fix suggested details and a few more

Author: fchapoton

src/sage/rings/rational.pyx

@@ -2043,8 +2043,8 @@ cdef class Rational(sage.structure.element.FieldElement):
             3.1415094339622641509433962264150943396226415094339622641509
         """
         d = self.denominator()
-        _, d = d.val_unit(2)
-        _, d  = d.val_unit(5)
+        d = d.val_unit(2)[1]
+        d = d.val_unit(5)[1]
         from sage.rings.finite_rings.integer_mod import Mod
         return Mod(10, d).multiplicative_order()
 

src/sage/rings/ring_extension.pyx

@@ -479,7 +479,7 @@ class RingExtensionFactory(UniqueFactory):
             sage: RingExtension.create_object((8,9,0), key, **extra_args)
             Rational Field over its base
         """
-        defining_morphism, _, _ = key
+        defining_morphism = key[0]
         constructors = extra_args['constructors']
         if len(constructors) == 0:
             raise NotImplementedError("no constructor available for this extension")

src/sage/rings/ring_extension_morphism.pyx

@@ -836,7 +836,7 @@ cdef class MapRelativeRingToFreeModule(Map):
         from sage.rings.ring_extension import common_base
         base = common_base(K, L, False)
         EK, iK, _ = K.free_module(base, map=True)
-        _, _, jL = L.free_module(base, map=True)
+        jL = L.free_module(base, map=True)[2]
 
         self._dimK = EK.dimension()
         self._iK = iK

src/sage/rings/tate_algebra_ideal.pyx

@@ -390,7 +390,7 @@ class TateAlgebraIdeal(Ideal_generic):
         if self.ring().base_ring().is_field():
             return self
         gb = self.groebner_basis()
-        gens = [ g.monic() for g in gb ]
+        gens = [g.monic() for g in gb]
         return self.ring().ideal(gens)
 
 
@@ -432,14 +432,14 @@ def groebner_basis_buchberger(I, prec, py_integral):
          ...0000000001*x^2*y + ...1210121020 + O(3^10 * <x, y>),
          ...000000001*y^2 + ...210121020*x + O(3^9 * <x, y>)]
     """
-    cdef list gb, rgb, indices, S = [ ]
+    cdef list gb, rgb, indices, S = []
     cdef int i, j, l
     cdef TateAlgebraTerm ti, tj, t
     cdef TateAlgebraElement f, g, r, s
     cdef bint do_reduce = True
     cdef bint integral = py_integral
 
-    gb = [ ]
+    gb = []
     l = 0
     for f in I.gens():
         if not f:
@@ -550,9 +550,10 @@ def groebner_basis_buchberger(I, prec, py_integral):
                 rgb[i] = g._positive_lshift_c(1)
                 _, rgb[i] = g._quo_rem_c(rgb, False, True, True)
         else:
-            rgb = [ g.monic() for g in rgb ]
+            rgb = [g.monic() for g in rgb]
     else:
-        rgb = [ g * base(g.leading_coefficient().unit_part()).inverse_of_unit() for g in rgb ]
+        rgb = [g * base(g.leading_coefficient().unit_part()).inverse_of_unit()
+               for g in rgb]
 
     rgb.sort(reverse=True)
     return rgb
@@ -638,7 +639,7 @@ cdef TateAlgebraElement regular_reduce(sgb, TateAlgebraTerm s, TateAlgebraElemen
     cdef dict coeffs = { }
     cdef TateAlgebraElement f
     cdef TateAlgebraTerm lt, factor
-    cdef list ltds = [ (<TateAlgebraElement>(d[1]))._terms_c()[0] for d in sgb ]
+    cdef list ltds = [(<TateAlgebraElement>(d[1]))._terms_c()[0] for d in sgb]
     cdef list terms = v._terms_c()
     cdef int index = 0
     cdef int i
@@ -711,7 +712,7 @@ cdef TateAlgebraElement reduce(gb, TateAlgebraElement v, stopval):
     cdef dict coeffs = { }
     cdef TateAlgebraElement f
     cdef TateAlgebraTerm lt, factor
-    cdef list ltds = [ (<TateAlgebraElement>d)._terms_c()[0] for d in gb ]
+    cdef list ltds = [(<TateAlgebraElement>d)._terms_c()[0] for d in gb]
     cdef list terms = v._terms_c()
     cdef int index = 0
     cdef int i
@@ -854,7 +855,7 @@ def groebner_basis_pote(I, prec, verbose=0):
     cdef TateAlgebraTerm term_one = I.ring().monoid_of_terms().one()
     cdef bint integral = not I.ring().base_ring().is_field()
 
