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19889 Fixing Style Errors
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rlmiller committed Feb 3, 2016
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3 changes: 1 addition & 2 deletions src/sage/schemes/affine/affine_homset.py
View file
@@ -1,5 +1,5 @@
r"""
Set of homomorphisms between two affine schemes.
Set of homomorphisms between two affine schemes
For schemes `X` and `Y`, this module implements the set of morphisms
`Hom(X,Y)`. This is done by :class:`SchemeHomset_generic`.
Expand Down Expand Up @@ -38,7 +38,6 @@
from sage.categories.number_fields import NumberFields
from sage.rings.finite_rings.constructor import is_FiniteField
from sage.rings.polynomial.polynomial_ring_constructor import PolynomialRing

import sage.schemes.generic.homset

#*******************************************************************
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117 changes: 59 additions & 58 deletions src/sage/schemes/affine/affine_morphism.py
View file
@@ -1,5 +1,5 @@
r"""
Morphisms on affine varieties.
Morphisms on affine varieties
A morphism of schemes determined by rational functions that define
what the morphism does on points in the ambient affine space.
Expand Down Expand Up @@ -30,23 +30,23 @@


from sage.calculus.functions import jacobian
from sage.categories.homset import Hom
from sage.matrix.constructor import matrix, identity_matrix
from sage.misc.cachefunc import cached_method
from sage.misc.all import prod
from sage.rings.all import Integer
from sage.arith.all import lcm, gcd
from sage.rings.complex_field import ComplexField
from sage.categories.homset import Hom
from sage.matrix.constructor import matrix, identity_matrix
from sage.misc.cachefunc import cached_method
from sage.misc.all import prod
from sage.rings.all import Integer
from sage.arith.all import lcm, gcd
from sage.rings.complex_field import ComplexField
from sage.rings.finite_rings.constructor import GF, is_PrimeFiniteField
from sage.rings.fraction_field import FractionField
from sage.rings.fraction_field import FractionField
from sage.rings.fraction_field_element import FractionFieldElement
from sage.rings.integer_ring import ZZ
from sage.rings.integer_ring import ZZ
from sage.rings.polynomial.polynomial_ring_constructor import PolynomialRing
from sage.rings.quotient_ring import QuotientRing_generic
from sage.rings.real_mpfr import RealField
from sage.rings.quotient_ring import QuotientRing_generic
from sage.rings.real_mpfr import RealField
from sage.schemes.generic.morphism import SchemeMorphism_polynomial
from sage.misc.lazy_attribute import lazy_attribute
from sage.ext.fast_callable import fast_callable
from sage.misc.lazy_attribute import lazy_attribute
from sage.ext.fast_callable import fast_callable
import sys

class SchemeMorphism_polynomial_affine_space(SchemeMorphism_polynomial):
Expand Down Expand Up @@ -173,7 +173,7 @@ def __call__(self, x, check=True):
except (TypeError, NotImplementedError):
raise TypeError("%s fails to convert into the map's domain %s, but a `pushforward` method is not properly implemented"%(x, self.domain()))
elif self.domain() != x.codomain():
raise TypeError("%s fails to convert into the map's domain %s, but a `pushforward` method is not properly implemented"%(x, self.domain()))
raise TypeError("%s fails to convert into the map's domain %s,but a `pushforward` method is not properly implemented"%(x, self.domain()))

# Passes the array of args to _fast_eval
P = self._fast_eval(x._coords)
Expand All @@ -189,7 +189,7 @@ def __eq__(self, right):
OUTPUT:
- Boolean - True if ``affine map`` and ``right`` define the same affine map. False otherwise.
- Boolean - True if the two affine maps defined the same map.
EXAMPLES::
Expand Down Expand Up @@ -226,7 +226,7 @@ def __ne__(self, right):
OUTPUT:
- Boolean -- True if ``affine map`` and ``right`` define different affine maps. False otherwise.
- Boolean -- True if the two affine maps defined the same map.
EXAMPLES::
Expand Down Expand Up @@ -327,7 +327,8 @@ def _fast_eval(self, x):

