As created just now. Enjoy!
-Alasdair
--
[image: http://www.facebook.com/alasdairmcandrew] [image:
https://twitter.com/amca01] <https://twitter.com/amca01>
<https://www.linkedin.com/in/alasdair-mcandrew-108178a>
<https://plus.google.com/+AlasdairMcAndrew/posts>
--
You received this message because you are subscribed to the Google Groups
"sage-support" group.
To unsubscribe from this group and stop receiving emails from it, send an email
to [email protected].
To post to this group, send email to [email protected].
Visit this group at https://groups.google.com/group/sage-support.
For more options, visit https://groups.google.com/d/optout.
***************************************************************************
IPython post-mortem report
{'commit_hash': u'5c9c918',
'commit_source': 'installation',
'default_encoding': 'UTF-8',
'ipython_path': '/opt/sage-8.1/local/lib/python2.7/site-packages/IPython',
'ipython_version': '5.1.0',
'os_name': 'posix',
'platform': 'Linux-4.15.7-1-ARCH-x86_64-with-glibc2.2.5',
'sys_executable': '/opt/sage-8.1/local/bin/python',
'sys_platform': 'linux2',
'sys_version': '2.7.14 (default, Dec 15 2017, 12:15:09) \n[GCC 7.2.0]'}
***************************************************************************
***************************************************************************
Crash traceback:
---------------------------------------------------------------------------
---------------------------------------------------------------------------
ImportError Python 2.7.14: /opt/sage-8.1/local/bin/python
Sat Mar 10 22:24:53 2018
A problem occurred executing Python code. Here is the sequence of function
calls leading up to the error, with the most recent (innermost) call last.
/opt/sage-8.1/src/bin/sage-ipython in <module>()
1 #!/usr/bin/env python
2 # -*- coding: utf-8 -*-
3 """
4 Sage IPython startup script.
5 """
6
7 from sage.repl.interpreter import SageTerminalApp
8
9 app = SageTerminalApp.instance()
---> 10 app.initialize()
global app.initialize = <bound method SageTerminalApp.initialize of
<sage.repl.interpreter.SageTerminalApp object at 0x7ff0aec1f550>>
11 app.start()
<decorator-gen-109> in initialize(self=<sage.repl.interpreter.SageTerminalApp
object>, argv=None)
/opt/sage-8.1/local/lib/python2.7/site-packages/traitlets/config/application.pyc
in catch_config_error(method=<function initialize>,
app=<sage.repl.interpreter.SageTerminalApp object>, *args=(None,), **kwargs={})
72 TRAITLETS_APPLICATION_RAISE_CONFIG_FILE_ERROR = False
73 else:
74 raise ValueError("Unsupported value for environment variable:
'TRAITLETS_APPLICATION_RAISE_CONFIG_FILE_ERROR' is set to '%s' which is none of
{'0', '1', 'false', 'true', ''}."% _envvar )
75
76
77 @decorator
78 def catch_config_error(method, app, *args, **kwargs):
79 """Method decorator for catching invalid config
(Trait/ArgumentErrors) during init.
80
81 On a TraitError (generally caused by bad config), this will print
the trait's
82 message, and exit the app.
83
84 For use on init methods, to prevent invoking excepthook on invalid
input.
85 """
86 try:
---> 87 return method(app, *args, **kwargs)
method = <function initialize at 0x7ff0a9896a28>
app = <sage.repl.interpreter.SageTerminalApp object at 0x7ff0aec1f550>
args = (None,)
kwargs = {}
88 except (TraitError, ArgumentError) as e:
89 app.print_help()
90 app.log.fatal("Bad config encountered during initialization:")
91 app.log.fatal(str(e))
92 app.log.debug("Config at the time: %s", app.config)
93 app.exit(1)
94
95
96 class ApplicationError(Exception):
97 pass
98
99
100 class LevelFormatter(logging.Formatter):
101 """Formatter with additional `highlevel` record
102
/opt/sage-8.1/local/lib/python2.7/site-packages/IPython/terminal/ipapp.pyc in
initialize(self=<sage.repl.interpreter.SageTerminalApp object>, argv=None)
294
295 return super(TerminalIPythonApp, self).parse_command_line(argv)
296
297 @catch_config_error
298 def initialize(self, argv=None):
299 """Do actions after construct, but before starting the app."""
