fix some typos in various places

src/sage/combinat/colored_permutations.py

@@ -1471,7 +1471,7 @@ def to_cycles(self, singletons=True, use_min=True, negative_cycles=True):
 
         .. WARNING::
 
-            The arugment ``negative_cycles`` does not refer to the usual
+            The argument ``negative_cycles`` does not refer to the usual
             definition of a negative cycle; see :meth:`cycle_type`.
 
         EXAMPLES::

src/sage/combinat/plane_partition.py

@@ -2180,7 +2180,7 @@ def from_antichain(self, acl) -> PP:
 
     def from_order_ideal(self, I) -> PP:
         r"""
-        Return the cylically symmetric plane partition corresponding
+        Return the cyclically symmetric plane partition corresponding
         to an order ideal in the poset given in :meth:`to_poset`.
 
         EXAMPLES::

src/sage/combinat/rsk.py

@@ -299,7 +299,7 @@ def forward_rule(self, obj1, obj2, check_standard=False, check=True):
 
           - any object ``obj1`` which has a method ``_rsk_iter()``,
             as long as this method returns an iterator yielding
-            pairs of numbers, which then are interperted as top
+            pairs of numbers, which then are interpreted as top
             entries and bottom entries in the biword (in this case,
             ``obj2`` is ``None``)
 
@@ -2173,7 +2173,7 @@ def forward_rule(self, obj1, obj2, check_standard=False, check=True):
 
           - any object ``obj1`` which has a method ``_rsk_iter()``,
             as long as this method returns an iterator yielding
-            pairs of numbers, which then are interperted as top
+            pairs of numbers, which then are interpreted as top
             entries and bottom entries in the biword (in this case,
             ``obj2`` is ``None``)
 

src/sage/combinat/t_sequences.py

@@ -18,7 +18,7 @@
 * the last element of `X` is -1
 * the last element of `U` is 1
 
-The nonperiodic autocorrelation of a familiy of sequences
+The nonperiodic autocorrelation of a family of sequences
 `X=\{A_1, A_2, ..., A_n\}` is defined as (see Definition 7.2 of [Seb2017]_):
 
 .. MATH::
@@ -45,7 +45,7 @@
 
 def _nonperiodic_autocorrelation(sequences, j):
     r"""
-    Compute the nonperiodic autocorrelation of a familiy of sequences.
+    Compute the nonperiodic autocorrelation of a family of sequences.
 
     Namely, given a family of sequences `X` it computes:
 

src/sage/combinat/triangles_FHM.py

@@ -62,7 +62,7 @@ def _matrix_display(self, variables=None):
 
     - ``variables`` -- (optional) choice of 2 variables
 
-    OUPUT:
+    OUTPUT:
 
     matrix
 

src/sage/crypto/block_cipher/des.py

@@ -1041,7 +1041,7 @@ def convert_to_vector(I, L):
 
     - ``I`` -- integer or bit list-like
 
-    - ``L`` -- integer; the desired bit length of the ouput
+    - ``L`` -- integer; the desired bit length of the output
 
     OUTPUT: the ``L``-bit vector representation of ``I``
 

src/sage/crypto/block_cipher/present.py

@@ -553,7 +553,7 @@ def sbox_layer(self, state, inverse=False):
             :mod:`sage.crypto.sbox` uses big endian by default whereas most of
             Sage uses little endian. So to use the big endian PRESENT Sbox from
             :mod:`sage.crypto.sboxes` :func:`sbox_layer` has to do some endian
-            conversion (i.e. reverse input and ouput of the Sbox). Keep this in
+            conversion (i.e. reverse input and output of the Sbox). Keep this in
             mind if you change the Sbox or :func:`sbox_layer`.
         """
         sbox = self.sbox if not inverse else self.sbox.inverse()
@@ -703,7 +703,7 @@ class PRESENT_KS(SageObject):
         :mod:`sage.crypto.sbox` uses big endian by default whereas most of Sage
         uses little endian. So to use the big endian PRESENT Sbox from
         :mod:`sage.crypto.sboxes` :class:`PRESENT_KS` has to do some endian
-        conversion (i.e. reverse input and ouput of the Sbox). Keep this in
+        conversion (i.e. reverse input and output of the Sbox). Keep this in
         mind if you change the Sbox or :func:`__call__`.
 
     .. automethod:: __init__
@@ -885,7 +885,7 @@ def convert_to_vector(I, L):
 
     - ``I`` -- integer or bit list-like
 
-    - ``L`` -- integer; the desired bit length of the ouput
+    - ``L`` -- integer; the desired bit length of the output
 
     OUTPUT: the ``L``-bit vector representation of ``I``
 

src/sage/dynamics/arithmetic_dynamics/projective_ds.py

@@ -4997,7 +4997,7 @@
         r"""
         Compute the ``n`` multiplier spectra of this dynamical system.
 
