.5,0):(   1.31695789692482, 3.14159265358979)
( 0.5,0):(   1.31695789692482, 0               )
( 1.0,0):(   0               , 0               )
( 2.0,0):(   0               , 1.04719755119660)

&asech
( 2, 3):(  0.23133469857397, -1.42041072246703)
(-2, 3):(  0.23133469857397, -1.72118193112276)
(-2,-3):(  0.23133469857397,  1.72118193112276)
( 2,-3):(  0.23133469857397,  1.42041072246703)

&acsch
(-2.0,0):(  -0.48121182505960, 0               )
(-1.0,0):(  -0.88137358701954, 0               )
(-0.5,0):(  -1.44363547517881, 0               )
( 0.5,0):(   1.44363547517881, 0               )
( 1.0,0):(   0.88137358701954, 0               )
( 2.0,0):(   0.48121182505960, 0               )

&acsch
( 2, 3):(  0.15735549884499, -0.22996290237721)
(-2, 3):( -0.15735549884499, -0.22996290237721)
(-2,-3):( -0.15735549884499,  0.22996290237721)
( 2,-3):(  0.15735549884499,  0.22996290237721)

&acoth
(-2.0,0):(  -0.54930614433405, 0               )
(-0.5,0):(  -0.54930614433405, 1.57079632679490)
( 0.5,0):(   0.54930614433405, 1.57079632679490)
( 2.0,0):(   0.54930614433405, 0               )

&acoth
( 2, 3):(  0.14694666622553, -0.23182380450040)
(-2, 3):( -0.14694666622553, -0.23182380450040)
(-2,-3):( -0.14694666622553,  0.23182380450040)
( 2,-3):(  0.14694666622553,  0.23182380450040)

# eof