300 super(TerminalIPythonApp, self).initialize(argv)
301 if self.subapp is not None:
302 # don't bother initializing further, starting subapp
303 return
304 # print self.extra_args
305 if self.extra_args and not self.something_to_run:
306 self.file_to_run = self.extra_args[0]
307 self.init_path()
308 # create the shell
--> 309 self.init_shell()
self.init_shell = <bound method SageTerminalApp.init_shell of
<sage.repl.interpreter.SageTerminalApp object at 0x7ff0aec1f550>>
310 # and draw the banner
311 self.init_banner()
312 # Now a variety of things that happen after the banner is
printed.
313 self.init_gui_pylab()
314 self.init_extensions()
315 self.init_code()
316
317 def init_shell(self):
318 """initialize the InteractiveShell instance"""
319 # Create an InteractiveShell instance.
320 # shell.display_banner should always be False for the terminal
321 # based app, because we call shell.show_banner() by hand below
322 # so the banner shows *before* all extension loading stuff.
323 self.shell = TerminalInteractiveShell.instance(parent=self,
324 profile_dir=self.profile_dir,
/opt/sage-8.1/local/lib/python2.7/site-packages/sage/repl/interpreter.pyc in
init_shell(self=<sage.repl.interpreter.SageTerminalApp object>)
747 self.shell.has_sage_extensions = SAGE_EXTENSION in
self.extensions
748
749 # Load the %lprun extension if available
750 try:
751 import line_profiler
752 except ImportError:
753 pass
754 else:
755 self.extensions.append('line_profiler')
756
757 if self.shell.has_sage_extensions:
758 self.extensions.remove(SAGE_EXTENSION)
759
760 # load sage extension here to get a crash if
761 # something is wrong with the sage library
--> 762 self.shell.extension_manager.load_extension(SAGE_EXTENSION)
self.shell.extension_manager.load_extension = <bound method
ExtensionManager.load_extension of <IPython.core.extensions.ExtensionManager
object at 0x7ff0a86f8050>>
global SAGE_EXTENSION = 'sage'
763
764
/opt/sage-8.1/local/lib/python2.7/site-packages/IPython/core/extensions.pyc in
load_extension(self=<IPython.core.extensions.ExtensionManager object>,
module_str='sage')
70
71 Returns the string "already loaded" if the extension is already
loaded,
72 "no load function" if the module doesn't have a
load_ipython_extension
73 function, or None if it succeeded.
74 """
75 if module_str in self.loaded:
76 return "already loaded"
77
78 from IPython.utils.syspathcontext import prepended_to_syspath
79
80 with self.shell.builtin_trap:
81 if module_str not in sys.modules:
82 with prepended_to_syspath(self.ipython_extension_dir):
83 __import__(module_str)
84 mod = sys.modules[module_str]
---> 85 if self._call_load_ipython_extension(mod):
self._call_load_ipython_extension = <bound method
ExtensionManager._call_load_ipython_extension of
<IPython.core.extensions.ExtensionManager object at 0x7ff0a86f8050>>
mod = <module 'sage' from
'/opt/sage-8.1/local/lib/python2.7/site-packages/sage/__init__.pyc'>
86 self.loaded.add(module_str)
87 else:
88 return "no load function"
89
90 def unload_extension(self, module_str):
91 """Unload an IPython extension by its module name.
92
93 This function looks up the extension's name in ``sys.modules``
and
94 simply calls ``mod.unload_ipython_extension(self)``.
95
96 Returns the string "no unload function" if the extension
doesn't define
97 a function to unload itself, "not loaded" if the extension
isn't loaded,
98 otherwise None.
