Merge branch 't/21180/cantor_product_comb' into t/21203/sequences/k-r…

…egular

* t/21180/cantor_product_comb: (135 commits)
  Updated SageMath version to 7.4.beta2
  Small change in a doctest
  Small fixes. All doctests pass (hopefully)
  Rewrite coerce_binop. Fix a bug exposed by this in fields.py
  removed base_ring option from abelian_variety() in ell_rational_field.py
  trac 21310 get rid of itervalues in the combinat folder
  trac 21308 better doc
  trac 21308 add one reference + more doc
  trac 21308 better doc
  implement the magnitude function of a graph
  12364: adding doctest
  removal of another bunch of useless .keys()
  Add traceback line to doctest
  formatting changes to automorphims in rational_field
  added automorphisms to rational_field
  detail
  18709: improve docstrings; make case of multiple roots more efficient
  Correct exception raising to Py3 format
  added abelian_variety() to ell_rational_field
  a bunch of typos, including "because"
  ...

COPYING.txt

@@ -801,7 +801,7 @@ at the notice in config.guess or ltmain.sh.)
 
 The atomic_ops library contains some code that is covered by the GNU General
 Public License, but is not needed by, nor linked into the collector library.
-It is included here only becuase the atomic_ops distribution is, for
+It is included here only because the atomic_ops distribution is, for
 simplicity, included in its entirety.
 
 ================================================================================

VERSION.txt

@@ -1 +1 @@
-SageMath version 7.4.beta1, Release Date: 2016-08-17
+SageMath version 7.4.beta2, Release Date: 2016-08-26

build/pkgs/bliss/dependencies

@@ -0,0 +1,5 @@
+# no dependencies
+
+----------
+All lines of this file are ignored except the first.
+It is copied by SAGE_ROOT/build/make/install into SAGE_ROOT/build/make/Makefile.

build/pkgs/configparser/SPKG.txt

@@ -0,0 +1,22 @@
+= configparser =
+
+== Description ==
+
+This library brings the updated configparser from Python 3.5 to Python 2.6-3.5.
+
+The ancient ConfigParser module available in the standard library 2.x
+has seen a major update in Python 3.2. This is a backport of those
+changes so that they can be used directly in Python 2.6 - 3.5.
+
+To use the configparser backport instead of the built-in version on both
+Python 2 and Python 3, simply import it explicitly as a backport:
+
+    from backports import configparser
+
+If you'd like to use the backport on Python 2 and the built-in version
+on Python 3, use that invocation instead:
+
+    import configparser
+
+For detailed documentation consult the vanilla version at
+http://docs.python.org/3/library/configparser.html.

build/pkgs/configparser/checksums.ini

@@ -0,0 +1,4 @@
+tarball=configparser-VERSION.tar.gz
+sha1=8ee6b29c6a11977c0e094da1d4f5f71e7e7ac78b
+md5=cfdd915a5b7a6c09917a64a573140538
+cksum=3139292895

build/pkgs/configparser/dependencies

@@ -0,0 +1,5 @@
+$(PYTHON) | pip
+
+----------
+All lines of this file are ignored except the first.
+It is copied by SAGE_ROOT/build/make/install into SAGE_ROOT/build/make/Makefile.

build/pkgs/configparser/package-version.txt

@@ -0,0 +1 @@
+3.5.0

build/pkgs/configparser/spkg-install

@@ -0,0 +1,3 @@
+#!/usr/bin/env bash
+
+cd src && pip install --verbose --no-index .

build/pkgs/configparser/type

@@ -0,0 +1 @@
+standard

build/pkgs/configure/checksums.ini

@@ -1,4 +1,4 @@
 tarball=configure-VERSION.tar.gz
-sha1=7bf585bca9e2ee124152b7ff7268e63bdee8d5ba
-md5=71088e94c8b154037848cbf03ff823c4
-cksum=2410748983
+sha1=3d13a8f9dcaef6c048d0d21f91338b0b3d0fe125
+md5=63fc727ca070844c580b5a722d177cb1
+cksum=3010448970

