fix some typos in manifolds

src/sage/manifolds/calculus_method.py

@@ -107,7 +107,7 @@ def _Sympy_to_SR(expression):
         # sympy abstract function
         a = expression._sage_()
         # As all sage objects have a ._sage_ operator, they have to be
-        # catched
+        # caught
         if type(a) is type(expression):
             raise TypeError
         return a

src/sage/manifolds/chart.py

@@ -2242,14 +2242,14 @@ def valid_coordinates_numerical(self, *coordinates):
                 else:
                     raise ValueError("restrictions must be in CNF (list of tuples)")
             list_of_fast_callable = []
-            for litteral in clause:
-                if not isinstance(litteral, Expression):
+            for literal in clause:
+                if not isinstance(literal, Expression):
                     raise ValueError("Restrictions must be in CNF (list of tuples)")
                 # End of checks
 
-                fl = fast_callable(litteral.lhs(), vars=self[:], domain=float)
-                fr = fast_callable(litteral.rhs(), vars=self[:], domain=float)
-                op = litteral.operator()
+                fl = fast_callable(literal.lhs(), vars=self[:], domain=float)
+                fr = fast_callable(literal.rhs(), vars=self[:], domain=float)
+                op = literal.operator()
                 list_of_fast_callable.append((fl, fr, op))
             list_of_clause.append(list_of_fast_callable)
 
@@ -3086,7 +3086,7 @@ def __eq__(self, other):
 
     def __ne__(self, other):
         r"""
-        Unequality operator.
+        Non-equality operator.
 
         TESTS::
 

src/sage/manifolds/differentiable/bundle_connection.py

@@ -1225,7 +1225,7 @@ def __setitem__(self, args, value):
                     raise TypeError("in case of [:] syntax, the list/tuple "
                                     "of value must contain lists/tuples")
                 else:
-                    # check lenghts:
+                    # check lengths:
                     rk = vb._rank
                     if len(value) != rk:
                         raise ValueError("value must have "

src/sage/manifolds/differentiable/chart.py

@@ -303,7 +303,7 @@ def transition_map(self, other, transformations, intersection_name=None,
         on `U\cap V`.
 
         By definition, the transition map `\psi\circ\varphi^{-1}` must be
-        of classe `C^k`, where `k` is the degree of differentiability of the
+        of class `C^k`, where `k` is the degree of differentiability of the
         manifold (cf.
         :meth:`~sage.manifolds.differentiable.manifold.DifferentiableManifold.diff_degree`).
 
@@ -1074,7 +1074,7 @@ class DiffCoordChange(CoordChange):
     charts intersect, i.e. on `U\cap V`.
 
     By definition, the transition map `\psi\circ\varphi^{-1}` must be
-    of classe `C^k`, where `k` is the degree of differentiability of the
+    of class `C^k`, where `k` is the degree of differentiability of the
     manifold (cf.
     :meth:`~sage.manifolds.differentiable.manifold.DifferentiableManifold.diff_degree`).
 

src/sage/manifolds/differentiable/degenerate_submanifold.py

@@ -426,7 +426,8 @@ def list_of_screens(self):
     def set_transverse(self, rigging=None, normal=None):
         r"""
         For setting a transversal distribution of the degenerate submanifold.
-        according to the type of the submanifold amoung the 4 possible types,
+
+        According to the type of the submanifold among the 4 possible types,
         one must enter a list of normal transversal vector fields and/or a
         list of transversal and not normal vector fields spanning a transverse
         distribution.
@@ -502,7 +503,7 @@ def set_transverse(self, rigging=None, normal=None):
                 rig.append(u)
                 l2 += 1
         if l1+l2!=self._codim:
-            raise ValueError("lenght of the transverse must be {}".format(self._codim))
+            raise ValueError("length of the transverse must be {}".format(self._codim))
         self._transverse['normal'] = tuple(nor)
         self._transverse['rigging'] = tuple(rig)
 
@@ -565,7 +566,7 @@ def screen(self, name, screen, rad, latex_name=None):
                 raise ValueError("a different screen distribution with the "
                                  "same name had already been set")
         if len(screen)+len(rad)!=self._dim:
-            raise ValueError("total lenght screen+rad must be {}".format(self._dim))
+            raise ValueError("total length screen+rad must be {}".format(self._dim))
         frame = self.default_frame()
         im = self.immersion()
         g = self.ambient_metric().along(im)

src/sage/manifolds/differentiable/examples/euclidean.py

@@ -790,15 +790,15 @@ def __init__(self, n, name=None, latex_name=None,
                 if coordinates == 'Cartesian':
                     symbols = 'x'
                 else:
-                    raise TypeError("unkown coordinate type")
+                    raise TypeError("unknown coordinate type")
             elif n > 3:
                 if coordinates == 'Cartesian':
                     symbols = ''
                     for i in self.irange():
                         symbols += "x{}".format(i) + r":x_{" + str(i) + r"} "
                     symbols = symbols[:-1]
                 else:
-                    raise TypeError("unkown coordinate type")
+                    raise TypeError("unknown coordinate type")
             else:
                 raise NotImplementedError("dimension not implemented yet")
         self._cartesian_chart = None  # to be constructed later if necessary
@@ -1195,7 +1195,7 @@ def __init__(self, name=None, latex_name=None, coordinates='Cartesian',
 
         """
         if coordinates not in ['Cartesian', 'polar']:
-            raise TypeError("unkown coordinate type")
+            raise TypeError("unknown coordinate type")
         if symbols is None:
             if coordinates == 'Cartesian':
                 symbols = 'x y'
@@ -1723,7 +1723,7 @@ def __init__(self, name=None, latex_name=None, coordinates='Cartesian',
 
         """
         if coordinates not in ['Cartesian', 'spherical', 'cylindrical']:
-            raise TypeError("unkown coordinate type")
+            raise TypeError("unknown coordinate type")
         if symbols is None:
             if coordinates == 'Cartesian':
                 symbols = 'x y z'

src/sage/manifolds/differentiable/integrated_curve.py

@@ -2951,7 +2951,7 @@ class IntegratedAutoparallelCurve(IntegratedCurve):
     line of latitude.
 
