Class a.complex
complex number
Tables
| a.complex | complex number |
Methods
| a.complex:new ([real[, imag]]) | constructor for complex number from real and imaginary parts |
| a.complex:rect ([real[, imag]]) | constructor for complex number from rectangular Cartesian components |
| a.complex:polar ([rho[, theta]]) | constructor for complex number from polar form |
| a.complex:eq (that) | complex number self is equal to complex number that |
| a.complex:ne (that) | complex number self is not equal to complex number that |
| a.complex:logabs () | computes the natural logarithm of magnitude of a complex number |
| a.complex:abs2 () | computes the squared magnitude of a complex number |
| a.complex:abs () | computes the magnitude of a complex number |
| a.complex:arg () | computes the phase angle of a complex number |
| a.complex:proj () | computes the projection on Riemann sphere |
| a.complex:conj () | computes the complex conjugate |
| a.complex:unm () | computes the complex negative |
| a.complex:inv () | inverse of a complex number |
| a.complex:add (z) | addition of complex numbers |
| a.complex:sub (z) | subtraction of complex numbers |
| a.complex:mul (z) | multiplication of complex numbers |
| a.complex:div (z) | division of complex numbers |
| a.complex:pow (a) | complex number z raised to complex power a |
| a.complex:logb (b) | computes the complex base-b logarithm |
| a.complex:exp () | computes the complex base-e exponential |
| a.complex:log () | computes the complex natural logarithm |
| a.complex:sqrt () | computes the complex square root |
| a.complex:log2 () | computes the complex base-2 logarithm |
| a.complex:log10 () | computes the complex base-10 logarithm |
| a.complex:sin () | computes the complex sine |
| a.complex:cos () | computes the complex cosine |
| a.complex:tan () | computes the complex tangent |
| a.complex:sec () | computes the complex secant |
| a.complex:csc () | computes the complex cosecant |
| a.complex:cot () | computes the complex cotangent |
| a.complex:asin () | computes the complex arc sine |
| a.complex:acos () | computes the complex arc cosine |
| a.complex:atan () | computes the complex arc tangent |
| a.complex:asec () | computes the complex arc secant |
| a.complex:acsc () | computes the complex arc cosecant |
| a.complex:acot () | computes the complex arc cotangent |
| a.complex:sinh () | computes the complex hyperbolic sine |
| a.complex:cosh () | computes the complex hyperbolic cosine |
| a.complex:tanh () | computes the complex hyperbolic tangent |
| a.complex:sech () | computes the complex hyperbolic secant |
| a.complex:csch () | computes the complex hyperbolic cosecant |
| a.complex:coth () | computes the complex hyperbolic cotangent |
| a.complex:asinh () | computes the complex arc hyperbolic sine |
| a.complex:acosh () | computes the complex arc hyperbolic cosine |
| a.complex:atanh () | computes the complex arc hyperbolic tangent |
| a.complex:asech () | computes the complex arc hyperbolic secant |
| a.complex:acsch () | computes the complex arc hyperbolic cosecant |
| a.complex:acoth () | computes the complex arc hyperbolic cotangent |
Tables
- a.complex
-
complex number
Fields:
- real real part of complex number
- imag imaginary part of complex number
- rho the magnitude of complex number
- theta the phase angle of complex number
Methods
- a.complex:new ([real[, imag]])
-
constructor for complex number from real and imaginary parts
Parameters:
- real number, string or a.complex real part of complex number (optional)
- imag number imaginary part of complex number (optional)
Returns:
-
a.complex
complex number userdata
- a.complex:rect ([real[, imag]])
-
constructor for complex number from rectangular Cartesian components
Parameters:
- real number real part of complex number (optional)
- imag number imaginary part of complex number (optional)
Returns:
-
a.complex
complex number userdata
- a.complex:polar ([rho[, theta]])
-
constructor for complex number from polar form
Parameters:
- rho number a distance from a reference point (optional)
- theta number an angle from a reference direction (optional)
Returns:
-
a.complex
complex number userdata
- a.complex:eq (that)
-
complex number self is equal to complex number that
Parameters:
- that a.complex complex number
Returns:
-
bool
result of comparison
- a.complex:ne (that)
-
complex number self is not equal to complex number that
Parameters:
- that a.complex complex number
Returns:
-
bool
result of comparison
- a.complex:logabs ()
-
computes the natural logarithm of magnitude of a complex number
Returns:
-
number