build/pkgs/configure/package-version.txt

@@ -1 +1 @@
-178
+179

build/pkgs/ecm/package-version.txt

@@ -1 +1 @@
-6.4.4
+6.4.4.p0

build/pkgs/ecm/patches/cygwin.patch

@@ -0,0 +1,26 @@
+Make sure the assembly routines use the appropriate calling convention
+for Windows in Cygwin as well.  See https://trac.sagemath.org/ticket/21223
+diff -ruN a/configure.in b/configure.in
+--- a/configure.in	2016-08-11 13:51:46.869520300 +0200
++++ b/configure.in	2016-08-11 13:52:46.240830400 +0200
+@@ -256,7 +256,7 @@
+   GMP_ASM_TYPE 
+
+   case $host in
+-    *-*-mingw32) GMP_DEFINE([WINDOWS64_ABI], 1)
++    *-*-mingw32|*cygwin*) GMP_DEFINE([WINDOWS64_ABI], 1)
+                  AC_DEFINE([WINDOWS64_ABI], 1,[Define to 1 if x86_64 mulredc*() functions should be called with Windows ABI]);;
+     *) ;;
+   esac
+diff -ruN a/configure b/configure
+--- a/configure	2016-08-11 13:51:46.936572300 +0200
++++ b/configure	2016-08-11 13:53:31.281801500 +0200
+@@ -12957,7 +12957,7 @@
+
+
+   case $host in
+-    *-*-mingw32)
++    *-*-mingw32|*cygwin*)
+ echo 'define(<WINDOWS64_ABI>, <1>)' >>$gmp_tmpconfigm4
+
+

build/pkgs/entrypoints/SPKG.txt

@@ -0,0 +1,17 @@
+= entrypoints =
+
+== Description ==
+
+Discover and load entry points from installed packages.
+
+== Upstream Contact ==
+
+https://github.com/takluyver/entrypoints
+
+== Special Update/Build Instructions ==
+
+Upstream does not provide a source tarball, so the tarball was taken
+from github and renamed.
+
+The source tarball does not contain setup.py, so we put the setup
+commands in spkg-install.

build/pkgs/entrypoints/checksums.ini

@@ -0,0 +1,4 @@
+tarball=entrypoints-VERSION.tar.gz
+sha1=75f43c6051e5d7b3bec7cf11fb7228d447efb06b
+md5=7dae980f7c6affd777dc60a51c8d0b0b
+cksum=2039305359

build/pkgs/entrypoints/dependencies

@@ -0,0 +1,5 @@
+$(PYTHON) | pip configparser
+
+----------
+All lines of this file are ignored except the first.
+It is copied by SAGE_ROOT/build/make/install into SAGE_ROOT/build/make/Makefile.

build/pkgs/entrypoints/package-version.txt

@@ -0,0 +1 @@
+0.2.2

build/pkgs/entrypoints/setup.py

@@ -0,0 +1,9 @@
+#!/usr/bin/env python
+#
+# Upstream does not have a setup.py file, so we use this instead
+#
+
+from entrypoints import __version__ as v
+
+from setuptools import setup
+setup(name="entrypoints", version=v, py_modules=["entrypoints"])

build/pkgs/entrypoints/spkg-install

@@ -0,0 +1,7 @@
+#!/usr/bin/env bash
+#
+# Upstream does not have a setup.py file, so we supply one with Sage
+#
+
+mv setup.py src
+cd src && pip install --verbose --no-index .

build/pkgs/entrypoints/type

@@ -0,0 +1 @@
+standard

build/pkgs/pari/checksums.ini

@@ -1,4 +1,4 @@
 tarball=pari-VERSION.tar.gz
-sha1=a936e0ed661c8e453578f3c129c3a454e2039e3e
-md5=59f2e4c3c51f7652182400489cd76e6a
-cksum=1366291737
+sha1=efd1eb6b8d87066b2b9f3b2c38ecb30bbfdb48d2
+md5=f3f3342913a3b3b306970b3462f4d47d
+cksum=1553747906

build/pkgs/pari/package-version.txt

@@ -1 +1 @@
-2.8-2771-gb70b447.p0
+2.8.0.alpha.p0

build/pkgs/r/patches/rcmd_exec.patch

@@ -0,0 +1,16 @@
+On Cygwin some of the scripts in $R_HOME/bin can fail to be recognized
+as executable, because they do no contain a shebang line and, depending
+on the ACL settings in the Cygwin mount, may not have an executable flag
+either.  This results in the scripts not being run properly.  It's fine
+to just check that they exist.  See https://trac.sagemath.org/ticket/20655
+--- a/src/scripts/Rcmd.in	2016-05-24 17:54:31.786568400 +0200
++++ b/src/scripts/Rcmd.in	2016-05-24 17:54:55.402067200 +0200
+@@ -50,7 +50,7 @@
+     exit 1
+     ;;
+   *)
+-    if test -x "${R_HOME}/bin/${1}"; then
++    if test -f "${R_HOME}/bin/${1}"; then
+       cmd="${R_HOME}/bin/${1}"
+     else
+       cmd="${1}"

build/pkgs/terminado/SPKG.txt

@@ -0,0 +1,10 @@
+= terminado =
+
+== Description ==
+
+This is a Tornado websocket backend for the term.js Javascript terminal
+emulator library.
+
+It evolved out of pyxterm, which was part of GraphTerm (as lineterm.py),
+v0.57.0 (2014-07-18), and ultimately derived from the public-domain
+Ajaxterm code, v0.11 (2008-11-13) (also on Github as part of QWeb).