-        This is the set of multipliers of all peroidic points of
+        This is the set of multipliers of all periodic points of
         period ``n`` included with the appropriate multiplicity.
         User can also specify to compute the formal ``n`` multiplier spectra
         instead which includes the multipliers of all formal periodic points
@@ -5413,7 +5413,7 @@
 
             \prod_{P \text{ period n}} ( w - c(P,t)),
 
-        where `c(P,t)` is the charateristic polynomial (variable `t`) of the
+        where `c(P,t)` is the characteristic polynomial (variable `t`) of the
         multiplier at `P`. Note that in dimension 1, only the coefficients
         of the constant term is returned.
 
@@ -6843,7 +6843,7 @@
     def Lattes_to_curve(self, return_conjugation=False, check_lattes=False):
         r"""
         Finds a Short Weierstrass Model Elliptic curve of self
-        self assumed to be Lattes map and not in charateristic 2 or 3
+        self assumed to be Lattes map and not in characteristic 2 or 3
 
         INPUT:
 
@@ -6974,7 +6974,7 @@
             sage: P.<x,y>=ProjectiveSpace(QQbar, 1)
             sage: E=EllipticCurve([1, 2])
             sage: f=P.Lattes_map(E, 2)
             sage: f.Lattes_to_curve(check_lattes=true)
             Elliptic Curve defined by y^2 = x^3 + x + 2 over Rational Field
 
         """

src/sage/geometry/polyhedron/combinatorial_polyhedron/base.pyx

@@ -3670,7 +3670,7 @@ cdef class CombinatorialPolyhedron(SageObject):
             # If ``not do_f_vector`` the iterator is set up
             # for ``output_dimension`` and
             # ``d < dim`` implies
-            # ``d == ouput_dimension``.
+            # ``d == output_dimension``.
             if not do_f_vector or d == output_dimension:
                 if do_atom_rep:
                     # Set up face_iter.atom_rep

src/sage/geometry/polyhedron/combinatorial_polyhedron/face_iterator.pyx

@@ -1591,7 +1591,7 @@ cdef class FaceIterator(FaceIterator_base):
         """
         if self.structure.output_dimension != -2:
             if self.dual:
-                # ouput_dimension is stored with respect to the dual
+                # output_dimension is stored with respect to the dual
                 intended_dimension = self.structure.dimension - 1 - self.structure.output_dimension
             else:
                 intended_dimension = self.structure.output_dimension

src/sage/graphs/graph_generators.py

@@ -1102,7 +1102,7 @@ def nauty_genbg(self, options='', debug=False, immutable=False):
 
         EXAMPLES:
 
-        The generator can be used to construct biparrtite graphs for testing,
+        The generator can be used to construct bipartite graphs for testing,
         one at a time (usually inside a loop).  Or it can be used to
         create an entire list all at once if there is sufficient memory
         to contain it::

src/sage/graphs/line_graph.pyx

@@ -403,7 +403,7 @@ def line_graph(g, labels=True, return_labels=False):
     multiple = g.has_multiple_edges()
 
     if multiple:
-        # As the edges of g are the vertices of its line graph, we need to distinguish between the mutliple edges of g.
+        # As the edges of g are the vertices of its line graph, we need to distinguish between the multiple edges of g.
         # To this aim, we assign to each edge of g an integer label (between 0 and g.size() - 1) and set labels to True
         # in order to keep these labels during the construction of the line graph.
         labels = True

src/sage/knots/knotinfo.py

@@ -15,7 +15,7 @@
 - ``sage -f database_knotinfo`` (installs even if the current version is present)
 
 This will install a `Python wrapper <https://github.com/soehms/database_knotinfo#readme>`__
-for the original databases in Sage. This wrapper perfoms an automatic progress
+for the original databases in Sage. This wrapper performs an automatic progress
 of version numbers. For more details and further install instructions please see
 the corresponding web-page.
 
@@ -2554,17 +2554,17 @@ def list(self, oriented=False, comp=None, det=None, homfly=None):
           keyword has to be set to ``True``.
 
         - ``comp`` -- (default: ``None``) if given an integer for this
-          keyword the list is restriced to links having the according number
+          keyword the list is restricted to links having the according number
           of components. This keyword implies ``oriented=True``.
 
