diff --git a/hipparchus-core/src/changes/changes.xml b/hipparchus-core/src/changes/changes.xml
index 46b583f76..8869ec88c 100644
--- a/hipparchus-core/src/changes/changes.xml
+++ b/hipparchus-core/src/changes/changes.xml
@@ -799,6 +799,9 @@ If the output is not quite correct, check for invisible trailing spaces!
       <action dev="psteitz" type="update">
         Forked from the Apache Commons Math library.
       </action>
+      <action dev="sean-g-rae" type="update">
+        Added some basic edge case unit tests.
+      </action>
     </release>
   </body>
 </document>
diff --git a/hipparchus-core/src/main/java/org/hipparchus/analysis/differentiation/TaylorMap.java b/hipparchus-core/src/main/java/org/hipparchus/analysis/differentiation/TaylorMap.java
index 67d6d7af9..da85686ed 100644
--- a/hipparchus-core/src/main/java/org/hipparchus/analysis/differentiation/TaylorMap.java
+++ b/hipparchus-core/src/main/java/org/hipparchus/analysis/differentiation/TaylorMap.java
@@ -41,7 +41,7 @@ public class TaylorMap implements DifferentialAlgebra {
 
     /** Simple constructor.
      * <p>
-     * The number of number of parameters and derivation orders of all
+     * The number of parameters and derivation orders of all
      * functions must match.
      * </p>
      * @param point point at which map is evaluated
diff --git a/hipparchus-core/src/test/java/org/hipparchus/analysis/FunctionUtilsTest.java b/hipparchus-core/src/test/java/org/hipparchus/analysis/FunctionUtilsTest.java
index b8e82ff19..d554d2ed9 100644
--- a/hipparchus-core/src/test/java/org/hipparchus/analysis/FunctionUtilsTest.java
+++ b/hipparchus-core/src/test/java/org/hipparchus/analysis/FunctionUtilsTest.java
@@ -118,6 +118,13 @@ void testAdd() {
         assertEquals(4 - 2, FunctionUtils.add(c, FunctionUtils.compose(m, id)).value(2), EPS);
     }
 
+    @Test
+    void testAddEmpty() {
+        assertThrows(ArrayIndexOutOfBoundsException.class, () -> {
+            FunctionUtils.add(new UnivariateFunction[0]).value(1.0);
+        });
+    }
+
     @Test
     void testAddDifferentiable() {
         UnivariateDifferentiableFunction sin = new Sin();
@@ -133,6 +140,13 @@ void testAddDifferentiable() {
         assertEquals(4 + FastMath.sin(1.2), FunctionUtils.add(sin, c).value(1.2), EPS);
     }
 
+    @Test
+    void testAddDifferentiableEmpty() {
+        assertThrows(ArrayIndexOutOfBoundsException.class, () -> {
+            FunctionUtils.add(new UnivariateDifferentiableFunction[0]).value(1.0);
+        });
+    }
+
     @Test
     void testMultiply() {
         UnivariateFunction c = new Constant(4);
@@ -143,6 +157,13 @@ void testMultiply() {
         assertEquals(1, FunctionUtils.multiply(FunctionUtils.compose(inv, pow), pow).value(3.5), EPS);
     }
 
+    @Test
+    void testMultiplyEmpty() {
+        assertThrows(ArrayIndexOutOfBoundsException.class, () -> {
+            FunctionUtils.multiply(new UnivariateFunction[0]).value(1.0);
+        });
+    }
+
     @Test
     void testMultiplyDifferentiable() {
         UnivariateDifferentiableFunction c = new Constant(4);
@@ -196,6 +217,14 @@ void testCollector() {
         assertEquals(-24, coll.value(new double[] {1, -2, 7.5, 10, -24, 9.99}), 0);
     }
 
+    @Test
+    void testCollectorEmpty() {
+        MultivariateFunction coll = FunctionUtils.collector(new Add(), 0);
+        assertThrows(ArrayIndexOutOfBoundsException.class, () -> {
+            coll.value(new double[0]);
+        });
+    }
+
     @Test
     void testSinc() {
         BivariateFunction div = new Divide();
@@ -278,6 +307,13 @@ void testToDifferentiableUnivariate() {
             assertEquals(2, ((Integer) e.getParts()[1]).intValue());
             assertEquals(3, ((Integer) e.getParts()[0]).intValue());
         }
+
+        try {
+            FunctionUtils.compose((UnivariateFunction) null).value(1.0);
+            fail("an exception should have been thrown");
+        } catch (NullPointerException e) {
+            // expected
+        }
     }
 
     @Test
@@ -340,6 +376,14 @@ void testToDifferentiableMultivariateInconsistentGradient() {
             assertEquals(3, ((Integer) e.getParts()[0]).intValue());
             assertEquals(2, ((Integer) e.getParts()[1]).intValue());
         }
+
+        try {
+            MultivariateFunction df = FunctionUtils.derivative(mdf, new int[] { 1 });
+            df.value(new double[] { 1.0, 2.0 });
+            fail("an exception should have been thrown");
+        } catch (MathIllegalArgumentException e) {
+            // expected dimension mismatch
+        }
     }
 