build/pkgs/terminado/checksums.ini

@@ -0,0 +1,4 @@
+tarball=terminado-VERSION.tar.gz
+sha1=5b2e42a23d6195474d320d4923c673866ccab07e
+md5=5b6c65da27fe1ed07a9f80f0588cdaba
+cksum=2602823520

build/pkgs/terminado/dependencies

@@ -0,0 +1,5 @@
+$(PYTHON) | pip ptyprocess tornado
+
+----------
+All lines of this file are ignored except the first.
+It is copied by SAGE_ROOT/build/make/install into SAGE_ROOT/build/make/Makefile.

build/pkgs/terminado/package-version.txt

@@ -0,0 +1 @@
+0.6

build/pkgs/terminado/spkg-install

@@ -0,0 +1,3 @@
+#!/usr/bin/env bash
+
+cd src && pip install --verbose --no-index .

build/pkgs/terminado/type

@@ -0,0 +1 @@
+standard

src/bin/sage-banner

@@ -1,5 +1,5 @@
 ┌────────────────────────────────────────────────────────────────────┐
-│ SageMath version 7.4.beta1, Release Date: 2016-08-17               │
+│ SageMath version 7.4.beta2, Release Date: 2016-08-26               │
 │ Type "notebook()" for the browser-based notebook interface.        │
 │ Type "help()" for help.                                            │
 └────────────────────────────────────────────────────────────────────┘

src/bin/sage-version.sh

@@ -1,4 +1,4 @@
 # Sage version information for shell scripts
 # This file is auto-generated by the sage-update-version script, do not edit!
-SAGE_VERSION='7.4.beta1'
-SAGE_RELEASE_DATE='2016-08-17'
+SAGE_VERSION='7.4.beta2'
+SAGE_RELEASE_DATE='2016-08-26'

src/doc/en/thematic_tutorials/lie/branching_rules.rst

@@ -641,8 +641,8 @@ Symmetric powers
 ----------------
 
 The `k`-th symmetric and exterior power homomorphisms map
-`GL(n) \to GL \left({n+k-1 \choose k} \right)` and
-`GL \left({n \choose k} \right)`. The corresponding branching rules
+`GL(n) \to GL \left(\binom{n+k-1}{k} \right)` and
+`GL \left(\binom{n}{k} \right)`. The corresponding branching rules
 are not implemented but a special case is. The `k`-th symmetric power
 homomorphism `SL(2) \to GL(k+1)` has its image inside of `SO(2r+1)` if
 `k = 2r` and inside of `Sp(2r)` if `k = 2r-1`. Hence there are

src/doc/en/thematic_tutorials/linear_programming.rst

@@ -319,7 +319,7 @@ the matching, which is a linear constraint. We will be solving:
 
 .. MATH::
     \text{Max: } & \sum_{e \in E(G)} m_e\\
-    \text{Such that: } & \forall v, \sum_{e \in E(G) \atop v \sim e} m_e \leq 1
+    \text{Such that: } & \forall v, \sum_{\substack{e \in E(G) \\ v \sim e}} m_e \leq 1
 
 Let us write the Sage code of this MILP::
 
@@ -385,7 +385,7 @@ following LP
 
 .. MATH::
     \text{Max: } & \sum_{sv \in G} f_{sv}\\
-    \text{Such that: } & \forall v \in G, {v \neq s \atop v \neq t}, \sum_{vu \in G} f_{vu} - \sum_{uv \in G} f_{uv} = 0\\
+    \text{Such that: } & \forall v \in G, {\substack{v \neq s \\ v \neq t}}, \sum_{vu \in G} f_{vu} - \sum_{uv \in G} f_{uv} = 0\\
     & \forall uv \in G, f_{uv} \leq 1\\
 
 We will solve the flow problem on an orientation of Chvatal's

src/doc/en/thematic_tutorials/tutorial-comprehensions.rst

@@ -227,15 +227,20 @@ Here is the analogue of list slicing::
     sage: list(itertools.islice(Permutations(3), 1, 4))
     [[1, 3, 2], [2, 1, 3], [2, 3, 1]]
 