99 """
100 if module_str not in self.loaded:
/opt/sage-8.1/local/lib/python2.7/site-packages/IPython/core/extensions.pyc in
_call_load_ipython_extension(self=<IPython.core.extensions.ExtensionManager
object>, mod=<module 'sage' from
'/opt/sage-8.1/local/lib/python2.7/site-packages/sage/__init__.pyc'>)
117 """
118 from IPython.utils.syspathcontext import prepended_to_syspath
119
120 if (module_str in self.loaded) and (module_str in sys.modules):
121 self.unload_extension(module_str)
122 mod = sys.modules[module_str]
123 with prepended_to_syspath(self.ipython_extension_dir):
124 reload(mod)
125 if self._call_load_ipython_extension(mod):
126 self.loaded.add(module_str)
127 else:
128 self.load_extension(module_str)
129
130 def _call_load_ipython_extension(self, mod):
131 if hasattr(mod, 'load_ipython_extension'):
--> 132 mod.load_ipython_extension(self.shell)
mod.load_ipython_extension = <function load_ipython_extension at
0x7ff0b0c746e0>
self.shell = <sage.repl.interpreter.SageTerminalInteractiveShell object
at 0x7ff0a96391d0>
133 return True
134
135 def _call_unload_ipython_extension(self, mod):
136 if hasattr(mod, 'unload_ipython_extension'):
137 mod.unload_ipython_extension(self.shell)
138 return True
139
140 def install_extension(self, url, filename=None):
141 """Download and install an IPython extension.
142
143 If filename is given, the file will be so named (inside the
extension
144 directory). Otherwise, the name from the URL will be used. The
file must
145 have a .py or .zip extension; otherwise, a ValueError will be
raised.
146
147 Returns the full path to the installed file.
/opt/sage-8.1/local/lib/python2.7/site-packages/sage/__init__.pyc in
load_ipython_extension(*args=(<sage.repl.interpreter.SageTerminalInteractiveShell
object>,))
1 __all__ = ['all']
2
3 # Make sure that the correct zlib library is loaded. This is needed
4 # to prevent the system zlib to be loaded instead of the Sage one.
5 # See https://trac.sagemath.org/ticket/23122
6 import zlib
7
8 # IPython calls this when starting up
9 def load_ipython_extension(*args):
10 import sage.repl.ipython_extension
---> 11 sage.repl.ipython_extension.load_ipython_extension(*args)
sage.repl.ipython_extension.load_ipython_extension = <function
load_ipython_extension at 0x7ff0a8263a28>
args = (<sage.repl.interpreter.SageTerminalInteractiveShell object at
0x7ff0a96391d0>,)
12
13
14 # Monkey-patch inspect.isfunction() to support Cython functions.
15 def isfunction(obj):
16 """
17 Check whether something is a function.
18
19 We assume that anything which has a genuine ``__code__``
20 attribute (not using ``__getattr__`` overrides) is a function.
21 This is meant to support Cython functions.
22
23 EXAMPLES::
24
25 sage: from inspect import isfunction
26 sage: def f(): pass
27 sage: isfunction(f)
28 True
29 sage: isfunction(lambda x:x)
30 True
31 sage: from sage.categories.coercion_methods import _mul_parent
/opt/sage-8.1/local/lib/python2.7/site-packages/sage/repl/ipython_extension.pyc
in wrapper(*args=(<sage.repl.interpreter.SageTerminalInteractiveShell
object>,), **kwargs={})
546 ....: if work:
547 ....: return 'foo worked'
548 ....: raise RuntimeError("foo didn't work")
549 sage: foo(False)
550 Traceback (most recent call last):
551 ...
552 RuntimeError: foo didn't work
553 sage: foo(True)
554 'foo worked'
555 sage: foo(False)
556 sage: foo(True)
557 """
558 @wraps(func)
559 def wrapper(*args, **kwargs):
560 if not wrapper.has_run:
--> 561 result = func(*args, **kwargs)
result = undefined
global func = undefined
args = (<sage.repl.interpreter.SageTerminalInteractiveShell object at
0x7ff0a96391d0>,)
kwargs = {}
562 wrapper.has_run = True
563 return result
564 wrapper.has_run = False
565 return wrapper
566
567
568 @run_once
569 def load_ipython_extension(ip):
570 """
571 Load the extension in IPython.
572 """
573 # this modifies ip
574 SageCustomizations(shell=ip)
/opt/sage-8.1/local/lib/python2.7/site-packages/sage/repl/ipython_extension.pyc
in
load_ipython_extension(ip=<sage.repl.interpreter.SageTerminalInteractiveShell
object>)
559 def wrapper(*args, **kwargs):
560 if not wrapper.has_run:
561 result = func(*args, **kwargs)
562 wrapper.has_run = True
563 return result
564 wrapper.has_run = False
565 return wrapper
566
567
568 @run_once
569 def load_ipython_extension(ip):
570 """