log|z|
- a.complex:abs2 ()
-
computes the squared magnitude of a complex number
Returns:
-
number
a^2+b^2
- a.complex:abs ()
-
computes the magnitude of a complex number
Returns:
-
number
sqrt{a^2+b^2}
- a.complex:arg ()
-
computes the phase angle of a complex number
Returns:
-
number
arctan(b/a)
- a.complex:proj ()
-
computes the projection on Riemann sphere
Returns:
-
a.complex
complex number userdata
- a.complex:conj ()
-
computes the complex conjugate
Returns:
-
a.complex
complex number userdata
- a.complex:unm ()
-
computes the complex negative
Returns:
-
a.complex
complex number userdata
- a.complex:inv ()
-
inverse of a complex number
Returns:
-
a.complex
complex number userdata
- a.complex:add (z)
-
addition of complex numbers
Parameters:
- z a.complex complex number userdata
Returns:
-
a.complex
complex number userdata
- a.complex:sub (z)
-
subtraction of complex numbers
Parameters:
- z a.complex complex number userdata
Returns:
-
a.complex
complex number userdata
- a.complex:mul (z)
-
multiplication of complex numbers
Parameters:
- z a.complex complex number userdata
Returns:
-
a.complex
complex number userdata
- a.complex:div (z)
-
division of complex numbers
Parameters:
- z a.complex complex number userdata
Returns:
-
a.complex
complex number userdata
- a.complex:pow (a)
-
complex number z raised to complex power a
Parameters:
- a a.complex complex number userdata
Returns:
-
a.complex
complex number userdata
- a.complex:logb (b)
-
computes the complex base-b logarithm
Parameters:
- b a.complex complex number userdata
Returns:
-
a.complex
complex number userdata
- a.complex:exp ()
-
computes the complex base-e exponential
Returns:
-
a.complex
complex number userdata
- a.complex:log ()
-
computes the complex natural logarithm
Returns:
-
a.complex
complex number userdata
- a.complex:sqrt ()
-
computes the complex square root
Returns:
-
a.complex
complex number userdata
- a.complex:log2 ()
-
computes the complex base-2 logarithm
Returns:
-
a.complex
complex number userdata
- a.complex:log10 ()
-
computes the complex base-10 logarithm
Returns:
-
a.complex
complex number userdata
- a.complex:sin ()
-
computes the complex sine
Returns:
-
a.complex
complex number userdata
- a.complex:cos ()
-
computes the complex cosine
Returns:
-
a.complex
complex number userdata
- a.complex:tan ()
-
computes the complex tangent
Returns:
-
a.complex
complex number userdata
- a.complex:sec ()
-
computes the complex secant
Returns:
-
a.complex
complex number userdata
- a.complex:csc ()
-
computes the complex cosecant
Returns:
-
a.complex
complex number userdata
- a.complex:cot ()
-
computes the complex cotangent
Returns:
-
a.complex
complex number userdata
- a.complex:asin ()
-
computes the complex arc sine
Returns:
-
a.complex
complex number userdata
- a.complex:acos ()
-
computes the complex arc cosine
Returns:
-
a.complex
complex number userdata
- a.complex:atan ()
-
computes the complex arc tangent
Returns:
-
a.complex
complex number userdata
- a.complex:asec ()
-
computes the complex arc secant
Returns:
-
a.complex
complex number userdata
- a.complex:acsc ()
-
computes the complex arc cosecant
Returns:
-
a.complex
complex number userdata
- a.complex:acot ()
-
computes the complex arc cotangent
Returns:
-
a.complex
complex number userdata
- a.complex:sinh ()
-
computes the complex hyperbolic sine
Returns:
-
a.complex
complex number userdata
- a.complex:cosh ()
-
computes the complex hyperbolic cosine
Returns:
-
a.complex
complex number userdata
- a.complex:tanh ()
-
computes the complex hyperbolic tangent
Returns:
-
a.complex
complex number userdata
- a.complex:sech ()
-
computes the complex hyperbolic secant
Returns:
-
a.complex
complex number userdata
- a.complex:csch ()
-
computes the complex hyperbolic cosecant
Returns:
-
a.complex
complex number userdata
- a.complex:coth ()
-
computes the complex hyperbolic cotangent
Returns:
-
a.complex
complex number userdata
- a.complex:asinh ()
-
computes the complex arc hyperbolic sine
Returns:
-
a.complex
complex number userdata
- a.complex:acosh ()
-
computes the complex arc hyperbolic cosine
Returns:
-
a.complex
complex number userdata
- a.complex:atanh ()
-
computes the complex arc hyperbolic tangent
Returns:
-
a.complex
complex number userdata
- a.complex:asech ()
-
computes the complex arc hyperbolic secant
Returns:
-
a.complex
complex number userdata
- a.complex:acsch ()
-
computes the complex arc hyperbolic cosecant
Returns:
-
a.complex
complex number userdata
- a.complex:acoth ()
-
computes the complex arc hyperbolic cotangent
Returns:
-
a.complex
complex number userdata