various ruff suggestions fixed in schemes

src/sage/schemes/curves/plane_curve_arrangement.py

@@ -200,13 +200,13 @@ def _repr_(self):
             Arrangement of 5 curves in Projective Space of dimension 2 over Rational Field
         """
         if not self:
-            return 'Empty curve arrangement in {0}'.format(self.parent().ambient_space())
+            return 'Empty curve arrangement in {}'.format(self.parent().ambient_space())
         elif len(self) < 5:
             curves = ', '.join(h.defining_polynomial()._repr_()
                                for h in self._curves)
-            return 'Arrangement ({0}) in {1}'.format(curves,
+            return 'Arrangement ({}) in {}'.format(curves,
                                                      self.parent().ambient_space())
-        return 'Arrangement of {0} curves in {1}'.format(len(self),
+        return 'Arrangement of {} curves in {}'.format(len(self),
                                                          self.parent().ambient_space())
 
     def _richcmp_(self, other, op):
@@ -574,7 +574,7 @@ def fundamental_group(self, simplified=True, vertical=True,
             if not vertical:
                 st = self._strands_nonvertical
                 d1 = prod(L).degree()
-                bd = (bm, st, dict(), d1)
+                bd = (bm, st, {}, d1)
             else:
                 st = self._strands_vertical
                 d1 = prod(L).degree(R.gen(1))
@@ -920,7 +920,7 @@ def fundamental_group(self, simplified=True):
                                        projective=proj)
         dic = C_affine.meridians(simplified=simplified, vertical=True)
         if infinity_in_C:
-            dic1 = dict()
+            dic1 = {}
             for k in range(j):
                 dic1[k] = dic[k]
             dic1[j] = dic[n - 1]
@@ -1023,7 +1023,7 @@ def __classcall__(cls, base, names=()):
         names = normalize_names(len(names), names)
         return super().__classcall__(cls, base, names)
 
-    def __init__(self, base_ring, names=tuple()):
+    def __init__(self, base_ring, names=()):
         """
         Initialize ``self``.
 
@@ -1115,7 +1115,7 @@ def _repr_(self):
             sage: L.<x, y> = AffinePlaneCurveArrangements(QQ);  L
             Curve arrangements in Affine Space of dimension 2 over Rational Field
         """
-        return 'Curve arrangements in {0}'.format(self.ambient_space())
+        return 'Curve arrangements in {}'.format(self.ambient_space())
 
     def _element_constructor_(self, *args, **kwds):
         """

src/sage/schemes/curves/zariski_vankampen.py

@@ -1524,14 +1524,15 @@ def braid2rels(L):
     k = min(T1) - 1
     B0 = BraidGroup(m)
     F0 = FreeGroup(m)
-    br0 = B0([j-k for j in T])
+    br0 = B0([j - k for j in T])
     br0_left = leftnormalform(br0)
     q, r = ZZ(br0_left[0][0]).quo_rem(2)
     br1 = B0.delta()**r * prod(map(B0, br0_left[1:]), B0.one())
     cox = prod(F0.gens())
     U0 = [cox**q * (f0 * br1) / cox**q / f0 for f0 in F0.gens()[:-1]]
     U = [tuple(sign(k1) * (abs(k1) + k) for k1 in br.Tietze()) for br in U0]
-    pasos = [B.one()] + list(reversed(L1))
+    pasos = [B.one()]
+    pasos.extend(reversed(L1))
     for C in pasos:
         U = [(F(a) * C.inverse()).Tietze() for a in U]
         ga = F / U
@@ -1884,13 +1885,13 @@ def fundamental_group_arrangement(flist, simplified=True, projective=False,
     x, y = R.gens()
     flist1 = tuple(flist)
     if vertical and vertical_lines_in_braidmon(flist1):
-        infinity = all([Curve(g).is_vertical_line() or
-                        g.degree(y) == g.degree() for g in flist1])
+        infinity = all(Curve(g).is_vertical_line() or
+                       g.degree(y) == g.degree() for g in flist1)
     else:
-        infinity = any([Curve(g).has_vertical_asymptote() or
-                        Curve(g).is_vertical_line() for g in flist1])
+        infinity = any(Curve(g).has_vertical_asymptote() or
+                       Curve(g).is_vertical_line() for g in flist1)
         if not infinity:
-            infinity = all([g.degree(y) == g.degree() for g in flist1])
+            infinity = all(g.degree(y) == g.degree() for g in flist1)
     if braid_data:
         bm, dic, dv, d1 = braid_data
     elif not flist:
@@ -1925,5 +1926,5 @@ def fundamental_group_arrangement(flist, simplified=True, projective=False,
     n = g1.ngens()
     rels = [rel.Tietze() for rel in g1.relations()]
     g1 = FreeGroup(n) / rels
-    dic1 = {i: list(set([g1(el.Tietze()) for el in dic1[i]])) for i in dic1}
+    dic1 = {i: list({g1(el.Tietze()) for el in dic1[i]}) for i in dic1}
     return (g1, dic1)

