gh-35317: fixing some E502 outside of schemes and combinat

    
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### 📚 Description

This fixes some pycodestyle warnings about

E502 the backslash is redundant between brackets

in py files outside the folders combinat/ and schemes/

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URL: #35317
Reported by: Frédéric Chapoton
Reviewer(s): Frédéric Chapoton, Matthias Köppe

src/sage/algebras/lie_conformal_algebras/affine_lie_conformal_algebra.py

@@ -107,24 +107,24 @@ def __init__(self, R, ct, names=None, prefix=None, bracket=None):
                 if S.rank(k2) <= S.rank(k1):
                     myb = B[k1].bracket(B[k2]).monomial_coefficients()
                     myf = R(2).inverse_of_unit()*R(hv).inverse_of_unit()\
-                          *g.killing_form(B[k1],B[k2])
+                          * g.killing_form(B[k1], B[k2])
                     if myb or myf:
-                        gdict[(k1,k2)] = {}
+                        gdict[(k1, k2)] = {}
                         if myb:
-                            gdict[(k1,k2)][0] = {(nk,0):v for nk,v in \
-                                                                    myb.items()}
+                            gdict[(k1, k2)][0] = {(nk, 0): v
+                                                  for nk, v in myb.items()}
                         if myf:
-                            gdict[(k1,k2)][1] = {('K',0):myf}
+                            gdict[(k1, k2)][1] = {('K', 0): myf}
 
-        weights = (1,)*B.cardinality()
+        weights = (1,) * B.cardinality()
         self._ct = ct
         if prefix is None and names is None:
             prefix = 'B'
 
         GradedLieConformalAlgebra.__init__(self,
-                    R, gdict, index_set=S,
-                    central_elements=('K',), weights=weights,
-                    names=names, prefix=prefix,bracket=bracket)
+            R, gdict, index_set=S,
+            central_elements=('K',), weights=weights,
+            names=names, prefix=prefix, bracket=bracket)
 
     def cartan_type(self):
         """

src/sage/algebras/lie_conformal_algebras/bosonic_ghosts_lie_conformal_algebra.py

@@ -87,29 +87,31 @@ def __init__(self, R, ngens=2, names=None, index_set=None):
         """
         from sage.rings.integer_ring import ZZ
         try:
-            assert (ngens in ZZ and ngens > 0 and ngens % 2 == 0)
+            assert (ngens in ZZ and ngens > 0 and not ngens % 2)
         except AssertionError:
             raise ValueError("ngens should be an even positive integer, " +
                              "got {}".format(ngens))
         latex_names = None
+        half = ngens // 2
         if (names is None) and (index_set is None):
             from sage.misc.defaults import variable_names as varnames
             from sage.misc.defaults import latex_variable_names as laxnames
-            names = varnames(ngens/2,'beta') + varnames(ngens/2,'gamma')
-            latex_names =  tuple(laxnames(ngens/2,r'\beta') +\
-                                          laxnames(ngens/2,r'\gamma')) + ('K',)
+            names = varnames(half, 'beta') + varnames(half, 'gamma')
+            latex_names = tuple(laxnames(half, r'\beta') +
+                                laxnames(half, r'\gamma')) + ('K',)
 
-        names,index_set = standardize_names_index_set(names=names,
+        names, index_set = standardize_names_index_set(names=names,
                                                       index_set=index_set,
                                                       ngens=ngens)
-        A = identity_matrix(R, ngens // 2)
+        A = identity_matrix(R, half)
         from sage.matrix.special import block_matrix
-        gram_matrix = block_matrix([[R.zero(),A],[-A,R.zero()]])
-        ghostsdict = { (i,j): {0: {('K',0): gram_matrix[index_set.rank(i),
-                    index_set.rank(j)]}} for i in index_set for j in index_set}
-        weights = (1,)*(ngens//2) + (0,)*(ngens//2)
+        gram_matrix = block_matrix([[R.zero(), A], [-A, R.zero()]])
+        ghostsdict = {(i, j): {0: {('K', 0): gram_matrix[index_set.rank(i),
+                                                         index_set.rank(j)]}}
+                      for i in index_set for j in index_set}
+        weights = (1,) * half + (0,) * half
         super().__init__(R,
-                         ghostsdict,names=names,
+                         ghostsdict, names=names,
                          latex_names=latex_names,
                          index_set=index_set,
                          weights=weights,

src/sage/algebras/lie_conformal_algebras/fermionic_ghosts_lie_conformal_algebra.py

