t-28012: collections.abc

src/sage/arith/misc.py

@@ -1,5 +1,5 @@
 # -*- coding: utf-8 -*-
-"""
+r"""
 Miscellaneous arithmetic functions
 """
 
@@ -13,16 +13,15 @@
 #                  https://www.gnu.org/licenses/
 # ****************************************************************************
 
-from __future__ import absolute_import, print_function
-
 import math
-import collections
+from collections.abc import Iterable
 
 from sage.misc.misc import powerset
 from sage.misc.misc_c import prod
 
 from sage.libs.pari.all import pari
-import sage.libs.flint.arith as flint_arith
+from sage.libs.flint.arith import (bernoulli_number as flint_bernoulli,
+                                   dedekind_sum as flint_dedekind_sum)
 
 from sage.structure.element import parent
 from sage.structure.coerce import py_scalar_to_element
@@ -34,16 +33,16 @@
 from sage.rings.real_mpfr import RealNumber
 from sage.rings.complex_number import ComplexNumber
 
-import sage.rings.fast_arith as fast_arith
-prime_range = fast_arith.prime_range
+from sage.rings.fast_arith import arith_int, arith_llong, prime_range
 
 
 ##################################################################
 # Elementary Arithmetic
 ##################################################################
 
 
-def algdep(z, degree, known_bits=None, use_bits=None, known_digits=None, use_digits=None, height_bound=None, proof=False):
+def algdep(z, degree, known_bits=None, use_bits=None, known_digits=None,
+           use_digits=None, height_bound=None, proof=False):
     """
     Return an irreducible polynomial of degree at most `degree` which
     is approximately satisfied by the number `z`.
@@ -367,7 +366,7 @@ def bernoulli(n, algorithm='default', num_threads=1):
         if n >= 100000:
             from warnings import warn
             warn("flint is known to not be accurate for large Bernoulli numbers")
-        return flint_arith.bernoulli_number(n)
+        return flint_bernoulli(n)
     elif algorithm == 'pari':
         x = pari(n).bernfrac()         # Use the PARI C library
         return Rational(x)
@@ -2108,9 +2107,9 @@ def get_gcd(order):
         <function gcd at ...>
     """
     if order <= 46340:   # todo: don't hard code
-        return fast_arith.arith_int().gcd_int
+        return arith_int().gcd_int
     elif order <= 2147483647:   # todo: don't hard code
-        return fast_arith.arith_llong().gcd_longlong
+        return arith_llong().gcd_longlong
     else:
         return gcd
 
@@ -2130,9 +2129,9 @@ def get_inverse_mod(order):
         <function inverse_mod at ...>
     """
     if order <= 46340:   # todo: don't hard code
-        return fast_arith.arith_int().inverse_mod_int
+        return arith_int().inverse_mod_int
     elif order <= 2147483647:   # todo: don't hard code
-        return fast_arith.arith_llong().inverse_mod_longlong
+        return arith_llong().inverse_mod_longlong
     else:
         return inverse_mod
 
@@ -3651,7 +3650,7 @@ def multinomial(*ks):
 
     - Gabriel Ebner
     """
-    if isinstance(ks[0], collections.Iterable):
+    if isinstance(ks[0], Iterable):
         if len(ks) > 1:
             raise ValueError("multinomial takes only one iterable argument")
         ks = ks[0]
@@ -5840,7 +5839,7 @@ def dedekind_sum(p, q, algorithm='default'):
     - :wikipedia:`Dedekind\_sum`
     """
     if algorithm == 'default' or algorithm == 'flint':
-        return flint_arith.dedekind_sum(p, q)
+        return flint_dedekind_sum(p, q)
 
