Add semimedium_axis property to sphere and ellipsoid (#192)

Add the `semimedium_axis` and `semimajor_axis_longitude` to the Sphere
and Ellipsoid classes for compatibility with the `TriaxialEllipsoid`.
Don't use mathematical symbols for the `semimedium_axis`. Remove the
"Added for compatibility with pymap3d" comment in some of the
properties.

boule/_ellipsoid.py

@@ -182,6 +182,23 @@ def semiminor_axis(self):
         """
         return self.semimajor_axis * (1 - self.flattening)
 
+    @property
+    def semimedium_axis(self):
+        """
+        The semimedium axis of the ellipsoid is equal to its semimajor axis.
+        Units: :math:`m`.
+        """
+        return self.semimajor_axis
+
+    @property
+    def semimajor_axis_longitude(self):
+        r"""
+        The semimajor axis longitude of the ellipsoid is equal to zero.
+        Definition: :math:`\lambda_a = 0`.
+        Units: :math:`m`.
+        """
+        return 0
+
     @property
     def thirdflattening(self):
         r"""

boule/_sphere.py

@@ -145,28 +145,40 @@ def _check_geocentric_grav_const(self, geocentric_grav_const, value):
     @property
     def semiminor_axis(self):
         """
-        The semiminor axis of the sphere is equal to its radius. Added for
-        compatibility with pymap3d.
-        Definition: :math:`b = R`.
+        The semiminor axis of the sphere is equal to its radius.
+        Units: :math:`m`.
+        """
+        return self.radius
+
+    @property
+    def semimedium_axis(self):
+        """
+        The semimedium axis of the sphere is equal to its radius.
         Units: :math:`m`.
         """
         return self.radius
 
     @property
     def semimajor_axis(self):
         """
-        The semimajor axis of the sphere is equal to its radius. Added for
-        compatibility with pymap3d.
-        Definition: :math:`a = R`.
+        The semimajor axis of the sphere is equal to its radius.
         Units: :math:`m`.
         """
         return self.radius
 
+    @property
+    def semimajor_axis_longitude(self):
+        r"""
+        The semimajor axis longitude of the sphere is equal to zero.
+        Definition: :math:`\lambda_a = 0`.
+        Units: :math:`m`.
+        """
+        return 0
+
     @property
     def flattening(self):
         r"""
-        The flattening of the sphere is equal to zero. Added for compatibility
-        with pymap3d.
+        The flattening of the sphere is equal to zero.
         Definition: :math:`f = \dfrac{a - b}{a}`.
         Units: adimensional.
         """
@@ -175,8 +187,7 @@ def flattening(self):
     @property
     def thirdflattening(self):
         r"""
-        The third flattening of the sphere is equal to zero. Added for
-        compatibility with pymap3d
+        The third flattening of the sphere is equal to zero.
         Definition: :math:`f^{\prime\prime}= \dfrac{a -b}{a + b}`.
         Units: adimensional.
         """
@@ -190,8 +201,7 @@ def eccentricity(self):
     @property
     def first_eccentricity(self):
         r"""
-        The (first) eccentricity of the sphere is equal to zero. Added for
-        compatibility with pymap3d.
+        The (first) eccentricity of the sphere is equal to zero.
         Definition: :math:`e = \dfrac{\sqrt{a^2 - b^2}}{a} = \sqrt{2f - f^2}`.
         Units: adimensional.
         """
@@ -209,8 +219,7 @@ def area(self):
     @property
     def mean_radius(self):
         """
-        The mean radius of the ellipsoid is equal to its radius. Added for
-        compatibility with pymap3d.
+        The mean radius of the ellipsoid is equal to its radius.
         Definition: :math:`R_0 = R`.
         Units: :math:`m`.
         """
@@ -220,7 +229,7 @@ def mean_radius(self):
     def semiaxes_mean_radius(self):
         """
         The arithmetic mean radius of the ellipsoid semi-axes is equal to its
-        radius. Added for compatibility with pymap3d.
+        radius.
         Definition: :math:`R_1 = R`.
         Units: :math:`m`.
         """

boule/tests/test_ellipsoid.py

@@ -104,6 +104,16 @@ def test_check_geocentric_grav_const():
         assert len(warn) >= 1
 
 
+@pytest.mark.parametrize("ellipsoid", ELLIPSOIDS, ids=ELLIPSOID_NAMES)
+def test_semiaxes(ellipsoid):
+    """
+    Check that the semimedium axis is equal to the semimajor axis and that
+    the longitude of the semimajor axis is zero.
+    """
+    assert ellipsoid.semimedium_axis == ellipsoid.semimajor_axis
+    assert ellipsoid.semimajor_axis_longitude == 0
+
+
 @pytest.mark.parametrize("ellipsoid", ELLIPSOIDS, ids=ELLIPSOID_NAMES)
 def test_geodetic_to_spherical_on_equator(ellipsoid):
     "Test geodetic to geocentric coordinates conversion on equator."

boule/tests/test_sphere.py

@@ -78,6 +78,17 @@ def test_check_geocentric_grav_const():
         assert len(warn) >= 1
 
 
+def test_semiaxes(sphere):
+    """
+    Check that the semiaxes are all equal to the sphere radius and that
+    the longitude of the semimajor axis is zero.
+    """
+    assert sphere.semimajor_axis == sphere.radius
+    assert sphere.semimedium_axis == sphere.radius
+    assert sphere.semiminor_axis == sphere.radius
+    assert sphere.semimajor_axis_longitude == 0
+
+
 @pytest.mark.parametrize("si_units", [False, True], ids=["mGal", "SI"])
 def test_normal_gravity_pole_equator(sphere, si_units):
     """