src/sage/schemes/elliptic_curves/ell_rational_field.py

@@ -5823,8 +5823,8 @@ def height(self, precision=None):
         c4 = self.c4()
         c6 = self.c6()
         j = self.j_invariant()
-        log_g2 = R((c4/12)).abs().log()
-        log_g3 = R((c6/216)).abs().log()
+        log_g2 = R(c4/12).abs().log()
+        log_g3 = R(c6/216).abs().log()
 
         if j == 0:
             h_j = R(1)
@@ -6348,7 +6348,7 @@ def point_preprocessing(free,tor):
             #new bound according to low_bound and upper bound
             #[c_5 exp((-c_2*H_q^2)/2)] provided by Corollary 8.7.3
             if low_bound != 0:
-                H_q_new = R((log(low_bound/c5)/(-c2/2))).sqrt()
+                H_q_new = R(log(low_bound/c5)/(-c2/2)).sqrt()
                 H_q_new = H_q_new.ceil()
                 if H_q_new == 1:
                     break_cond = 1 # stops reduction
@@ -7025,9 +7025,8 @@ def S_integral_x_coords_with_abs_bounded_by(abs_bound):
             else:
                 bound_list.append(H_q)
 
-         ##reduction for finite places in S
-            for p in S:
-                bound_list.append(reduction_at(p))
+            # reduction for finite places in S
+            bound_list.extend(reduction_at(p) for p in S)
 
             if verbose:
                 print('bound_list', bound_list)

src/sage/schemes/elliptic_curves/gal_reps_number_field.py

@@ -739,9 +739,7 @@ def _exceptionals(E, L, patience=1000):
         if (not D) or (patience == 0):
             break
 
-    for l in D:
-        output.append(l)
-
+    output.extend(D)
     output.sort()
     return output
 

src/sage/schemes/elliptic_curves/heegner.py

@@ -7055,7 +7055,7 @@ def _heegner_index_in_EK(self, D):
     basis = [G(z) for z in E.gens()] + [G(phi(z)) for z in F.gens()]
     # Make a list of the 2-power order torsion points in E(K), including 0.
     T = [G(z) for z in G.torsion_subgroup().list() if z.order() == 1 or
-            ((z.order() % 2 == 0 and len(z.order().factor()) == 1))]
+            (z.order() % 2 == 0 and len(z.order().factor()) == 1)]
 
     r = len(basis)   # rank
     V = QQ**r
@@ -7066,9 +7066,8 @@ def _heegner_index_in_EK(self, D):
         if not v:
             continue
         P = sum([basis[i] for i in range(r) if v[i]])
-        for t in T:
-            if (P+t).is_divisible_by(2):
-                B.append(V(v)/2)
+        w = V(v) / 2
+        B.extend(w for t in T if (P + t).is_divisible_by(2))
 
     A = ZZ**r
     # Take span of our vectors in (1/2)*ZZ^r, along with ZZ^r.  This is E(K)/tor.