     if algorithm == 'pari':
         import sage.interfaces.gp

src/sage/categories/poor_man_map.py

@@ -1,17 +1,17 @@
 # -*- coding: utf-8 -*-
-"""
+r"""
 Poor Man's map
 """
-#*****************************************************************************
+# ****************************************************************************
 #       Copyright (C) 2009 Nicolas M. Thiery <nthiery at users.sf.net>
 #                     2016 Julian Rüth <julian.rueth@fsfe.org>
 #
 # This program is free software: you can redistribute it and/or modify
 # it under the terms of the GNU General Public License as published by
 # the Free Software Foundation, either version 2 of the License, or
 # (at your option) any later version.
-#                  http://www.gnu.org/licenses/
-#*****************************************************************************
+#                  https://www.gnu.org/licenses/
+# ****************************************************************************
 import sage.structure.sage_object
 
 class PoorManMap(sage.structure.sage_object.SageObject):
@@ -69,7 +69,7 @@ def __init__(self, function, domain = None, codomain = None, name = None):
             sage: TestSuite(f*g).run()
 
         """
-        from collections import Iterable
+        from collections.abc import Iterable
         if not isinstance(function, Iterable):
             function = (function,)
         self._functions = tuple(function)

src/sage/combinat/finite_state_machine.py

@@ -924,16 +924,17 @@
 #               2012--2015 Daniel Krenn <dev@danielkrenn.at>
 #               2012--2015 Sara Kropf <sara.kropf@aau.at>
 #
-#  Distributed under the terms of the GNU General Public License (GPL)
-#  as published by the Free Software Foundation; either version 2 of
-#  the License, or (at your option) any later version.
-#                https://www.gnu.org/licenses/
+# This program is free software: you can redistribute it and/or modify
+# it under the terms of the GNU General Public License as published by
+# the Free Software Foundation, either version 2 of the License, or
+# (at your option) any later version.
+#                  https://www.gnu.org/licenses/
 # ****************************************************************************
-from __future__ import print_function
 
 from IPython.lib.pretty import pretty
-import collections
 import itertools
+from collections import defaultdict, deque, namedtuple, OrderedDict
+from collections.abc import Iterator
 from copy import copy, deepcopy
 
 from sage.calculus.var import var
@@ -964,13 +965,13 @@ def full_group_by(l, key=lambda x: x):
     A list of pairs ``(k, elements)`` such that ``key(e)=k`` for all
     ``e`` in ``elements``.
 
-    This is similar to ``itertools.groupby`` except that lists are
+    This is similar to :func:`itertools.groupby` except that lists are
     returned instead of iterables and no prior sorting is required.
 
     We do not require
 
     - that the keys are sortable (in contrast to the
-      approach via ``sorted`` and ``itertools.groupby``) and
+      approach via :func:`sorted` and :func:`itertools.groupby`) and
     - that the keys are hashable (in contrast to the
       implementation proposed in `<https://stackoverflow.com/a/15250161>`_).
 
@@ -998,13 +999,13 @@ def full_group_by(l, key=lambda x: x):
         1/x [1]
         2/x [2]
 
-    Note that the behavior is different from ``itertools.groupby``
+    Note that the behavior is different from :func:`itertools.groupby`
     because neither `1/x<2/x` nor `2/x<1/x` does hold.
 
     Here, the result ``r`` has been sorted in order to guarantee a
     consistent order for the doctest suite.
     """
-    elements = collections.defaultdict(list)
+    elements = defaultdict(list)
     original_keys = {}
     for item in l:
         k = key(item)
@@ -4924,7 +4925,7 @@ def key_function(s):
         # transitions have to be sorted anyway, the performance
         # penalty should be bearable; nevertheless, this is only
         # required for doctests.
-        adjacent = collections.OrderedDict(
+        adjacent = OrderedDict(
             (pair, list(transitions))
             for pair, transitions in
             itertools.groupby(
@@ -13143,7 +13144,7 @@ def __init__(self, tape_cache_manager, tape, tape_ended,
 
         self.tape_cache_manager = tape_cache_manager
         self.tape_cache_manager.append(self)
-        self.cache = tuple(collections.deque() for _ in self.tape)
+        self.cache = tuple(deque() for _ in self.tape)
 
     def _repr_(self):
         """
@@ -13927,8 +13928,7 @@ def is_FSMProcessIterator(PI):
 # ****************************************************************************
 
