feat(math): Upgrade Derivative Calculator to Complete Calculus Engine

Author: Kunwartejpal Sidhu

math/Complete-Calculus-Engine/Complete-Calculus-Engine.py

@@ -0,0 +1,252 @@
+import re
+import math
+
+def parse_polynomial(raw):
+    clean_str = raw.replace(" ", "")
+    if not clean_str:
+        return None
+    
+    term_pattern = r'([+-]?\d*\.?\d*\*?x(?:\^[+-]?\d+)?|[+-]?\d+\.?\d*)'
+    matches = re.findall(term_pattern, clean_str)
+    
+    if not matches:
+        return None
+        
+    terms_map = {}
+    for term in matches:
+        if not term or term in ('+', '-'):
+            continue
+            
+        coeff = 1.0
+        power = 0
+        
+        if 'x' in term:
+            parts = term.split('x')
+            coeff_str = parts[0].replace('*', '')
+            if coeff_str == '+' or coeff_str == '':
+                coeff = 1.0
+            elif coeff_str == '-':
+                coeff = -1.0
+            else:
+                try:
+                    coeff = float(coeff_str)
+                except ValueError:
+                    return None
+                
+            if len(parts) > 1 and parts[1].startswith('^'):
+                try:
+                    power = int(parts[1][1:])
+                except ValueError:
+                    return None
+            else:
+                power = 1
+        else:
+            try:
+                coeff = float(term)
+            except ValueError:
+                return None
+            power = 0
+            
+        if power not in terms_map:
+            terms_map[power] = 0.0
+        terms_map[power] += coeff
+        
+    result = []
+    for p in sorted(terms_map.keys(), reverse=True):
+        c = terms_map[p]
+        if abs(c) > 1e-12:
+            result.append({"coeff": c, "power": p, "is_ln": False})
+            
+    if not result:
+        result.append({"coeff": 0.0, "power": 0, "is_ln": False})
+        
+    return result
+
+def poly_to_string(terms, is_integral=False):
+    if not terms:
+        return "C" if is_integral else "0"
+        
+    parts = []
+    for i, term in enumerate(terms):
+        c = term['coeff']
+        p = term['power']
+        is_ln = term['is_ln']
+        
+        if abs(c) < 1e-12:
+            continue
+            
+        sign = "+" if c >= 0 else "-"
+        abs_c = abs(c)
+        c_str = str(int(round(abs_c))) if abs(abs_c - round(abs_c)) < 1e-9 else f"{abs_c:.6f}".rstrip("0").rstrip(".")
+        
+        if is_ln:
+            body = "ln|x|" if abs(abs_c - 1.0) < 1e-12 else f"{c_str}ln|x|"
+        else:
+            if p == 0:
+                body = c_str
+            elif p == 1:
+                body = "x" if abs(abs_c - 1.0) < 1e-12 else f"{c_str}x"
+            else:
+                body = f"x^{p}" if abs(abs_c - 1.0) < 1e-12 else f"{c_str}x^{p}"
+                
+        if len(parts) == 0:
+            parts.append(body if sign == "+" else f"-{body}")
+        else:
+            parts.append(f"{sign} {body}")
+            
+    res = " ".join(parts)
+    if not res:
+        res = "0"
+        
+    if is_integral:
+        if res == "0":
+            res = "C"
+        else:
+            res += " + C"
+    return res
+
+def derivative(terms):
+    res = []
+    for t in terms:
+        c = t['coeff']
+        p = t['power']
+        if p != 0:
+            res.append({"coeff": c * p, "power": p - 1, "is_ln": False})
+    if not res:
+        res.append({"coeff": 0.0, "power": 0, "is_ln": False})
+    return res
+
+def integral(terms):
+    res = []
+    for t in terms:
+        c = t['coeff']
+        p = t['power']
+        if p == -1:
+            res.append({"coeff": c, "power": 0, "is_ln": True})
+        else:
+            res.append({"coeff": c / (p + 1), "power": p + 1, "is_ln": False})
+    if not res:
+        res.append({"coeff": 0.0, "power": 0, "is_ln": False})
+    
+    # Sort for consistent display (ln at the end or powers sorted)
+    res.sort(key=lambda x: (x['is_ln'], -x['power']))
+    return res
+
+def evaluate(terms, x):
+    val = 0.0
+    for t in terms:
+        c = t['coeff']
+        p = t['power']
+        is_ln = t['is_ln']
+        if is_ln:
+            if x == 0:
+                raise ValueError("Cannot evaluate ln|0|")
