CONTRIBUTORS.md

@@ -1,10 +0,0 @@
-## Contributors
-
-<!-- ALL-CONTRIBUTORS-LIST:START - Do not remove or modify this section -->
-<!-- prettier-ignore-start -->
-<!-- markdownlint-disable -->
-[![All Contributors](https://img.shields.io/github/all-contributors/jono-rams/PolySolve?color=ee8449&style=flat-square)](#contributors)
-<!-- markdownlint-restore -->
-<!-- prettier-ignore-end -->
-
-<!-- ALL-CONTRIBUTORS-LIST:END -->

README.md

@@ -56,17 +56,22 @@ print(f"Value of f1 at x=5 is: {y_val}")
 # > Value of f1 at x=5 is: 30.0
 
 # 3. Get the derivative: 4x - 3
-df1 = f1.differential()
+df1 = f1.derivative()
 print(f"Derivative of f1: {df1}")
 # > Derivative of f1: 4x - 3
 
-# 4. Find roots analytically using the quadratic formula
+# 4. Get the 2nd derivative: 4
+df1 = f1.nth_derivative(2)
+print(f"2nd Derivative of f1: {df1}")
+# > Derivative of f1: 4
+
+# 5. Find roots analytically using the quadratic formula
 #    This is exact and fast for degree-2 polynomials.
 roots_analytic = quadratic_solve(f1)
 print(f"Analytic roots: {sorted(roots_analytic)}")
 # > Analytic roots: [-1.0, 2.5]
 
-# 5. Find roots with the genetic algorithm (CPU)
+# 6. Find roots with the genetic algorithm (CPU)
 #    This can solve polynomials of any degree.
 ga_opts = GA_Options(num_of_generations=20)
 roots_ga = f1.get_real_roots(ga_opts, use_cuda=False)

pyproject.toml

@@ -5,7 +5,7 @@ build-backend = "setuptools.build_meta"
 [project]
 # --- Core Metadata ---
 name = "polysolve"
-version = "0.1.1"
+version = "0.2.0"
 authors = [
   { name="Jonathan Rampersad", email="jonathan@jono-rams.work" },
 ]

src/polysolve/__init__.py

@@ -1,7 +1,7 @@
 import math
 import numpy as np
 from dataclasses import dataclass
-from typing import List, Optional
+from typing import List, Optional, Union
 import warnings
 
 # Attempt to import CuPy for CUDA acceleration.
@@ -109,6 +109,11 @@ class Function:
         """Returns the largest exponent of the function."""
         return self._largest_exponent
     
+    @property
+    def degree(self) -> int:
+        """Returns the largest exponent of the function."""
+        return self._largest_exponent
+
     def solve_y(self, x_val: float) -> float:
         """
         Solves for y given an x value. (i.e., evaluates the polynomial at x).
@@ -126,6 +131,26 @@ class Function:
         """
         Calculates the derivative of the function.
 
+        Returns:
+            Function: A new Function object representing the derivative.
+        """
+        warnings.warn(
+            "The 'differential' function has been renamed. Please use 'derivative' instead.",
+            DeprecationWarning,
+            stacklevel=2
+        )
+
+        self._check_initialized()
+        if self._largest_exponent == 0:
+            raise ValueError("Cannot differentiate a constant (Function of degree 0).")
+
+        return self.derivitive()
+        
+    
+    def derivative(self) -> 'Function':
+        """
+        Calculates the derivative of the function.
+
         Returns:
             Function: A new Function object representing the derivative.
         """
@@ -139,6 +164,37 @@ class Function:
         diff_func.set_coeffs(derivative_coefficients.tolist())
         return diff_func
     
+
+    def nth_derivative(self, n: int) -> 'Function':
+        """
+        Calculates the nth derivative of the function.
+
+        Args:
+            n (int): The order of the derivative to calculate.
+
+        Returns:
+           Function: A new Function object representing the nth derivative.
+        """
+        self._check_initialized()
+        
+        if not isinstance(n, int) or n < 1:
+            raise ValueError("Derivative order 'n' must be a positive integer.")
+
+        if n > self.largest_exponent:
+            function = Function(0)
+            function.set_coeffs([0])
+            return function
+
+        if n == 1:
+            return self.derivative()
+        
+        function = self
+        for _ in range(n):
+            function = function.derivative()
+
+        return function
+
+
     def get_real_roots(self, options: GA_Options = GA_Options(), use_cuda: bool = False) -> np.ndarray:
         """
         Uses a genetic algorithm to find the approximate real roots of the function (where y=0).
@@ -337,13 +393,14 @@ class Function:
         result_func.set_coeffs(new_coefficients.tolist())
         return result_func
     
-    def __mul__(self, scalar: int) -> 'Function':
-        """Multiplies the function by a scalar constant."""
-        self._check_initialized()
-        if not isinstance(scalar, (int, float)):
-            return NotImplemented
+    def _multiply_by_scalar(self, scalar: Union[int, float]) -> 'Function':
+        """Helper method to multiply the function by a scalar constant."""
+        self._check_initialized() # It's good practice to check here too
+
         if scalar == 0:
-            raise ValueError("Cannot multiply a function by 0.")
+            result_func = Function(0)
+            result_func.set_coeffs([0])
+            return result_func
     
         new_coefficients = self.coefficients * scalar
     
@@ -351,19 +408,39 @@ class Function:
         result_func.set_coeffs(new_coefficients.tolist())
         return result_func
 