         - ``det`` -- (default: ``None``) if given an integer for this
-          keyword the list is restriced to links having the according value
+          keyword the list is restricted to links having the according value
           for its determinant. This keyword implies ``oriented=True``.
 
         - ``homfly`` -- (default: ``None``) if given a HOMFLY-PT polynomial
-          having ``normalization='vz'`` for this keyword the list is restriced to
-          links having the according value for its HOMFLY-PT polynomial. This
-          keyword implies ``oriented=True``.
+          having ``normalization='vz'`` for this keyword the list is restricted
+          to links having the according value for its HOMFLY-PT
+          polynomial. This keyword implies ``oriented=True``.
 
         EXAMPLES::
 

src/sage/knots/link.py

@@ -3949,7 +3949,7 @@ def _markov_move_cmp(self, braid):
             return sb.is_conjugated(ob)
 
         if sb_ind > ob_ind:
-            # if the braid of self has more strands we have to perfom
+            # if the braid of self has more strands we have to perform
             # Markov II moves
             B = sb.parent()
             g = B.gen(ob_ind-1)

src/sage/modular/arithgroup/arithgroup_perm.py

@@ -2488,7 +2488,7 @@ def one_odd_subgroup(self, random=False):
             sage: Go == G
             True
 
-        Strating from `\Gamma(6)` we get a different group::
+        Starting from `\Gamma(6)` we get a different group::
 
             sage: G = Gamma(6).as_permutation_group()
             sage: G.is_odd(), G.index()

src/sage/modular/drinfeld_modform/ring.py

@@ -102,7 +102,7 @@ class DrinfeldModularForms(Parent, UniqueRepresentation):
 
       If this parameter is a single character, for example ``f``, and a
       rank is specified, then the names will be of the form
-      ``f1, f2, ..., fr``. Finally, if this parameter is a list, a tupe
+      ``f1, f2, ..., fr``. Finally, if this parameter is a list, a tuple
       or a string of comma separated characters, then each character
       will corresponds to a generator. Note that in this case, it not
       necessary to specify the rank.

src/sage/modules/with_basis/invariant.py

@@ -997,7 +997,7 @@ def project_ambient(self, x):
         but you still may pass elements of ``M``, which is an instance of
         :class:`~sage.combinat.free_module.CombinatorialFreeModule`,
         because the underlying ``Representation`` is built off of ``M``
-        and we can cannonically construct elements of the ``Representation``
+        and we can canonically construct elements of the ``Representation``
         from elements of ``M``.
 
         ::

src/sage/quivers/ar_quiver.py

@@ -192,7 +192,7 @@ def __init__(self, quiver):
         cat = Sets().Enumerated().Finite() if self._is_finite else Sets().Infinite()
         super().__init__(self, category=cat)
 
-    def _repr_(self):
+    def _repr_(self) -> str:
         """
         Return a string representation of ``self``.
 
@@ -361,7 +361,7 @@ def edge_options(data):
 
     def digraph_preprojectives(self, max_depth, with_translations=False):
         r"""
-        Return the diagraph of preprojectives of ``self`` up to ``max_depth``.
+        Return the digraph of preprojectives of ``self`` up to ``max_depth``.
 
         EXAMPLES::
 
@@ -400,7 +400,7 @@ def digraph_preprojectives(self, max_depth, with_translations=False):
 
     def digraph_postinjectives(self, max_depth, with_translations=False):
         """
-        Return the diagraph of postinjectives of ``self`` up to ``max_depth``.
+        Return the digraph of postinjectives of ``self`` up to ``max_depth``.
 
         EXAMPLES::
 
@@ -440,12 +440,12 @@ def digraph_postinjectives(self, max_depth, with_translations=False):
     @cached_method
     def digraph(self, with_translations=False):
         r"""
-        Return the diagraph of ``self``.
+        Return the digraph of ``self``.
 
         INPUT:
 
-        - ``with_translations`` -- boolean (default: ``False``); if ``True``, then
-          include the arrows corresponding to the translations
+        - ``with_translations`` -- boolean (default: ``False``); if ``True``,
+          then include the arrows corresponding to the translations
 
         EXAMPLES::
 
@@ -697,7 +697,7 @@ def __init__(self, parent, vertex, level):
             self._level = ZZ(level)
             Element.__init__(self, parent)
 
-        def _repr_(self):
+        def _repr_(self) -> str:
             r"""
             Return a string representation of ``self``.
 
@@ -710,7 +710,7 @@ def _repr_(self):
             """
             return f"<{self._vertex}, {self._level}>"
 
-        def _latex_(self):
+        def _latex_(self) -> str:
             r"""
             Return a latex representation of ``self``.
 