@@ -80,33 +80,35 @@ def __init__(self,R,ngens=2,names=None,index_set=None):
             sage: TestSuite(V).run()
         """
         try:
-            assert (ngens > 0 and ngens % 2 == 0)
+            assert (ngens > 0 and not ngens % 2)
         except AssertionError:
             raise ValueError("ngens should be an even positive integer, " +
                              "got {}".format(ngens))
         latex_names = None
+        half = ngens // 2
         if (names is None) and (index_set is None):
             from sage.misc.defaults import variable_names as varnames
             from sage.misc.defaults import latex_variable_names as laxnames
-            names = varnames(ngens/2,'b') + varnames(ngens/2,'c')
-            latex_names =  tuple(laxnames(ngens/2,'b') +\
-                                          laxnames(ngens/2,'c')) + ('K',)
+            names = varnames(half, 'b') + varnames(half, 'c')
+            latex_names = tuple(laxnames(half, 'b') +
+                                laxnames(half, 'c')) + ('K',)
 
         from sage.structure.indexed_generators import \
-                                                standardize_names_index_set
-        names,index_set = standardize_names_index_set(names=names,
-                                                      index_set=index_set,
-                                                      ngens=ngens)
+            standardize_names_index_set
+        names, index_set = standardize_names_index_set(names=names,
+                                                       index_set=index_set,
+                                                       ngens=ngens)
         from sage.matrix.special import identity_matrix
-        A = identity_matrix(R, ngens // 2)
+        A = identity_matrix(R, half)
         from sage.matrix.special import block_matrix
-        gram_matrix = block_matrix([[R.zero(),A],[A,R.zero()]])
-        ghostsdict = { (i,j): {0: {('K',0): gram_matrix[index_set.rank(i),
-                    index_set.rank(j)]}} for i in index_set for j in index_set}
-        weights = (1,)*(ngens//2) + (0,)*(ngens//2)
-        parity = (1,)*ngens
+        gram_matrix = block_matrix([[R.zero(), A], [A, R.zero()]])
+        ghostsdict = {(i, j): {0: {('K', 0): gram_matrix[index_set.rank(i),
+                                                         index_set.rank(j)]}}
+                      for i in index_set for j in index_set}
+        weights = (1,) * half + (0,) * half
+        parity = (1,) * ngens
         super().__init__(R,
-                         ghostsdict,names=names,
+                         ghostsdict, names=names,
                          latex_names=latex_names,
                          index_set=index_set,
                          weights=weights,

