# HG changeset patch
# User Andrey Novoseltsev
# 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/sage/geometry/polyhedron/lattice_euclidean_group_element.py
+++ b/sage/geometry/polyhedron/lattice_euclidean_group_element.py
@@ -137,7 +137,7 @@
def domain_dim(self):
"""
- Return the rank of the domain lattice
+ Return the dimension of the domain lattice
EXAMPLES::
@@ -158,7 +158,7 @@
def codomain_dim(self):
"""
- Return the rank of the codomain lattice
+ Return the dimension of the codomain lattice
EXAMPLES::
diff --git a/sage/schemes/toric/weierstrass.py b/sage/schemes/toric/weierstrass.py
--- a/sage/schemes/toric/weierstrass.py
+++ b/sage/schemes/toric/weierstrass.py
@@ -361,16 +361,16 @@
- ``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.
@@ -386,7 +386,7 @@
.. 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.
@@ -432,7 +432,7 @@
(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()
diff --git a/sage/schemes/toric/weierstrass_covering.py b/sage/schemes/toric/weierstrass_covering.py
--- a/sage/schemes/toric/weierstrass_covering.py
+++ b/sage/schemes/toric/weierstrass_covering.py
@@ -1,14 +1,14 @@
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
@@ -20,7 +20,7 @@
.. math::
- Y^2 = X^3 + f X Z^4 + Z^6
+ Y^2 = X^3 + f X Z^4 + g Z^6
EXAMPLES::
@@ -30,7 +30,7 @@
(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::
@@ -71,7 +71,8 @@
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)
@@ -134,12 +135,12 @@
- ``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.
@@ -151,7 +152,7 @@
.. 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.
@@ -356,7 +357,7 @@
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::
@@ -399,7 +400,6 @@
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) )