mathExampleLibrary.py

# Common Math Functions for Algebra & Precalc
# Requires: pip install sympy matplotlib
# Disclaimer use this as a way to check your work or practice
# math. Do NOT use for cheating, homework, etc. Always
# check your work. There is no gurantee these functions are 
# correct, check your work.
import sympy as sp
import matplotlib.pyplot as plt
import numpy as np

# Define a common symbol
x = sp.symbols('x')

# ---------------- Algebra Basics ----------------
def simplify_expr(expr):
    """Simplify an algebraic expression"""
    return sp.simplify(expr)

def expand_expr(expr):
    """Expand an algebraic expression"""
    return sp.expand(expr)

def factor_expr(expr):
    """Factor an algebraic expression"""
    return sp.factor(expr)

def solve_equation(expr, variable=x):
    """Solve equation expr = 0 for variable"""
    return sp.solve(expr, variable)

# ---------------- Precalc Functions ----------------
def derivative(expr, variable=x):
    """Find derivative of expression"""
    return sp.diff(expr, variable)

def integral(expr, variable=x):
    """Find indefinite integral of expression"""
    return sp.integrate(expr, variable)

def definite_integral(expr, a, b, variable=x):
    """Find definite integral from a to b"""
    return sp.integrate(expr, (variable, a, b))

def limit(expr, point, variable=x):
    """Find the limit of an expression as variable -> point"""
    return sp.limit(expr, variable, point)

# ---------------- Graphing ----------------
def plot_function(expr, xmin=-10, xmax=10):
    """Graph a function using matplotlib"""
    f = sp.lambdify(x, expr, 'numpy')
    xs = np.linspace(xmin, xmax, 400)
    ys = f(xs)
    plt.plot(xs, ys, label=str(expr))
    plt.axhline(0, color='black', lw=0.5)
    plt.axvline(0, color='black', lw=0.5)
    plt.legend()
    plt.grid(True)
    plt.show()

# ---------------- Examples ----------------
if __name__ == "__main__":
    expr = x**2 - 5*x + 6
    
    print("Simplify:", simplify_expr((x**2 + 2*x + 1)/(x+1)))
    print("Expand:", expand_expr((x-2)*(x+3)))
    print("Factor:", factor_expr(expr))
    print("Solve:", solve_equation(expr))
    print("Derivative:", derivative(sp.sin(x)))
    print("Integral:", integral(sp.cos(x)))
    print("Definite Integral:", definite_integral(x**2, 0, 3))
    print("Limit:", limit(sp.sin(x)/x, 0))
    
    plot_function(expr)