gh-39048: pep8 cleanup in libs
    
just fixing most pep8 warning in the `libs` folder

### 📝 Checklist

- [x] The title is concise and informative.
- [x] The description explains in detail what this PR is about.
    
URL: #39048
Reported by: Frédéric Chapoton
Reviewer(s): Travis Scrimshaw

Author: Release Manager

src/sage/libs/coxeter3/coxeter_group.py

@@ -279,7 +279,7 @@ def m(self, i, j):
         """
         from sage.misc.superseded import deprecation
         deprecation(30237, "the .m(i, j) method has been deprecated; use .coxeter_matrix()[i,j] instead.")
-        return self.coxeter_matrix()[i,j]
+        return self.coxeter_matrix()[i, j]
 
     def kazhdan_lusztig_polynomial(self, u, v, constant_term_one=True):
         r"""
@@ -354,8 +354,9 @@ def kazhdan_lusztig_polynomial(self, u, v, constant_term_one=True):
             return p
         ZZq = PolynomialRing(ZZ, 'q', sparse=True)
         # This is the same as q**len_diff * p(q**(-2))
-        len_diff = v.length()-u.length()
-        d = {-2*deg+len_diff: coeff for deg,coeff in enumerate(p) if coeff != 0}
+        len_diff = v.length() - u.length()
+        d = {-2 * deg + len_diff: coeff for deg, coeff in enumerate(p)
+             if coeff != 0}
         return ZZq(d)
 
     def parabolic_kazhdan_lusztig_polynomial(self, u, v, J, constant_term_one=True):
@@ -414,11 +415,11 @@ def parabolic_kazhdan_lusztig_polynomial(self, u, v, J, constant_term_one=True):
         WOI = self.weak_order_ideal(lambda x: J_set.issuperset(x.descents()))
         if constant_term_one:
             P = PolynomialRing(ZZ, 'q')
-            return P.sum((-1)**(z.length()) * self.kazhdan_lusztig_polynomial(u*z,v)
-                         for z in WOI if (u*z).bruhat_le(v))
+            return P.sum((-1)**(z.length()) * self.kazhdan_lusztig_polynomial(u * z, v)
+                         for z in WOI if (u * z).bruhat_le(v))
         P = PolynomialRing(ZZ, 'q', sparse=True)
-        return P.sum((-1)**(z.length()) * self.kazhdan_lusztig_polynomial(u*z,v, constant_term_one=False).shift(z.length())
-                     for z in WOI if (u*z).bruhat_le(v))
+        return P.sum((-1)**(z.length()) * self.kazhdan_lusztig_polynomial(u * z, v, constant_term_one=False).shift(z.length())
+                     for z in WOI if (u * z).bruhat_le(v))
 
     class Element(ElementWrapper):
         wrapped_class = CoxGroupElement
@@ -701,7 +702,7 @@ def action_on_rational_function(self, f):
 
                 for exponent in exponents:
                     # Construct something in the root lattice from the exponent vector
-                    exponent = sum(e*b for e, b in zip(exponent, basis_elements))
+                    exponent = sum(e * b for e, b in zip(exponent, basis_elements))
                     exponent = self.action(exponent)
 
                     monomial = 1

src/sage/libs/eclib/interface.py

@@ -247,8 +247,11 @@ def __repr__(self):
         """
         a1, a2, a3, a4, a6 = self.__ainvs
         # we do not assume a1, a2, a3 are reduced to {0,1}, {-1,0,1}, {0,1}
-        coeff = lambda a: ''.join([" +" if a > 0 else " -",
-                                   " " + str(abs(a)) if abs(a) > 1 else ""])
+
+        def coeff(a):
+            return ''.join([" +" if a > 0 else " -",
+                            " " + str(abs(a)) if abs(a) > 1 else ""])
+
         return ''.join(['y^2',
                         ' '.join([coeff(a1), 'xy']) if a1 else '',
                         ' '.join([coeff(a3), 'y']) if a3 else '',
@@ -614,12 +617,14 @@ def certain(self):
         """
         return bool(self.__two_descent_data().getcertain())
 
-    #def fullmw(self):
-    #    return self.__two_descent_data().getfullmw()
+    # def fullmw(self):
+    #     return self.__two_descent_data().getfullmw()
 
     def CPS_height_bound(self):
         r"""
-        Return the Cremona-Prickett-Siksek height bound.  This is a
+        Return the Cremona-Prickett-Siksek height bound.
+
+        This is a
         floating point number `B` such that if `P` is a point on the
         curve, then the naive logarithmic height `h(P)` is less than
         `B+\hat{h}(P)`, where `\hat{h}(P)` is the canonical height of
@@ -1290,9 +1295,9 @@ def search(self, height_limit=18, verbose=False):
         """
         height_limit = float(height_limit)
         int_bits = sys.maxsize.bit_length()
-        max_height_limit = int_bits * 0.693147 # log(2.0) = 0.693147 approx
+        max_height_limit = int_bits * 0.693147  # log(2.0) = 0.693147 approx
         if height_limit >= max_height_limit:
-            raise ValueError("The height limit must be < {} = {}log(2) on a {}-bit machine.".format(max_height_limit, int_bits, int_bits+1))
+            raise ValueError("The height limit must be < {} = {}log(2) on a {}-bit machine.".format(max_height_limit, int_bits, int_bits + 1))
 
