sagemath · vbraun · Jan 4, 2025 · Nov 24, 2024 · Dec 11, 2024 · Dec 11, 2024
diff --git a/src/doc/de/tutorial/programming.rst b/src/doc/de/tutorial/programming.rst
@@ -263,15 +263,9 @@ aussehen könnten. Hier sind einige Beispiele:
     sqrt(2)
     sage: V = VectorSpace(QQ,2)
     sage: V.basis()
-        [
-        (1, 0),
-        (0, 1)
-        ]
+        [(1, 0), (0, 1)]
     sage: basis(V)
-        [
-        (1, 0),
-        (0, 1)
-        ]
+        [(1, 0), (0, 1)]
     sage: M = MatrixSpace(GF(7), 2); M
     Full MatrixSpace of 2 by 2 dense matrices over Finite Field of size 7
     sage: A = M([1,2,3,4]); A
@@ -425,11 +419,7 @@ Vektorräumen. Es ist wichtig, dass sie nicht verändert werden können.
 ::
 
     sage: V = QQ^3; B = V.basis(); B
-    [
-    (1, 0, 0),
-    (0, 1, 0),
-    (0, 0, 1)
-    ]
+    [(1, 0, 0), (0, 1, 0), (0, 0, 1)]
     sage: type(B)
     <class 'sage.structure.sequence.Sequence_generic'>
     sage: B[0] = B[1]

diff --git a/src/doc/de/tutorial/tour_advanced.rst b/src/doc/de/tutorial/tour_advanced.rst
@@ -20,12 +20,10 @@ die Kurven als irreduzible Komponenten der Vereinigung zurück erhalten.
     Affine Plane Curve over Rational Field defined by
        x^5 + x^3*y^2 + x^2*y^3 + y^5 - x^3 - y^3 - x^2 - y^2 + 1
     sage: D.irreducible_components()
-    [
-    Closed subscheme of Affine Space of dimension 2 over Rational Field defined by:
-      x^2 + y^2 - 1,
-    Closed subscheme of Affine Space of dimension 2 over Rational Field defined by:
-      x^3 + y^3 - 1
-    ]
+    [Closed subscheme of Affine Space of dimension 2 over Rational Field defined by:
+       x^2 + y^2 - 1,
+     Closed subscheme of Affine Space of dimension 2 over Rational Field defined by:
+       x^3 + y^3 - 1]
 
 Wir können auch alle Punkte im Schnitt der beiden Kurven finden, indem
 wir diese schneiden und dann die irreduziblen Komponenten berechnen.
@@ -36,17 +34,15 @@ wir diese schneiden und dann die irreduziblen Komponenten berechnen.
 
     sage: V = C2.intersection(C3)
     sage: V.irreducible_components()
-    [
-    Closed subscheme of Affine Space of dimension 2 over Rational Field defined by:
-      y,
-      x - 1,
-    Closed subscheme of Affine Space of dimension 2 over Rational Field defined by:
-      y - 1,
-      x,
-    Closed subscheme of Affine Space of dimension 2 over Rational Field defined by:
-      x + y + 2,
-      2*y^2 + 4*y + 3
-    ]
+    [Closed subscheme of Affine Space of dimension 2 over Rational Field defined by:
+       y,
+       x - 1,
+     Closed subscheme of Affine Space of dimension 2 over Rational Field defined by:
+       y - 1,
+       x,
+     Closed subscheme of Affine Space of dimension 2 over Rational Field defined by:
+       x + y + 2,
+       2*y^2 + 4*y + 3]
 