     Now, set an affine connection with respect to such fields that are
-    parallely transported in all directions, that is:
+    parallelly transported in all directions, that is:
     `\nabla \hat{e}_{\theta} = \nabla \hat{e}_{\phi} = 0`.
     This is equivalent to setting all the connection coefficients to
     zero with respect to this frame::

src/sage/manifolds/differentiable/manifold.py

@@ -3073,7 +3073,7 @@ def vector_frame(self, *args, **kwargs):
             Vector field f_0 on the 2-dimensional differentiable manifold M
 
         Thanks to the keywords ``dest_map`` and ``from_frame``, one can also
-        define a vector frame from one prexisting on another manifold, via a
+        define a vector frame from one preexisting on another manifold, via a
         differentiable map (here provided by the curve ``c``)::
 
             sage: fc = I.vector_frame(dest_map=c, from_frame=f); fc

src/sage/manifolds/differentiable/mixed_form.py

@@ -982,7 +982,7 @@ def exterior_derivative(self):
         resu = self._new_instance()
         resu[0] = self._domain.zero_scalar_field()
         resu[1:] = [self[j].exterior_derivative()
-                    for j in range(0, self._max_deg)]
+                    for j in range(self._max_deg)]
         # Compose name:
         from sage.tensor.modules.format_utilities import (format_unop_txt,
                                                           format_unop_latex)

src/sage/manifolds/differentiable/scalarfield.py

@@ -525,7 +525,7 @@ class DiffScalarField(ScalarField):
            (x, y) |--> x*y*H(x, y)
         on W: (u, v) |--> u*v*H(u/(u^2 + v^2), v/(u^2 + v^2))/(u^4 + 2*u^2*v^2 + v^4)
 
-    Thanks to the coercion `C^k(M)\rightarrow C^k(U)` mentionned
+    Thanks to the coercion `C^k(M)\rightarrow C^k(U)` mentioned
     above, it is possible to multiply a scalar field defined on `M` by a
     scalar field defined on `U`, the result being a scalar field defined on
     `U`::

src/sage/manifolds/differentiable/tensorfield.py

@@ -3983,10 +3983,10 @@ def down(self, metric, pos=None):
             False
 
         """
-        n_con = self._tensor_type[0] # number of contravariant indices = k
+        n_con = self._tensor_type[0]  # number of contravariant indices = k
         if pos is None:
             result = self
-            for p in range(0, n_con):
+            for p in range(n_con):
                 k = result._tensor_type[0]
                 result = result.down(metric, k-1)
             return result

src/sage/manifolds/differentiable/tensorfield_paral.py

@@ -2362,8 +2362,8 @@ def truncate(self, symbol, order):
             [ 0  0  e  1]
 
         """
-        ser = self.series_expansion(symbol, order)
-        return sum(symbol**i*s for (i, s) in enumerate(ser))
+        series = self.series_expansion(symbol, order)
+        return sum(symbol**i * s for i, s in enumerate(series))
 
     def set_calc_order(self, symbol, order, truncate=False):
         r"""

src/sage/manifolds/differentiable/vectorframe.py

@@ -479,7 +479,7 @@ class VectorFrame(FreeModuleBasis):
     immersion and `\Phi` being a curve in `M` (`U` is then an open interval
     of `\RR`).
 
-    For each instanciation of a vector frame, a coframe is automatically
+    For each instantiation of a vector frame, a coframe is automatically
     created, as an instance of the class :class:`CoFrame`. It is returned by
     the method :meth:`coframe`.
 

src/sage/manifolds/local_frame.py

@@ -422,7 +422,7 @@ class LocalFrame(FreeModuleBasis):
     of the base space `M`, such that `e(p)` is a basis of the fiber `E_p` for
     any `p \in U`.
 
-    For each instanciation of a local frame, a local coframe is automatically
+    For each instantiation of a local frame, a local coframe is automatically
     created, as an instance of the class :class:`LocalCoFrame`. It is returned
     by the method :meth:`coframe`.
 

src/sage/manifolds/point.py

@@ -649,7 +649,7 @@ def __eq__(self, other):
                     common_chart = chart
                     break
         if common_chart is None:
-            # A commont chart is searched via a coordinate transformation,
+            # A common chart is searched via a coordinate transformation,
             # privileging the default chart
             if def_chart in self._coordinates:
                 try:
@@ -665,7 +665,7 @@ def __eq__(self, other):
                 except ValueError:
                     pass
         if common_chart is None:
-            # At this stage, a commont chart is searched via a coordinate
+            # At this stage, a common chart is searched via a coordinate
             # transformation from any chart
             for chart in self._coordinates:
                 try:

src/sage/manifolds/topological_submanifold.py

@@ -434,7 +434,7 @@ def set_embedding(self, phi, inverse=None, var=None,
             sage: N.set_embedding(phi, inverse=phi_inv, var=t,
             ....:                 t_inverse={t: phi_inv_t})
 
-        Now ``N`` appears as an embbeded submanifold::
+        Now ``N`` appears as an embedded submanifold::
 
             sage: N
             2-dimensional topological submanifold N embedded in the

src/sage/manifolds/trivialization.py

@@ -733,7 +733,7 @@ def __eq__(self, other):
 
     def __ne__(self, other):
         r"""
-        Unequality operator.
+        Non-equality operator.
 
         TESTS::