src/sage/algebras/lie_conformal_algebras/lie_conformal_algebra_element.py

@@ -60,14 +60,14 @@ def T(self, n=1):
             raise ValueError("n must be a nonnegative Integer")
         if n == 0 or self.is_zero():
             return self
-        #it's faster to sum than to use recursion
+        # it's faster to sum than to use recursion
         if self.is_monomial():
             p = self.parent()
-            a,m = self.index()
-            coef = self._monomial_coefficients[(a,m)]
-            if (a,m+n) in p._indices:
-                return coef*prod(j for j in range(m+1,m+n+1))\
-                        *p.monomial((a,m+n))
+            a, m = self.index()
+            coef = self._monomial_coefficients[(a, m)]
+            if (a, m + n) in p._indices:
+                return coef * prod(j for j in range(m + 1, m + n + 1))\
+                    * p.monomial((a, m + n))
             else:
                 return p.zero()
         return sum(mon.T(n) for mon in self.terms())
@@ -121,23 +121,25 @@ def _bracket_(self, right):
             if self.is_zero() or right.is_zero():
                 return {}
             s_coeff = p._s_coeff
-            a,k = self.index()
-            coefa = self.monomial_coefficients()[(a,k)]
-            b,m = right.index()
-            coefb = right.monomial_coefficients()[(b,m)]
+            a, k = self.index()
+            coefa = self.monomial_coefficients()[(a, k)]
+            b, m = right.index()
+            coefb = right.monomial_coefficients()[(b, m)]
             try:
-                mbr = dict(s_coeff[(a,b)])
+                mbr = dict(s_coeff[(a, b)])
             except KeyError:
                 return {}
             pole = max(mbr.keys())
-            ret =  {l: coefa*coefb*(-1)**k/factorial(k)*sum(factorial(l)\
-                    /factorial(m+k+j-l)/factorial(l-k-j)/factorial(j)*\
-                    mbr[j].T(m+k+j-l) for j in mbr if j >= l-m-k and\
-                    j <= l-k) for l in range(m+k+pole+1)}
+            ret = {l: coefa * coefb * (-1)**k / factorial(k) *
+                   sum(factorial(l) / factorial(m + k + j - l)
+                       / factorial(l - k - j) / factorial(j)
+                       * mbr[j].T(m + k + j - l)
+                       for j in mbr if l - m - k <= j <= l - k)
+                   for l in range(m + k + pole + 1)}
             return {k: v for k, v in ret.items() if v}
 
-        diclist = [i._bracket_(j) for i in self.terms() for
-                   j in right.terms()]
+        diclist = [i._bracket_(j) for i in self.terms()
+                   for j in right.terms()]
         ret = {}
         pz = p.zero()
         for d in diclist:

src/sage/algebras/lie_conformal_algebras/lie_conformal_algebra_with_structure_coefs.py

@@ -158,18 +158,18 @@ def _standardize_s_coeff(s_coeff, index_set, ce, parity=None):
                 if lth_product:
                     vals[l]=lth_product
 
-            myvals = tuple([(k,tuple(v.items())) for k,v in vals.items() if v])
+            myvals = tuple((k, tuple(v.items())) for k, v in vals.items() if v)
 
             if key in sc.keys() and sorted(sc[key]) != sorted(myvals):
-                raise ValueError("two distinct values given for one "\
-                                 "and the same bracket, skew-symmetry"\
+                raise ValueError("two distinct values given for one "
+                                 "and the same bracket, skew-symmetry"
                                  "is not satisfied?")
             if myvals:
                 sc[key] = myvals
 
-            #We now add the skew-symmetric part to optimize
-            #brackets computations later
-            key=(mypair[1],mypair[0])
+            # We now add the skew-symmetric part to optimize
+            # brackets computations later
+            key = (mypair[1], mypair[0])
             if index_to_parity[mypair[0]]*index_to_parity[mypair[1]]:
                 parsgn = -1
             else:
@@ -191,11 +191,11 @@ def _standardize_s_coeff(s_coeff, index_set, ce, parity=None):
                 if kth_product:
                     vals[k]=kth_product
 
-            myvals = tuple([(k,tuple(v.items())) for k,v in vals.items() if v])
+            myvals = tuple((k, tuple(v.items())) for k, v in vals.items() if v)
 
             if key in sc.keys() and sorted(sc[key]) != sorted(myvals):
-                raise ValueError("two distinct values given for one "\
-                                 "and the same bracket. "\
+                raise ValueError("two distinct values given for one "
+                                 "and the same bracket. "
                                  "Skew-symmetry is not satisfied?")
             if myvals:
                 sc[key] = myvals
@@ -233,31 +233,31 @@ def __init__(self, R, s_coeff, index_set=None, central_elements=None,
                 # index_set
                 pass
 