@@ -739,7 +739,7 @@ def _latex_(self):
                 return dim_vec
             return r"\begin{{gathered}} {} \\ {} \end{{gathered}}".format(node, dim_vec)
 
-        def _richcmp_(self, other, op):
+        def _richcmp_(self, other, op) -> bool:
             r"""
             Rich comparison of ``self`` to ``other`` by ``op``.
 
@@ -752,7 +752,7 @@ def _richcmp_(self, other, op):
             """
             return richcmp((self._level, self._vertex), (other._level, other._vertex), op)
 
-        def __hash__(self):
+        def __hash__(self) -> int:
             r"""
             Return the hash of ``self``.
 

src/sage/rings/continued_fraction.py

@@ -2375,7 +2375,7 @@ def continued_fraction_list(x, type='std', partial_convergents=False,
 
     OUTPUT:
 
-    A lits of integers, the coefficients in the continued fraction expansion of
+    A list of integers, the coefficients in the continued fraction expansion of
     ``x``. If ``partial_convergents`` is set to ``True``, then return a pair
     containing the coefficient list and the partial convergents list is
     returned.

src/sage/rings/number_field/number_field.py

@@ -10441,7 +10441,7 @@ def hilbert_symbol_negative_at_S(self, S, b, check=True):
         # symbol is negative for all primes in S and positive
         # at all primes in S'
         # For technical reasons, a Hilbert symbol of -1 is
-        # respresented as 1 and a Hilbert symbol of 1
+        # represented as 1 and a Hilbert symbol of 1
         # is represented as 0
         V = VectorSpace(GF(2), len(SL))
         v = V([1]*len(S) + [0]*len(L))

src/sage/rings/polynomial/pbori/randompoly.py

@@ -47,7 +47,7 @@ def sparse_random_system(ring, number_of_polynomials, variables_per_polynomial,
     Generate a sparse random system.
 
     Generate a system, which is sparse in the sense, that each polynomial
-    contains only a small subset of variables. In each variable that occurrs
+    contains only a small subset of variables. In each variable that occurs
     in a polynomial it is dense in the terms up to the given degree
     (every term occurs with probability 1/2).
 

src/sage/rings/rational_field.py

@@ -889,7 +889,7 @@ def hilbert_symbol_negative_at_S(self, S, b, check=True):
         # Compute the map phi of Hilbert symbols at all the primes
         # in S and S'
         # For technical reasons, a Hilbert symbol of -1 is
-        # respresented as 1 and a Hilbert symbol of 1
+        # represented as 1 and a Hilbert symbol of 1
         # is represented as 0
         def phi(x):
             v = [(1-hilbert_symbol(x, b, p))//2 for p in P]

src/sage/rings/semirings/tropical_polynomial.py

@@ -930,9 +930,9 @@ def interpolation(self, points):
             ...
             ValueError: the slope is not an integer
 
-        For max-plus algebra, the slope of the componenets has to be
+        For max-plus algebra, the slope of the components has to be
         increasing as we move from left to right. Conversely for min-plus
-        algebra, the slope of the componenets has to be decreasing from
+        algebra, the slope of the components has to be decreasing from
         left to right::
 
             sage: T = TropicalSemiring(QQ, use_min=False)

src/sage/rings/semirings/tropical_variety.py

@@ -534,7 +534,7 @@ def update_result(result):
 
     def weight_vectors(self):
         r"""
-        Return the weight vectors for each unique intesection of
+        Return the weight vectors for each unique intersection of
         components of ``self``.
 
         Weight vectors are a list of vectors associated with each

src/sage/schemes/generic/algebraic_scheme.py

@@ -1122,7 +1122,7 @@ def normalize_defining_polynomials(self):
             initial_polys = list(self.__polys)
 
             for P in initial_polys:
-                # stores value which need to be mutliplied to make all coefficient integers
+                # stores value which need to be multiplied to make all coefficient integers
                 mult = lcm([c.denominator() for c in P.coefficients()])
                 P = mult*P
                 # stores the common factor from all coefficients

src/sage/schemes/riemann_surfaces/riemann_surface.py

@@ -2972,7 +2972,7 @@ def _integrate_differentials_iteratively(
         mp_list = [reparameterize_differential_minpoly(mp, z_start) for mp in mp_list]
 
         # Depending on whether we have reparameterized about infinity or not,
-        # we initialise some values we will need in the calculation, inclduing
+        # we initialise some values we will need in the calculation, including
         # the function `initalize', which at a given value of zbar, calculates
         # the starting value for the i-th differential so it can be iterated
         # from via homotopy continuation.