algolib.core package

Submodules

algolib.core.complex module

A lightweight Complex number implementation (without using Python’s built-in complex).

This module provides a small, well-documented Complex class suitable for learning and algorithmic implementations. It supports algebraic form (a + bi) and polar form (r·e^{iθ}), with common operations.

Notes

This class uses plain floats and is immutable.
We intentionally avoid Python’s built-in complex to practice fundamentals.

Examples

>>> z1 = Complex(3, 4)
>>> z1.modulus()
5.0
>>> z2 = Complex.from_polar(2, math.pi/2)
>>> (z1 + z2).re  
3.0
>>> (z1.conjugate()).im
-4.0

class algolib.core.complex.Complex(re: float, im: float)[source]

Bases: object

Complex number in algebraic form \(a + b \mathrm{i}\).

Parameters:

re (float) – Real part \(a\).
im (float) – Imaginary part \(b\).

Raises:

InvalidTypeError – If either part is not a real number (int/float).

almost_equal(other: Complex, tol: float = 1e-12) → bool[source]

Return True if each component differs by at most tol (absolute).

This is safer than exact float equality.

argument() → float[source]

Compute the principal argument of the complex number.

Returns:: The argument (angle in radians) in the range \((-\pi, \pi]\).
Return type:: float

Examples

>>> z = Complex(0, 1)
>>> z.argument()
1.5707963267948966

conjugate() → Complex[source]

Compute the complex conjugate of the number.

Returns:: The conjugate \(a - b \mathrm{i}\).
Return type:: Complex

Examples

>>> z = Complex(3, 4)
>>> z.conjugate()
Complex(re=3.0, im=-4.0)

static from_cartesian(re: float, im: float) → Complex[source]

Construct a complex number from Cartesian coordinates.

Parameters:

re (float) – The real part of the complex number.
im (float) – The imaginary part of the complex number.

Returns:

The complex number corresponding to the Cartesian coordinates.

Return type:

Complex

Examples

>>> z = Complex.from_cartesian(3, 4)
>>> z
Complex(re=3.0, im=4.0)

static from_iterable(pair: Iterable[float]) → Complex[source]

Construct a complex number from an iterable of two numbers.

Parameters:: pair (Iterable[float]) – An iterable containing exactly two elements: the real and imaginary parts.
Returns:: The complex number constructed from the iterable.
Return type:: Complex
Raises:: InvalidTypeError – If the iterable does not contain exactly two numeric elements.

Examples

>>> z = Complex.from_iterable([3, 4])
>>> z
Complex(re=3.0, im=4.0)

static from_polar(r: float, theta: float) → Complex[source]

Construct a complex number from polar coordinates.

Parameters:

r (float) – The modulus (radius) of the complex number. Must be non-negative.
theta (float) – The argument (angle in radians) of the complex number.

Returns:

The complex number corresponding to the polar coordinates.

Return type:

Complex

Raises:

InvalidTypeError – If r or theta is not a real number.
InvalidValueError – If r is negative.

Examples

>>> z = Complex.from_polar(2, math.pi / 2)
>>> z
Complex(re=1.2246467991473532e-16, im=2.0)

im: float

modulus() → float[source]

Compute the modulus (absolute value) of the complex number.

Returns:: The modulus \(\sqrt{a^2 + b^2}\).
Return type:: float

Examples

>>> z = Complex(3, 4)
>>> z.modulus()
5.0

normalized() → Complex[source]

Normalize the complex number by \(z/|z|\) to have a modulus of 1.

Returns:: The normalized complex number.
Return type:: Complex
Raises:: InvalidValueError – If the complex number is zero.

Examples

>>> z = Complex(3, 4)
>>> z.normalized()
Complex(re=0.6, im=0.8)

re: float

to_polar() → Tuple[float, float][source]

Convert the complex number to polar coordinates.

Returns:: A tuple (r, theta) where r is the modulus and theta is the argument.
Return type:: tuple of float

Examples

>>> z = Complex(3, 4)
>>> z.to_polar()
(5.0, 0.9272952180016122)

to_tuple() → Tuple[float, float][source]

Convert the complex number to a tuple of its real and imaginary parts.