-The functions :func:`map` and :func:`filter` also have an analogue::
-
-    sage: list(itertools.imap(lambda z: z.cycle_type(), Permutations(3)))
+The behaviour of the functions :func:`map` and :func:`filter` has
+changed between Python 2 and Python 3. In Python 3, they return an
+iterator. If you want to use this new behaviour in Python 2, and keep
+your code compatible with Python3, you can use the compatibility
+library ``six`` as follows::
+
+    sage: from six.moves import map
+    sage: list(map(lambda z: z.cycle_type(), Permutations(3)))
     [[1, 1, 1], [2, 1], [2, 1], [3], [3], [2, 1]]
 
-    sage: list(itertools.ifilter(lambda z: z.has_pattern([1,2]), Permutations(3)))
+    sage: from six.moves import filter
+    sage: list(filter(lambda z: z.has_pattern([1,2]), Permutations(3)))
     [[1, 2, 3], [1, 3, 2], [2, 1, 3], [2, 3, 1], [3, 1, 2]]
 
-
 .. TOPIC:: Exercises
 
     #.  Define an iterator for the `i`-th prime for `5<i<10`::

src/fpickle_setup.py

@@ -1,44 +1,46 @@
 """
 The purpose of this file is to allow instancemethods to be pickable.
 This is needed in setup.py only and not installed anywhere, thus is not
-a library file. It solves the issue from #11874.
+a library file. It solves the issue from :trac:`11874`.
 """
-
 import types
-from six.moves import copyreg
 import copy
-
+from six.moves import copyreg
+from six import get_method_function, get_method_self
 
 # The following four methods are taken from twisted.persisted.styles
 # into sage.misc.fpickle, and then here. It was needed due to
 # chicken vs egg issue, as we cannot use sage.misc.fpickle in
 # setup.py of sage-***.spkg
+
+
 def pickleMethod(method):
     'support function for copyreg to pickle method refs'
-    return unpickleMethod, (method.im_func.__name__,
-                             method.im_self,
-                             method.im_class)
+    return unpickleMethod, (get_method_function(method).__name__,
+                            get_method_self(method),
+                            get_method_self(method).__class__)
+
 
 def unpickleMethod(im_name,
-                    im_self,
-                    im_class):
+                   im_self,
+                   im_class):
     'support function for copyreg to unpickle method refs'
     try:
-        unbound = getattr(im_class,im_name)
+        unbound = getattr(im_class, im_name)
         if im_self is None:
             return unbound
-        bound=types.MethodType(unbound.im_func,
+        bound = types.MethodType(get_method_function(unbound),
                                  im_self)
         return bound
     except AttributeError:
         # assert im_self is not None,"No recourse: no instance to guess from."
         # Attempt a common fix before bailing -- if classes have
         # changed around since we pickled this method, we may still be
         # able to get it by looking on the instance's current class.
-        unbound = getattr(im_self.__class__,im_name)
+        unbound = getattr(im_self.__class__, im_name)
         if im_self is None:
             return unbound
-        bound=types.MethodType(unbound.im_func,
+        bound = types.MethodType(get_method_function(unbound),
                                  im_self)
         return bound
 
@@ -48,15 +50,18 @@ def unpickleMethod(im_name,
 
 oldModules = {}
 
+
 def pickleModule(module):
     'support function for copyreg to pickle module refs'
     return unpickleModule, (module.__name__,)
 
+
 def unpickleModule(name):
     'support function for copyreg to unpickle module refs'
     if name in oldModules:
         name = oldModules[name]
-    return __import__(name,{},{},'x')
+    return __import__(name, {}, {}, 'x')
+
 
 copyreg.pickle(types.ModuleType,
                pickleModule,

src/sage/algebras/letterplace/free_algebra_letterplace.pyx

@@ -833,7 +833,7 @@ cdef class FreeAlgebra_letterplace(Algebra):
         if not D:
             return self.zero()
         cdef int l
-        for e in D.iterkeys():
+        for e in D:
             l = len(e)
             break
         cdef dict out = {}

src/sage/categories/action.pyx

@@ -57,13 +57,14 @@ AUTHOR:
 #
 #                  http://www.gnu.org/licenses/
 #*****************************************************************************
+from __future__ import absolute_import
 
-from functor cimport Functor
-from morphism cimport Morphism
-from map cimport Map
+from .functor cimport Functor
+from .morphism cimport Morphism
+from .map cimport Map
 from sage.structure.parent cimport Parent
 
-import homset
+from . import homset
 import sage.structure.element
 from weakref import ref
 from sage.misc.constant_function import ConstantFunction
@@ -79,7 +80,7 @@ cdef inline category(x):
 cdef class Action(Functor):
 
     def __init__(self, G, S, bint is_left = 1, op=None):
-        from groupoid import Groupoid
+        from .groupoid import Groupoid
         Functor.__init__(self, Groupoid(G), category(S))
         self.G = G
         self.US = ref(S)