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20697: Missed name changes.
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Grayson Jorgenson committed Jun 2, 2016
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2 changes: 1 addition & 1 deletion src/doc/de/tutorial/tour_advanced.rst
Expand Up @@ -17,7 +17,7 @@ die Kurven als irreduzible Komponenten der Vereinigung zurück erhalten.
sage: C3 = Curve(x^3 + y^3 - 1)
sage: D = C2 + C3
sage: D
Affine Curve over Rational Field defined by
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()
[
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4 changes: 2 additions & 2 deletions src/doc/en/constructions/algebraic_geometry.rst
Expand Up @@ -32,7 +32,7 @@ algorithm. Here is an example of the syntax:

sage: x,y,z = PolynomialRing(GF(5), 3, 'xyz').gens()
sage: C = Curve(y^2*z^7 - x^9 - x*z^8); C
Projective Curve over Finite Field of size 5 defined by -x^9 + y^2*z^7 - x*z^8
Projective Plane Curve over Finite Field of size 5 defined by -x^9 + y^2*z^7 - x*z^8
sage: C.rational_points()
[(0 : 0 : 1), (0 : 1 : 0), (2 : 2 : 1), (2 : 3 : 1), (3 : 1 : 1), (3 : 4 : 1)]
sage: C.rational_points(algorithm="bn")
Expand All @@ -49,7 +49,7 @@ Klein's quartic over :math:`GF(8)`.
sage: x, y, z = PolynomialRing(GF(8,'a'), 3, 'xyz').gens()
sage: f = x^3*y+y^3*z+x*z^3
sage: C = Curve(f); C
Projective Curve over Finite Field in a of size 2^3 defined by x^3*y + y^3*z + x*z^3
Projective Plane Curve over Finite Field in a of size 2^3 defined by x^3*y + y^3*z + x*z^3
sage: C.rational_points()
[(0 : 0 : 1),
(0 : 1 : 0),
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2 changes: 1 addition & 1 deletion src/doc/en/tutorial/tour_advanced.rst
Expand Up @@ -17,7 +17,7 @@ of the union.
sage: C3 = Curve(x^3 + y^3 - 1)
sage: D = C2 + C3
sage: D
Affine Curve over Rational Field defined by
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()
[
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2 changes: 1 addition & 1 deletion src/doc/fr/tutorial/tour_advanced.rst
Expand Up @@ -17,7 +17,7 @@ en tant que composante irréductible de la réunion.
sage: C3 = Curve(x^3 + y^3 - 1)
sage: D = C2 + C3
sage: D
Affine Curve over Rational Field defined by
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()
[
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4 changes: 2 additions & 2 deletions src/doc/ja/tutorial/tour_advanced.rst
Expand Up @@ -17,7 +17,7 @@ Sageでは,任意の代数多様体を定義することができるが,そ
sage: C3 = Curve(x^3 + y^3 - 1)
sage: D = C2 + C3
sage: D
Affine Curve over Rational Field defined by
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()
[
Expand Down Expand Up @@ -81,7 +81,7 @@ Sageでは,3次元射影空間における捻れ3次曲線のトーリック
---------------

Sageの楕円曲線部門にはPARIの楕円曲線機能の大部分が取り込まれており,Cremonaの管理するオンラインデータベースに接続することもできる(これにはデータベースパッケージを追加する必要がある).
さらに、Second-descentによって楕円曲線の完全Mordell-Weil群を計算するmwrankの機能が使えるし,SEAアルゴリズムの実行や同種写像全ての計算なども可能だ.
さらに、Second-descentによって楕円曲線の完全Mordell-Weil群を計算するmwrankの機能が使えるし,SEAアルゴリズムの実行や同種写像全ての計算なども可能だ.
:math:`\QQ` 上の曲線群を扱うためのコードは大幅に更新され,Denis Simonによる代数的降下法ソフトウェアも取り込まれている.


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56 changes: 28 additions & 28 deletions src/doc/pt/tutorial/tour_advanced.rst
Expand Up @@ -17,7 +17,7 @@ componentes irredutíveis da união.
sage: C3 = Curve(x^3 + y^3 - 1)
sage: D = C2 + C3
sage: D
Affine Curve over Rational Field defined by
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()
[
Expand Down Expand Up @@ -126,19 +126,19 @@ Agora ilustramos cada uma dessas construções:

sage: EllipticCurve([0,0,1,-1,0])
Elliptic Curve defined by y^2 + y = x^3 - x over Rational Field

sage: EllipticCurve([GF(5)(0),0,1,-1,0])
Elliptic Curve defined by y^2 + y = x^3 + 4*x over Finite Field of size 5

sage: EllipticCurve([1,2])
Elliptic Curve defined by y^2 = x^3 + x + 2 over Rational Field

sage: EllipticCurve('37a')
Elliptic Curve defined by y^2 + y = x^3 - x over Rational Field

sage: EllipticCurve_from_j(1)
Elliptic Curve defined by y^2 + x*y = x^3 + 36*x + 3455 over Rational Field

sage: EllipticCurve(GF(5), [0,0,1,-1,0])
Elliptic Curve defined by y^2 + y = x^3 + 4*x over Finite Field of size 5

