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 b  
    137137
    138138    def domain_dim(self):
    139139        """
    140         Return the rank of the domain lattice
     140        Return the dimension of the domain lattice
    141141
    142142        EXAMPLES::
    143143
     
    158158
    159159    def codomain_dim(self):
    160160        """
    161         Return the rank of the codomain lattice
     161        Return the dimension of the codomain lattice
    162162
    163163        EXAMPLES::
    164164
  • sage/schemes/toric/weierstrass.py

    diff --git a/sage/schemes/toric/weierstrass.py b/sage/schemes/toric/weierstrass.py
    a b  
    361361    - ``polynomial`` -- a polynomial. The toric hypersurface
    362362      equation. Can be either a cubic, a biquadric, or the
    363363      hypersurface in `\mathbb{P}^2[1,1,2]`. The equation need not be
    364       in any standard form, only its Newton polynomial is used.
     364      in any standard form, only its Newton polyhedron is used.
    365365
    366366    - ``variables`` -- a list of variables of the parent polynomial
    367367      ring or ``None`` (default). In the latter case, all variables
    368368      are taken to be polynomial ring variables. If a subset of
    369       polynomial ring variables are given, the Weierstras form is
     369      polynomial ring variables are given, the Weierstrass form is
    370370      determined over the function field generated by the remaining
    371371      variables.
    372372
    373     - ``transformation`` -- boolean (default: ``True``). Whether to
     373    - ``transformation`` -- boolean (default: ``False``). Whether to
    374374      return the new variables that bring ``polynomial`` into
    375375      Weierstrass form.
    376376
     
    386386
    387387    .. math::
    388388
    389         Y^2 = X^3 + f X Z^4 + Z^6
     389        Y^2 = X^3 + f X Z^4 + g Z^6
    390390
    391391    when restricted to the toric hypersurface.
    392392
     
    432432        (0, -27/4)
    433433
    434434    This allows you to work with either homogeneous or inhomogeneous
    435     variables. For exmple, here is the del Pezzo surface of degree 8::
     435    variables. For example, here is the del Pezzo surface of degree 8::
    436436
    437437        sage: dP8 = toric_varieties.dP8()
    438438        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 b  
    11r"""
    22Map to the Weierstrass form of a toric elliptic curve.
    33
    4 There are 16 reflexive polygons in 2-d. Each defines a toric fano
    5 variety, which (in 2-d) has a unique crepant resolution to a smooth
    6 toric surface. An anticanonical hypersurface defines a genus-one curve
     4There are 16 reflexive polygons in 2-d. Each defines a toric Fano
     5variety, which (since it is 2-d) has a unique crepant resolution to a smooth
     6toric surface. An anticanonical hypersurface defines a genus one curve
    77`C` in this ambient space, with Jacobian elliptic curve `J(C)` which
    88can be defined by the Weierstrass model `y^2 = x^3 + f x + g`. The
    9 coefficients `f`, `g` can be computed with the
     9coefficients `f` and `g` can be computed with the
    1010:mod:`~sage.schemes.toric.weierstrass` module. The purpose of this
    11 model is to give an explicit rational map `C \to J(C)`. This is a
     11model is to give an explicit rational map `C \to J(C)`. This is an
    1212`n^2`-cover, where `n` is the minimal multi-section of `C`.
    1313
    1414Since it is technically often easier to deal with polynomials than
     
    2020
    2121.. math::
    2222
    23     Y^2 = X^3 + f X Z^4 + Z^6
     23    Y^2 = X^3 + f X Z^4 + g Z^6
    2424
    2525EXAMPLES::
    2626
     
    3030    (0, -27/4)
    3131
    3232That is, this hypersurface `C \in \mathbb{P}^2` has a Weierstrass
    33 equation `-Y^2 = X^3 + 0 \cdot X Z^4 - \frac{27}{4} Z^6` where
     33equation `Y^2 = X^3 + 0 \cdot X Z^4 - \frac{27}{4} Z^6` where
    3434`[X:Y:Z]` are projective coordinates on `\mathbb{P}^2[2,3,1]`. The
    3535form of the map `C\to J(C)` is::
    3636
     
    7171
    7272    sage: P2_112 = toric_varieties.P2_112()
    7373    sage: C = P2_112.anticanonical_hypersurface(coefficients=[1]*4);  C
    74     Closed subscheme of 2-d CPR-Fano toric variety covered by 3 affine patches defined by:
     74    Closed subscheme of 2-d CPR-Fano toric variety
     75    covered by 3 affine patches defined by:
    7576      z0^4 + z2^4 + z0*z1*z2 + z1^2
    7677    sage: eq = C.defining_polynomials()[0]
    7778    sage: f, g = WeierstrassForm(eq)
     
    134135    - ``polynomial`` -- a polynomial. The toric hypersurface
    135136      equation. Can be either a cubic, a biquadric, or the
    136137      hypersurface in `\mathbb{P}^2[1,1,2]`. The equation need not be
    137       in any standard form, only its Newton polynomial is used.
     138      in any standard form, only its Newton polyhedron is used.
    138139
    139140    - ``variables`` -- a list of variables of the parent polynomial
    140141      ring or ``None`` (default). In the latter case, all variables
    141142      are taken to be polynomial ring variables. If a subset of
    142       polynomial ring variables are given, the Weierstras form is
     143      polynomial ring variables are given, the Weierstrass form is
    143144      determined over the function field generated by the remaining
    144145      variables.
    145146
     
    151152
    152153    .. math::
    153154
    154         Y^2 = X^3 + f X Z^4 + Z^6
     155        Y^2 = X^3 + f X Z^4 + g Z^6
    155156
    156157    when restricted to the toric hypersurface.
    157158
     
    356357
    357358    Input/output is the same as :func:`WeierstrassMap`, except that
    358359    the input polynomial must be a standard anticanonical hypersurface
    359     in weighted projective space `\mathbb{P}^1 \times \mathbb{P}^1`:
     360    in the toric surface `\mathbb{P}^1 \times \mathbb{P}^1`:
    360361
    361362    EXAMPLES::
    362363
     
    399400    h = Q.h_covariant()
    400401    if t is None:
    401402        t = 1
    402         #return ( 4*g*(a00*s+V/2), 4*h, (a00*s+V/2)**3 )
    403403    return ( 4*g*t**2, 4*h*t**3, (a00*s+V/2) )
    404404
    405405