 Also sind zum Beispiel :math:`(1,0)` und :math:`(0,1)` auf beiden
 Kurven (wie man sofort sieht), genauso wie bestimmte (quadratischen)
@@ -333,10 +329,8 @@ Faktorisierung des Moduls entsprechen.
     [1, 2, 2, 1, 1, 2, 2, 1]
 
     sage: G.decomposition()
-    [
-    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
-    ]
+    [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
 mod 20, jedoch mit Werten in :math:`\QQ(i)`:
@@ -465,9 +459,7 @@ Nun berechnen wir ein paar charakteristische Polynome und
     [-2  0]
     [ 0 -2]
     sage: S.q_expansion_basis(10)
-    [
-        q - 2*q^2 - q^3 + 2*q^4 + q^5 + 2*q^6 - 2*q^7 - 2*q^9 + O(q^10)
-    ]
+    [q - 2*q^2 - q^3 + 2*q^4 + q^5 + 2*q^6 - 2*q^7 - 2*q^9 + O(q^10)]
 
 Wir können sogar Räume von Modulsymbolen mit Charakteren berechnen.
 
@@ -487,10 +479,7 @@ Wir können sogar Räume von Modulsymbolen mit Charakteren berechnen.
     sage: S.T(2).charpoly('x').factor()
     (x + zeta6 + 1)^2
     sage: S.q_expansion_basis(10)
-    [
-    q + (-zeta6 - 1)*q^2 + (2*zeta6 - 2)*q^3 + zeta6*q^4 + (-2*zeta6 + 1)*q^5
-      + (-2*zeta6 + 4)*q^6 + (2*zeta6 - 1)*q^8 - zeta6*q^9 + O(q^10)
-    ]
+    [q + (-zeta6 - 1)*q^2 + (2*zeta6 - 2)*q^3 + zeta6*q^4 + (-2*zeta6 + 1)*q^5 + (-2*zeta6 + 4)*q^6 + (2*zeta6 - 1)*q^8 - zeta6*q^9 + O(q^10)]
 
 Hier ist ein weiteres Beispiel davon wie Sage mit den Operationen von
 Hecke-Operatoren auf dem Raum von Modulformen rechnen kann.

diff --git a/src/doc/de/tutorial/tour_linalg.rst b/src/doc/de/tutorial/tour_linalg.rst
@@ -63,11 +63,7 @@ Sage kann auch Eigenwerte und Eigenvektoren berechnen::
     [-2*I, 2*I]
     sage: B = matrix([[1, 3], [3, 1]])
     sage: B.eigenvectors_left()
-    [(4, [
-    (1, 1)
-    ], 1), (-2, [
-    (1, -1)
-    ], 1)]
+    [(4, [(1, 1)], 1), (-2, [(1, -1)], 1)]
 
 (Die Syntax der Ausgabe von ``eigenvectors_left`` ist eine Liste von
 Tripeln: (Eigenwert, Eigenvektor, Vielfachheit).) Eigenwerte und

diff --git a/src/doc/en/constructions/linear_algebra.rst b/src/doc/en/constructions/linear_algebra.rst
@@ -22,10 +22,7 @@ one can create a subspace. Note the basis computed by Sage is
     sage: V = VectorSpace(GF(2),8)
     sage: S = V.subspace([V([1,1,0,0,0,0,0,0]),V([1,0,0,0,0,1,1,0])])
     sage: S.basis()
-    [
-    (1, 0, 0, 0, 0, 1, 1, 0),
-    (0, 1, 0, 0, 0, 1, 1, 0)
-    ]
+    [(1, 0, 0, 0, 0, 1, 1, 0), (0, 1, 0, 0, 0, 1, 1, 0)]
     sage: S.dimension()
     2
 
