gh-35392: partial cython linting in algebras/

    
using --ignore=E501,E731,E741

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### 📚 Description

Making use of the `cython-lint` command, and fixing manually the issues.
Done here in `algebras` outside of `quatalg`

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URL: #35392
Reported by: Frédéric Chapoton
Reviewer(s): David Coudert

src/sage/algebras/clifford_algebra_element.pxd

@@ -1,7 +1,6 @@
 """
 Clifford algebra elements
 """
-
 from sage.modules.with_basis.indexed_element cimport IndexedFreeModuleElement
 from sage.data_structures.bitset cimport FrozenBitset
 
@@ -14,4 +13,3 @@ cdef class ExteriorAlgebraElement(CliffordAlgebraElement):
 
 cdef class CohomologyRAAGElement(CliffordAlgebraElement):
     pass
-

src/sage/algebras/clifford_algebra_element.pyx

@@ -6,8 +6,7 @@ AUTHORS:
 - Travis Scrimshaw (2013-09-06): Initial version
 - Trevor Karn (2022-07-10): Rewrite multiplication using bitsets
 """
-
-#*****************************************************************************
+# ****************************************************************************
 #       Copyright (C) 2022 Trevor K. Karn <karnx018 at umn.edu>
 #                 (C) 2022 Travis Scrimshaw <tcscrims at gmail.com>
 #
@@ -16,8 +15,7 @@ AUTHORS:
 # the Free Software Foundation, either version 2 of the License, or
 # (at your option) any later version.
 #                  http://www.gnu.org/licenses/
-#*****************************************************************************
-
+# ****************************************************************************
 from sage.structure.parent cimport Parent
 from sage.data_structures.bitset cimport Bitset
 from sage.algebras.weyl_algebra import repr_from_monomials
@@ -125,7 +123,7 @@ cdef class CliffordAlgebraElement(IndexedFreeModuleElement):
 
         for ml, cl in self:
             # Distribute the current term ``cl`` * ``ml`` over ``other``.
-            cur = copy(other._monomial_coefficients) # The current distribution of the term
+            cur = copy(other._monomial_coefficients)  # The current distribution of the term
             for i in reversed(ml):
                 # Distribute the current factor ``e[i]`` (the ``i``-th
                 # element of the standard basis).
@@ -142,10 +140,10 @@ cdef class CliffordAlgebraElement(IndexedFreeModuleElement):
                             break
                         # Add the additional term from the commutation
                         # get a non-frozen bitset to manipulate
-                        t = Bitset(mr) # a mutable copy
+                        t = Bitset(mr)  # a mutable copy
                         t.discard(j)
                         t = FrozenBitset(t)
-                        next_level[t] = next_level.get(t, zero) + cr * Q[i,j]
+                        next_level[t] = next_level.get(t, zero) + cr * Q[i, j]
                         # Note: ``Q[i,j] == Q(e[i]+e[j]) - Q(e[i]) - Q(e[j])`` for
                         # ``i != j``, where ``e[k]`` is the ``k``-th standard
                         # basis vector.
@@ -154,16 +152,16 @@ cdef class CliffordAlgebraElement(IndexedFreeModuleElement):
                             del next_level[t]
 
                     # Check to see if we have a squared term or not
-                    mr = Bitset(mr) # temporarily mutable
+                    mr = Bitset(mr)  # temporarily mutable
                     if i in mr:
                         mr.discard(i)
-                        cr *= Q[i,i]
+                        cr *= Q[i, i]
                         # Note: ``Q[i,i] == Q(e[i])`` where ``e[i]`` is the
                         # ``i``-th standard basis vector.
                     else:
                         # mr is implicitly sorted
                         mr.add(i)
-                    mr = FrozenBitset(mr) # refreeze it
+                    mr = FrozenBitset(mr)  # refreeze it
                     next_level[mr] = next_level.get(mr, zero) + cr
                     if next_level[mr] == zero:
                         del next_level[mr]
@@ -213,11 +211,6 @@ cdef class CliffordAlgebraElement(IndexedFreeModuleElement):
             sage: r * 2  # indirect doctest
             2*x*y*z + 2*x*y + 2*x*z + 2*y*z + 2*x + 2*y + 2*z + 2
         """
-        cdef dict d
-        cdef list to_remove
-        cdef Py_ssize_t num_cross, tot_cross, i, j
-        cdef FrozenBitset ml
-
         if supp.isempty():  # Multiplication by a base ring element
             if coeff == self._parent._base.one():
                 return self
@@ -315,7 +308,8 @@ cdef class CliffordAlgebraElement(IndexedFreeModuleElement):
             sage: all(x.reflection().reflection() == x for x in Cl.basis())
             True
         """
-        return self.__class__(self._parent, {m: (-1)**len(m) * c for m,c in self})
+        return self.__class__(self._parent,
+                              {m: (-1)**len(m) * c for m, c in self})
 
