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