AlComplex

AlComplex

A Complex Number library. It uses its own complex number implementation. Its main goal it's to provide a more complete API, compared to the default complex number implementation in Python.

It's as simple as:

>>> from AlComplex import I, AlComplex, pi
>>> 2 + 3*I
2.0 + 3.0i
>>> AlComplex(2,3)
2.0 + 3.0i
>>> AlComplex(1)
1.0 + 0.0i
>>> # You can also use Polar Coordinates
>>> AlComplex.polar(2, pi)
0 - 2i

Installation

Just run

pip install AlComplex

It has no external dependencies.

Details

Basic operations with complex and real numbers are supported

>>> -I + 4 + 3*I
4 + 2i
>>> (25+35*I)/5
5.0 + 7.0i
>>> (-8 + 14*I)/(2+3*I)
2.0000000000000018 + 4.000000000000001i
>>> I**I
.20787957635076193 + 0.0i

Note that since Floats behave weirdly, we use relative equality. Two Complex numbers are equal if their real and imaginary parts are close by at least 1e-14. You can change this by modifying AlComplex.precission to 0.

>>> (-8 + 14*I)/(2+3*I)
2.0000000000000018 + 4.000000000000001i
>>> (-8 + 14*I)/(2+3*I) == 2 + 4*I
True

AlComplex objects have a basic but complete API:

>>> z = 1 + I
>>> z.real
1.0
>>> z.imag
1.0
>>> z.abs()
1.4142135623730951
>>> z.phase()
0.7853981633974483
>>> z.to_polar()
(1.4142135623730951, 0.7853981633974483)
>>> z.to_rect_coord()
(1,1)
>>> z.conjugate()
1 - i

Note that there many aliases and ways to get the same value:

from AlComplex import phase, module, conjugate, real, imaginary
z.phase() == z.arg() == z.angle() == phase(z)
z.abs() == z.magnitude() == z.module() == abs(z) == module(z)
z.real == real(z)
z.imag == imaginary(z)
z.conjugate() == conjugate(z)

There's also basic math functions, optimized for Complex objects.

>>> from AlComplex import sin, exp, Ln
>>> from math import pi
>>> exp(2*pi*I)
1.0 + 0.0i
>>> sin(2*pi)
0.0 + 0.0i
>>> sin(2 + I)
1.4031192506220411 - 0.48905625904129324i
>>> Ln(exp(I)) 
0.0 + 1.0*I

Note that these functions work differently to cmath functions, since very small numbers are rounded to zero automatically.

>>> import cmath
>>> import AlComplex
>>> from math import pi
>>> cmath.sin(2*pi)
(-2.4492935982947064e-16+0j)
>>> AlComplex.sin(2*pi)
0.0 + 0.0i
>>> cmath.sin(2*pi) == 0
False
>>> AlComplex.sin(2*pi) == 0
True

The functions available are sin, cos, tan, sec, csc, cot, asin, acos, atan, sinh, cosh, tanh, sech, csch, coth, asinh, acosh, atanh, exp, Ln, sqrt and inverse.

You can set representation of complex numbers with j, if you prefer.

>>> from AlComplex import J, use_j
>>> J
0.0 + 1.0i
>>> use_j(True)
>>> 2 + J
2.0 + 1.0j
>>> use_j(False)
>>> 2 + J
2.0 + 1.0i

There's also partial support for multiple valued functions. They all create generators.

>>> from AlComplex import int_roots, ln_values
>>> from math import pi
>>> list(int_roots(I, 3))
[0.866025403784439 + 0.5i, -0.866025403784438 + 0.5i, 0.0 - 1.0i]
>>> # Gives log(z.abs()) + (z.phase() + 2*pi*n)*I, where n takes the values from 0 to 2
>>> list(ln_values(I, 0, 3))
[0.0 + 1.5707963267948966i, 0.0 + 7.853981633974483i, 0.0 + 14.137166941154069i]

Currently only int_roots of a function and complex logarithm are supported. More to come.

You can also get the n-th value of the log directly

>>> from AlComplex import ln_n_branch
>>> ln_n_branch(I, 2)
0.0 + 14.137166941154069i