src/sage/schemes/elliptic_curves/isogeny_small_degree.py

@@ -564,7 +564,7 @@ def _sporadic_Q_data(j):
     w = w1 # real period
     if j in [-121, -24729001, -162677523113838677, QQ(-882216989)/131072]:
         w = 2*w2-w1 # imaginary period
-    kerpol = prod(([X-L.elliptic_exponential(n*w/ell)[0] for n in range(1,(ell+1)//2)]))
+    kerpol = prod([X-L.elliptic_exponential(n*w/ell)[0] for n in range(1,(ell+1)//2)])
     if j == -162677523113838677:
         kerpolcoeffs = [(37*c.real()).round()/37 for c in list(kerpol)]
     else:
@@ -2110,7 +2110,7 @@ def isogenies_prime_degree_genus_plus_0_j0(E, l, minimal_models=True):
         raise ValueError("%s must be one of %s." % (l,hyperelliptic_primes))
     F = E.base_field()
     if E.j_invariant() != 0:
-        raise ValueError(("j-invariant must be 0."))
+        raise ValueError("j-invariant must be 0.")
     if F.characteristic() in [2,3,l]:
         raise NotImplementedError("Not implemented in characteristic 2, 3 or l.")
 

src/sage/schemes/elliptic_curves/padic_lseries.py

@@ -1554,7 +1554,7 @@ def __phi_bpr(self, prec=0):
         if prec > 10:
             print("Warning: Very large value for the precision.")
         if prec == 0:
-            prec = floor((log(10000)/log(p)))
+            prec = floor(log(10000)/log(p))
             verbose("prec set to %s" % prec)
         eh = E.formal()
         om = eh.differential(prec=p**prec+3)

src/sage/schemes/elliptic_curves/weierstrass_morphism.py

@@ -32,7 +32,7 @@
 from sage.rings.integer import Integer
 from sage.rings.polynomial.polynomial_ring_constructor import PolynomialRing
 
-class baseWI():
+class baseWI:
     r"""
     This class implements the basic arithmetic of isomorphisms between
     Weierstrass models of elliptic curves.

src/sage/schemes/product_projective/space.py

@@ -256,7 +256,7 @@ def _repr_(self):
             Product of projective spaces P^1 x P^1 x P^1 over Integer Ring
         """
         return ''.join(['Product of projective spaces ',
-                        ' x '.join('P^{0}'.format(d) for d in self._dims),
+                        ' x '.join('P^{}'.format(d) for d in self._dims),
                         ' over ', str(self.base_ring())])
 
     def _repr_generic_point(self, v=None):
@@ -1197,8 +1197,8 @@ def points_of_bounded_height(self, **kwds):
         P = []
         for i in range(m):
             pt = next(iters[i])
-            for j in range(dim[i]):
-                P.append(pt[j]) # initial value of P
+            P.extend(pt[j] for j in range(dim[i]))
+            # initial value of P
         yield self(P)
 
         i = 0
@@ -1248,9 +1248,7 @@ def __iter__(self):
              (1 : 0 : 0 , 1 : 0)]
         """
         iters = [iter(T) for T in self._components]
-        L = []
-        for x in iters:
-            L.append(next(x))  # put at zero
+        L = [next(x) for x in iters]  # put at zero
         yield self(L)
         j = 0
         while j < self.num_components():

src/sage/schemes/projective/projective_morphism.py

@@ -1233,9 +1233,8 @@ def dehomogenize(self, n):
             G = phi(self._polys[ind[1]])
             # ind[1] is relative to codomain
             M = self.codomain().ambient_space().dimension_relative()
-            for i in range(0, M + 1):
-                if i != ind[1]:
-                    F.append(phi(self._polys[i]) / G)
+            F.extend(phi(self._polys[i]) / G
+                     for i in range(M + 1) if i != ind[1])
             H = Hom(Aff_domain, self.codomain().affine_patch(ind[1]))
             # since often you dehomogenize at the same coordinate in domain
             # and codomain it should be stored appropriately.
@@ -1720,17 +1719,13 @@ def rational_preimages(self, Q, k=1):
             L2 = []
             for P in L:
                 I = list(self.domain().defining_polynomials())
-                for i in range(N+1):
-                    for j in range(i+1, N+1):
-                        I.append(P[i]*self[j] - P[j]*self[i])
+                I.extend(P[i] * self[j] - P[j] * self[i]
+                         for i in range(N + 1) for j in range(i + 1, N + 1))
                 X = PS.subscheme(I)
                 if X.dimension() > 0:
                     return X
-                preimages = []
-                for T in X.rational_points():
-                    if not all(g(tuple(T)) == 0 for g in self):
-                        preimages.append(PS(T))
-                L2 = L2 + preimages
+                L2.extend(PS(T) for T in X.rational_points()
+                          if not all(g(tuple(T)) == 0 for g in self))
             L = L2
         return L
 
