From b3809671bae3c03fe2407471a1e908cdbdc22a00 Mon Sep 17 00:00:00 2001 From: Grayson Jorgenson Date: Thu, 2 Jun 2016 01:59:30 -0400 Subject: [PATCH] 20697: Missed name changes. --- src/doc/de/tutorial/tour_advanced.rst | 2 +- .../en/constructions/algebraic_geometry.rst | 4 +- src/doc/en/tutorial/tour_advanced.rst | 2 +- src/doc/fr/tutorial/tour_advanced.rst | 2 +- src/doc/ja/tutorial/tour_advanced.rst | 4 +- src/doc/pt/tutorial/tour_advanced.rst | 56 +++++++++---------- src/doc/ru/tutorial/tour_advanced.rst | 2 +- 7 files changed, 36 insertions(+), 36 deletions(-) diff --git a/src/doc/de/tutorial/tour_advanced.rst b/src/doc/de/tutorial/tour_advanced.rst index 7e6c6a7cfc6..8d69303b9e2 100644 --- a/src/doc/de/tutorial/tour_advanced.rst +++ b/src/doc/de/tutorial/tour_advanced.rst @@ -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() [ diff --git a/src/doc/en/constructions/algebraic_geometry.rst b/src/doc/en/constructions/algebraic_geometry.rst index 4932833f94b..eb712b0a6e4 100644 --- a/src/doc/en/constructions/algebraic_geometry.rst +++ b/src/doc/en/constructions/algebraic_geometry.rst @@ -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") @@ -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), diff --git a/src/doc/en/tutorial/tour_advanced.rst b/src/doc/en/tutorial/tour_advanced.rst index 27b8b1e526e..80b637383ef 100644 --- a/src/doc/en/tutorial/tour_advanced.rst +++ b/src/doc/en/tutorial/tour_advanced.rst @@ -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() [ diff --git a/src/doc/fr/tutorial/tour_advanced.rst b/src/doc/fr/tutorial/tour_advanced.rst index 6eba3c2b0b9..188135f058d 100644 --- a/src/doc/fr/tutorial/tour_advanced.rst +++ b/src/doc/fr/tutorial/tour_advanced.rst @@ -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() [ diff --git a/src/doc/ja/tutorial/tour_advanced.rst b/src/doc/ja/tutorial/tour_advanced.rst index b18e6df216b..a27e97bd53d 100644 --- a/src/doc/ja/tutorial/tour_advanced.rst +++ b/src/doc/ja/tutorial/tour_advanced.rst @@ -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() [ @@ -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． diff --git a/src/doc/pt/tutorial/tour_advanced.rst b/src/doc/pt/tutorial/tour_advanced.rst index f61b2cb53ef..bac50f9192a 100644 --- a/src/doc/pt/tutorial/tour_advanced.rst +++ b/src/doc/pt/tutorial/tour_advanced.rst @@ -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() [ @@ -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 @@ -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 @@ -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`: @@ -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 @@ -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 @@ -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 @@ -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, @@ -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] @@ -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 @@ -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() @@ -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) ] @@ -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 @@ -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 diff --git a/src/doc/ru/tutorial/tour_advanced.rst b/src/doc/ru/tutorial/tour_advanced.rst index aef6425e7b6..673b49a9ab1 100644 --- a/src/doc/ru/tutorial/tour_advanced.rst +++ b/src/doc/ru/tutorial/tour_advanced.rst @@ -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() [