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import numpy as np
import pandas as pd
from scipy.optimize import linprog
from statsmodels.tsa.arima.model import ARIMA
import matplotlib.pyplot as plt
def run_math_analysis(topic: str):
if topic == "linear_algebra":
linear_algebra_demo()
elif topic == "probability":
probability_demo()
elif topic == "optimization":
optimization_demo()
elif topic == "game_theory":
game_theory_demo()
elif topic == "time_series":
time_series_demo()
elif topic == "markov":
markov_process_demo()
else:
print("❌ Unknown topic. Available: linear_algebra, probability, optimization, game_theory, time_series, markov")
def linear_algebra_demo():
print("📐 Linear Algebra: Matrix-Vector Multiplication")
A = np.array([[1, 2], [3, 4]])
B = np.array([[2], [1]])
result = np.dot(A, B)
print("Matrix A:\n", A)
print("Vector B:\n", B)
print("A · B:\n", result)
def probability_demo():
print("📊 Probability & Bayesian Inference Example")
prior = 0.3
likelihood = 0.8
evidence = 0.6
posterior = (likelihood * prior) / evidence
print(f"Bayesian Posterior = P(H|E) = {posterior:.2f}")
def optimization_demo():
print("🔧 Optimization: Linear Programming (Maximize 3x + 5y)")
c = [-3, -5] # Maximize 3x + 5y → minimize -3x -5y
A = [[1, 0], [0, 2], [3, 2]]
b = [4, 12, 18]
result = linprog(c, A_ub=A, b_ub=b)
if result.success:
print("Optimal values of x and y:", result.x)
print("Maximum value of objective function:", -result.fun)
else:
print("❌ Optimization failed:", result.message)
def game_theory_demo():
print("🎲 Game Theory: Payoff Matrix")
matrix = np.array([[3, 0], [5, 1]])
print("Player A vs Player B Payoff Matrix:")
print(matrix)
print("Interpret rows as Player A strategies and columns as Player B.")
def time_series_demo():
print("📈 Time Series: ARIMA(1,1,1) Forecast")
np.random.seed(42)
series = pd.Series(np.random.randn(100).cumsum())
model = ARIMA(series, order=(1, 1, 1))
fit = model.fit()
forecast = fit.forecast(steps=10)
print("Forecasted next 10 values:")
print(forecast)
series.plot(label="Historical")
forecast.plot(label="Forecast", legend=True)
plt.title("Time Series Forecast (ARIMA)")
plt.xlabel("Time")
plt.ylabel("Value")
plt.grid(True)
plt.show()
def markov_process_demo():
print("🔁 Markov Chain Simulation: Sunny vs Rainy")
transition_matrix = np.array([[0.9, 0.1], [0.5, 0.5]]) # [Sunny, Rainy]
state = np.array([1, 0]) # Start in Sunny
for day in range(5):
state = np.dot(state, transition_matrix)
print(f"Day {day + 1}: P(Sunny) = {state[0]:.2f}, P(Rainy) = {state[1]:.2f}")
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