@@ -205,26 +202,21 @@ gives matrices :math:`D` and :math:`P` such that :math:`AP=PD` (resp.
     sage: A.eigenvalues()
     [3, 2, 1]
     sage: A.eigenvectors_right()
-    [(3, [
-    (0, 0, 1)
-    ], 1), (2, [
-    (1, 1, 0)
-    ], 1), (1, [
-    (1, 0, 0)
-    ], 1)]
+    [(3, [(0, 0, 1)], 1), (2, [(1, 1, 0)], 1), (1, [(1, 0, 0)], 1)]
 
     sage: A.eigenspaces_right()
-    [
-    (3, Vector space of degree 3 and dimension 1 over Rational Field
-    User basis matrix:
-    [0 0 1]),
-    (2, Vector space of degree 3 and dimension 1 over Rational Field
-    User basis matrix:
-    [1 1 0]),
-    (1, Vector space of degree 3 and dimension 1 over Rational Field
-    User basis matrix:
-    [1 0 0])
-    ]
+    [(3,
+      Vector space of degree 3 and dimension 1 over Rational Field
+      User basis matrix:
+      [0 0 1]),
+     (2,
+      Vector space of degree 3 and dimension 1 over Rational Field
+      User basis matrix:
+      [1 1 0]),
+     (1,
+      Vector space of degree 3 and dimension 1 over Rational Field
+      User basis matrix:
+      [1 0 0])]
 
     sage: D, P = A.eigenmatrix_right()
     sage: D
@@ -256,20 +248,19 @@ floating point entries (over ``CDF`` and ``RDF``) can be obtained with the
     sage: MS = MatrixSpace(QQ, 2, 2)
     sage: A = MS([1,-4,1, -1])
     sage: A.eigenspaces_left(format='all')
-    [
-    (-1.732050807568878?*I, Vector space of degree 2 and dimension 1 over Algebraic Field
-    User basis matrix:
-    [                        1 -1 - 1.732050807568878?*I]),
-    (1.732050807568878?*I, Vector space of degree 2 and dimension 1 over Algebraic Field
-    User basis matrix:
-    [                        1 -1 + 1.732050807568878?*I])
-    ]
+    [(-1.732050807568878?*I,
+      Vector space of degree 2 and dimension 1 over Algebraic Field
+      User basis matrix:
+      [                        1 -1 - 1.732050807568878?*I]),
+     (1.732050807568878?*I,
+      Vector space of degree 2 and dimension 1 over Algebraic Field
+      User basis matrix:
+      [                        1 -1 + 1.732050807568878?*I])]
     sage: A.eigenspaces_left(format='galois')
-    [
-    (a0, Vector space of degree 2 and dimension 1 over Number Field in a0 with defining polynomial x^2 + 3
-    User basis matrix:
-    [     1 a0 - 1])
-    ]
+    [(a0,
+      Vector space of degree 2 and dimension 1 over Number Field in a0 with defining polynomial x^2 + 3
+      User basis matrix:
+      [     1 a0 - 1])]
 
 Another approach is to use the interface with Maxima:
 

diff --git a/src/doc/en/prep/Quickstarts/Graphs-and-Discrete.rst b/src/doc/en/prep/Quickstarts/Graphs-and-Discrete.rst
@@ -325,11 +325,7 @@ Start with a generator matrix over :math:`\ZZ/2\ZZ`.
 ::
 
     sage: D.basis()
-    [
-    (1, 0, 1, 0, 1, 0, 1),
-    (0, 1, 1, 0, 0, 1, 1),
-    (0, 0, 0, 1, 1, 1, 1)
-    ]
+    [(1, 0, 1, 0, 1, 0, 1), (0, 1, 1, 0, 0, 1, 1), (0, 0, 0, 1, 1, 1, 1)]
 
 ::
 

diff --git a/src/doc/en/prep/Quickstarts/Linear-Algebra.rst b/src/doc/en/prep/Quickstarts/Linear-Algebra.rst
@@ -256,10 +256,7 @@ of the matrix)::
 Or we can get the basis vectors explicitly as a list of vectors::
 
     sage: V.basis()
-    [
-    (1, 0, -1/3),
-    (0, 1, -2/3)
-    ]
+    [(1, 0, -1/3), (0, 1, -2/3)]
 