-        issuper=kwds.pop('super', False)
+        issuper = kwds.pop('super', False)
         if parity is None:
-            parity = (0,)*index_set.cardinality()
+            parity = (0,) * index_set.cardinality()
         else:
             issuper = True
 
         try:
             assert len(parity) == index_set.cardinality()
         except AssertionError:
-            raise ValueError("parity should have the same length as the "\
-                             "number of generators, got {}".format(parity))
+            raise ValueError("parity should have the same length as the "
+                             f"number of generators, got {parity}")
 
         s_coeff = LieConformalAlgebraWithStructureCoefficients\
-                    ._standardize_s_coeff(s_coeff, index_set, central_elements,
-                                          parity)
+            ._standardize_s_coeff(s_coeff, index_set, central_elements,
+                                  parity)
 
         if names is not None and central_elements is not None:
             names += tuple(central_elements)
 
-        self._index_to_pos = {k: i for i,k in enumerate(index_set)}
-        #Add central parameters to index_to_pos so that we can
-        #represent names
+        self._index_to_pos = {k: i for i, k in enumerate(index_set)}
+        # Add central parameters to index_to_pos so that we can
+        # represent names
         if central_elements is not None:
-            for i,ce in enumerate(central_elements):
-                self._index_to_pos[ce] = len(index_set)+i
+            for i, ce in enumerate(central_elements):
+                self._index_to_pos[ce] = len(index_set) + i
 
         default_category = LieConformalAlgebras(R).WithBasis().FinitelyGenerated()
         if issuper:

src/sage/algebras/lie_conformal_algebras/neveu_schwarz_lie_conformal_algebra.py

@@ -57,15 +57,17 @@ def __init__(self, R):
             sage: V = lie_conformal_algebras.NeveuSchwarz(QQ)
             sage: TestSuite(V).run()
         """
-        nsdict =  {('L','L'):{0:{('L',1):1}, 1:{('L',0): 2},
-                    3:{('C', 0):R(2).inverse_of_unit()}},
-                   ('L','G'):{0:{('G',1):1}, 1:{('G',0):R(3)*R(2).\
-                    inverse_of_unit()}}, ('G','G'): {0:{('L',0):2},
-                    2:{('C',0):R(2)*R(3).inverse_of_unit()}}}
+        nsdict = {('L', 'L'): {0: {('L', 1): 1},
+                               1: {('L', 0): 2},
+                               3: {('C', 0): R(2).inverse_of_unit()}},
+                  ('L', 'G'): {0: {('G', 1): 1},
+                               1: {('G', 0): R(3) * R(2).inverse_of_unit()}},
+                  ('G', 'G'): {0: {('L', 0): 2},
+                               2: {('C', 0): R(2) * R(3).inverse_of_unit()}}}
         from sage.rings.rational_field import QQ
-        weights = (2,QQ(3/2))
-        parity = (0,1)
-        GradedLieConformalAlgebra.__init__(self, R, nsdict, names=('L','G'),
+        weights = (2, QQ((3, 2)))
+        parity = (0, 1)
+        GradedLieConformalAlgebra.__init__(self, R, nsdict, names=('L', 'G'),
                     central_elements=('C',), weights=weights, parity=parity)
 
     def _repr_(self):

