Update tools/math_tools.py

tools/math_tools.py

@@ -20,41 +20,43 @@ def run_math_analysis(topic: str):
     elif topic == "markov":
         markov_process_demo()
     else:
-        print("❌ Unknown topic. Available topics are:")
-        print("linear_algebra, probability, optimization, game_theory, time_series, markov")
+        print("❌ Unknown topic. Available: linear_algebra, probability, optimization, game_theory, time_series, markov")
 
 def linear_algebra_demo():
-    print("📐 Linear Algebra: Matrix-vector multiplication (embeddings, transformations)")
+    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)
+    print("Matrix A:\n", A)
+    print("Vector B:\n", B)
+    print("A · B:\n", result)
 
 def probability_demo():
-    print("📊 Probability & Bayesian Inference")
+    print("📊 Probability & Bayesian Inference Example")
     prior = 0.3
     likelihood = 0.8
     evidence = 0.6
     posterior = (likelihood * prior) / evidence
-    print(f"P(H|E) = (P(E|H) * P(H)) / P(E) = {posterior:.2f}")
+    print(f"Bayesian Posterior = P(H|E) = {posterior:.2f}")
 
 def optimization_demo():
-    print("🔧 Optimization: Linear Programming Example")
-    c = [-3, -5]  # Maximize 3x + 5y
+    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)
-    print("Optimal solution (x, y):", result.x)
-    print("Maximized objective value:", -result.fun)
+    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: Simple 2x2 Payoff Matrix")
-    payoff_matrix = np.array([[3, 0], [5, 1]])
-    print("Payoff Matrix (A vs B):")
-    print(payoff_matrix)
-    print("Interpretation: Rows = Player A strategies, Columns = Player B")
+    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")
@@ -63,17 +65,21 @@ def time_series_demo():
     model = ARIMA(series, order=(1, 1, 1))
     fit = model.fit()
     forecast = fit.forecast(steps=10)
-    print("Forecast for next 10 steps:")
+    print("Forecasted next 10 values:")
     print(forecast)
+
     series.plot(label="Historical")
     forecast.plot(label="Forecast", legend=True)
-    plt.title("ARIMA Forecast")
+    plt.title("Time Series Forecast (ARIMA)")
+    plt.xlabel("Time")
+    plt.ylabel("Value")
+    plt.grid(True)
     plt.show()
 
 def markov_process_demo():
-    print("🔁 Markov Model: Weather Simulation (Sunny/Rainy)")
-    transition_matrix = np.array([[0.9, 0.1], [0.5, 0.5]])
-    state = np.array([1, 0])  # Start with Sunny
+    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}")
+        print(f"Day {day + 1}: P(Sunny) = {state[0]:.2f}, P(Rainy) = {state[1]:.2f}")