         moduli_option = 0  # Use Stoll's sieving program... see strategies in ratpoints-1.4.c
 

src/sage/libs/gap/gap_globals.py

@@ -15,34 +15,34 @@
 
 
 # selected gap globals to use in tab completion
-common_gap_globals = set([
-  'Assert',
-  'Cyclotomics',
-  'GaussianIntegers',
-  'GaussianRationals',
-  'GlobalMersenneTwister',
-  'GlobalRandomSource',
-  'InfoAlgebra',
-  'InfoAttributes',
-  'InfoBckt',
-  'InfoCharacterTable',
-  'InfoCoh',
-  'InfoComplement',
-  'InfoCoset',
-  'InfoFpGroup',
-  'InfoGroebner',
-  'InfoGroup',
-  'InfoLattice',
-  'InfoMatrix',
-  'InfoMonomial',
-  'InfoNumtheor',
-  'InfoOptions',
-  'InfoPackageLoading',
-  'InfoPcSubgroup',
-  'InfoWarning',
-  'Integers',
-  'NiceBasisFiltersInfo',
-  'Primes',
-  'Rationals',
-  'TableOfMarksComponents'
-]) | common_gap_functions
+common_gap_globals = {
+    'Assert',
+    'Cyclotomics',
+    'GaussianIntegers',
+    'GaussianRationals',
+    'GlobalMersenneTwister',
+    'GlobalRandomSource',
+    'InfoAlgebra',
+    'InfoAttributes',
+    'InfoBckt',
+    'InfoCharacterTable',
+    'InfoCoh',
+    'InfoComplement',
+    'InfoCoset',
+    'InfoFpGroup',
+    'InfoGroebner',
+    'InfoGroup',
+    'InfoLattice',
+    'InfoMatrix',
+    'InfoMonomial',
+    'InfoNumtheor',
+    'InfoOptions',
+    'InfoPackageLoading',
+    'InfoPcSubgroup',
+    'InfoWarning',
+    'Integers',
+    'NiceBasisFiltersInfo',
+    'Primes',
+    'Rationals',
+    'TableOfMarksComponents'
+} | common_gap_functions

src/sage/libs/gap/test_long.py

@@ -28,7 +28,7 @@ def test_loop_2():
     G = libgap.FreeGroup(2)
     a, b = G.GeneratorsOfGroup()
     for i in range(100):
-        rel = libgap([a**2, b**2, a*b*a*b])
+        rel = libgap([a**2, b**2, a * b * a * b])
         H = G / rel
         H1 = H.GeneratorsOfGroup()[0]
         n = H1.Order()

src/sage/libs/giac/__init__.py

@@ -287,7 +287,7 @@ def groebner_basis(gens, proba_epsilon=None, threads=None, prot=False,
         return PolynomialSequence([P(0)], P, immutable=True)
 
     # check for name confusions
-    blackgiacconstants = ['i', 'e'] # NB e^k is expanded to exp(k)
+    blackgiacconstants = ['i', 'e']  # NB e^k is expanded to exp(k)
     blacklist = blackgiacconstants + [str(j) for j in libgiac.VARS()]
     problematicnames = sorted(set(P.gens_dict()).intersection(blacklist))
 
@@ -336,8 +336,8 @@ def groebner_basis(gens, proba_epsilon=None, threads=None, prot=False,
                 var_names = var_names[:len(blocks[0])]
             else:
                 raise NotImplementedError(
-                        "%s is not a supported term order in "
-                        "Giac Groebner bases." % P.term_order())
+                    "%s is not a supported term order in "
+                    "Giac Groebner bases." % P.term_order())
 
         # compute de groebner basis with giac
         gb_giac = F.gbasis(list(var_names), giac_order)

src/sage/libs/pari/__init__.py

@@ -182,8 +182,8 @@ def _get_pari_instance():
         Interface to the PARI C library
     """
     from cypari2 import Pari
-    stack_initial = 1024*1024
-    stack_max = 1024*stack_initial
+    stack_initial = 1024 * 1024
+    stack_max = 1024 * stack_initial
     P = Pari(stack_initial, stack_max)
 
     # pari_init_opts() overrides MPIR's memory allocation functions,

src/sage/libs/singular/standard_options.py

@@ -96,7 +96,7 @@ def __exit__(self, typ, value, tb):
               b - 3*d^6 + 2*d^4 + d^3 + 2*d^2 - 3*d,
               a - 2*d^6 + d^5 - 2*d^4 + 3*d^3 + 3*d^2 - 2*d - 1]
         """
-        self.libsingular_option_context.__exit__(typ,value,tb)
+        self.libsingular_option_context.__exit__(typ, value, tb)
 
 
 def libsingular_gb_standard_options(func):