@@ -2224,8 +2219,8 @@ def reduce_base_field(self):
                         # find the right subfield and it's embedding
                         if M.degree() == da:
                             break
-                    c = M((str(c).replace(c.as_finite_field_element()[0].variable_name(),
-                                          M.variable_name())))
+                    c = M(str(c).replace(c.as_finite_field_element()[0].variable_name(),
+                                          M.variable_name()))
                     new_c.append(M_to_L(c))
                 # reconstruct as a poly in the new domain
                 new_f.append(sum([new_c[i] * prod(new_R.gen(j)**mon_deg[i][j]
@@ -2613,9 +2608,8 @@ def self_with_domain(C):
         polys = list(X.defining_polynomials())
 
         for r in self.representatives():
-            r_proj = r if emb is None else emb*r
-            for p in r_proj:
-                polys.append(p)
+            r_proj = r if emb is None else emb * r
+            polys.extend(r_proj)
 
         return Amb.subscheme(polys).reduce()
 

src/sage/schemes/riemann_surfaces/riemann_surface.py

@@ -481,7 +481,7 @@ def reparameterize_differential_minpoly(minpoly, z0):
     return mt
 
 
-class RiemannSurface():
+class RiemannSurface:
     r"""
     Construct a Riemann Surface. This is specified by the zeroes of a bivariate
     polynomial with rational coefficients `f(z,w) = 0`.

src/sage/schemes/toric/divisor.py

@@ -346,7 +346,7 @@ def ToricDivisor(toric_variety, arg=None, ring=None, check=True, reduce=True):
     except (AssertionError, TypeError):
         n_rays = toric_variety.fan().nrays()
         assert len(arg) == n_rays, \
-            'Argument list {0} is not of the required length {1}!' \
+            'Argument list {} is not of the required length {}!' \
             .format(arg, n_rays)
         arg = list(zip(arg, toric_variety.gens()))
         reduce = False

src/sage/schemes/toric/morphism.py

@@ -1537,12 +1537,11 @@ def fiber_dimension(self, codomain_cone):
         dim = []
         fm = self.fan_morphism()
         base_dim = codomain_cone.dim()
-        for c in fm.primitive_preimage_cones(codomain_cone):
-            dim.append(base_dim - c.dim())
+        dim.extend(base_dim - c.dim()
+                   for c in fm.primitive_preimage_cones(codomain_cone))
         if dim:
             return max(dim) + self.domain().dimension() - self.codomain().dimension()
-        else:
-            return ZZ(-1)
+        return ZZ(-1)
 
     def fiber_graph(self, codomain_cone):
         r"""

src/sage/schemes/toric/points.py

@@ -44,7 +44,7 @@
 from sage.parallel.decorate import Parallel
 
 
-class InfinitePointEnumerator():
+class InfinitePointEnumerator:
 
     def __init__(self, fan, ring):
         """
@@ -105,7 +105,7 @@ def __iter__(self):
                 yield tuple(p)
 
 
-class NaiveFinitePointEnumerator():
+class NaiveFinitePointEnumerator:
 
     def __init__(self, fan, ring):
         """
@@ -756,7 +756,7 @@ def cardinality(self):
         return n
 
 
-class NaiveSubschemePointEnumerator():
+class NaiveSubschemePointEnumerator:
 
     def __init__(self, polynomials, ambient):
         """

src/sage/schemes/toric/sheaf/constructor.py

@@ -138,7 +138,7 @@ def LineBundle(X, D):
     return klyachko.Bundle(X, filtrations, check=True)
 
 
-class SheafLibrary():
+class SheafLibrary:
 
     def __init__(self, toric_variety):
         """