 .. note::
    Kernels are **vector spaces** and bases are "\ **echelonized**\ "

diff --git a/...doc/en/thematic_tutorials/explicit_methods_in_number_theory/level_one_forms.rst b/...doc/en/thematic_tutorials/explicit_methods_in_number_theory/level_one_forms.rst
@@ -47,22 +47,31 @@ rather nice diagonal shape.
 ::
 
     sage: victor_miller_basis(24, 6)
-    [
-    1 + 52416000*q^3 + 39007332000*q^4 + 6609020221440*q^5 + O(q^6),
-    q + 195660*q^3 + 12080128*q^4 + 44656110*q^5 + O(q^6),
-    q^2 - 48*q^3 + 1080*q^4 - 15040*q^5 + O(q^6)
-    ]
+    [1 + 52416000*q^3 + 39007332000*q^4 + 6609020221440*q^5 + O(q^6),
+     q + 195660*q^3 + 12080128*q^4 + 44656110*q^5 + O(q^6),
+     q^2 - 48*q^3 + 1080*q^4 - 15040*q^5 + O(q^6)]
     sage: from sage.modular.dims import dimension_modular_forms
     sage: dimension_modular_forms(1,200)
     17
     sage: B = victor_miller_basis(200, 18) #5 seconds
     sage: B
-    [
-    1 + 79288314420681734048660707200000*q^17 + O(q^18),
-    q + 2687602718106772837928968846869*q^17 + O(q^18),
-    ...
-    ]
+    [1 + 79288314420681734048660707200000*q^17 + O(q^18),
+     q + 2687602718106772837928968846869*q^17 + O(q^18),
+     q^2 + 85789116961248834349485762560*q^17 + O(q^18),
+     q^3 + 2567045661341737693075080984*q^17 + O(q^18),
+     q^4 + 71629117222531314878690304*q^17 + O(q^18),
+     q^5 + 1852433650992110376992650*q^17 + O(q^18),
+     q^6 + 44081333191517147315712*q^17 + O(q^18),
+     q^7 + 956892703246212300900*q^17 + O(q^18),
+     q^8 + 18748755998771700480*q^17 + O(q^18),
+     q^9 + 327218645736859401*q^17 + O(q^18),
+     q^10 + 5001104379048960*q^17 + O(q^18),
+     q^11 + 65427591611128*q^17 + O(q^18),
+     q^12 + 709488619776*q^17 + O(q^18),
+     q^13 + 6070433286*q^17 + O(q^18),
+     q^14 + 37596416*q^17 + O(q^18),
+     q^15 + 138420*q^17 + O(q^18),
+     q^16 + 96*q^17 + O(q^18)]
 
 Note: Craig Citro has made the above computation an order of
 magnitude faster in code he has not quite got into Sage yet.

diff --git a/src/doc/en/thematic_tutorials/explicit_methods_in_number_theory/modabvar.rst b/src/doc/en/thematic_tutorials/explicit_methods_in_number_theory/modabvar.rst
@@ -35,10 +35,8 @@ compute some basic invariants.
 ::
 
     sage: D = J0(39).decomposition(); D
-    [
-    Simple abelian subvariety 39a(1,39) of dimension 1 of J0(39),
-    Simple abelian subvariety 39b(1,39) of dimension 2 of J0(39)
-    ]
+    [Simple abelian subvariety 39a(1,39) of dimension 1 of J0(39),
+     Simple abelian subvariety 39b(1,39) of dimension 2 of J0(39)]
     sage: D[1].lattice()
     Free module of degree 6 and rank 4 over Integer Ring
     Echelon basis matrix:

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
@@ -142,13 +142,11 @@ and :math:`k` is the weight.
     sage: S = CuspForms(Gamma0(25),4, prec=15); S
     Cuspidal subspace of dimension 5 of Modular Forms space ...
     sage: S.basis()
-    [
-    q + q^9 - 8*q^11 - 8*q^14 + O(q^15),
-    q^2 - q^7 - q^8 - 7*q^12 + 7*q^13 + O(q^15),
-    q^3 + q^7 - 2*q^8 - 6*q^12 - 5*q^13 + O(q^15),
-    q^4 - q^6 - 3*q^9 + 5*q^11 - 2*q^14 + O(q^15),
-    q^5 - 4*q^10 + O(q^15)
-    ]
+    [q + q^9 - 8*q^11 - 8*q^14 + O(q^15),
+     q^2 - q^7 - q^8 - 7*q^12 + 7*q^13 + O(q^15),
+     q^3 + q^7 - 2*q^8 - 6*q^12 - 5*q^13 + O(q^15),
+     q^4 - q^6 - 3*q^9 + 5*q^11 - 2*q^14 + O(q^15),
+     q^5 - 4*q^10 + O(q^15)]
 
 Dimension Formulas
 ~~~~~~~~~~~~~~~~~~
@@ -200,9 +198,7 @@ described later.
 ::
 
     sage: CuspForms(DirichletGroup(5).0, 5).basis()
-    [
-    q + (-zeta4 - 1)*q^2 + (6*zeta4 - 6)*q^3 - ... + O(q^6)
-    ]
+    [q + (-zeta4 - 1)*q^2 + (6*zeta4 - 6)*q^3 - 14*zeta4*q^4 + (15*zeta4 + 20)*q^5 + O(q^6)]
 
 
 Dirichlet Characters
@@ -296,12 +292,10 @@ Hecke operator :math:`T_n`, and to compute the subspace
 
     sage: M = ModularForms(Gamma0(11),4)
     sage: M.basis()
-    [
-    q + 3*q^3 - 6*q^4 - 7*q^5 + O(q^6),
-    q^2 - 4*q^3 + 2*q^4 + 8*q^5 + O(q^6),
-    1 + O(q^6),
-    q + 9*q^2 + 28*q^3 + 73*q^4 + 126*q^5 + O(q^6)
-    ]
+    [q + 3*q^3 - 6*q^4 - 7*q^5 + O(q^6),
+     q^2 - 4*q^3 + 2*q^4 + 8*q^5 + O(q^6),
+     1 + O(q^6),
+     q + 9*q^2 + 28*q^3 + 73*q^4 + 126*q^5 + O(q^6)]
     sage: M.hecke_matrix(2)
     [0 2 0 0]
     [1 2 0 0]

diff --git a/...oc/en/thematic_tutorials/explicit_methods_in_number_theory/nf_galois_groups.rst b/...oc/en/thematic_tutorials/explicit_methods_in_number_theory/nf_galois_groups.rst
@@ -101,20 +101,18 @@ You can also enumerate all complex embeddings of a number field:
 ::
 
     sage: K.complex_embeddings()
-    [
-    Ring morphism:
-      From: Number Field in a with defining polynomial x^3 - 2
-      To:   Complex Field with 53 bits of precision
-      Defn: a |--> -0.629960524947437 - 1.09112363597172*I,
-    Ring morphism:
-      From: Number Field in a with defining polynomial x^3 - 2
-      To:   Complex Field with 53 bits of precision
-      Defn: a |--> -0.629960524947437 + 1.09112363597172*I,
-    Ring morphism:
-      From: Number Field in a with defining polynomial x^3 - 2
-      To:   Complex Field with 53 bits of precision
-      Defn: a |--> 1.25992104989487
-    ]
+    [Ring morphism:
+       From: Number Field in a with defining polynomial x^3 - 2
+       To:   Complex Field with 53 bits of precision
+       Defn: a |--> -0.629960524947437 - 1.09112363597172*I,
+     Ring morphism:
+       From: Number Field in a with defining polynomial x^3 - 2
+       To:   Complex Field with 53 bits of precision
+       Defn: a |--> -0.629960524947437 + 1.09112363597172*I,
+     Ring morphism:
+       From: Number Field in a with defining polynomial x^3 - 2
+       To:   Complex Field with 53 bits of precision
+       Defn: a |--> 1.25992104989487]
 
 
 Class Numbers and Class Groups