     degree_negation = reflection
 
@@ -361,7 +355,7 @@ cdef class CliffordAlgebraElement(IndexedFreeModuleElement):
         if not self._monomial_coefficients:
             return P.zero()
         g = P.gens()
-        return P.sum(c * P.prod(g[i] for i in reversed(m)) for m,c in self)
+        return P.sum(c * P.prod(g[i] for i in reversed(m)) for m, c in self)
 
     def conjugate(self):
         r"""
@@ -475,7 +469,7 @@ cdef class ExteriorAlgebraElement(CliffordAlgebraElement):
         ml = FrozenBitset()
         if ml in self._monomial_coefficients:
             const_coeff = self._monomial_coefficients[ml]
-            d = dict(rhs._monomial_coefficients) # Make a shallow copy
+            d = dict(rhs._monomial_coefficients)  # Make a shallow copy
             to_remove = []
             if const_coeff != P._base.one():
                 for k in d:
@@ -488,10 +482,12 @@ cdef class ExteriorAlgebraElement(CliffordAlgebraElement):
             d = {}
 
         n = P.ngens()
-        for ml, cl in self._monomial_coefficients.items(): # ml for "monomial on the left"
+        for ml, cl in self._monomial_coefficients.items():
+            # ml for "monomial on the left"
             if ml.isempty():  # We already handled the trivial element
                 continue
-            for mr,cr in rhs._monomial_coefficients.items(): # mr for "monomial on the right"
+            for mr, cr in rhs._monomial_coefficients.items():
+                # mr for "monomial on the right"
                 if mr.isempty():
                     t = ml
                 else:
@@ -502,7 +498,7 @@ cdef class ExteriorAlgebraElement(CliffordAlgebraElement):
                     it = iter(mr)
                     j = next(it)
 
-                    num_cross = 0 # keep track of the number of signs
+                    num_cross = 0  # keep track of the number of signs
                     tot_cross = 0
                     for i in ml:
                         while i > j:
@@ -576,15 +572,16 @@ cdef class ExteriorAlgebraElement(CliffordAlgebraElement):
 
         n = self._parent.ngens()
         d = {}
-        for ml, cl in self._monomial_coefficients.items(): # ml for "monomial on the left"
+        for ml, cl in self._monomial_coefficients.items():
+            # ml for "monomial on the left"
             if not ml.isdisjoint(supp):
                 # if they intersect nontrivially, move along.
                 continue
             t = <FrozenBitset> ml._union(supp)
             it = iter(supp)
             j = next(it)
 
-            num_cross = 0 # keep track of the number of signs
+            num_cross = 0  # keep track of the number of signs
             tot_cross = 0
             for i in ml:
                 while i > j:
@@ -668,15 +665,16 @@ cdef class ExteriorAlgebraElement(CliffordAlgebraElement):
             const_coeff = self._monomial_coefficients.pop(mr)
             d[supp] = const_coeff
 
-        for mr, cr in self._monomial_coefficients.items(): # mr for "monomial on the right"
+        for mr, cr in self._monomial_coefficients.items():
+            # mr for "monomial on the right"
             if not supp.isdisjoint(mr):
                 # if they intersect nontrivially, move along.
                 continue
             t = <FrozenBitset> supp._union(mr)
             it = iter(mr)
             j = next(it)  # We assume mr is non-empty here
 