Expand Down Expand Up @@ -175,7 +175,7 @@ seguinte forma:
sage: E.conductor()
2368
sage: E.j_invariant()
110592/37
110592/37

Se criarmos uma curva com o mesmo invariante :math:`j` que a curva
:math:`E`, ela não precisa ser isomórfica a :math:`E`. No seguinte
Expand Down Expand Up @@ -210,10 +210,10 @@ PARI.
::

sage: E = EllipticCurve([0,0,1,-1,0])
sage: E.anlist(30)
[0, 1, -2, -3, 2, -2, 6, -1, 0, 6, 4, -5, -6, -2, 2, 6, -4, 0, -12, 0, -4,
sage: E.anlist(30)
[0, 1, -2, -3, 2, -2, 6, -1, 0, 6, 4, -5, -6, -2, 2, 6, -4, 0, -12, 0, -4,
3, 10, 2, 0, -1, 4, -9, -2, 6, -12]
sage: v = E.anlist(10000)
sage: v = E.anlist(10000)

Leva apenas um segundo para calcular todos os :math:`a_n` para
:math:`n\leq 10^5`:
Expand All @@ -234,7 +234,7 @@ sobre o seu posto, números de Tomagawa, regulador, etc.

sage: E = EllipticCurve("37b2")
sage: E
Elliptic Curve defined by y^2 + y = x^3 + x^2 - 1873*x - 31833 over Rational
Elliptic Curve defined by y^2 + y = x^3 + x^2 - 1873*x - 31833 over Rational
Field
sage: E = EllipticCurve("389a")
sage: E
Expand Down Expand Up @@ -281,12 +281,12 @@ Um *caractere de Dirichlet* é a extensão de um homomorfismo

sage: G = DirichletGroup(12)
sage: G.list()
[Dirichlet character modulo 12 of conductor 1 mapping 7 |--> 1, 5 |--> 1,
Dirichlet character modulo 12 of conductor 4 mapping 7 |--> -1, 5 |--> 1,
Dirichlet character modulo 12 of conductor 3 mapping 7 |--> 1, 5 |--> -1,
[Dirichlet character modulo 12 of conductor 1 mapping 7 |--> 1, 5 |--> 1,
Dirichlet character modulo 12 of conductor 4 mapping 7 |--> -1, 5 |--> 1,
Dirichlet character modulo 12 of conductor 3 mapping 7 |--> 1, 5 |--> -1,
Dirichlet character modulo 12 of conductor 12 mapping 7 |--> -1, 5 |--> -1]
sage: G.gens()
(Dirichlet character modulo 12 of conductor 4 mapping 7 |--> -1, 5 |--> 1,
(Dirichlet character modulo 12 of conductor 4 mapping 7 |--> -1, 5 |--> 1,
Dirichlet character modulo 12 of conductor 3 mapping 7 |--> 1, 5 |--> -1)
sage: len(G)
4
Expand All @@ -302,7 +302,7 @@ cálculos com ele.
sage: chi = G.1; chi
Dirichlet character modulo 21 of conductor 7 mapping 8 |--> 1, 10 |--> zeta6
sage: chi.values()
[0, 1, zeta6 - 1, 0, -zeta6, -zeta6 + 1, 0, 0, 1, 0, zeta6, -zeta6, 0, -1,
[0, 1, zeta6 - 1, 0, -zeta6, -zeta6 + 1, 0, 0, 1, 0, zeta6, -zeta6, 0, -1,
0, 0, zeta6 - 1, zeta6, 0, -zeta6 + 1, -1]
sage: chi.conductor()
7
Expand All @@ -327,11 +327,11 @@ módulo.
sage: chi.galois_orbit()
[Dirichlet character modulo 21 of conductor 7 mapping 8 |--> 1, 10 |--> -zeta6 + 1,
Dirichlet character modulo 21 of conductor 7 mapping 8 |--> 1, 10 |--> zeta6]

