From 94723dcb88b533bf2b31830187a8ad92489f9d9c Mon Sep 17 00:00:00 2001
From: Jonathan Rampersad <rampersad.jonathan@gmail.com>
Date: Sun, 2 Nov 2025 12:50:48 -0400
Subject: [PATCH] feat(Function): Add __eq__ method and improve quadratic_solve
 stability

Implements two features for the Function class:

1.  Adds the `__eq__` operator (`==`) to allow for logical comparison of two Function objects based on their coefficients.
2.  Replaces the standard quadratic formula with a numerically stable version in `quadratic_solve` to prevent "catastrophic cancellation" errors and improve accuracy.
---
 pyproject.toml            |  2 +-
 src/polysolve/__init__.py | 45 +++++++++++++++++++++++++++++++++++++--
 tests/test_polysolve.py   | 32 ++++++++++++++++++++++++++++
 3 files changed, 76 insertions(+), 3 deletions(-)

diff --git a/pyproject.toml b/pyproject.toml
index cfed628..7797a57 100644
--- a/pyproject.toml
+++ b/pyproject.toml
@@ -5,7 +5,7 @@ build-backend = "setuptools.build_meta"
 [project]
 # --- Core Metadata ---
 name = "polysolve"
-version = "0.6.1"
+version = "0.6.2"
 authors = [
   { name="Jonathan Rampersad", email="jonathan@jono-rams.work" },
 ]
diff --git a/src/polysolve/__init__.py b/src/polysolve/__init__.py
index 30f00eb..35f9537 100644
--- a/src/polysolve/__init__.py
+++ b/src/polysolve/__init__.py
@@ -746,6 +746,21 @@ class Function:
             return NotImplemented
         
         return self
+    
+    def __eq__(self, other: object) -> bool:
+        """
+        Checks if two Function objects are equal by comparing
+        their coefficients.
+        """
+        # Check if the 'other' object is even a Function
+        if not isinstance(other, Function):
+            return NotImplemented
+        
+        # Ensure both are initialized before trying to access .coefficients
+        if not self._initialized or not other._initialized:
+            return False
+
+        return np.array_equal(self.coefficients, other.coefficients)
 
 
     def quadratic_solve(self) -> Optional[List[float]]:
@@ -770,9 +785,35 @@ class Function:
             return None  # No real roots
 
         sqrt_discriminant = math.sqrt(discriminant)
-        root1 = (-b + sqrt_discriminant) / (2 * a)
-        root2 = (-b - sqrt_discriminant) / (2 * a)
+        
+        # 1. Calculate the first root.
+        # We use math.copysign(val, sign) to get the sign of b.
+        # This ensures (-b - sign*sqrt) is always an *addition*
+        # (or subtraction of a smaller from a larger number),
+        # avoiding catastrophic cancellation.
+        root1 = (-b - math.copysign(sqrt_discriminant, b)) / (2 * a)
 
+        # 2. Calculate the second root using Vieta's formulas.
+        # We know that root1 * root2 = c / a.
+        # This is just a division, which is numerically stable.
+
+        # Handle the edge case where c=0.
+        # If c=0, then root1 is 0.0, and root2 is -b/a
+        # We can't divide by root1=0, so we check.
+        if root1 == 0.0:
+            # If c is also 0, the other root is -b/a
+            if c == 0.0: 
+                root2 = -b / a
+            else:
+                # This case (root1=0 but c!=0) shouldn't happen
+                # with real numbers, but it's safe to just
+                # return the one root we found.
+                return [0.0] 
+        else:
+            # Standard case: Use Vieta's formula
+            root2 = (c / a) / root1
+
+        # Return roots in a consistent order
         return [root1, root2]
 
 # Example Usage
diff --git a/tests/test_polysolve.py b/tests/test_polysolve.py
index 00bdb37..dcef499 100644
--- a/tests/test_polysolve.py
+++ b/tests/test_polysolve.py
@@ -37,6 +37,12 @@ def m_func_2() -> Function:
     f.set_coeffs([5, -4])
     return f
 
+@pytest.fixture
+def base_func():
+    f = Function(2)
+    f.set_coeffs([1, 2, 3])
+    return f
+
 # --- Core Functionality Tests ---
 
 def test_solve_y(quadratic_func):
@@ -95,6 +101,32 @@ def test_function_multiplication(m_func_1, m_func_2):
     assert result.largest_exponent == 3
     assert np.array_equal(result.coefficients, [10, 7, -7, -4])
 
+def test_equality(base_func):
+    """Tests the __eq__ method for the Function class."""
+    
+    # 1. Test for equality with a new, identical object
+    f_identical = Function(2)
+    f_identical.set_coeffs([1, 2, 3])
+    assert base_func == f_identical
+
+    # 2. Test for inequality (different coefficients)
+    f_different = Function(2)
+    f_different.set_coeffs([1, 9, 3])
+    assert base_func != f_different
+
+    # 3. Test for inequality (different degree)
+    f_diff_degree = Function(1)
+    f_diff_degree.set_coeffs([1, 2])
+    assert base_func != f_diff_degree
+
+    # 4. Test against a different type
+    assert base_func != "some_string"
+    assert base_func != 123
+
+    # 5. Test against an uninitialized Function
+    f_uninitialized = Function(2)
+    assert base_func != f_uninitialized
+
 # --- Genetic Algorithm Root-Finding Tests ---
 
 def test_get_real_roots_numpy(quadratic_func):
-- 
2.49.1