Ticket #10642: trac_10642.patch

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  • sage/calculus/calculus.py 

    # HG changeset patch
# User Ivo Hedtke <hedtke@me.com>
# Date 1311443640 -7200
# Node ID cae7699b764ad7c507060a8109317d81ca1d75bc
# Parent  ce324e28c3334398d3552640e2cb1520d22465a3
trac 10642: deleted additional point in some headings

diff -r ce324e28c333 -r cae7699b764a sage/calculus/calculus.py
    a b  
    11r"""
    2 Symbolic Computation.
     2Symbolic Computation
    33
    44AUTHORS:
    55

  • sage/calculus/functional.py 

    diff -r ce324e28c333 -r cae7699b764a sage/calculus/functional.py
    a b  
    11"""
    2 Functional notation support for common calculus methods.
     2Functional notation support for common calculus methods
    33
    44EXAMPLES: We illustrate each of the calculus functional functions.
    55

  • sage/calculus/tests.py 

    diff -r ce324e28c333 -r cae7699b764a sage/calculus/tests.py
    a b  
    11r"""
    2 Calculus Tests and Examples.
     2Calculus Tests and Examples
    33
    44Compute the Christoffel symbol.
    55

  • sage/categories/category_types.py 

    diff -r ce324e28c333 -r cae7699b764a sage/categories/category_types.py
    a b  
    11"""
    2 Specific category classes.
     2Specific category classes
    33
    44This is placed in a separate file from categories.py to avoid circular imports
    55(as morphisms must be very low in the hierarchy with the new coercion model).

  • sage/categories/pushout.py 

    diff -r ce324e28c333 -r cae7699b764a sage/categories/pushout.py
    a b  
    11"""
    2 Coercion via Construction Functors.
     2Coercion via Construction Functors
    33"""
    44from functor import Functor, IdentityFunctor_generic
    55from basic import *

  • sage/coding/code_constructions.py 

    diff -r ce324e28c333 -r cae7699b764a sage/coding/code_constructions.py
    a b  
    11r"""
    2 Linear code constructions.
     2Linear code constructions
    33
    44AUTHOR:
    55

  • sage/combinat/combinat.py 

    diff -r ce324e28c333 -r cae7699b764a sage/combinat/combinat.py
    a b  
    11r"""
    2 Combinatorial Functions.
     2Combinatorial Functions
    33 
    44AUTHORS:
    55

  • sage/combinat/expnums.pyx 

    diff -r ce324e28c333 -r cae7699b764a sage/combinat/expnums.pyx
    a b  
    11r"""
    2 Compute Bell and Uppuluri-Carpenter numbers.
     2Compute Bell and Uppuluri-Carpenter numbers
    33
    44AUTHORS:
    55

  • sage/combinat/integer_list.py 

    diff -r ce324e28c333 -r cae7699b764a sage/combinat/integer_list.py
    a b  
    11r"""
    2 Tools for generating lists of integers in lexicographic order.
     2Tools for generating lists of integers in lexicographic order
    33
    44IMPORTANT NOTE (2009/02):
    55The internal functions in this file will be deprecated soon.

  • sage/crypto/mq/mpolynomialsystem.py 

    diff -r ce324e28c333 -r cae7699b764a sage/crypto/mq/mpolynomialsystem.py
    a b  
    11"""
    2 Multivariate Polynomial Systems.
     2Multivariate Polynomial Systems
    33
    44We call a finite set of multivariate polynomials an ``MPolynomialSystem``.
    55

  • sage/crypto/mq/sr.py 

    diff -r ce324e28c333 -r cae7699b764a sage/crypto/mq/sr.py
    a b  
    11r"""
    2 Small Scale Variants of the AES (SR) Polynomial System Generator.
     2Small Scale Variants of the AES (SR) Polynomial System Generator
    33
    44Sage supports polynomial system generation for small scale (and full
    55scale) AES variants over `\GF{2}` and `\GF{2^e}`. Also, Sage supports

  • sage/databases/conway.py 

    diff -r ce324e28c333 -r cae7699b764a sage/databases/conway.py
    a b  
    11"""
    2 Frank Luebeck's tables of Conway polynomials over finite fields.
     2Frank Luebeck's tables of Conway polynomials over finite fields
    33"""
    44
    55

  • sage/databases/cremona.py 

    diff -r ce324e28c333 -r cae7699b764a sage/databases/cremona.py
    a b  
    11"""
    2 Cremona's tables of elliptic curves.
     2Cremona's tables of elliptic curves
    33
    44Sage includes John Cremona's tables of elliptic curves in an
    55easy-to-use format. The unique instance of the class

  • sage/databases/odlyzko.py 

    diff -r ce324e28c333 -r cae7699b764a sage/databases/odlyzko.py
    a b  
    11"""
    2 Tables of zeros of the Riemann-Zeta function.
     2Tables of zeros of the Riemann-Zeta function
    33"""
    44
    55#*****************************************************************************

  • sage/databases/stein_watkins.py 

    diff -r ce324e28c333 -r cae7699b764a sage/databases/stein_watkins.py
    a b  
    11r"""
    2 The Stein-Watkins table of elliptic curves.
     2The Stein-Watkins table of elliptic curves
    33
    44Sage gives access to the Stein-Watkins table of elliptic curves,
    55via an optional package that you must install. This is a huge