P = []
for i in range(len(self._fastpolys[0])):
# Check if denominator is the identity; if not, then must append the fraction evaluated at the point
# Check if denominator is the identity;
#if not, then must append the fraction evaluated at the point
if self._fastpolys[1][i] is R.one():
P.append(self._fastpolys[0][i](*x))
else:
Expand All @@ -344,8 +345,8 @@ def homogenize(self, n):
INPUT:
- ``n`` -- a tuple of nonnegative integers. If ``n`` is an integer, then the two values of
the tuple are assumed to be the same.
- ``n`` -- a tuple of nonnegative integers. If ``n`` is an integer,
then the two values of the tuple are assumed to be the same.
OUTPUT:
Expand All @@ -355,7 +356,7 @@ def homogenize(self, n):
sage: A.<x,y> = AffineSpace(ZZ, 2)
sage: H = Hom(A, A)
sage: f = H([(x^2-2)/x^5,y^2])
sage: f = H([(x^2-2)/x^5, y^2])
sage: f.homogenize(2)
Scheme endomorphism of Projective Space of dimension 2 over Integer Ring
Defn: Defined on coordinates by sending (x0 : x1 : x2) to
Expand All @@ -380,7 +381,8 @@ def homogenize(self, n):
sage: H = Hom(X, X)
sage: f = H([9*y^2, 3*y])
sage: f.homogenize(2)
Scheme endomorphism of Closed subscheme of Projective Space of dimension 2 over Integer Ring defined by:
Scheme endomorphism of Closed subscheme of Projective Space
of dimension 2 over Integer Ring defined by:
-x1^2 + x0*x2
Defn: Defined on coordinates by sending (x0 : x1 : x2) to
(9*x0*x2 : 3*x1*x2 : x2^2)
Expand Down Expand Up @@ -436,7 +438,8 @@ def homogenize(self, n):
sage: A.<x> = AffineSpace(K, 1)
sage: f = Hom(A, A)([x^2 + c])
sage: f.homogenize(1)
Scheme endomorphism of Projective Space of dimension 1 over Rational function field in c over Rational Field
Scheme endomorphism of Projective Space of
dimension 1 over Rational function field in c over Rational Field
Defn: Defined on coordinates by sending (x0 : x1) to
(x0^2 + c*x1^2 : x1^2)
"""
Expand Down Expand Up @@ -498,7 +501,8 @@ def dynatomic_polynomial(self, period):
INPUT:
- ``period`` -- a positive integer or a list/tuple `[m,n]` where `m` is the preperiod and `n` is the period.
- ``period`` -- a positive integer or a list/tuple `[m,n]`,
where `m` is the preperiod and `n` is the period.
OUTPUT:
Expand Down Expand Up @@ -580,7 +584,7 @@ def dynatomic_polynomial(self, period):

def nth_iterate_map(self, n):
r"""
This function returns the nth iterate of the map.
This function returns the ``n``th iterate of the map.
ALGORITHM:
Expand Down Expand Up @@ -655,16 +659,17 @@ def nth_iterate_map(self, n):

def nth_iterate(self, P, n):
r"""
Returns the nth iterate of the point ``P`` by this map.
Returns the ``n``th iterate of the point ``P`` by this map.
INPUT:
- ``P`` -- a point in the maps domain.
- ``P`` -- a point in the map's domain.
- ``n`` -- a positive integer.
OUTPUT:
- a point in the maps codomain.
- a point in the map's codomain.
EXAMPLES::
Expand Down Expand Up @@ -700,12 +705,12 @@ def orbit(self, P, n):
Returns the orbit of ``P`` by the map.
If `n` is an integer it returns `[P,self(P),\ldots,self^n(P)]`.
If `n` is a list or tuple `n=[m,k]` it returns `[self^m(P),\ldots,self^k(P)]`.
INPUT:
- ``P`` -- a point in the map domain.
- ``n`` -- a non-negative integer or list or tuple of two non-negative integers.
OUTPUT:
Expand Down Expand Up @@ -740,7 +745,7 @@ def orbit(self, P, n):
::
sage: R.<t> = PolynomialRing(QQ)
sage: A.<x,y>= AffineSpace(FractionField(R), 2)
sage: A.<x,y> = AffineSpace(FractionField(R), 2)
sage: H = Hom(A, A)
sage: f = H([(x-t*y^2)/x, t*x*y])
sage: f.orbit(A(1, t), 3)
Expand All @@ -750,9 +755,10 @@ def orbit(self, P, n):
"""
return(P.orbit(self, n))