-    gb = [ ]
+    gb = []
 
     for f in sorted(I.gens()):
         sig_check()
@@ -869,10 +870,10 @@ def groebner_basis_pote(I, prec, verbose=0):
             print("new generator: %s + ..." % f.leading_term())
         # Initial strong Grobner basis:
         # we add signatures
-        sgb = [ (None, g) for g in gb if g ]
+        sgb = [(None, g) for g in gb if g]
         # We compute initial J-pairs
         p = (term_one, f.add_bigoh(prec))
-        Jpairs = [ ]
+        Jpairs = []
         for P in sgb:
             sig_check()
             J = Jpair(p, P)
@@ -881,7 +882,7 @@ def groebner_basis_pote(I, prec, verbose=0):
         sgb.append(p)
 
         # For the syzygy criterium
-        gb0 = [ g.leading_term() for g in gb ]
+        gb0 = [g.leading_term() for g in gb]
 
         if verbose > 1:
             print("%s initial J-pairs" % len(Jpairs))
@@ -1003,7 +1004,7 @@ def groebner_basis_pote(I, prec, verbose=0):
                 print("| %s" % g)
 
     if not integral:
-        gb = [ f.monic() for f in gb ]
+        gb = [f.monic() for f in gb]
     gb.sort(reverse=True)
     return gb
 
@@ -1098,9 +1099,9 @@ def groebner_basis_vapote(I, prec, verbose=0, interrupt_red_with_val=False, inte
     cdef list terms
     cdef bint do_reduce, integral
     term_one = I.ring().monoid_of_terms().one()
-    gb = [ ]
+    gb = []
 
-    gens = [ ]
+    gens = []
     for f in I.gens():
         if f:
             val = f.valuation()
@@ -1155,18 +1156,18 @@ def groebner_basis_vapote(I, prec, verbose=0, interrupt_red_with_val=False, inte
 
         # Initial strong Grobner basis:
         # we add signatures
-        sgb = [ (None, g) for g in gb if g ]
+        sgb = [(None, g) for g in gb if g]
         # We compute initial J-pairs
         p = (term_one, f.add_bigoh(prec))
-        Jpairs = [ ]
+        Jpairs = []
         for P in sgb:
             J = Jpair(p, P)
             if J is not None:
                 heappush(Jpairs, J)
         sgb.append(p)
 
         # For the syzygy criterium
-        gb0 = [ g.leading_term() for g in gb ]
+        gb0 = [g.leading_term() for g in gb]
 
         if verbose > 1:
             print("%s initial J-pairs" % len(Jpairs))
@@ -1254,8 +1255,8 @@ def groebner_basis_vapote(I, prec, verbose=0, interrupt_red_with_val=False, inte
                 sgb.append(p)
 
         # We forget signatures
-        # gb = [ v.monic() for (s,v) in sgb ]
-        gb = [ v for (s,v) in sgb ]
+        # gb = [v.monic() for s, v in sgb]
+        gb = [v for s, v in sgb]
         if verbose > 1:
             print("%s elements in GB before minimization" % len(gb))
         if verbose > 3:
@@ -1297,7 +1298,7 @@ def groebner_basis_vapote(I, prec, verbose=0, interrupt_red_with_val=False, inte
         for g in gb:
             print("| %s" % g)
     if not integral:
-        gb = [ f.monic() for f in gb ]
+        gb = [f.monic() for f in gb]
     gb.sort(reverse=True)
 
     return gb