  • sage/functions/piecewise.py 

    diff -r ce324e28c333 -r cae7699b764a sage/functions/piecewise.py
    a b  
    11r"""
    2 Piecewise-defined Functions.
     2Piecewise-defined Functions
    33
    44Sage implements a very simple class of piecewise-defined functions.
    55Functions may be any type of symbolic expression. Infinite

  • sage/interfaces/gnuplot.py 

    diff -r ce324e28c333 -r cae7699b764a sage/interfaces/gnuplot.py
    a b  
    11r"""
    2 Interface to the Gnuplot interpreter.
     2Interface to the Gnuplot interpreter
    33"""
    44
    55#*****************************************************************************

  • sage/interfaces/gp.py 

    diff -r ce324e28c333 -r cae7699b764a sage/interfaces/gp.py
    a b  
    11r"""
    2 Interface to the GP calculator of PARI/GP.
     2Interface to the GP calculator of PARI/GP
    33
    44Type ``gp.[tab]`` for a list of all the functions
    55available from your Gp install. Type ``gp.[tab]?`` for

  • sage/libs/singular/function.pyx 

    diff -r ce324e28c333 -r cae7699b764a sage/libs/singular/function.pyx
    a b  
    11"""
    2 libSingular: Functions.
     2libSingular: Functions
    33
    44Sage implements a C wrapper around the Singular interpreter which
    55allows to call any function directly from Sage without string parsing

  • sage/libs/singular/option.pyx 

    diff -r ce324e28c333 -r cae7699b764a sage/libs/singular/option.pyx
    a b  
    11"""
    2 libSingular: Options.
     2libSingular: Options
    33
    44Singular uses a set of global options to determine verbosity and the
    55behavior of certain algorithms. We provide an interface to these

  • sage/matrix/matrix.pyx 

    diff -r ce324e28c333 -r cae7699b764a sage/matrix/matrix.pyx
    a b  
    11"""
    2 Abstract base class for matrices.
     2Abstract base class for matrices
    33
    44For design documentation see matrix/docs.py.
    55"""

  • sage/matrix/matrix_integer_dense.pyx 

    diff -r ce324e28c333 -r cae7699b764a sage/matrix/matrix_integer_dense.pyx
    a b  
    11"""
    2 Dense matrices over the integer ring.
     2Dense matrices over the integer ring
    33
    44AUTHORS:
    55

  • sage/matrix/matrix_modn_dense.pyx 

    diff -r ce324e28c333 -r cae7699b764a sage/matrix/matrix_modn_dense.pyx
    a b  
    11r"""
    2 Dense matrices over `\ZZ/n\ZZ` for `n` small.
     2Dense matrices over `\ZZ/n\ZZ` for `n` small
    33
    44AUTHORS:
    55

  • sage/matrix/matrix_modn_sparse.pyx 

    diff -r ce324e28c333 -r cae7699b764a sage/matrix/matrix_modn_sparse.pyx
    a b  
    11r"""
    2 Sparse matrices over `\ZZ/n\ZZ` for `n` small.
     2Sparse matrices over `\ZZ/n\ZZ` for `n` small
    33
    44This is a compiled implementation of sparse matrices over
    55`\ZZ/n\ZZ` for `n` small.

  • sage/matrix/matrix_rational_dense.pyx 

    diff -r ce324e28c333 -r cae7699b764a sage/matrix/matrix_rational_dense.pyx
    a b  
    11"""
    2 Dense matrices over the rational field.
     2Dense matrices over the rational field
    33
    44EXAMPLES:
    55

  • sage/matrix/matrix_space.py 

    diff -r ce324e28c333 -r cae7699b764a sage/matrix/matrix_space.py
    a b  
    11r"""
    2 Matrix Spaces.
     2Matrix Spaces
    33
    44You can create any space `\text{Mat}_{n\times m}(R)` of
    55either dense or sparse matrices with given number of rows and

  • sage/misc/classcall_metaclass.py 

    diff -r ce324e28c333 -r cae7699b764a sage/misc/classcall_metaclass.py
    a b  
    11r"""
    2 Special Methods for Classes.
     2Special Methods for Classes
    33"""
    44#*****************************************************************************
    55#  Copyright (C) 2009    Nicolas M. Thiery <nthiery at users.sf.net>

  • sage/misc/func_persist.py 

    diff -r ce324e28c333 -r cae7699b764a sage/misc/func_persist.py
    a b  
    11r"""
    2 Support for persistent functions in .sage files.
     2Support for persistent functions in .sage files
    33
    44Persistent functions are functions whose values are stored on disk
    55so they do not have to be recomputed.

  • sage/misc/log.py 

    diff -r ce324e28c333 -r cae7699b764a sage/misc/log.py
    a b  
    11r"""
    2 Logging of Sage sessions.
     2Logging of Sage sessions
    33
    44TODO: Pressing "control-D" can mess up the I/O sequence because of
    55a known bug.