     @Test
diff --git a/hipparchus-core/src/test/java/org/hipparchus/analysis/polynomials/PolynomialsUtilsTest.java b/hipparchus-core/src/test/java/org/hipparchus/analysis/polynomials/PolynomialsUtilsTest.java
index 3fef40bd6..11c2e6a83 100644
--- a/hipparchus-core/src/test/java/org/hipparchus/analysis/polynomials/PolynomialsUtilsTest.java
+++ b/hipparchus-core/src/test/java/org/hipparchus/analysis/polynomials/PolynomialsUtilsTest.java
@@ -26,11 +26,13 @@
 import org.hipparchus.util.CombinatoricsUtils;
 import org.hipparchus.util.FastMath;
 import org.hipparchus.util.Precision;
+import org.junit.jupiter.api.Assertions;
 import org.junit.jupiter.api.Test;
 
 import static org.junit.jupiter.api.Assertions.assertEquals;
 import static org.junit.jupiter.api.Assertions.assertNotEquals;
 import static org.junit.jupiter.api.Assertions.assertTrue;
+import static org.junit.jupiter.api.Assertions.fail;
 
 /**
  * Tests the PolynomialsUtils class.
@@ -265,6 +267,16 @@ void testHighDegreeLegendre() {
         }
     }
 
+    @Test
+    void testNegativeDegree() {
+        try {
+            PolynomialsUtils.createChebyshevPolynomial(-1);
+            fail("Expected MathIllegalArgumentException");
+        } catch (org.hipparchus.exception.MathIllegalArgumentException e) {
+            // expected
+        }
+    }
+
     @Test
     void testJacobiLegendre() {
         for (int i = 0; i < 10; ++i) {
@@ -348,6 +360,26 @@ void testShift() {
         PolynomialFunction f2x3
             = new PolynomialFunction(PolynomialsUtils.shift(f2x.getCoefficients(), 3));
         checkPolynomial(f2x3, "29648 + 49239 x + 32745 x^2 + 10898 x^3 + 1815 x^4 + 121 x^5");
+
+        // Zero shift
+        double[] coeffs = { 1.0, 2.0, 3.0 };
+        Assertions.assertArrayEquals(coeffs, PolynomialsUtils.shift(coeffs, 0), 1e-15);
+
+        // Empty coeffs
+        double[] empty = new double[0];
+        Assertions.assertArrayEquals(empty, PolynomialsUtils.shift(empty, 1.0), 1e-15);
+
+        // Single coeff
+        double[] single = { 5.0 };
+        Assertions.assertArrayEquals(single, PolynomialsUtils.shift(single, 10.0), 1e-15);
+
+        // Null coeffs
+        try {
+            PolynomialsUtils.shift(null, 1.0);
+            fail("Expected NullPointerException");
+        } catch (NullPointerException e) {
+            // expected
+        }
     }
 
 
diff --git a/hipparchus-core/src/test/java/org/hipparchus/complex/QuaternionTest.java b/hipparchus-core/src/test/java/org/hipparchus/complex/QuaternionTest.java
index 97e909b1c..d5de93602 100644
--- a/hipparchus-core/src/test/java/org/hipparchus/complex/QuaternionTest.java
+++ b/hipparchus-core/src/test/java/org/hipparchus/complex/QuaternionTest.java
@@ -407,4 +407,64 @@ final void testToString() {
         final Quaternion q = new Quaternion(1, 2, 3, 4);
         assertEquals("[1.0 2.0 3.0 4.0]", q.toString());
     }
+
+    @Test
+    final void testGetPositivePolarForm() {
+        final Quaternion q = new Quaternion(-3, 1, -2, 1);
+        final Quaternion p = q.getPositivePolarForm();
+        assertTrue(p.getQ0() > 0);
+        assertEquals(1.0, p.getNorm(), EPS);
+
+        final Quaternion q2 = new Quaternion(3, 1, -2, 1);
+        final Quaternion p2 = q2.getPositivePolarForm();
+        assertTrue(p2.getQ0() > 0);
+        assertEquals(1.0, p2.getNorm(), EPS);
+
+        final Quaternion q3 = new Quaternion(0, 1, -2, 1);
+        final Quaternion p3 = q3.getPositivePolarForm();
+        assertEquals(0, p3.getQ0(), EPS);
+        assertEquals(1.0, p3.getNorm(), EPS);
+    }
+
+    @Test
+    final void testHashCode() {
+        final Quaternion q1 = new Quaternion(1, 2, 3, 4);
+        final Quaternion q2 = new Quaternion(1, 2, 3, 4);
+        assertEquals(q1.hashCode(), q2.hashCode());
+
+        final Quaternion q3 = new Quaternion(1, 2, 3, 5);
+        assertNotEquals(q1.hashCode(), q3.hashCode());
+    }
+
+    @Test
+    final void testObjectEqualsMore() {
+        final Quaternion q1 = new Quaternion(1, 2, 3, 4);
+        assertEquals(q1, q1);
+        assertNotEquals(null, q1);
+        assertNotEquals(q1, "not a quaternion");
+        final Quaternion q2 = new Quaternion(1, 2, 3, 4);
+        assertEquals(q1, q2);
+    }
+
+    @Test
+    final void testInstanceMethods() {
+        final Quaternion q1 = new Quaternion(1, 2, 3, 4);
+        final Quaternion q2 = new Quaternion(5, 6, 7, 8);
+
+        // multiply(Quaternion)
+        final Quaternion qM = q1.multiply(q2);
+        assertEquals(Quaternion.multiply(q1, q2), qM);
+
+        // add(Quaternion)
+        final Quaternion qA = q1.add(q2);
+        assertEquals(Quaternion.add(q1, q2), qA);
+
+        // subtract(Quaternion)
+        final Quaternion qS = q1.subtract(q2);
+        assertEquals(Quaternion.subtract(q1, q2), qS);
+
+        // dotProduct(Quaternion)
+        final double d = q1.dotProduct(q2);
+        assertEquals(Quaternion.dotProduct(q1, q2), d, EPS);
+    }
 }