Returns:: A tuple (re, im) representing the real and imaginary parts.
Return type:: tuple of float

Examples

>>> z = Complex(3, 4)
>>> z.to_tuple()
(3.0, 4.0)

Module contents

class algolib.core.Complex(re: float, im: float)[source]

Bases: object

Complex number in algebraic form \(a + b \mathrm{i}\).

Parameters:

re (float) – Real part \(a\).
im (float) – Imaginary part \(b\).

Raises:

InvalidTypeError – If either part is not a real number (int/float).

almost_equal(other: Complex, tol: float = 1e-12) → bool[source]

Return True if each component differs by at most tol (absolute).

This is safer than exact float equality.

argument() → float[source]

Compute the principal argument of the complex number.

Returns:: The argument (angle in radians) in the range \((-\pi, \pi]\).
Return type:: float

Examples

>>> z = Complex(0, 1)
>>> z.argument()
1.5707963267948966

conjugate() → Complex[source]

Compute the complex conjugate of the number.

Returns:: The conjugate \(a - b \mathrm{i}\).
Return type:: Complex

Examples

>>> z = Complex(3, 4)
>>> z.conjugate()
Complex(re=3.0, im=-4.0)

static from_cartesian(re: float, im: float) → Complex[source]

Construct a complex number from Cartesian coordinates.

Parameters:

re (float) – The real part of the complex number.
im (float) – The imaginary part of the complex number.

Returns:

The complex number corresponding to the Cartesian coordinates.

Return type:

Complex

Examples

>>> z = Complex.from_cartesian(3, 4)
>>> z
Complex(re=3.0, im=4.0)

static from_iterable(pair: Iterable[float]) → Complex[source]

Construct a complex number from an iterable of two numbers.

Parameters:: pair (Iterable[float]) – An iterable containing exactly two elements: the real and imaginary parts.
Returns:: The complex number constructed from the iterable.
Return type:: Complex
Raises:: InvalidTypeError – If the iterable does not contain exactly two numeric elements.

Examples

>>> z = Complex.from_iterable([3, 4])
>>> z
Complex(re=3.0, im=4.0)

static from_polar(r: float, theta: float) → Complex[source]

Construct a complex number from polar coordinates.

Parameters:

r (float) – The modulus (radius) of the complex number. Must be non-negative.
theta (float) – The argument (angle in radians) of the complex number.

Returns:

The complex number corresponding to the polar coordinates.

Return type:

Complex

Raises:

InvalidTypeError – If r or theta is not a real number.
InvalidValueError – If r is negative.

Examples

>>> z = Complex.from_polar(2, math.pi / 2)
>>> z
Complex(re=1.2246467991473532e-16, im=2.0)

im: float

modulus() → float[source]

Compute the modulus (absolute value) of the complex number.

Returns:: The modulus \(\sqrt{a^2 + b^2}\).
Return type:: float

Examples

>>> z = Complex(3, 4)
>>> z.modulus()
5.0

normalized() → Complex[source]

Normalize the complex number by \(z/|z|\) to have a modulus of 1.

Returns:: The normalized complex number.
Return type:: Complex
Raises:: InvalidValueError – If the complex number is zero.

Examples

>>> z = Complex(3, 4)
>>> z.normalized()
Complex(re=0.6, im=0.8)

re: float

to_polar() → Tuple[float, float][source]

Convert the complex number to polar coordinates.

Returns:: A tuple (r, theta) where r is the modulus and theta is the argument.
Return type:: tuple of float

Examples

>>> z = Complex(3, 4)
>>> z.to_polar()
(5.0, 0.9272952180016122)

to_tuple() → Tuple[float, float][source]

Convert the complex number to a tuple of its real and imaginary parts.

Returns:: A tuple (re, im) representing the real and imaginary parts.
Return type:: tuple of float

Examples

>>> z = Complex(3, 4)
>>> z.to_tuple()
(3.0, 4.0)