  • sage/misc/nested_class.py 

    diff -r ce324e28c333 -r cae7699b764a sage/misc/nested_class.py
    a b  
    11"""
    2 Fixing Pickle for Nested Classes.
     2Fixing Pickle for Nested Classes
    33
    44As of Python 2.6, names for nested classes are set by Python in  a
    55way which is incompatible with the pickling of such classes (pickling by name)::

  • sage/misc/random_testing.py 

    diff -r ce324e28c333 -r cae7699b764a sage/misc/random_testing.py
    a b  
    11r"""
    2 Random testing.
     2Random testing
    33
    44Some Sage modules do random testing in their doctests; that is, they
    55construct test cases using a random number generator.  To get the

  • sage/modular/abvar/constructor.py 

    diff -r ce324e28c333 -r cae7699b764a sage/modular/abvar/constructor.py
    a b  
    11"""
    2 Constructors for certain modular abelian varieties.
     2Constructors for certain modular abelian varieties
    33
    44AUTHORS:
    55

  • sage/modular/abvar/homology.py 

    diff -r ce324e28c333 -r cae7699b764a sage/modular/abvar/homology.py
    a b  
    11r"""
    2 Homology of modular abelian varieties.
     2Homology of modular abelian varieties
    33
    44Sage can compute with homology groups associated to modular abelian
    55varieties with coefficients in any commutative ring. Supported

  • sage/modular/abvar/homspace.py 

    diff -r ce324e28c333 -r cae7699b764a sage/modular/abvar/homspace.py
    a b  
    11"""
    2 Spaces of homomorphisms between modular abelian varieties.
     2Spaces of homomorphisms between modular abelian varieties
    33
    44EXAMPLES:
    55

  • sage/modular/abvar/morphism.py 

    diff -r ce324e28c333 -r cae7699b764a sage/modular/abvar/morphism.py
    a b  
    11r"""
    2 Morphisms between modular abelian varieties, including Hecke operators acting on modular abelian varieties.
     2Morphisms between modular abelian varieties, including Hecke operators acting on modular abelian varieties
    33
    44Sage can compute with Hecke operators on modular abelian varieties.
    55A Hecke operator is defined by given a modular abelian variety and

  • sage/modular/abvar/torsion_subgroup.py 

    diff -r ce324e28c333 -r cae7699b764a sage/modular/abvar/torsion_subgroup.py
    a b  
    11"""
    2 Torsion subgroups of modular abelian varieties.
     2Torsion subgroups of modular abelian varieties
    33
    44Sage can compute information about the structure of the torsion
    55subgroup of a modular abelian variety. Sage computes a multiple of

  • sage/modular/cusps_nf.py 

    diff -r ce324e28c333 -r cae7699b764a sage/modular/cusps_nf.py
    a b  
    11r"""
    2 The set `\mathbb{P}^1(K)` of cusps of a number field K.
     2The set `\mathbb{P}^1(K)` of cusps of a number field K
    33
    44AUTHORS:
    55

  • sage/modular/etaproducts.py 

    diff -r ce324e28c333 -r cae7699b764a sage/modular/etaproducts.py
    a b  
    11r"""
    2 Eta-products on modular curves :math:`X_0(N)`.
     2Eta-products on modular curves :math:`X_0(N)`
    33
    44This package provides a class for representing eta-products, which
    55are meromorphic functions on modular curves of the form

  • sage/modular/modform/ambient.py 

    diff -r ce324e28c333 -r cae7699b764a sage/modular/modform/ambient.py
    a b  
    11# -*- coding: utf-8 -*-
    22r"""
    3 Ambient Spaces of Modular Forms.
     3Ambient Spaces of Modular Forms
    44
    55EXAMPLES:
    66

  • sage/modular/modform/ambient_g1.py 

    diff -r ce324e28c333 -r cae7699b764a sage/modular/modform/ambient_g1.py
    a b  
    11r"""
    2 Modular Forms for `\Gamma_1(N)` and `\Gamma_H(N)` over `\QQ`.
     2Modular Forms for `\Gamma_1(N)` and `\Gamma_H(N)` over `\QQ`
    33
    44EXAMPLES::
    55

  • sage/modular/modform/element.py 

    diff -r ce324e28c333 -r cae7699b764a sage/modular/modform/element.py
    a b  
    11# -*- coding: utf-8 -*-
    22"""
    3 Elements of modular forms spaces.
     3Elements of modular forms spaces
    44"""
    55
    66#########################################################################

  • sage/modular/modform/half_integral.py 

    diff -r ce324e28c333 -r cae7699b764a sage/modular/modform/half_integral.py
    a b  
    11r"""
    2 Compute spaces of half-integral weight modular forms.
     2Compute spaces of half-integral weight modular forms
    33
    44Based on an algorithm in Basmaji's thesis.
    55

  • sage/modular/modsym/ambient.py 

    diff -r ce324e28c333 -r cae7699b764a sage/modular/modsym/ambient.py
    a b  
    11# -*- coding: utf-8 -*-
    22r"""
    3 Ambient spaces of modular symbols.
     3Ambient spaces of modular symbols
    44
    55This module defines the following classes.  There is an abstract base
    66class ``ModularSymbolsAmbient``, derived from

  • sage/modular/modsym/boundary.py 

    diff -r ce324e28c333 -r cae7699b764a sage/modular/modsym/boundary.py
    a b  
    11# -*- coding: utf-8 -*-
    22r"""
    3 Space of boundary modular symbols.
     3Space of boundary modular symbols
    44
    55Used mainly for computing the cuspidal subspace of modular symbols. The space
    66of boundary symbols of sign 0 is isomorphic as a Hecke module to the dual of