+            val += c * math.log(abs(x))
+        else:
+            if x == 0 and p < 0:
+                raise ValueError("Division by zero in negative exponent")
+            val += c * math.pow(x, p)
+    return val
+
+def main():
+    print("=" * 58)
+    print("📈 COMPLETE CALCULUS ENGINE 📈")
+    print("=" * 58)
+
+    while True:
+        print("\nChoose an option:")
+        print("1️⃣  Find 1st derivative")
+        print("2️⃣  Find nth derivative")
+        print("3️⃣  Evaluate derivative at x")
+        print("4️⃣  Find indefinite integral")
+        print("5️⃣  Evaluate definite integral")
+        print("6️⃣  Exit")
+
+        choice = input("🎯 Enter your choice (1-6): ").strip()
+
+        if choice == "6":
+            print("\n👋 Thanks for using Complete Calculus Engine! Goodbye! ✨\n")
+            break
+
+        if choice not in {"1", "2", "3", "4", "5"}:
+            print("❌ Please choose between 1 and 6.")
+            continue
+
+        raw = input("\n📝 Enter equation (e.g. 3x^2 - x^-1 + 5): ").strip()
+        if not raw:
+            print("❌ Error: Input cannot be empty.")
+            continue
+
+        terms = parse_polynomial(raw)
+        if terms is None:
+            print("❌ Error: Could not parse equation. Check your formatting.")
+            continue
+            
+        print(f"\n✨ Equation: {poly_to_string(terms)}")
+
+        if choice == "1":
+            derived = derivative(terms)
+            print(f"✅ First derivative: {poly_to_string(derived)}")
+
+        elif choice == "2":
+            try:
+                n_order = int(input("🎯 Enter derivative order n (>= 1): ").strip())
+                if n_order < 1:
+                    raise ValueError
+            except ValueError:
+                print("❌ n must be an integer >= 1.")
+                continue
+
+            derived = terms
+            for _ in range(n_order):
+                derived = derivative(derived)
+            print(f"✅ {n_order}th derivative: {poly_to_string(derived)}")
+
+        elif choice == "3":
+            try:
+                x_val = float(input("🎯 Enter x value: ").strip())
+                order = int(input("🎯 Derivative order to evaluate (>= 1): ").strip())
+                if order < 1:
+                    raise ValueError
+            except ValueError:
+                print("❌ Enter valid numeric x and integer order >= 1.")
+                continue
+
+            derived = terms
+            for _ in range(order):
+                derived = derivative(derived)
+                
+            try:
+                val_eval = evaluate(derived, x_val)
+                x_str = str(int(round(x_val))) if abs(x_val - round(x_val)) < 1e-9 else f"{x_val:.6f}".rstrip("0").rstrip(".")
+                val_eval_str = str(int(round(val_eval))) if abs(val_eval - round(val_eval)) < 1e-9 else f"{val_eval:.6f}".rstrip("0").rstrip(".")
+                print(f"🔍 Derivative used: {poly_to_string(derived)}")
+                print(f"✅ Value at x = {x_str}: {val_eval_str}")
+            except ValueError as e:
+                print(f"❌ Error during evaluation: {e}")
+
+        elif choice == "4":
+            integral_terms = integral(terms)
+            print(f"✅ Indefinite integral: {poly_to_string(integral_terms, is_integral=True)}")
+
+        elif choice == "5":
+            try:
+                lower = float(input("🎯 Enter lower bound: ").strip())
+                upper = float(input("🎯 Enter upper bound: ").strip())
+            except ValueError:
+                print("❌ Enter valid numeric bounds.")
+                continue
+
+            integral_terms = integral(terms)
+            try:
+                val_upper = evaluate(integral_terms, upper)
+                val_lower = evaluate(integral_terms, lower)
+                result = val_upper - val_lower
+                result_str = str(int(round(result))) if abs(result - round(result)) < 1e-9 else f"{result:.6f}".rstrip("0").rstrip(".")
+                print(f"🔍 Integral used: {poly_to_string(integral_terms)}")
+                print(f"✅ Definite integral from {lower} to {upper}: {result_str}")
+            except ValueError as e:
+                print(f"❌ Error during evaluation: {e}")
+
+if __name__ == "__main__":
+    main()