PyPoSolver

PyPoSolver is a Python library for performing mathematical and physics calculations, including numerical integration, root-finding, linear algebra operations, and basic mechanics.

Installation

pip install pyposolver 

Usage

Mathematics

Integration

Use the trapezoidal_rule function to perform numerical integration:

from pyposolver.maths.integration import trapezoidal_rule

def f(x):
    return x**2

result = trapezoidal_rule(f, 0, 1, 100)  # Integrate f(x) from 0 to 1 using 100 intervals
print(result)  # Expected: 0.333...

Root-Finding

• Bisection Method

Use bisection_method to find the root of a function within a specified interval:

from pyposolver.maths.root_finding import bisection_method

def f(x):
    return x**2 - 4

root = bisection_method(f, 0, 3)  # Find root of f(x) in the interval [0, 3]
print(root)  # Expected: 2.0

• Newton-Raphson Method

Use newton_raphson_method for root-finding with an initial guess and the function's derivative:

from pyposolver.maths.root_finding import newton_raphson_method

def f(x):
    return x**3 - 2*x - 5

def df(x):
    return 3*x**2 - 2

root = newton_raphson_method(f, df, 2)  # Initial guess: 2
print(root)  # Expected: 2.094...

Linear Algebra

• Dot Product

Calculate the dot product of two vectors:

from pyposolver.maths.linear_algebra import dot_product

vector1 = [1, 2, 3]
vector2 = [4, 5, 6]

result = dot_product(vector1, vector2)
print(result)  # Expected: 32

• Cross Product

Compute the cross product of two 3D vectors:

from pyposolver.maths.linear_algebra import cross_product

vector1 = [1, 2, 3]
vector2 = [4, 5, 6]

result = cross_product(vector1, vector2)
print(result)  # Expected: [-3, 6, -3]

• Matrix Multiplication

Multiply two matrices:

from pyposolver.maths.linear_algebra import matrix_multiply

matrix1 = [[1, 2], [3, 4]]
matrix2 = [[5, 6], [7, 8]]

result = matrix_multiply(matrix1, matrix2)
print(result)  # Expected: [[19, 22], [43, 50]]

Physics

• Velocity

Calculate velocity given initial velocity, acceleration, and time:

from pyposolver.physics.mechanics import velocity

initial_velocity = 5
acceleration = 2
time = 3

result = velocity(initial_velocity, acceleration, time)
print(result)  # Expected: 11

• Force

Calculate force using mass and acceleration:

from pyposolver.physics.mechanics import force

mass = 10
acceleration = 5

result = force(mass, acceleration)
print(result)  # Expected: 50