Massive modularization fixes

Author: Matthias Koeppe

src/sage/rings/number_field/S_unit_solver.py

@@ -982,11 +982,12 @@ def minimal_vector(A, y, prec=106):
     ALLLinv = ALLL.inverse()
     ybrace = [ abs(R(a-a.round())) for a in y * ALLLinv if (a-a.round()) != 0]
 
+    v = ALLL.rows()[0]
     if len(ybrace) == 0:
-        return (ALLL.rows()[0].norm())**2 / c1
+        return v.dot_product(v) / c1
     else:
         sigma = ybrace[len(ybrace)-1]
-        return ((ALLL.rows()[0].norm())**2 * sigma) / c1
+        return v.dot_product(v) * sigma / c1
 
 
 def reduction_step_complex_case(place, B0, list_of_gens, torsion_gen, c13):

src/sage/rings/number_field/galois_group.py

@@ -46,17 +46,18 @@ class GaloisGroup_v1(SageObject):
     EXAMPLES::
 
         sage: from sage.rings.number_field.galois_group import GaloisGroup_v1
-        sage: K = QQ[2^(1/3)]
-        sage: G = GaloisGroup_v1(K.absolute_polynomial().galois_group(pari_group=True), K); G
+        sage: K = QQ[2^(1/3)]                                                           # optional - sage.symbolic
+        sage: pK = K.absolute_polynomial()                                              # optional - sage.symbolic
+        sage: G = GaloisGroup_v1(pK.galois_group(pari_group=True), K); G                # optional - sage.symbolic
         ...DeprecationWarning: GaloisGroup_v1 is deprecated; please use GaloisGroup_v2
         See https://github.com/sagemath/sage/issues/28782 for details.
         Galois group PARI group [6, -1, 2, "S3"] of degree 3 of the
          Number Field in a with defining polynomial x^3 - 2 with a = 1.259921049894873?
-        sage: G.order()
+        sage: G.order()                                                                 # optional - sage.symbolic
         6
-        sage: G.group()
+        sage: G.group()                                                                 # optional - sage.symbolic
         PARI group [6, -1, 2, "S3"] of degree 3
-        sage: G.number_field()
+        sage: G.number_field()                                                          # optional - sage.symbolic
         Number Field in a with defining polynomial x^3 - 2 with a = 1.259921049894873?
     """
 
@@ -96,11 +97,11 @@ def __eq__(self, other):
             sage: G = GaloisGroup_v1(K.absolute_polynomial().galois_group(pari_group=True), K)
             ...DeprecationWarning: GaloisGroup_v1 is deprecated; please use GaloisGroup_v2
             See https://github.com/sagemath/sage/issues/28782 for details.
-            sage: L = QQ[sqrt(2)]
-            sage: H = GaloisGroup_v1(L.absolute_polynomial().galois_group(pari_group=True), L)
-            sage: H == G
+            sage: L = QQ[sqrt(2)]                                                               # optional - sage.symbolic
+            sage: H = GaloisGroup_v1(L.absolute_polynomial().galois_group(pari_group=True), L)  # optional - sage.symbolic
+            sage: H == G                                                                        # optional - sage.symbolic
             False
-            sage: H == H
+            sage: H == H                                                                        # optional - sage.symbolic
             True
             sage: G == G
             True
@@ -125,11 +126,11 @@ def __ne__(self, other):
             sage: G = GaloisGroup_v1(K.absolute_polynomial().galois_group(pari_group=True), K)
             ...DeprecationWarning: GaloisGroup_v1 is deprecated; please use GaloisGroup_v2
             See https://github.com/sagemath/sage/issues/28782 for details.
-            sage: L = QQ[sqrt(2)]
-            sage: H = GaloisGroup_v1(L.absolute_polynomial().galois_group(pari_group=True), L)
-            sage: H != G
+            sage: L = QQ[sqrt(2)]                                                               # optional - sage.symbolic
+            sage: H = GaloisGroup_v1(L.absolute_polynomial().galois_group(pari_group=True), L)  # optional - sage.symbolic
+            sage: H != G                                                                        # optional - sage.symbolic
             True
-            sage: H != H
+            sage: H != H                                                                        # optional - sage.symbolic
             False
             sage: G != G
             False

src/sage/rings/number_field/maps.py

@@ -79,7 +79,7 @@ def _repr_type(self):
 
     def is_injective(self):
         r"""
-         EXAMPLES::
+        EXAMPLES::
 
             sage: x = polygen(ZZ, 'x')
             sage: K.<a> = NumberField(x^4 + 3*x + 1)
@@ -91,7 +91,7 @@ def is_injective(self):
 
     def is_surjective(self):
         r"""
-         EXAMPLES::
+        EXAMPLES::
 
             sage: x = polygen(ZZ, 'x')
             sage: K.<a> = NumberField(x^4 + 3*x + 1)