  • sage/modular/modsym/element.py 

    diff -r ce324e28c333 -r cae7699b764a sage/modular/modsym/element.py
    a b  
    11"""
    2 A single element of an ambient space of modular symbols.
     2A single element of an ambient space of modular symbols
    33"""
    44
    55#*****************************************************************************

  • sage/modular/modsym/g1list.py 

    diff -r ce324e28c333 -r cae7699b764a sage/modular/modsym/g1list.py
    a b  
    11r"""
    2 List of coset representatives for `\Gamma_1(N)` in `{\rm SL}_2(\ZZ)`.
     2List of coset representatives for `\Gamma_1(N)` in `{\rm SL}_2(\ZZ)`
    33"""
    44
    55#*****************************************************************************

  • sage/modular/modsym/ghlist.py 

    diff -r ce324e28c333 -r cae7699b764a sage/modular/modsym/ghlist.py
    a b  
    11r"""
    2 List of coset representatives for `\Gamma_H(N)` in `{\rm SL}_2(\ZZ)`.
     2List of coset representatives for `\Gamma_H(N)` in `{\rm SL}_2(\ZZ)`
    33"""
    44
    55###########################################################################

  • sage/modular/modsym/p1list.pyx 

    diff -r ce324e28c333 -r cae7699b764a sage/modular/modsym/p1list.pyx
    a b  
    11r"""
    2 Lists of Manin symbols (elements of `\mathbb{P}^1(\ZZ/N\ZZ)`) over `\QQ`.
     2Lists of Manin symbols (elements of `\mathbb{P}^1(\ZZ/N\ZZ)`) over `\QQ`
    33"""
    44
    55from sage.misc.search import search

  • sage/modular/modsym/p1list_nf.py 

    diff -r ce324e28c333 -r cae7699b764a sage/modular/modsym/p1list_nf.py
    a b  
    11r"""
    2 Lists of Manin symbols (elements of `\mathbb{P}^1(R/N)`) over number fields.
     2Lists of Manin symbols (elements of `\mathbb{P}^1(R/N)`) over number fields
    33
    44Lists of elements of `\mathbb{P}^1(R/N)` where `R` is the ring of integers of a number
    55field `K` and `N` is an integral ideal.

  • sage/modules/complex_double_vector.py 

    diff -r ce324e28c333 -r cae7699b764a sage/modules/complex_double_vector.py
    a b  
    11r"""
    2 Pickling for the old CDF vector class.
     2Pickling for the old CDF vector class
    33
    44AUTHORS:
    55

  • sage/modules/fg_pid/fgp_element.py 

    diff -r ce324e28c333 -r cae7699b764a sage/modules/fg_pid/fgp_element.py
    a b  
    11r"""
    2 Elements of finitely generated modules over a PID.
     2Elements of finitely generated modules over a PID
    33
    44AUTHOR:
    55    - William Stein, 2009

  • sage/modules/fg_pid/fgp_module.py 

    diff -r ce324e28c333 -r cae7699b764a sage/modules/fg_pid/fgp_module.py
    a b  
    11r"""
    2 Finitely generated modules over a PID.
     2Finitely generated modules over a PID
    33
    44You can use Sage to compute with finitely generated modules (FGM's)
    55over a principal ideal domain R presented as a quotient V/W, where V

  • sage/modules/fg_pid/fgp_morphism.py 

    diff -r ce324e28c333 -r cae7699b764a sage/modules/fg_pid/fgp_morphism.py
    a b  
    11r"""
    2 Morphisms between finitely generated modules over a PID.
     2Morphisms between finitely generated modules over a PID
    33
    44AUTHOR:
    55- William Stein, 2009

  • sage/modules/free_module_morphism.py 

    diff -r ce324e28c333 -r cae7699b764a sage/modules/free_module_morphism.py
    a b  
    11"""
    2 Morphisms of free modules.
     2Morphisms of free modules
    33
    44AUTHORS:
    55    - William Stein: initial version

  • sage/modules/matrix_morphism.py 

    diff -r ce324e28c333 -r cae7699b764a sage/modules/matrix_morphism.py
    a b  
    11r"""
    2 Morphisms defined by a matrix.
     2Morphisms defined by a matrix
    33
    44A matrix morphism is a morphism that is defined by multiplication
    55by a matrix. Elements of domain must either have a method

  • sage/modules/real_double_vector.py 

    diff -r ce324e28c333 -r cae7699b764a sage/modules/real_double_vector.py
    a b  
    11"""
    2 Pickling for the old RDF vector class.
     2Pickling for the old RDF vector class
    33
    44AUTHORS:
    55

  • sage/plot/plot3d/examples.py 

    diff -r ce324e28c333 -r cae7699b764a sage/plot/plot3d/examples.py
    a b  
    11r"""
    2 Introduction.
     2Introduction
    33
    44EXAMPLES::
    55

  • sage/plot/plot3d/platonic.py 

    diff -r ce324e28c333 -r cae7699b764a sage/plot/plot3d/platonic.py
    a b  
    11r"""
    2 Platonic Solids.
     2Platonic Solids
    33
    44EXAMPLES: The five platonic solids in a row;
    55

  • sage/plot/plot3d/plot3d.py 

    diff -r ce324e28c333 -r cae7699b764a sage/plot/plot3d/plot3d.py
    a b  
    11r"""
    2 Plotting Functions.
     2Plotting Functions
    33
    44EXAMPLES::
    55

  • sage/quadratic_forms/binary_qf.py 

    diff -r ce324e28c333 -r cae7699b764a sage/quadratic_forms/binary_qf.py
    a b  
    11r"""
    2 Binary Quadratic Forms with Integer Coefficients.
     2Binary Quadratic Forms with Integer Coefficients
    33
    44This module provides a specialized class for working with a binary quadratic
    55form `a x^2 + b x y + c y^2`, stored as a triple of integers `(a, b, c)`.

