Trac #30821: some typos found using "sage --tox"

of various kinds

URL: https://trac.sagemath.org/30821
Reported by: chapoton
Ticket author(s): Frédéric Chapoton
Reviewer(s): Matthias Koeppe

Author: Release Manager

src/sage/algebras/letterplace/letterplace_ideal.pyx

@@ -249,9 +249,8 @@ class LetterplaceIdeal(Ideal_nc):
             sage: J.groebner_basis()
             [b*a^2 - c^3, b^2*a + c*a^2, c*a^3 + c^3*b, c^3*b^2 + c^4*a]
 
-        Aparently, the results are compatible, by sending `a` to `x`, `b`
+        Apparently, the results are compatible, by sending `a` to `x`, `b`
         to `y` and `c` to `z`.
-
         """
         cdef FreeAlgebra_letterplace A = self.ring()
         cdef FreeAlgebraElement_letterplace x

src/sage/algebras/lie_algebras/affine_lie_algebra.py

@@ -178,7 +178,7 @@ def __classcall_private__(cls, arg0, cartan_type=None, kac_moody=True):
 
     def __init__(self, g, kac_moody):
         """
-        Initalize ``self``.
+        Initialize ``self``.
 
         EXAMPLES::
 

src/sage/algebras/lie_algebras/morphism.py

@@ -259,6 +259,7 @@ def _call_(self, x):
         """
         return x._im_gens_(self.codomain(), self.im_gens(), base_map=self.base_map())
 
+
 class LieAlgebraHomset(Homset):
     """
     Homset between two Lie algebras.
@@ -270,7 +271,7 @@ class LieAlgebraHomset(Homset):
     """
     def __init__(self, X, Y, category=None, base=None, check=True):
         """
-        Initalize ``self``.
+        Initialize ``self``.
 
         EXAMPLES::
 

src/sage/algebras/lie_algebras/verma_module.py

@@ -812,7 +812,7 @@ def _call_(self, x):
             sage: v = Mpp.highest_weight_vector()
             sage: psi(v)
             0
-        """ 
+        """
         if not self._scalar or self.parent().singular_vector() is None:
             return self.codomain().zero()
         mc = x.monomial_coefficients(copy=False)
@@ -1321,4 +1321,3 @@ def _convert_wt_to_root(wt):
     b = b[0]  # Get the actual vector that gives the linear dependency
     # Get v as a linear combination of the simple roots
     return vector(QQ, [-x / b[0] for x in b[1:]])
-

src/sage/algebras/splitting_algebra.py

@@ -4,7 +4,7 @@
 
 *Splitting algebras* have been considered by Dan Laksov, Anders Thorup,
 Torsten Ekedahl and others (see references below) in order to study
-intersection theory of Grassmann and other flag schemes. Similarily as
+intersection theory of Grassmann and other flag schemes. Similarly as
 *splitting fields* they can be considered as extensions of rings containing
 all the roots of a given monic polynomial over that ring under the
 assumption that its Galois group is the symmetric group of order equal
@@ -151,7 +151,7 @@ class SplittingAlgebra(PolynomialQuotientRing_domain):
         sage: Lc.<w> = LaurentPolynomialRing(ZZ)
         sage: PabLc.<u,v> = Lc[]; t = polygen(PabLc)
         sage: S.<x, y> = SplittingAlgebra(t^3 - u*t^2 + v*t - w)
-        doctest:...: UserWarning: Asuming x^3 - u*x^2 + v*x - w to have maximal
+        doctest:...: UserWarning: Assuming x^3 - u*x^2 + v*x - w to have maximal
                                   Galois group!
 
         sage: roots = S.splitting_roots(); roots
@@ -261,7 +261,7 @@ def __init__(self, monic_polynomial, names='X', iterate=True, warning=True):
             # assuming this has been checked mathematically before
             self._set_modulus_irreducible_ = True
             if warning:
-                warn('Asuming %s to have maximal Galois group!' % (monic_polynomial))
+                warn('Assuming %s to have maximal Galois group!' % (monic_polynomial))
                 warning = False # one warning must be enough
 
         verbose("P %s defined:" % (P))
@@ -569,7 +569,7 @@ def lifting_map(self):
 
     def splitting_roots(self):
         r"""
-        Return the roots of the splitted equation.
+        Return the roots of the split equation.
 
