Trac 6018: improve repr() of Dirichlet groups

sagemath · Jul 20, 2015 · 1431319 · 1431319
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diff --git a/src/doc/de/tutorial/tour_advanced.rst b/src/doc/de/tutorial/tour_advanced.rst
@@ -334,10 +334,8 @@ Faktorisierung des Moduls entsprechen.
 
     sage: G.decomposition()
     [
-    Group of Dirichlet characters of modulus 3 over Cyclotomic Field of order
-    6 and degree 2,
-    Group of Dirichlet characters of modulus 7 over Cyclotomic Field of order
-    6 and degree 2
+    Group of Dirichlet characters modulo 3 with values in Cyclotomic Field of order 6 and degree 2,
+    Group of Dirichlet characters modulo 7 with values in Cyclotomic Field of order 6 and degree 2
     ]
 
 Als nächstes konstruieren wir die Gruppe der Dirichlet-Charaktere
@@ -348,7 +346,7 @@ mod 20, jedoch mit Werten in :math:`\QQ(i)`:
     sage: K.<i> = NumberField(x^2+1)
     sage: G = DirichletGroup(20,K)
     sage: G
-    Group of Dirichlet characters of modulus 20 over Number Field in i with defining polynomial x^2 + 1
+    Group of Dirichlet characters modulo 20 with values in Number Field in i with defining polynomial x^2 + 1
 
 
 Nun berechnen wir mehrere Invarianten von ``G``:
@@ -381,8 +379,7 @@ Argument von ``DirichletGroup`` an.
     sage: K
     Number Field in a with defining polynomial x^4 + 1
     sage: G = DirichletGroup(5, K, a); G
-    Group of Dirichlet characters of modulus 5 over Number Field in a with
-    defining polynomial x^4 + 1 with values in the group of order 8 generated by a
+    Group of Dirichlet characters modulo 5 with values in the group of order 8 generated by a in Number Field in a with defining polynomial x^4 + 1
     sage: chi = G.0; chi
     Dirichlet character modulo 5 of conductor 5 mapping 2 |--> a^2
     sage: [(chi^i)(2) for i in range(4)]

diff --git a/...torials/explicit_methods_in_number_theory/modular_forms_and_hecke_operators.rst b/...torials/explicit_methods_in_number_theory/modular_forms_and_hecke_operators.rst
@@ -216,8 +216,7 @@ cyclotomic field.
 ::
 
     sage: G = DirichletGroup(8); G
-    Group of Dirichlet characters of modulus 8 over Cyclotomic
-    Field of order 2 and degree 1
+    Group of Dirichlet characters modulo 8 with values in Cyclotomic Field of order 2 and degree 1
     sage: v = G.list(); v
     [Dirichlet character modulo 8 of conductor 1 mapping 7 |--> 1, 5 |--> 1,
     Dirichlet character modulo 8 of conductor 4 mapping 7 |--> -1, 5 |--> 1,
@@ -230,7 +229,7 @@ cyclotomic field.
 
 Sage both represents Dirichlet characters by giving a "matrix",
 i.e., the list of images of canonical generators of
-:math:`(\ZZ/N\ZZ)^*`, and as vectors modulo and
+:math:`(\ZZ/N\ZZ)^*`, and as vectors modulo an
 integer :math:`n`. For years, I was torn between these two
 representations, until J. Quer and I realized that the best
 approach is to use both and make it easy to convert between them.

diff --git a/src/doc/en/tutorial/tour_advanced.rst b/src/doc/en/tutorial/tour_advanced.rst
@@ -332,10 +332,8 @@ factorization of the modulus.
 
     sage: G.decomposition()
     [
-    Group of Dirichlet characters of modulus 3 over Cyclotomic Field of order
-    6 and degree 2,
-    Group of Dirichlet characters of modulus 7 over Cyclotomic Field of order
-    6 and degree 2
+    Group of Dirichlet characters modulo 3 with values in Cyclotomic Field of order 6 and degree 2,
+    Group of Dirichlet characters modulo 7 with values in Cyclotomic Field of order 6 and degree 2
     ]
 