  • sage/rings/finite_rings/element_base.pyx 

    diff -r ce324e28c333 -r cae7699b764a sage/rings/finite_rings/element_base.pyx
    a b  
    11"""
    2 Base class for finite field elements.
     2Base class for finite field elements
    33
    44AUTHORS::
    55

  • sage/rings/homset.py 

    diff -r ce324e28c333 -r cae7699b764a sage/rings/homset.py
    a b  
    11"""
    2 Space of homomorphisms between two rings.
     2Space of homomorphisms between two rings
    33"""
    44
    55#*****************************************************************************

  • sage/rings/number_field/number_field_base.pyx 

    diff -r ce324e28c333 -r cae7699b764a sage/rings/number_field/number_field_base.pyx
    a b  
    11"""
    2 Base class for all number fields.
     2Base class for all number fields
    33
    44
    55TESTS::

  • sage/rings/padics/eisenstein_extension_generic.py 

    diff -r ce324e28c333 -r cae7699b764a sage/rings/padics/eisenstein_extension_generic.py
    a b  
    11"""
    2 Eisenstein Extension Generic.
     2Eisenstein Extension Generic
    33
    44This file implements the shared functionality for Eisenstein extensions.
    55

  • sage/rings/padics/factory.py 

    diff -r ce324e28c333 -r cae7699b764a sage/rings/padics/factory.py
    a b  
    11"""
    2 Factory.
     2Factory
    33
    44This file contains the constructor classes and functions for `p`-adic rings and fields.
    55

  • sage/rings/padics/generic_nodes.py 

    diff -r ce324e28c333 -r cae7699b764a sage/rings/padics/generic_nodes.py
    a b  
    11"""
    2 `p`-Adic Generic Nodes.
     2`p`-Adic Generic Nodes
    33
    44This file contains a bunch of intermediate classes for the `p`-adic
    55parents, allowing a function to be implemented at the right level of

  • sage/rings/padics/local_generic.py 

    diff -r ce324e28c333 -r cae7699b764a sage/rings/padics/local_generic.py
    a b  
    11"""
    2 Local Generic.
     2Local Generic
    33
    44Superclass for `p`-adic and power series rings.
    55

  • sage/rings/padics/local_generic_element.pyx 

    diff -r ce324e28c333 -r cae7699b764a sage/rings/padics/local_generic_element.pyx
    a b  
    11"""
    2 Local Generic Element.
     2Local Generic Element
    33
    44This file contains a common superclass for `p`-adic elements and power
    55series elements.

  • sage/rings/padics/misc.py 

    diff -r ce324e28c333 -r cae7699b764a sage/rings/padics/misc.py
    a b  
    11"""
    2 Miscellaneous Functions.
     2Miscellaneous Functions
    33
    44This file contains some miscellaneous functions used by p-adics.
    55

  • sage/rings/padics/padic_ZZ_pX_CA_element.pyx 

    diff -r ce324e28c333 -r cae7699b764a sage/rings/padics/padic_ZZ_pX_CA_element.pyx
    a b  
    11"""
    2 `p`-Adic ``ZZ_pX`` CA Element.
     2`p`-Adic ``ZZ_pX`` CA Element
    33
    44This file implements elements of eisenstein and unramified extensions
    55of ``Zp`` with capped absolute precision.

  • sage/rings/padics/padic_ZZ_pX_CR_element.pyx 

    diff -r ce324e28c333 -r cae7699b764a sage/rings/padics/padic_ZZ_pX_CR_element.pyx
    a b  
    11"""
    2 `p`-Adic ``ZZ_pX`` CR Element.
     2`p`-Adic ``ZZ_pX`` CR Element
    33
    44This file implements elements of Eisenstein and unramified extensions
    55of `\mathbb{Z}_p` and `\mathbb{Q}_p` with capped relative precision.

  • sage/rings/padics/padic_ZZ_pX_FM_element.pyx 

    diff -r ce324e28c333 -r cae7699b764a sage/rings/padics/padic_ZZ_pX_FM_element.pyx
    a b  
    11"""
    2 `p`-Adic ``ZZ_pX`` FM Element.
     2`p`-Adic ``ZZ_pX`` FM Element
    33
    44This file implements elements of Eisenstein and unramified extensions
    55of `\mathbb{Z}_p` with fixed modulus precision.

  • sage/rings/padics/padic_ZZ_pX_element.pyx 

    diff -r ce324e28c333 -r cae7699b764a sage/rings/padics/padic_ZZ_pX_element.pyx
    a b  
    11"""
    2 `p`-Adic ``ZZ_pX Element``.
     2`p`-Adic ``ZZ_pX Element``
    33
    44A common superclass implementing features shared by all elements that
    55use NTL's ``ZZ_pX`` as the fundamental data type.