 
-class FSMProcessIterator(SageObject,
-                         collections.Iterator):
+class FSMProcessIterator(SageObject, Iterator):
     """
     This class takes an input, feeds it into a finite state machine
     (automaton or transducer, in particular), tests whether this was
@@ -14215,7 +14215,7 @@ def __repr__(self):
             return result
 
 
-    FinishedBranch = collections.namedtuple('Branch', 'accept, state, output')
+    FinishedBranch = namedtuple('Branch', 'accept, state, output')
     r"""
     A :func:`named tuple <collections.namedtuple>` representing the
     attributes of a branch, once
@@ -14311,7 +14311,7 @@ def __init__(self, fsm,
         self._finished_ = []  # contains (accept, state, output)
 
 
-    _branch_ = collections.namedtuple('Branch', 'tape_cache, outputs')
+    _branch_ = namedtuple('Branch', 'tape_cache, outputs')
     r"""
     A :func:`named tuple <collections.namedtuple>` representing the
     attributes of a branch at a particular state during processing.

src/sage/combinat/finite_state_machine_generators.py

@@ -1,3 +1,4 @@
+# -*- coding: utf-8 -*-
 r"""
 Common Automata and Transducers (Finite State Machines Generators)
 
@@ -76,19 +77,19 @@
 ---------------------
 
 """
-#*****************************************************************************
+# ****************************************************************************
 #       Copyright (C) 2014--2015 Clemens Heuberger <clemens.heuberger@aau.at>
 #                     2014--2015 Daniel Krenn <dev@danielkrenn.at>
 #                     2014 Sara Kropf <sara.kropf@aau.at>
 #
-#  Distributed under the terms of the GNU General Public License (GPL)
-#  as published by the Free Software Foundation; either version 2 of
-#  the License, or (at your option) any later version.
-#                http://www.gnu.org/licenses/
-#*****************************************************************************
-from __future__ import print_function
-
-import collections
+# This program is free software: you can redistribute it and/or modify
+# it under the terms of the GNU General Public License as published by
+# the Free Software Foundation, either version 2 of the License, or
+# (at your option) any later version.
+#                  https://www.gnu.org/licenses/
+# ****************************************************************************
+
+from collections import namedtuple
 import operator
 
 from sage.combinat.finite_state_machine import Automaton, Transducer
@@ -1058,8 +1059,7 @@ def GrayCode(self):
                           with_final_word_out=[0])
 
 
-    RecursionRule = collections.namedtuple('RecursionRule',
-                                           ['K', 'r', 'k', 's', 't'])
+    RecursionRule = namedtuple('RecursionRule', ['K', 'r', 'k', 's', 't'])
 
 
     def _parse_recursion_equation_(self, equation, base, function, var,
@@ -1800,7 +1800,7 @@ def Recursion(self, recursions, base, function=None, var=None,
 
         if is_zero is None:
             is_zero = lambda x: not x
-        RuleRight = collections.namedtuple('Rule', ['k', 's', 't'])
+        RuleRight = namedtuple('Rule', ['k', 's', 't'])
         initial_values = {}
         rules = []
         if input_alphabet is None and base in ZZ:

src/sage/combinat/ranker.py

@@ -1,24 +1,20 @@
-"""
+# -*- coding: utf-8 -*-
+r"""
 Rankers
 """
 #*****************************************************************************
 #       Copyright (C) 2007 Mike Hansen <mhansen@gmail.com>,
 #                          Nicolas M. Thiery <nthiery at users.sf.net>
 #  Ported from MuPAD-Combinat (combinat::rankers)
 #
-#  Distributed under the terms of the GNU General Public License (GPL)
-#
-#    This code is distributed in the hope that it will be useful,
-#    but WITHOUT ANY WARRANTY; without even the implied warranty of
-#    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
-#    General Public License for more details.
-#
-#  The full text of the GPL is available at:
-#
-#                  http://www.gnu.org/licenses/
-#*****************************************************************************
-
-from collections import Iterable, Sequence
+# This program is free software: you can redistribute it and/or modify
+# it under the terms of the GNU General Public License as published by
+# the Free Software Foundation, either version 2 of the License, or
+# (at your option) any later version.
+#                  https://www.gnu.org/licenses/
+# ****************************************************************************
+
+from collections.abc import Iterable, Sequence
 from sage.misc.cachefunc import cached_function
 from sage.misc.callable_dict import CallableDict
 from sage.structure.parent import Parent
@@ -188,14 +184,14 @@ def unrank(L, i):
 
     The purpose of this utility is to give a uniform idiom to recover
     the `i`-th element of an object ``L``, whether ``L`` is a list,
-    tuple (or more generally a :class:`collections.Sequence`), an
+    tuple (or more generally a :class:`collections.abc.Sequence`), an
     enumerated set, some old parent of Sage still implementing
     unranking in the method ``__getitem__``, or an iterable (see
-    :class:`collections.Iterable`). See :trac:`15919`.
+    :class:`collections.abc.Iterable`). See :trac:`15919`.
 
     EXAMPLES:
 
-    Lists, tuples, and other :class:`sequences <collections.Sequence>`::
+    Lists, tuples, and other :class:`sequences <collections.abc.Sequence>`::
 
         sage: from sage.combinat.ranker import unrank
         sage: unrank(['a','b','c'], 2)

src/sage/combinat/shuffle.py

@@ -45,16 +45,17 @@
 
  - Jean-Baptiste Priez
 """
-#*****************************************************************************
+# ****************************************************************************
 #       Copyright (C) 2014 Jean-Baptiste Priez <jbp@kerios.fr>
 #
-#  Distributed under the terms of the GNU General Public License (GPL)
-#
-#  The full text of the GPL is available at:
-#
-#                  http://www.gnu.org/licenses/
-#*****************************************************************************
-import collections
+# This program is free software: you can redistribute it and/or modify
+# it under the terms of the GNU General Public License as published by
+# the Free Software Foundation, either version 2 of the License, or
+# (at your option) any later version.
+#                  https://www.gnu.org/licenses/
+# ****************************************************************************
+
+from collections.abc import Iterable
 import itertools
 import operator
 
@@ -116,11 +117,11 @@ def __init__(self, l1, l2, element_constructor=None):
             [[2, 3, 4, 5], [2, 5, 3, 4], [5, 2, 3, 4], [2, 3, 5, 4], [1, 2, 3, 5], [1, 5, 2, 3],
              [5, 1, 2, 3], [1, 2, 5, 3]]
         """
-        assert(isinstance(l1, collections.Iterable) and
-               isinstance(l2, collections.Iterable)
+        assert(isinstance(l1, Iterable) and
+               isinstance(l2, Iterable)
         )
-        assert(all(isinstance(elem, collections.Iterable) for elem in l1))
-        assert(all(isinstance(elem, collections.Iterable) for elem in l2))
+        assert(all(isinstance(elem, Iterable) for elem in l1))
+        assert(all(isinstance(elem, Iterable) for elem in l2))
         self._l1 = list(l1)
         self._l2 = list(l2)
 
@@ -259,8 +260,8 @@ def __init__(self, l1, l2, element_constructor=None):
              word: bbbaa, word: bbaba, word: babba, word: abbba]
 
         """
-        assert(isinstance(l1, collections.Iterable) and
-               isinstance(l2, collections.Iterable)
+        assert(isinstance(l1, Iterable) and
+               isinstance(l2, Iterable)
         )
         self._l1 = list(l1)
         self._l2 = list(l2)