This package contains implementation of the library "MPComplex". MPComplex is a data type supporting complex numbers which allow comparison and sorting operations.
Project description
MPComplex
MPComplex is a data type which support complex numbers which allow comparison and sorting operations. This library extends 'mpc' in 'mpmath' library (https://pypi.org/project/mpmath/) by allowing comparisons and sorting.
MPComplex Operations
The operations supported by MPComplex are addition, subtraction, multiplication, division, power, comparisons, and sorting.
Addition
Input: MPComplex(4, 2) + MPComplex(5, 3) Output: MPComplex(9, 5)
Subtraction
Input: MPComplex(7, 9) - MPComplex(3, 3) Output: MPComplex(4, 6)
Multiplication
Input: MPComplex(5, 4) * MPComplex(4, 6) Output: MPComplex(-4, 46)
Division
Input: MPComplex(5, 4) / MPComplex(4, 6) Output: MPComplex(0.846153846153846, -0.269230769230769)
Power
Input: MPComplex(4, 2) ** 5 Output: MPComplex(-1216, 1312)
Comparisons in General
MPComplex objects are compared to each other in the following order:
- real part value
- imaginary part value
For example, to check whether MPComplex object a is greater than MPComplex object b or not, the program does the following steps:
- Checks if the real part of a is greater than the real part of b or not. If yes, 'True' is returned.
- If the real part of a is equal to the real part of b, go to step 3. Else, go to step 4.
- Return true if the imaginary part of a is greater than the imaginary part of b. Else, return 'False'.
- Return 'False' immediately.
The similar process applies to the operations 'less than', 'less than or equal to', and 'greater than or equal to' as well.
For checking equality of two complex numbers, equality applies if the real and imaginary parts of both numbers are equal.
Greater Than
Input: MPComplex(5, 4) > MPComplex(4, 6) Output: True
Greater Than or Equal To
Input: MPComplex(5, 4) >= MPComplex(4, 6) Output: True
Less Than
Input: MPComplex(5, 4) < MPComplex(4, 6) Output: False
Less Than or Equal To
Input: MPComplex(5, 4) <= MPComplex(4, 6) Output: False
Equal To
Input: MPComplex(4, 2) == MPComplex(4, 1) Output: False
Not Equal To
Input: MPComplex(4, 2) != MPComplex(4, 1) Output: True
Sorting
If a list of MPComplex objects is called with sort() method, the list will be sorted in ascending order.
Input: [MPComplex(4, 2), MPComplex(4, 1), MPComplex(5, 3), MPComplex(2, 7)].sort() Output: [MPComplex(2, 7), MPComplex(4, 1), MPComplex(4, 2), MPComplex(5, 3)]
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