diff --git a/quaternions/__init__.py b/quaternions/__init__.py
index fd54ad8..af65e04 100644
--- a/quaternions/__init__.py
+++ b/quaternions/__init__.py
@@ -1,3 +1,6 @@
 from quaternions.quaternion import Quaternion  # NOQA
 from quaternions.general_quaternion import GeneralQuaternion, QuaternionError  # NOQA
 from quaternions.version import __version__  # NOQA
+
+import warnings
+warnings.simplefilter('once')
diff --git a/quaternions/quaternion.py b/quaternions/quaternion.py
index 5636f22..4f3fc58 100644
--- a/quaternions/quaternion.py
+++ b/quaternions/quaternion.py
@@ -8,6 +8,8 @@
     GeneralQuaternion, QuaternionError, DEFAULT_TOLERANCE, exp
 )
 
+import warnings
+
 
 class Quaternion(GeneralQuaternion):
     ''' A class that holds unit quaternions (norm==1, aka versors). It actually holds Q^op, as
@@ -119,6 +121,7 @@ def average(cls, *quaternions, weights=None):
 
     @property
     def basis(self):
+        warnings.warn('This property will be deprecated. Use matrix instead', DeprecationWarning)
         m = self.matrix
         return m[0, :], m[1, :], m[2, :]
 
@@ -156,6 +159,7 @@ def astrometry_ra_dec_roll(self):
         Notice that Tetra gives a different roll angle, so this is not
         a fixed standard.
         '''
+        warnings.warn('This method will be deprecated', DeprecationWarning)
         twisted = self.OpticalAxisFirst() * self
         ra, dec, roll = twisted.ra_dec_roll
         return np.array([-ra, dec, roll - 180])
diff --git a/tests/test_general_quaternion.py b/tests/test_general_quaternion.py
index ccbbae5..0939ca0 100644
--- a/tests/test_general_quaternion.py
+++ b/tests/test_general_quaternion.py
@@ -121,3 +121,7 @@ def test_log_identical_both_ways(self, arr):
         assume(np.linalg.norm(arr) > DEFAULT_TOLERANCE)
         q = GeneralQuaternion(*arr)
         assert log(q) == q.log()
+
+    def test_repr(self):
+        gen_quat = GeneralQuaternion(1, 2, 3, 4)
+        assert repr(gen_quat) == 'GeneralQuaternion(1, 2, 3, 4)'
diff --git a/tests/test_quaternion.py b/tests/test_quaternion.py
index bda2be8..9fd1f17 100644
--- a/tests/test_quaternion.py
+++ b/tests/test_quaternion.py
@@ -161,11 +161,29 @@ def test_ra_dec_roll(self, arr):
     def test_qmethod(self):
         v1, v2 = [2 / 3, 2 / 3, 1 / 3], [2 / 3, -1 / 3, -2 / 3]
         w1, w2 = [0.8, 0.6, 0], [-0.6, 0.8, 0]
-        q = Quaternion.from_qmethod(np.array([v1, v2]).T, np.array([w1, w2]).T, np.ones(2))
+        q = Quaternion.from_qmethod(np.array([v1, v2]).T, np.array([w1, w2]).T)
 
         np.testing.assert_allclose(q(v1), w1, atol=1e-10)
         np.testing.assert_allclose(q(v2), w2, atol=1e-10)
 
+    def test_weights_change_in_qmethod(self):
+        v1, v2 = [1, 0, 0], [0, 1, 0]
+        w1, w2 = [1, 0, 0], [-1/2, np.sqrt(3) / 2, 0]
+
+        previous_cos_1 = np.inf
+        previous_cos_2 = -np.inf
+        for second_weight in np.linspace(0.1, 2, 10):
+            q = Quaternion.from_qmethod(np.array([v1, v2]).T, np.array([w1, w2]).T, [1, second_weight])
+            current_cos_1 = q(v1).dot(w1)
+            current_cos_2 = q(v2).dot(w2)
+
+            # since first weight is constant and second weight increases, correlation with
+            # first vector should go down and correlation with second vector should go up
+            assert current_cos_1 < previous_cos_1
+            assert current_cos_2 > previous_cos_2
+
+            previous_cos_1, previous_cos_2 = current_cos_1, current_cos_2
+
     @given(ANY_ROTATION_VECTOR)
     def test_from_qmethod_with_noise(self, r):
         assume(np.linalg.norm(r) > Quaternion.tolerance)
@@ -253,6 +271,19 @@ def test_apply_wrong_type(self):
         with pytest.raises(QuaternionError):
             q({1, 2, 3})
 
+    def test_repr(self):
+        unit_quat = Quaternion(1, 2, 3, 4)
+        assert repr(unit_quat).startswith('Quaternion(')
+        assert eval(repr(unit_quat)) == unit_quat
+
+    @given(strategies.integers(min_value=1, max_value=5))
+    def test_integrate(self, number_of_vectors):
+        vectors = [np.array([0, 0, i / 10]) for i in range(1, number_of_vectors + 1)]
+        v = Quaternion.integrate_from_velocity_vectors(vectors)
+        expected = [0, 0, number_of_vectors * (number_of_vectors + 1) / 20]
+        np.testing.assert_allclose(expected, v)
+
+
 class QuaternionStdDevTests(unittest.TestCase):
     # tolerance is this big because average_and_std_naive gives slightly different results than matlab implementation
     # this may be due to the way weights are taken into account, as in matlab implementation weights were not being used