# Ticket #13458: trac_13458_reviewer.patch

File trac_13458_reviewer.patch, 6.0 KB (added by novoselt, 8 years ago)
• ## sage/geometry/polyhedron/lattice_euclidean_group_element.py

# HG changeset patch
# User Andrey Novoseltsev <novoselt@gmail.com>
# Date 1372975788 21600
# Node ID f2ba3bc3c4773ef332b2140375e9a9b5943fd499
# Parent  4d62717de85ef513af7b7f9b7d50e1eabf841084
Fixes for typos.

diff --git a/sage/geometry/polyhedron/lattice_euclidean_group_element.py b/sage/geometry/polyhedron/lattice_euclidean_group_element.py
 a def domain_dim(self): """ Return the rank of the domain lattice Return the dimension of the domain lattice EXAMPLES:: def codomain_dim(self): """ Return the rank of the codomain lattice Return the dimension of the codomain lattice EXAMPLES::
• ## sage/schemes/toric/weierstrass.py

diff --git a/sage/schemes/toric/weierstrass.py b/sage/schemes/toric/weierstrass.py
 a - polynomial -- a polynomial. The toric hypersurface equation. Can be either a cubic, a biquadric, or the hypersurface in \mathbb{P}^2[1,1,2]. The equation need not be in any standard form, only its Newton polynomial is used. in any standard form, only its Newton polyhedron is used. - variables -- a list of variables of the parent polynomial ring or None (default). In the latter case, all variables are taken to be polynomial ring variables. If a subset of polynomial ring variables are given, the Weierstras form is polynomial ring variables are given, the Weierstrass form is determined over the function field generated by the remaining variables. - transformation -- boolean (default: True). Whether to - transformation -- boolean (default: False). Whether to return the new variables that bring polynomial into Weierstrass form. .. math:: Y^2 = X^3 + f X Z^4 + Z^6 Y^2 = X^3 + f X Z^4 + g Z^6 when restricted to the toric hypersurface. (0, -27/4) This allows you to work with either homogeneous or inhomogeneous variables. For exmple, here is the del Pezzo surface of degree 8:: variables. For example, here is the del Pezzo surface of degree 8:: sage: dP8 = toric_varieties.dP8() sage: dP8.inject_variables()
• ## sage/schemes/toric/weierstrass_covering.py

diff --git a/sage/schemes/toric/weierstrass_covering.py b/sage/schemes/toric/weierstrass_covering.py
 a r""" Map to the Weierstrass form of a toric elliptic curve. There are 16 reflexive polygons in 2-d. Each defines a toric fano variety, which (in 2-d) has a unique crepant resolution to a smooth toric surface. An anticanonical hypersurface defines a genus-one curve There are 16 reflexive polygons in 2-d. Each defines a toric Fano variety, which (since it is 2-d) has a unique crepant resolution to a smooth toric surface. An anticanonical hypersurface defines a genus one curve C in this ambient space, with Jacobian elliptic curve J(C) which can be defined by the Weierstrass model y^2 = x^3 + f x + g. The coefficients f, g can be computed with the coefficients f and g can be computed with the :mod:~sage.schemes.toric.weierstrass module. The purpose of this model is to give an explicit rational map C \to J(C). This is a model is to give an explicit rational map C \to J(C). This is an n^2-cover, where n is the minimal multi-section of C. Since it is technically often easier to deal with polynomials than .. math:: Y^2 = X^3 + f X Z^4 + Z^6 Y^2 = X^3 + f X Z^4 + g Z^6 EXAMPLES:: (0, -27/4) That is, this hypersurface C \in \mathbb{P}^2 has a Weierstrass equation -Y^2 = X^3 + 0 \cdot X Z^4 - \frac{27}{4} Z^6 where equation Y^2 = X^3 + 0 \cdot X Z^4 - \frac{27}{4} Z^6 where [X:Y:Z] are projective coordinates on \mathbb{P}^2[2,3,1]. The form of the map C\to J(C) is:: sage: P2_112 = toric_varieties.P2_112() sage: C = P2_112.anticanonical_hypersurface(coefficients=[1]*4);  C Closed subscheme of 2-d CPR-Fano toric variety covered by 3 affine patches defined by: Closed subscheme of 2-d CPR-Fano toric variety covered by 3 affine patches defined by: z0^4 + z2^4 + z0*z1*z2 + z1^2 sage: eq = C.defining_polynomials()[0] sage: f, g = WeierstrassForm(eq) - polynomial -- a polynomial. The toric hypersurface equation. Can be either a cubic, a biquadric, or the hypersurface in \mathbb{P}^2[1,1,2]. The equation need not be in any standard form, only its Newton polynomial is used. in any standard form, only its Newton polyhedron is used. - variables -- a list of variables of the parent polynomial ring or None (default). In the latter case, all variables are taken to be polynomial ring variables. If a subset of polynomial ring variables are given, the Weierstras form is polynomial ring variables are given, the Weierstrass form is determined over the function field generated by the remaining variables. .. math:: Y^2 = X^3 + f X Z^4 + Z^6 Y^2 = X^3 + f X Z^4 + g Z^6 when restricted to the toric hypersurface. Input/output is the same as :func:WeierstrassMap, except that the input polynomial must be a standard anticanonical hypersurface in weighted projective space \mathbb{P}^1 \times \mathbb{P}^1: in the toric surface \mathbb{P}^1 \times \mathbb{P}^1: EXAMPLES:: h = Q.h_covariant() if t is None: t = 1 #return ( 4*g*(a00*s+V/2), 4*h, (a00*s+V/2)**3 ) return ( 4*g*t**2, 4*h*t**3, (a00*s+V/2) )