def global_height(self,prec=None):
def global_height(self, prec=None):
r"""
Returns the maximum of the heights of the coefficients in any of the coordinate functions of the affine morphism.
Returns the maximum of the heights of the coefficients in any
of the coordinate functions of the affine morphism.
INPUT:
Expand All @@ -767,7 +773,7 @@ def global_height(self,prec=None):
sage: A.<x> = AffineSpace(QQ, 1)
sage: H = Hom(A, A)
sage: f = H([1/1331*x^2+4000]);
sage: f = H([1/1331*x^2 + 4000]);
sage: f.global_height()
8.29404964010203
Expand All @@ -777,25 +783,18 @@ def global_height(self,prec=None):
sage: k.<w> = NumberField(x^2 + 5)
sage: A.<x,y> = AffineSpace(k, 2)
sage: H = Hom(A, A)
sage: f = H([13*w*x^2+4*y, 1/w*y^2]);
sage: f = H([13*w*x^2 + 4*y, 1/w*y^2]);
sage: f.global_height(prec=100)
3.3696683136785869233538671082
.. TODO::
::
Add heights to integer.pyx and remove special case.
sage: A.<x> = AffineSpace(ZZ, 1)
sage: H = Hom(A, A)
sage: f = H([7*x^2 + 1513]);
sage: f.global_height()
7.32184971378836
"""
if self.domain().base_ring() == ZZ:
if prec is None:
R = RealField()
else:
R = RealField(prec)
H = R(0)
for i in range(self.domain().ambient_space().dimension_relative()):
C = self[i].coefficients()
h = max([c.abs() for c in C])
H = max(H, R(h).log())
return(H)
H=0
for i in range(self.domain().ambient_space().dimension_relative()):
C = self[i].coefficients()
Expand All @@ -810,8 +809,8 @@ def jacobian (self):
r"""
Returns the Jacobian matrix of partial derivitive of this map.
The ``(i, j)`` entry of the Jacobian matrix is the partial derivative
``diff(functions[i], variables[j])``.
The `(i, j)` entry of the Jacobian matrix is the partial derivative
`diff(functions[i], variables[j])`.
OUTPUT:
Expand All @@ -821,7 +820,7 @@ def jacobian (self):
sage: A.<z> = AffineSpace(QQ, 1)
sage: H = End(A)
sage: f = H([z^2-3/4])
sage: f = H([z^2 - 3/4])
sage: f.jacobian()
[2*z]
Expand Down Expand Up @@ -866,7 +865,7 @@ def multiplier(self, P, n, check=True):
OUTPUT:
- a square matrix of size ``self.codomain().dimension_relative()`` in
the ``base_ring`` of the map.
the ``base_ring`` of the map.
EXAMPLES::
Expand Down Expand Up @@ -993,12 +992,14 @@ class SchemeMorphism_polynomial_affine_space_finite_field(SchemeMorphism_polynom

def orbit_structure(self, P):
r"""
Every point is preperiodic over a finite field. This function returns the pair `[m,n]` where `m` is the
Every point is preperiodic over a finite field.
This function returns the pair `[m,n]` where `m` is the
preperiod and `n` is the period of the point ``P`` by this map.
INPUT:
- ``P`` -- a point in the maps domain.
- ``P`` -- a point in the map's domain.
OUTPUT:
Expand All @@ -1024,7 +1025,7 @@ def orbit_structure(self, P):

def _fast_eval(self, x):
"""
Evaluate affine morphism at point described by x.
Evaluate affine morphism at point described by ``x``.
EXAMPLES::
Expand Down Expand Up @@ -1063,12 +1064,12 @@ def _fast_eval(self, x):

def cyclegraph(self):
r"""
Returns digraph of all orbits of this morphism mod `p`. For subschemes, only points on the subscheme whose
image are also on the subscheme are in the digraph.
Returns digraph of all orbits of this morphism mod `p`.
OUTPUT:
For subschemes, only points on the subscheme whose
image are also on the subscheme are in the digraph.
- a digraph.
OUTPUT: A digraph.
EXAMPLES::
Expand Down

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