-    def __rmul__(self, scalar: int) -> 'Function':
+    def _multiply_by_function(self, other: 'Function') -> 'Function':
+        """Helper method for polynomial multiplication (Function * Function)."""
+        self._check_initialized()
+        other._check_initialized()
+
+        # np.polymul performs convolution of coefficients to multiply polynomials
+        new_coefficients = np.polymul(self.coefficients, other.coefficients)
+    
+        # The degree of the resulting polynomial is derived from the new coefficients
+        new_degree = len(new_coefficients) - 1
+    
+        result_func = Function(new_degree)
+        result_func.set_coeffs(new_coefficients.tolist())
+        return result_func
+        
+    def __mul__(self, other: Union['Function', int, float]) -> 'Function':
+        """Multiplies the function by a scalar constant."""
+        if isinstance(other, (int, float)):
+            return self._multiply_by_scalar(other)
+        elif isinstance(other, self.__class__):
+            return self._multiply_by_function(other)
+        else:
+            return NotImplemented
+
+    def __rmul__(self, scalar: Union[int, float]) -> 'Function':
         """Handles scalar multiplication from the right (e.g., 3 * func)."""
+
         return self.__mul__(scalar)
         
-    def __imul__(self, scalar: int) -> 'Function':
+    def __imul__(self, other: Union['Function', int, float]) -> 'Function':
         """Performs in-place multiplication by a scalar (func *= 3)."""
-        self._check_initialized()
-        if not isinstance(scalar, (int, float)):
-            return NotImplemented
-        if scalar == 0:
-            raise ValueError("Cannot multiply a function by 0.")
 
-        self.coefficients *= scalar
+        self.coefficients *= other
         return self
 
 
@@ -408,9 +485,13 @@ if __name__ == '__main__':
     print(f"Value of f1 at x=5 is: {y}") # Expected: 2*(25) - 3*(5) - 5 = 50 - 15 - 5 = 30
 
     # Find the derivative: 4x - 3
-    df1 = f1.differential()
+    df1 = f1.derivative()
     print(f"Derivative of f1: {df1}")
 
+    # Find the second derivative: 4
+    ddf1 = f1.nth_derivative(2)
+    print(f"Second derivative of f1: {ddf1}")
+
     # --- Root Finding ---
     # 1. Analytical solution for quadratic
     roots_analytic = quadratic_solve(f1)
@@ -449,3 +530,17 @@ if __name__ == '__main__':
     # Multiplication: (x + 10) * 3 = 3x + 30
     f_mul = f2 * 3
     print(f"f2 * 3 = {f_mul}")
+
+    # f3 represents 2x^2 + 3x + 1
+    f3 = Function(2)
+    f3.set_coeffs([2, 3, 1]) 
+    print(f"Function f3: {f3}")
+
+    # f4 represents 5x - 4
+    f4 = Function(1)
+    f4.set_coeffs([5, -4])
+    print(f"Function f4: {f4}")
+
+    # Multiply the two functions
+    product_func = f3 * f4
+    print(f"f3 * f4 = {product_func}")

tests/test_polysolve.py

@@ -24,6 +24,18 @@ def linear_func() -> Function:
     f.set_coeffs([1, 10])
     return f
 
+@pytest.fixture
+def m_func_1() -> Function:
+    f = Function(2)
+    f.set_coeffs([2, 3, 1])
+    return f
+
+@pytest.fixture
+def m_func_2() -> Function:
+    f = Function(1)
+    f.set_coeffs([5, -4])
+    return f
+
 # --- Core Functionality Tests ---
 
 def test_solve_y(quadratic_func):
@@ -32,13 +44,20 @@ def test_solve_y(quadratic_func):
     assert quadratic_func.solve_y(0) == -5.0
     assert quadratic_func.solve_y(-1) == 0.0
 
-def test_differential(quadratic_func):
+def test_derivative(quadratic_func):
     """Tests the calculation of the function's derivative."""
-    derivative = quadratic_func.differential()
+    derivative = quadratic_func.derivative()
     assert derivative.largest_exponent == 1
     # The derivative of 2x^2 - 3x - 5 is 4x - 3
     assert np.array_equal(derivative.coefficients, [4, -3])
 
+def test_nth_derivative(quadratic_func):
+    """Tests the calculation of the function's 2nd derivative."""
+    derivative = quadratic_func.nth_derivative(2)
+    assert derivative.largest_exponent == 0
+    # The derivative of 2x^2 - 3x - 5 is 4x - 3
+    assert np.array_equal(derivative.coefficients, [4])
+
 def test_quadratic_solve(quadratic_func):
     """Tests the analytical quadratic solver for exact roots."""
     roots = quadratic_solve(quadratic_func)
@@ -61,13 +80,20 @@ def test_subtraction(quadratic_func, linear_func):
     assert result.largest_exponent == 2
     assert np.array_equal(result.coefficients, [2, -4, -15])
 
-def test_multiplication(linear_func):
+def test_scalar_multiplication(linear_func):
     """Tests the multiplication of a Function object by a scalar."""
     # (x + 10) * 3 = 3x + 30
     result = linear_func * 3
     assert result.largest_exponent == 1
     assert np.array_equal(result.coefficients, [3, 30])
 
+def test_function_multiplication(m_func_1, m_func_2):
+    """Tests the multiplication of two Function objects."""
+    # (2x^2 + 3x + 1) * (5x -4) = 10x^3 + 7x^2 - 7x -4
+    result = m_func_1 * m_func_2
+    assert result.largest_exponent == 3
+    assert np.array_equal(result.coefficients, [10, 7, -7, -4])
+
 # --- Genetic Algorithm Root-Finding Tests ---
 
 def test_get_real_roots_numpy(quadratic_func):