mathWiz 0.2.2

A python math module designed for complex math.

MathWiz

Description

MathWiz is a Python library that was written in Python. It is specifically designed for use in various aspects of mathematics, as per listed below. Other common python math modules such as numpy provide similiar (overlapping) services, however there are many unique advantages and processes offered by this module.

Installation

The module mathWiz is available to install via pip:

pip install mathWiz

Use the following command to upgrade to the most recent version (Recommended due to bug fixes and new features)

pip install --upgrade mathWiz

Version

MathWiz is currently on version 0.2.2

Latest Additions

• Simultaneous Equations:

  • Solving of any order

• Matrices:

  • Adjoint Matrix Function
  • Cofactor Matrix Function

See Changelogs in (CHANELOG.md) for more information

Features

Complex Numbers

• Operations
• Conjugates
• Polar Form

Polynomials

• Roots
• Turning Points
• Substitution (Real and Complex)
• Derivatives
• Gradient
• Integrals
• Area Under Curve

Matrices

• Addition and Subtraction
• Multiplication
• Determinants
• Transposition
• Adjoint Matrix Function
• Cofactor Matrix Function
• Inverse Matrices

Simulataneous Equations

• Solving with any amount of variables

Vectors

• 2D Vectors
• 3D Vectors
• Unit Vectors
• Scalar Multiplication
• Dot Products
• Cross Multiplication
• Scalar Projection
• Vector Projection

More Features will be coming soon

Usage / Documentation

Here are some examples on how you can use the above mentioned features with mathWiz.

Complex Numbers

z = Complex(3, 4)

z
# 3 + 4i

z.conjugate()
# 3 - 4i

z.polarForm()
# 5cis(0.9272952180016122)

z + Complex(4,-2)
# 7 + 2i

z * Complex(2, 4)
# -10 + 20i

z ** 5
# -237 - 3116i

Polynomials

x = Variable('x')
poly = Polynomial(3, 2*x**3 - 4*x**2 + 12)

poly
# 2x^3 - 4x^2 + 12

poly.subIn(2)
# 12

poly.subIn(Complex(2,-3))
# -60 + 30i

poly.roots()
# [(1.670125415064549 + 1.2990208027107955i, 0), (1.670125415064549 - 1.2990208027107955i, 0), (-1.3402508301290976, 0)]

poly.turningPoints()
# [(1.3333333333333333, 9.62962962962963), (0.0, 12.0)]

poly.derivative()
# 6x^2 - 8x

poly.gradientAt(x=4)
# 64

poly.integral()
# 0.5x^4 - 1.33x^3 + 12.0x

poly.definiteIntegral(lowerBound=1, upperBound=3)
# 29.333333333333336

Matrices

matrix = Matrix([[1,-4.89,5,7], [6,3,2,5], [1,4,3,-2.53], [8,7,3,5]])
matrix2 = Matrix([[2,-3,4,8],[1,1,0,0],[9,2,1,-3.42],[8,1,7,1]])

matrix
"""
 _                  _
| 1  -4.89  5      7 |
| 6      3  2      5 |
| 1      4  3  -2.53 |
|_8      7  3      5_| 
"""
matrix.rows 
# 4

matrix.columns 
# 4

matrix + matrix2
"""
 _                    _
|  3  -7.89   9     15 |
|  7      4   2      5 |
| 10      6   4  -5.95 |
|_16      8  10      6_|
"""

matrix * matrix2
"""
 _                          _
| 98.11  9.11    58.0   -2.1 |
|    73    -6      61  46.16 |
| 12.76  4.47  -10.71  -4.79 |
|_   90    -6      70  58.74_|
"""

matrix.determinant()
# 264.54339999999985

matrix.transpose()
"""
 _                  _
|     1  6      1  8 |
| -4.89  3      4  7 |
|     5  2      3  3 |
|_    7  5  -2.53  5_|
"""

matrix.inverse()
"""
 _                         _
| -0.2   1.37   0.34  -0.92 |
| 0.08  -0.95  -0.22   0.73 |
|  0.1   0.05   0.22  -0.08 |
|_0.15  -0.89  -0.36    0.7_|
"""

matrix.inverse()*matrix
"""
 _                    _
| 1.0  -0.0  0.0   0.0 |
| 0.0   1.0  0.0  -0.0 |
| 0.0   0.0  1.0  -0.0 |
|_0.0   0.0  0.0   1.0_|
"""

Simultaneous Equations

solveSim('2x+3y-z=7', '-x+4y+2z =1', '3x-5y+z=-8')
# [{'x': 0.36}, {'y': 1.39}, {'z': -2.11}]

Vectors

vectorL = Vector2(2, 3)

vectorL
# (2, 3)

vectorL.i
# 2

vectorL.j
# 3

vectorL.magnitude 
# 3.605551275463989

vectorL.direction
# 0.982793723247329

vectorL * 3
# (6, 9)

vectorL.unitVector()
# (0.5547, 0.8321)

dotProduct(vectorL, Vector2(1,2))
# 8

vectorA = Vector3(4, 3, -5)
vectorB = Vector3(-5.4, 7, 2)

vectorA.k
# -5

vectorA * vectorB:
# (41, 19.0, 44.2)

scalarProjection(vectorA, vectorB) # vector A on vector B
# -1.1689

vectorProjection(vectorA, vectorB) # vector A on vector B
# (0.6967, -0.9031, -0.258) 

License

This project is licensed under the MIT License. See the LICENSE file for more details.

Credits

This module was created by William E.