sage: go = G.galois_orbits()
sage: [len(orbit) for orbit in go]
[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,
Expand Down Expand Up @@ -420,7 +420,7 @@ símbolos modulares de nível :math:`1` e peso :math:`12`.
([X^8*Y^2,(0,0)], [X^9*Y,(0,0)], [X^10,(0,0)])
sage: t2 = M.T(2)
sage: t2
Hecke operator T_2 on Modular Symbols space of dimension 3 for Gamma_0(1)
Hecke operator T_2 on Modular Symbols space of dimension 3 for Gamma_0(1)
of weight 12 with sign 0 over Rational Field
sage: t2.matrix()
[ -24 0 0]
Expand All @@ -443,7 +443,7 @@ Podemos também criar espaços para :math:`\Gamma_0(N)` e
Modular Symbols space of dimension 3 for Gamma_0(11) of weight 2 with sign
0 over Rational Field
sage: ModularSymbols(Gamma1(11),2)
Modular Symbols space of dimension 11 for Gamma_1(11) of weight 2 with
Modular Symbols space of dimension 11 for Gamma_1(11) of weight 2 with
sign 0 and over Rational Field

Vamos calcular alguns polinômios característicos e expansões
Expand All @@ -453,10 +453,10 @@ Vamos calcular alguns polinômios característicos e expansões

sage: M = ModularSymbols(Gamma1(11),2)
sage: M.T(2).charpoly('x')
x^11 - 8*x^10 + 20*x^9 + 10*x^8 - 145*x^7 + 229*x^6 + 58*x^5 - 360*x^4
x^11 - 8*x^10 + 20*x^9 + 10*x^8 - 145*x^7 + 229*x^6 + 58*x^5 - 360*x^4
+ 70*x^3 - 515*x^2 + 1804*x - 1452
sage: M.T(2).charpoly('x').factor()
(x - 3) * (x + 2)^2 * (x^4 - 7*x^3 + 19*x^2 - 23*x + 11)
(x - 3) * (x + 2)^2 * (x^4 - 7*x^3 + 19*x^2 - 23*x + 11)
* (x^4 - 2*x^3 + 4*x^2 + 2*x + 11)
sage: S = M.cuspidal_submodule()
sage: S.T(2).matrix()
Expand All @@ -474,19 +474,19 @@ Podemos até mesmo calcular espaços de símbolos modulares com carácter.
sage: G = DirichletGroup(13)
sage: e = G.0^2
sage: M = ModularSymbols(e,2); M
Modular Symbols space of dimension 4 and level 13, weight 2, character
Modular Symbols space of dimension 4 and level 13, weight 2, character
[zeta6], sign 0, over Cyclotomic Field of order 6 and degree 2
sage: M.T(2).charpoly('x').factor()
(x - zeta6 - 2) * (x - 2*zeta6 - 1) * (x + zeta6 + 1)^2
sage: S = M.cuspidal_submodule(); S
Modular Symbols subspace of dimension 2 of Modular Symbols space of
dimension 4 and level 13, weight 2, character [zeta6], sign 0, over
Modular Symbols subspace of dimension 2 of Modular Symbols space of
dimension 4 and level 13, weight 2, character [zeta6], sign 0, over
Cyclotomic Field of order 6 and degree 2
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
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)
]

Expand All @@ -497,7 +497,7 @@ operadores de Hecke em um espaço de formas modulares.

sage: T = ModularForms(Gamma0(11),2)
sage: T
Modular Forms space of dimension 2 for Congruence Subgroup Gamma0(11) of
Modular Forms space of dimension 2 for Congruence Subgroup Gamma0(11) of
weight 2 over Rational Field
sage: T.degree()
2
Expand All @@ -511,7 +511,7 @@ operadores de Hecke em um espaço de formas modulares.
Cuspidal subspace of dimension 1 of Modular Forms space of dimension 2 for
Congruence Subgroup Gamma0(11) of weight 2 over Rational Field
sage: T.eisenstein_subspace()
Eisenstein subspace of dimension 1 of Modular Forms space of dimension 2
Eisenstein subspace of dimension 1 of Modular Forms space of dimension 2
for Congruence Subgroup Gamma0(11) of weight 2 over Rational Field
sage: M = ModularSymbols(11); M
Modular Symbols space of dimension 3 for Gamma_0(11) of weight 2 with sign
Expand Down
2 changes: 1 addition & 1 deletion src/doc/ru/tutorial/tour_advanced.rst
Expand Up @@ -16,7 +16,7 @@ Sage позволяет создавать любые алгебраически
sage: C3 = Curve(x^3 + y^3 - 1)
sage: D = C2 + C3
sage: D
Affine Curve over Rational Field defined by
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()
[
Expand Down

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