src/sage/algebras/lie_conformal_algebras/weyl_lie_conformal_algebra.py

@@ -119,7 +119,7 @@ class WeylLieConformalAlgebra(LieConformalAlgebraWithStructureCoefficients):
         [0 1 0]
         [0 0 1]
     """
-    def __init__(self,R,ngens=None, gram_matrix=None, names=None,
+    def __init__(self, R, ngens=None, gram_matrix=None, names=None,
                  index_set=None):
         """
         Initialize self.
@@ -131,31 +131,29 @@ def __init__(self,R,ngens=None, gram_matrix=None, names=None,
         """
         from sage.matrix.matrix_space import MatrixSpace
         if ngens:
-            try:
-                from sage.rings.integer_ring import ZZ
-                assert ngens in ZZ and ngens % 2 == 0
-            except AssertionError:
-                raise ValueError("ngens needs to be an even positive "+
-                                 "Integer, got {}".format(ngens))
-        if (gram_matrix is not None):
+            from sage.rings.integer_ring import ZZ
+            if not(ngens in ZZ and not ngens % 2):
+                raise ValueError("ngens needs to be an even positive Integer, "
+                                 f"got {ngens}")
+        if gram_matrix is not None:
             if ngens is None:
                 ngens = gram_matrix.dimensions()[0]
             try:
-                assert (gram_matrix in MatrixSpace(R,ngens,ngens))
+                assert (gram_matrix in MatrixSpace(R, ngens, ngens))
             except AssertionError:
-                raise ValueError("The gram_matrix should be a skew-symmetric "+
-                    "{0} x {0} matrix, got {1}".format(ngens,gram_matrix))
-            if (not gram_matrix.is_skew_symmetric()) or \
-                                                (gram_matrix.is_singular()):
-                raise ValueError("The gram_matrix should be a non degenerate " +
-                                 "skew-symmetric {0} x {0} matrix, got {1}"\
-                                 .format(ngens,gram_matrix))
-        elif (gram_matrix is None):
+                raise ValueError("The gram_matrix should be a skew-symmetric "
+                    "{0} x {0} matrix, got {1}".format(ngens, gram_matrix))
+            if (not gram_matrix.is_skew_symmetric() or
+                    gram_matrix.is_singular()):
+                raise ValueError("The gram_matrix should be a non degenerate "
+                                 "skew-symmetric {0} x {0} matrix, got {1}"
+                                 .format(ngens, gram_matrix))
+        elif gram_matrix is None:
             if ngens is None:
                 ngens = 2
             A = identity_matrix(R, ngens // 2)
             from sage.matrix.special import block_matrix
-            gram_matrix = block_matrix([[R.zero(),A],[-A,R.zero()]])
+            gram_matrix = block_matrix([[R.zero(), A], [-A, R.zero()]])
 
         latex_names = None
         if (names is None) and (index_set is None):

src/sage/categories/drinfeld_modules.py

@@ -425,7 +425,7 @@ def characteristic(self):
             0
         """
         if self._characteristic is None:
-            raise NotImplementedError('function ring characteristic not ' \
+            raise NotImplementedError('function ring characteristic not '
                                       'implemented in this case')
         return self._characteristic
 
@@ -498,7 +498,7 @@ def object(self, gen):
         gen = self._ore_polring(gen)
         T = self._function_ring.gen()
         if gen[0] != self._base_morphism(T):
-            raise ValueError('constant coefficient must equal that of the ' \
+            raise ValueError('constant coefficient must equal that of the '
                              'category')
         return DrinfeldModule(self._function_ring, gen)
 

src/sage/coding/linear_code_no_metric.py

@@ -265,9 +265,9 @@ def __eq__(self, other):
             False
         """
         # Fail without computing the generator matrix if possible:
-        if not (isinstance(other, AbstractLinearCodeNoMetric)\
-                and self.length() == other.length()\
-                and self.dimension() == other.dimension()\
+        if not (isinstance(other, AbstractLinearCodeNoMetric)
+                and self.length() == other.length()
+                and self.dimension() == other.dimension()
                 and self.base_ring() == other.base_ring()):
             return False
         # Check that basis elements of `other` are all in `self.`
@@ -276,10 +276,7 @@ def __eq__(self, other):
         # This implementation may avoid linear algebra altogether, if `self`
         # implements an efficient way to obtain a parity check matrix, and in
         # the worst case does only one system solving.
-        for c in other.gens():
-            if not (c in self):
-                return False
-        return True
+        return all(c in self for c in other.gens())
 
     def __ne__(self, other):
         r"""