 Next, we construct the group of Dirichlet characters mod 20, but
@@ -346,7 +344,7 @@ with values in :math:`\QQ(i)`:
     sage: K.<i> = NumberField(x^2+1)
     sage: G = DirichletGroup(20,K)
     sage: G
-    Group of Dirichlet characters of modulus 20 over Number Field in i with defining polynomial x^2 + 1
+    Group of Dirichlet characters modulo 20 with values in Number Field in i with defining polynomial x^2 + 1
 
 
 We next compute several invariants of ``G``:
@@ -379,8 +377,7 @@ the third argument to ``DirichletGroup`` below.
     sage: K
     Number Field in a with defining polynomial x^4 + 1
     sage: G = DirichletGroup(5, K, a); G
-    Group of Dirichlet characters of modulus 5 over Number Field in a with
-    defining polynomial x^4 + 1 with values in the group of order 8 generated by a
+    Group of Dirichlet characters modulo 5 with values in the group of order 8 generated by a in Number Field in a with defining polynomial x^4 + 1
     sage: chi = G.0; chi
     Dirichlet character modulo 5 of conductor 5 mapping 2 |--> a^2
     sage: [(chi^i)(2) for i in range(4)]

diff --git a/src/doc/fr/tutorial/tour_advanced.rst b/src/doc/fr/tutorial/tour_advanced.rst
@@ -333,10 +333,8 @@ caractères, de même qu'une décomposition en produit direct correspondant
 
     sage: G.decomposition()
     [
-    Group of Dirichlet characters of modulus 3 over Cyclotomic Field of order
-    6 and degree 2,
-    Group of Dirichlet characters of modulus 7 over Cyclotomic Field of order
-    6 and degree 2
+    Group of Dirichlet characters modulo 3 with values in Cyclotomic Field of order 6 and degree 2,
+    Group of Dirichlet characters modulo 7 with values in Cyclotomic Field of order 6 and degree 2
     ]
 
 Construisons à present le groupe de caractères de Dirichlet modulo 20,
@@ -347,7 +345,7 @@ mais à valeur dans  :math:`\QQ(i)`:
     sage: K.<i> = NumberField(x^2+1)
     sage: G = DirichletGroup(20,K)
     sage: G
-    Group of Dirichlet characters of modulus 20 over Number Field in i with defining polynomial x^2 + 1
+    Group of Dirichlet characters modulo 20 with values in Number Field in i with defining polynomial x^2 + 1
 
 Nous calculons ensuite différents invariants de ``G``:
 
@@ -380,8 +378,7 @@ de la racine de l'unité par le troisième argument de la fonction
     sage: K
     Number Field in a with defining polynomial x^4 + 1
     sage: G = DirichletGroup(5, K, a); G
-    Group of Dirichlet characters of modulus 5 over Number Field in a with
-    defining polynomial x^4 + 1 with values in the group of order 8 generated by a
+    Group of Dirichlet characters modulo 5 with values in the group of order 8 generated by a in Number Field in a with defining polynomial x^4 + 1
     sage: chi = G.0; chi
     Dirichlet character modulo 5 of conductor 5 mapping 2 |--> a^2
     sage: [(chi^i)(2) for i in range(4)]

diff --git a/src/doc/pt/tutorial/tour_advanced.rst b/src/doc/pt/tutorial/tour_advanced.rst
@@ -334,10 +334,8 @@ módulo.
     
     sage: G.decomposition()
     [
-    Group of Dirichlet characters of modulus 3 over Cyclotomic Field of order 
-    6 and degree 2,
-    Group of Dirichlet characters of modulus 7 over Cyclotomic Field of order 
-    6 and degree 2
+    Group of Dirichlet characters modulo 3 with values in Cyclotomic Field of order 6 and degree 2,
+    Group of Dirichlet characters modulo 7 with values in Cyclotomic Field of order 6 and degree 2
     ]
 