  • sage/rings/padics/padic_base_coercion.pyx 

    diff -r ce324e28c333 -r cae7699b764a sage/rings/padics/padic_base_coercion.pyx
    a b  
    11"""
    2 This file contains morphisms implementing coercion between base p-adic rings and fields as well as ZZ and QQ.
     2This file contains morphisms implementing coercion between base p-adic rings and fields as well as ZZ and QQ
    33
    44AUTHOR:
    55-- David Roe (initial version: 2010-8-25)

  • sage/rings/padics/padic_base_generic.py 

    diff -r ce324e28c333 -r cae7699b764a sage/rings/padics/padic_base_generic.py
    a b  
    11"""
    2 `p`-Adic Base Generic.
     2`p`-Adic Base Generic
    33
    44A superclass for implementations of `\mathbb{Z}_p` and `\mathbb{Q}_p`.
    55

  • sage/rings/padics/padic_base_generic_element.pyx 

    diff -r ce324e28c333 -r cae7699b764a sage/rings/padics/padic_base_generic_element.pyx
    a b  
    11"""
    2 `p`-Adic Base Generic Element.
     2`p`-Adic Base Generic Element
    33
    44A common superclass for features shared among all elements of `\mathbb{Z}_p` and
    55`\mathbb{Q}_p` (regardless of implementation).

  • sage/rings/padics/padic_base_leaves.py 

    diff -r ce324e28c333 -r cae7699b764a sage/rings/padics/padic_base_leaves.py
    a b  
    11"""
    2 `p`-Adic Base Leaves.
     2`p`-Adic Base Leaves
    33
    44Implementations of `\mathbb{Z}_p` and `\mathbb{Q}_p`
    55

  • sage/rings/padics/padic_capped_absolute_element.pyx 

    diff -r ce324e28c333 -r cae7699b764a sage/rings/padics/padic_capped_absolute_element.pyx
    a b  
    11"""
    2 `p`-Adic Capped Absolute Element.
     2`p`-Adic Capped Absolute Element
    33
    44Elements of `p`-Adic Rings with Absolute Precision Cap
    55

  • sage/rings/padics/padic_capped_relative_element.pyx 

    diff -r ce324e28c333 -r cae7699b764a sage/rings/padics/padic_capped_relative_element.pyx
    a b  
    11"""
    2 p-Adic Capped Relative Element.
     2p-Adic Capped Relative Element
    33
    44Elements of p-Adic Rings with Capped Relative Precision
    55

  • sage/rings/padics/padic_ext_element.pyx 

    diff -r ce324e28c333 -r cae7699b764a sage/rings/padics/padic_ext_element.pyx
    a b  
    11"""
    2 p-Adic Extension Element.
     2p-Adic Extension Element
    33
    44A common superclass for all elements of extension rings and field of Zp and Qp.
    55

  • sage/rings/padics/padic_extension_generic.py 

    diff -r ce324e28c333 -r cae7699b764a sage/rings/padics/padic_extension_generic.py
    a b  
    11"""
    2 p-Adic Extension Generic.
     2p-Adic Extension Generic
    33
    44A common superclass for all extensions of Qp and Zp.
    55

  • sage/rings/padics/padic_extension_leaves.py 

    diff -r ce324e28c333 -r cae7699b764a sage/rings/padics/padic_extension_leaves.py
    a b  
    11"""
    2 p-Adic Extension Leaves.
     2p-Adic Extension Leaves
    33
    44The final classes for extensions of Zp and Qp (ie classes that are not
    55just designed to be inherited from).

  • sage/rings/padics/padic_fixed_mod_element.pyx 

    diff -r ce324e28c333 -r cae7699b764a sage/rings/padics/padic_fixed_mod_element.pyx
    a b  
    11"""
    2 p-Adic Fixed-Mod Element.
     2p-Adic Fixed-Mod Element
    33
    44Elements of p-Adic Rings with Fixed Modulus
    55

  • sage/rings/padics/padic_generic.py 

    diff -r ce324e28c333 -r cae7699b764a sage/rings/padics/padic_generic.py
    a b  
    11"""
    2 p-Adic Generic.
     2p-Adic Generic
    33
    44A generic superclass for all p-adic parents.
    55

  • sage/rings/padics/padic_generic_element.pyx 

    diff -r ce324e28c333 -r cae7699b764a sage/rings/padics/padic_generic_element.pyx
    a b  
    11"""
    2 p-Adic Generic Element.
     2p-Adic Generic Element
    33
    44Elements of p-Adic Rings and Fields
    55

  • sage/rings/padics/padic_printing.pyx 

    diff -r ce324e28c333 -r cae7699b764a sage/rings/padics/padic_printing.pyx
    a b  
    11"""
    2 p-Adic Printing.
     2p-Adic Printing
    33
    44This file contains code for printing p-adic elements.
    55

  • sage/rings/padics/pow_computer.pyx 

    diff -r ce324e28c333 -r cae7699b764a sage/rings/padics/pow_computer.pyx
    a b  
    11"""
    2 PowComputer.
     2PowComputer
    33
    44A class for computing and caching powers of the same integer.
    55

  • sage/rings/padics/pow_computer_ext.pyx 

    diff -r ce324e28c333 -r cae7699b764a sage/rings/padics/pow_computer_ext.pyx
    a b  
    11"""
    2 PowComputer_ext.
     2PowComputer_ext
    33
    44The classes in this file are designed to be attached to p-adic parents
    55and elements for Cython access to properties of the parent.