         EXAMPLES::
 
@@ -750,10 +750,10 @@ def create_roots(monic_polynomial, warning=True):
         roots = create_roots(monic_polynomial, warning=warning)
 
     else:
-        # ------------------------------------------------------------------------------
-        # root calculation was possible but maybe some more roots in an apropriate
-        # extension ring can be constructed.
-        # ------------------------------------------------------------------------------
+        # ------------------------------------------------------------------
+        # root calculation was possible but maybe some more roots in
+        # an appropriate extension ring can be constructed.
+        # ------------------------------------------------------------------
         num_roots = sum(m for r, m in root_list)
         if num_roots < deg_pol:
             h = monic_polynomial.variables()[0]

src/sage/algebras/yokonuma_hecke_algebra.py

@@ -161,7 +161,7 @@ def __init__(self, d, n, q, R):
         self._assign_names(self.algebra_generators().keys())
 
     def _repr_(self):
-        """ 
+        """
         Return a string representation of ``self``.
 
         EXAMPLES::

src/sage/categories/algebras_with_basis.py

@@ -340,10 +340,10 @@ def one(self):
                 else:
                     return NotImplemented
 
-            #def product_on_basis(self, t1, t2):
+            # def product_on_basis(self, t1, t2):
             # would be easy to implement, but without a special
             # version of module morphism, this would not take
-            # advantage of the bloc structure
+            # advantage of the block structure
 
 
     class TensorProducts(TensorProductsCategory):

src/sage/categories/category.py

@@ -2388,7 +2388,7 @@ def join(categories, as_list=False, ignore_axioms=(), axioms=()):
             sage: Category.join([Groups() & Posets()], as_list=True)
             [Category of groups, Category of posets]
 
-        Support for axiom categories (TODO: put here meaningfull examples)::
+        Support for axiom categories (TODO: put here meaningful examples)::
 
             sage: Sets().Facade() & Sets().Infinite()
             Category of facade infinite sets

src/sage/categories/complex_reflection_or_generalized_coxeter_groups.py

@@ -691,7 +691,7 @@ def from_reduced_word(self, word, word_type='simple'):
 
                 sage: W.from_reduced_word([1, 2, 3]).reduced_word()
                 [1, 2, 3]
-                              
+
                 sage: W = WeylGroup("A3", prefix='s')
                 sage: AS = W.domain()
                 sage: r1 = AS.roots()[4]
@@ -702,7 +702,7 @@ def from_reduced_word(self, word, word_type='simple'):
                 (0, 0, 1, -1)
                 sage: W.from_reduced_word([r1, r2], word_type='all')
                 s3*s2
-                
+
                 sage: W = WeylGroup("G2", prefix='s')
                 sage: W.from_reduced_word(W.domain().positive_roots(), word_type='all')
                 s1*s2
@@ -1077,8 +1077,8 @@ def apply_reflections(self, word, side='right', word_type='all'):
                 (0, 0, 1, -1)
                 sage: w.apply_reflections([r1, r2], word_type='all')
                 s1
-                
-                
+
+
                 sage: W = ReflectionGroup((1,1,3))          # optional - gap3
                 sage: W.one().apply_reflections([1], word_type='distinguished')   # optional - gap3
                 (1,4)(2,3)(5,6)
@@ -1227,7 +1227,6 @@ def is_reflection(self):
             """
             return self.reflection_length() == 1
 
-
     class Irreducible(CategoryWithAxiom):
         class ParentMethods:
             def irreducible_components(self):
@@ -1242,4 +1241,3 @@ def irreducible_components(self):
                     [4-colored permutations of size 3]
                 """
                 return [self]
-

src/sage/categories/coxeter_groups.py

@@ -1205,8 +1205,8 @@ def has_left_descent(self, i):
 
         def first_descent(self, side='right', index_set=None, positive=False):
             """
-            Returns the first left (resp. right) descent of self, as
-            ane element of ``index_set``, or ``None`` if there is none.
+            Return the first left (resp. right) descent of self, as
+            an element of ``index_set``, or ``None`` if there is none.
 
             See :meth:`.descents` for a description of the options.