 A seguir, construímos o grupo de caracteres de Dirichlet mod 20, mas
@@ -348,7 +346,7 @@ com valores em :math:`\QQ(i)`:
     sage: K.<i> = NumberField(x^2+1)
     sage: G = DirichletGroup(20,K)
     sage: G
-    Group of Dirichlet characters of modulus 20 over Number Field in i with defining polynomial x^2 + 1
+    Group of Dirichlet characters modulo 20 with values in Number Field in i with defining polynomial x^2 + 1
 
 Agora calculamos diversos invariantes de ``G``:
 
@@ -380,8 +378,7 @@ unidade no terceiro argumento do comando ``DirichletGroup`` abaixo.
     sage: K
     Number Field in a with defining polynomial x^4 + 1
     sage: G = DirichletGroup(5, K, a); G
-    Group of Dirichlet characters of modulus 5 over Number Field in a with 
-    defining polynomial x^4 + 1 with values in the group of order 8 generated by a
+    Group of Dirichlet characters modulo 5 with values in the group of order 8 generated by a in Number Field in a with defining polynomial x^4 + 1
     sage: chi = G.0; chi
     Dirichlet character modulo 5 of conductor 5 mapping 2 |--> a^2
     sage: [(chi^i)(2) for i in range(4)]

diff --git a/src/doc/ru/tutorial/tour_advanced.rst b/src/doc/ru/tutorial/tour_advanced.rst
@@ -297,10 +297,8 @@ Sage может вычислить тороидальный идеал непл
 
     sage: G.decomposition()
     [
-    Group of Dirichlet characters of modulus 3 over Cyclotomic Field of order
-    6 and degree 2,
-    Group of Dirichlet characters of modulus 7 over Cyclotomic Field of order
-    6 and degree 2
+    Group of Dirichlet characters modulo 3 with values in Cyclotomic Field of order 6 and degree 2,
+    Group of Dirichlet characters modulo 7 with values in Cyclotomic Field of order 6 and degree 2
     ]
 
 Далее надо построить группу символов Дирихле по модулю 20, но со значениями
@@ -311,7 +309,7 @@ Sage может вычислить тороидальный идеал непл
     sage: K.<i> = NumberField(x^2+1)
     sage: G = DirichletGroup(20,K)
     sage: G
-    Group of Dirichlet characters of modulus 20 over Number Field in i with defining polynomial x^2 + 1
+    Group of Dirichlet characters modulo 20 with values in Number Field in i with defining polynomial x^2 + 1
 
 
 Теперь посчитаем несколько инвариант ``G``:
@@ -343,8 +341,7 @@ Sage может вычислить тороидальный идеал непл
     sage: K
     Number Field in a with defining polynomial x^4 + 1
     sage: G = DirichletGroup(5, K, a); G
-    Group of Dirichlet characters of modulus 5 over Number Field in a with
-    defining polynomial x^4 + 1 with values in the group of order 8 generated by a
+    Group of Dirichlet characters modulo 5 with values in the group of order 8 generated by a in Number Field in a with defining polynomial x^4 + 1
     sage: chi = G.0; chi
     Dirichlet character modulo 5 of conductor 5 mapping 2 |--> a^2
     sage: [(chi^i)(2) for i in range(4)]

diff --git a/src/sage/misc/functional.py b/src/sage/misc/functional.py
@@ -230,7 +230,7 @@ def decomposition(x):
         [Dirichlet character modulo 4 of conductor 4 mapping 3 |--> -1,
         Dirichlet character modulo 5 of conductor 5 mapping 2 |--> zeta4]
         sage: d[0].parent()
-        Group of Dirichlet characters of modulus 4 over Cyclotomic Field of order 4 and degree 2
+        Group of Dirichlet characters modulo 4 with values in Cyclotomic Field of order 4 and degree 2
     """
     return x.decomposition()