-            num_cross = 0 # keep track of the number of signs
+            num_cross = 0  # keep track of the number of signs
             tot_cross = 0
             for i in supp:
                 while i > j:
@@ -839,7 +837,7 @@ cdef class ExteriorAlgebraElement(CliffordAlgebraElement):
         """
         P = self._parent
         return P.sum([c * cx * P.interior_product_on_basis(m, mx)
-                      for m,c in self for mx,cx in x])
+                      for m, c in self for mx, cx in x])
 
     antiderivation = interior_product
 
@@ -968,7 +966,8 @@ cdef class CohomologyRAAGElement(CliffordAlgebraElement):
                 tp = tuple(sorted(mr + ml))
                 if any(tp[i] == tp[i+1] for i in range(len(tp)-1)):  # e_i ^ e_i = 0
                     continue
-                if tp not in I: # not an independent set, so this term is also 0
+                if tp not in I:
+                    # not an independent set, so this term is also 0
                     continue
 
                 t = list(mr)

src/sage/algebras/exterior_algebra_groebner.pxd

@@ -1,7 +1,6 @@
 """
 Exterior algebras Gröbner bases
 """
-
 from sage.data_structures.bitset cimport FrozenBitset
 from sage.rings.integer cimport Integer
 from sage.algebras.clifford_algebra_element cimport CliffordAlgebraElement
@@ -53,4 +52,3 @@ cdef class GroebnerStrategyDegRevLex(GroebnerStrategy):
 
 cdef class GroebnerStrategyDegLex(GroebnerStrategy):
     pass
-

src/sage/algebras/exterior_algebra_groebner.pyx

@@ -21,8 +21,8 @@ AUTHORS:
 # ****************************************************************************
 
 from cysignals.signals cimport sig_check
-from sage.libs.gmp.mpz cimport mpz_sizeinbase, mpz_setbit, mpz_tstbit, mpz_cmp_si, mpz_sgn
-from sage.data_structures.bitset_base cimport (bitset_t, bitset_init, bitset_first,
+from sage.libs.gmp.mpz cimport mpz_sizeinbase, mpz_setbit, mpz_tstbit, mpz_sgn
+from sage.data_structures.bitset_base cimport (bitset_init, bitset_first,
                                                bitset_next, bitset_set_to, bitset_len)
 from sage.structure.parent cimport Parent
 from sage.structure.richcmp cimport richcmp, rich_to_bool
@@ -175,8 +175,8 @@ cdef class GroebnerStrategy:
         Convert ``f`` into a ``GBElement``.
         """
         cdef dict mc = <dict> f._monomial_coefficients
-        #if not mc:
-        #    return GBElement(f, FrozenBitset(), -1)
+        # if not mc:
+        #     return GBElement(f, FrozenBitset(), -1)
         cdef Integer r = <Integer> max(self.bitset_to_int(k) for k in mc)
         return GBElement(f, self.int_to_bitset(r), r)
 