  • sage/rings/padics/precision_error.py 

    diff -r ce324e28c333 -r cae7699b764a sage/rings/padics/precision_error.py
    a b  
    11"""
    2 Precision Error.
     2Precision Error
    33
    44The errors in this file indicate various styles of precision problems
    55that can go wrong for p-adics and power series.

  • sage/rings/padics/unramified_extension_generic.py 

    diff -r ce324e28c333 -r cae7699b764a sage/rings/padics/unramified_extension_generic.py
    a b  
    11"""
    2 Unramified Extension Generic.
     2Unramified Extension Generic
    33
    44This file implements the shared functionality for unramified extensions.
    55

  • sage/rings/polynomial/convolution.py 

    diff -r ce324e28c333 -r cae7699b764a sage/rings/polynomial/convolution.py
    a b  
    11r"""
    2 Generic Convolution.
     2Generic Convolution
    33
    44Asymptotically fast convolution of lists over any commutative ring
    55in which the multiply-by-two map is injective. (More precisely, if

  • sage/rings/rational_field.py 

    diff -r ce324e28c333 -r cae7699b764a sage/rings/rational_field.py
    a b  
    11r"""
    2 Field `\QQ` of Rational Numbers.
     2Field `\QQ` of Rational Numbers
    33
    44The class ``RationalField`` represents the field
    55`\QQ` of (arbitrary precision) rational numbers.

  • sage/schemes/elliptic_curves/ell_generic.py 

    diff -r ce324e28c333 -r cae7699b764a sage/schemes/elliptic_curves/ell_generic.py
    a b  
    11r"""
    2 Elliptic curves over a general ring.
     2Elliptic curves over a general ring
    33
    44Sage defines an elliptic curve over a ring `R` as a 'Weierstrass Model' with
    55five coefficients `[a_1,a_2,a_3,a_4,a_6]` in `R` given by

  • sage/schemes/elliptic_curves/ell_torsion.py 

    diff -r ce324e28c333 -r cae7699b764a sage/schemes/elliptic_curves/ell_torsion.py
    a b  
    11# -*- coding: utf-8 -*-
    22r"""
    3 Torsion subgroups of elliptic curves over number fields (including `\QQ`).
     3Torsion subgroups of elliptic curves over number fields (including `\QQ`)
    44
    55AUTHORS:
    66

  • sage/schemes/elliptic_curves/ell_wp.py 

    diff -r ce324e28c333 -r cae7699b764a sage/schemes/elliptic_curves/ell_wp.py
    a b  
    11r"""
    2 Weierstrass `\wp` function for elliptic curves.
     2Weierstrass `\wp` function for elliptic curves
    33
    44The Weierstrass `\wp` function associated to an elliptic curve over a field `k` is a Laurent series
    55of the form

  • sage/schemes/elliptic_curves/formal_group.py 

    diff -r ce324e28c333 -r cae7699b764a sage/schemes/elliptic_curves/formal_group.py
    a b  
    11# -*- coding: utf-8 -*-
    22r"""
    3 Formal groups of elliptic curves.
     3Formal groups of elliptic curves
    44
    55AUTHORS:
    66

  • sage/schemes/elliptic_curves/kodaira_symbol.py 

    diff -r ce324e28c333 -r cae7699b764a sage/schemes/elliptic_curves/kodaira_symbol.py
    a b  
    11r"""
    2 Kodaira symbols.
     2Kodaira symbols
    33
    44Kodaira symbols encode the type of reduction of an elliptic curve at a
    55(finite) place.

  • sage/schemes/elliptic_curves/modular_parametrization.py 

    diff -r ce324e28c333 -r cae7699b764a sage/schemes/elliptic_curves/modular_parametrization.py
    a b  
    11# -*- coding: utf-8 -*-
    22r"""
    3 Modular parametrization of elliptic curves over `\QQ`.
     3Modular parametrization of elliptic curves over `\QQ`
    44
    55By the work of Taylor--Wiles et al. it is known that there
    66is a surjective morphism

  • sage/schemes/elliptic_curves/monsky_washnitzer.py 

    diff -r ce324e28c333 -r cae7699b764a sage/schemes/elliptic_curves/monsky_washnitzer.py
    a b  
    11r"""
    2 Computation of Frobenius matrix on Monsky-Washnitzer cohomology.
     2Computation of Frobenius matrix on Monsky-Washnitzer cohomology
    33
    44The most interesting functions to be exported here are
    55matrix_of_frobenius() and adjusted_prec().

  • sage/schemes/elliptic_curves/period_lattice.py 

    diff -r ce324e28c333 -r cae7699b764a sage/schemes/elliptic_curves/period_lattice.py
    a b  
    11# -*- coding: utf-8 -*-
    22r"""
    3 Period lattices of elliptic curves and related functions.
     3Period lattices of elliptic curves and related functions
    44
    55Let `E` be an elliptic curve defined over a number field `K`
    66(including `\QQ`).  We attach a period lattice (a discrete rank 2

  • sage/schemes/generic/affine_space.py 

    diff -r ce324e28c333 -r cae7699b764a sage/schemes/generic/affine_space.py
    a b  
    11"""
    2 Affine `n` space over a ring.
     2Affine `n` space over a ring
    33"""
    44
    55#*****************************************************************************

  • sage/schemes/generic/projective_space.py 

    diff -r ce324e28c333 -r cae7699b764a sage/schemes/generic/projective_space.py
    a b  
    11r"""
    2 Projective `n` space over a ring.
     2Projective `n` space over a ring
    33
    44EXAMPLES: We construct projective space over various rings of
    55various dimensions.