@@ -232,7 +232,7 @@ cdef class GroebnerStrategy:
                 if self.build_S_poly(f0, f1):
                     L.add(self.partial_S_poly_right(f0, f1))
                     L.add(self.partial_S_poly_right(f1, f0))
-        else: # We compute a left Gröbner basis for two-sided ideals
+        else:  # We compute a left Gröbner basis for two-sided ideals
             for f0, f1 in P:
                 if self.build_S_poly(f0, f1):
                     L.add(self.partial_S_poly_left(f0, f1))
@@ -272,14 +272,14 @@ cdef class GroebnerStrategy:
         cdef set L = self.preprocessing(P, G)
         cdef Py_ssize_t i
         from sage.matrix.constructor import matrix
-        cdef Integer r = Integer(2) ** self.rank - Integer(1) # r for "rank" or "reverso"
+        cdef Integer r = Integer(2) ** self.rank - Integer(1)  # r for "rank" or "reverso"
         M = matrix({(i, r - self.bitset_to_int(<FrozenBitset> m)): c
-                    for i,f in enumerate(L)
-                    for m,c in (<GBElement> f).elt._monomial_coefficients.items()},
+                    for i, f in enumerate(L)
+                    for m, c in (<GBElement> f).elt._monomial_coefficients.items()},
                    sparse=True)
         M.echelonize()  # Do this in place
         lead_supports = set((<GBElement> f).lsi for f in L)
-        return [GBElement(self.E.element_class(self.E, {self.int_to_bitset(r - Integer(j)): c for j,c in M[i].iteritems()}),
+        return [GBElement(self.E.element_class(self.E, {self.int_to_bitset(r - Integer(j)): c for j, c in M[i].iteritems()}),
                           self.int_to_bitset(Integer(r - p)),
                           Integer(r - p))
                 for i, p in enumerate(M.pivots())
@@ -309,8 +309,7 @@ cdef class GroebnerStrategy:
         """
         cdef FrozenBitset p0, p1
         cdef long deg
-        cdef Py_ssize_t i, j, k
-        cdef set additions
+        cdef Py_ssize_t i, j
         cdef GBElement f0, f1
         cdef list G = [], Gp
         cdef dict constructed = {}
@@ -321,7 +320,7 @@ cdef class GroebnerStrategy:
                 continue
             f0 = self.build_elt(f)
             if f0.lsi in constructed:
-                if f0 in constructed[f0.lsi]: # Already there
+                if f0 in constructed[f0.lsi]:  # Already there
                     continue
                 constructed[f0.lsi].add(f0)
             else:
@@ -338,7 +337,7 @@ cdef class GroebnerStrategy:
                         continue
                     f1 = self.build_elt(f)
                     if f1.lsi in constructed:
-                        if f1 in constructed[f1.lsi]: # Already there
+                        if f1 in constructed[f1.lsi]:  # Already there
                             continue
                         constructed[f1.lsi].add(f1)
                     else:
@@ -367,7 +366,7 @@ cdef class GroebnerStrategy:
             # Add the elements Gp to G when a new element is found
             for f0 in Gp:
                 if f0.lsi in constructed:
-                    if f0 in constructed[f0.lsi]: # Already there
+                    if f0 in constructed[f0.lsi]:  # Already there
                         continue
                     constructed[f0.lsi].add(f0)
                 else:
@@ -402,20 +401,16 @@ cdef class GroebnerStrategy:
         cdef GBElement f0, f1
 
         # Now that we have a Gröbner basis, we make this into a reduced Gröbner basis
-        cdef tuple supp
-        cdef bint did_reduction
-        cdef FrozenBitset lm, s
-        cdef Integer r
         cdef Py_ssize_t num_zeros = 0
         cdef Py_ssize_t n = len(G)
         cdef set pairs = set((i, j) for i in range(n) for j in range(n) if i != j)
 
         while pairs:
             sig_check()
-            i,j = pairs.pop()
+            i, j = pairs.pop()
             f0 = <GBElement> G[i]
             f1 = <GBElement> G[j]
-            assert f0.elt._monomial_coefficients is not f1.elt._monomial_coefficients, (i,j)
+            assert f0.elt._monomial_coefficients is not f1.elt._monomial_coefficients, (i, j)
             # We perform the classical reduction algorithm here on each pair
             # TODO: Make this faster by using the previous technique?
             if self.reduce_single(f0.elt, f1.elt):
@@ -500,7 +495,6 @@ cdef class GroebnerStrategy:
         """
         cdef FrozenBitset lm = self.leading_support(g), s, t
         cdef bint did_reduction = True, was_reduced=False
-        cdef tuple supp
         cdef CliffordAlgebraElement gp
 
         one = self.E._base.one()
@@ -521,7 +515,6 @@ cdef class GroebnerStrategy:
                 iaxpy(-coeff, gp._monomial_coefficients, f._monomial_coefficients)
         return was_reduced
 
-
     cdef Integer bitset_to_int(self, FrozenBitset X):
         raise NotImplementedError
 
@@ -658,8 +651,6 @@ cdef class GroebnerStrategyDegRevLex(GroebnerStrategy):
         """
         Convert a nonnegative integer ``n`` to a :class:`FrozenBitset`.
         """
-        cdef size_t i
-
         if mpz_sgn(n.value) == 0:
             return FrozenBitset()
 
@@ -701,8 +692,6 @@ cdef class GroebnerStrategyDegLex(GroebnerStrategy):
         """
         Convert a nonnegative integer ``n`` to a :class:`FrozenBitset`.
         """
-        cdef size_t i
-
         if mpz_sgn(n.value) == 0:
             return FrozenBitset()