  • sage/schemes/hyperelliptic_curves/jacobian_g2.py 

    diff -r ce324e28c333 -r cae7699b764a sage/schemes/hyperelliptic_curves/jacobian_g2.py
    a b  
    11"""
    2 Jacobian of a Hyperelliptic curve of Genus 2.
     2Jacobian of a Hyperelliptic curve of Genus 2
    33"""
    44
    55#*****************************************************************************

  • sage/schemes/hyperelliptic_curves/jacobian_morphism.py 

    diff -r ce324e28c333 -r cae7699b764a sage/schemes/hyperelliptic_curves/jacobian_morphism.py
    a b  
    11r"""
    2 Jacobian 'morphism' as a class in the Picard group.
     2Jacobian 'morphism' as a class in the Picard group
    33
    44This module implements the group operation in the Picard group of a
    55hyperelliptic curve, represented as divisors in Mumford

  • sage/schemes/plane_conics/con_field.py 

    diff -r ce324e28c333 -r cae7699b764a sage/schemes/plane_conics/con_field.py
    a b  
    11r"""
    2 Projective plane conics over a field.
     2Projective plane conics over a field
    33
    44AUTHORS:
    55

  • sage/schemes/plane_conics/con_finite_field.py 

    diff -r ce324e28c333 -r cae7699b764a sage/schemes/plane_conics/con_finite_field.py
    a b  
    11r"""
    2 Projective plane conics over finite fields.
     2Projective plane conics over finite fields
    33
    44AUTHORS:
    55

  • sage/schemes/plane_conics/con_number_field.py 

    diff -r ce324e28c333 -r cae7699b764a sage/schemes/plane_conics/con_number_field.py
    a b  
    11r"""
    2 Projective plane conics over a number field.
     2Projective plane conics over a number field
    33
    44AUTHORS:
    55

  • sage/schemes/plane_conics/con_prime_finite_field.py 

    diff -r ce324e28c333 -r cae7699b764a sage/schemes/plane_conics/con_prime_finite_field.py
    a b  
    11r"""
    2 Projective plane conics over prime finite fields.
     2Projective plane conics over prime finite fields
    33
    44AUTHORS:
    55

  • sage/schemes/plane_conics/con_rational_field.py 

    diff -r ce324e28c333 -r cae7699b764a sage/schemes/plane_conics/con_rational_field.py
    a b  
    11r"""
    2 Projective plane conics over `\QQ`.
     2Projective plane conics over `\QQ`
    33
    44AUTHORS:
    55

  • sage/schemes/plane_conics/constructor.py 

    diff -r ce324e28c333 -r cae7699b764a sage/schemes/plane_conics/constructor.py
    a b  
    11r"""
    2 Plane conic constructor.
     2Plane conic constructor
    33
    44AUTHORS:
    55

  • sage/structure/category_object.pyx 

    diff -r ce324e28c333 -r cae7699b764a sage/structure/category_object.pyx
    a b  
    11r"""
    2 Base class for objects of a category.
     2Base class for objects of a category
    33
    44CLASS HIERARCHY:
    55

  • sage/structure/parent_gens.pyx 

    diff -r ce324e28c333 -r cae7699b764a sage/structure/parent_gens.pyx
    a b  
    11r"""
    2 Base class for parent objects with generators.
     2Base class for parent objects with generators
    33
    44.. note::
    55

  • sage/symbolic/relation.py 

    diff -r ce324e28c333 -r cae7699b764a sage/symbolic/relation.py
    a b  
    11r"""
    2 Symbolic Equations and Inequalities.
     2Symbolic Equations and Inequalities
    33
    44Sage can solve symbolic equations and inequalities. For
    55example, we derive the quadratic formula as follows::

  • sage/tensor/coordinate_patch.py 

    diff -r ce324e28c333 -r cae7699b764a sage/tensor/coordinate_patch.py
    a b  
    11r"""
    2 Open subset of Euclidian space with coordinates.
     2Open subset of Euclidian space with coordinates
    33
    44An open subset of Euclidian space with a specific set of coordinates.  This
    55is the background on which differential forms can be defined.

  • sage/tensor/differential_form_element.py 

    diff -r ce324e28c333 -r cae7699b764a sage/tensor/differential_form_element.py
    a b  
    11r"""
    2 Elements of the algebra of differential forms.
     2Elements of the algebra of differential forms
    33
    44AUTHORS:
    55

  • sage/tensor/differential_forms.py 

    diff -r ce324e28c333 -r cae7699b764a sage/tensor/differential_forms.py
    a b  
    11r"""
    2 Algebra of differential forms.
     2Algebra of differential forms
    33
    44Algebra of differential forms defined on a CoordinatePatch (an open subset of
    55Euclidian space, see ``CoordinatePatch`` for details).