571 Load the extension in IPython.
572 """
573 # this modifies ip
--> 574 SageCustomizations(shell=ip)
global SageCustomizations = <class
'sage.repl.ipython_extension.SageCustomizations'>
global shell = undefined
ip = <sage.repl.interpreter.SageTerminalInteractiveShell object at
0x7ff0a96391d0>
/opt/sage-8.1/local/lib/python2.7/site-packages/sage/repl/ipython_extension.pyc
in __init__(self=<sage.repl.ipython_extension.SageCustomizations object>,
shell=<sage.repl.interpreter.SageTerminalInteractiveShell object>)
417 def __init__(self, shell=None):
418 """
419 Initialize the Sage plugin.
420 """
421 self.shell = shell
422
423 self.auto_magics = SageMagics(shell)
424 self.shell.register_magics(self.auto_magics)
425
426 import sage.misc.edit_module as edit_module
427 self.shell.set_hook('editor', edit_module.edit_devel)
428
429 self.init_inspector()
430 self.init_line_transforms()
431
--> 432 import sage.all # until sage's import hell is fixed
sage.all = undefined
433
434 self.shell.verbose_quit = True
435 self.set_quit_hook()
436
437 self.register_interface_magics()
438
439 if SAGE_IMPORTALL == 'yes':
440 self.init_environment()
441
442 def register_interface_magics(self):
443 """
444 Register magics for each of the Sage interfaces
445 """
446 from sage.repl.interface_magic import InterfaceMagic
447 InterfaceMagic.register_all(self.shell)
/opt/sage-8.1/local/lib/python2.7/site-packages/sage/all.py in <module>()
83
84 from time import sleep
85
86 import sage.misc.lazy_import
87 from sage.misc.all import * # takes a while
88 from sage.typeset.all import *
89 from sage.repl.all import *
90
91 from sage.misc.sh import sh
92
93 from sage.libs.all import *
94 from sage.data_structures.all import *
95 from sage.doctest.all import *
96
97 from sage.structure.all import *
---> 98 from sage.rings.all import *
global sage.rings.all = undefined
99 from sage.arith.all import *
100 from sage.matrix.all import *
101
102 from sage.symbolic.all import *
103 from sage.modules.all import *
104 from sage.monoids.all import *
105 from sage.algebras.all import *
106 from sage.modular.all import *
107 from sage.sat.all import *
108 from sage.schemes.all import *
109 from sage.graphs.all import *
110 from sage.groups.all import *
111 from sage.databases.all import *
112 from sage.categories.all import *
113 from sage.sets.all import *
/opt/sage-8.1/local/lib/python2.7/site-packages/sage/rings/all.py in <module>()
39
40 # Rational numbers
41 from .rational_field import RationalField, QQ
42 from .rational import Rational
43 Rationals = RationalField
44
45 # Integers modulo n.
46 from sage.rings.finite_rings.integer_mod_ring import IntegerModRing,
Zmod
47 from sage.rings.finite_rings.integer_mod import IntegerMod, Mod, mod
48 Integers = IntegerModRing
49
50 # Finite fields
51 from .finite_rings.all import *
52
53 # Number field
---> 54 from .number_field.all import *
global number_field.all = undefined
55
56 # Function field
57 from .function_field.all import *
58
59 # Finite residue fields
60 from .finite_rings.residue_field import ResidueField
61
62 # p-adic field
63 from .padics.all import *
64 from .padics.padic_printing import _printer_defaults as padic_printing
65
66 # Semirings
67 from .semirings.all import *
68
69 # Real numbers
/opt/sage-8.1/local/lib/python2.7/site-packages/sage/rings/number_field/all.py
in <module>()
1 from __future__ import absolute_import
2
3 from .number_field import (NumberField, NumberFieldTower,
CyclotomicField, QuadraticField,
4 is_fundamental_discriminant, is_real_place)
5 from .number_field_element import NumberFieldElement
6
7 from .order import EquationOrder, GaussianIntegers, EisensteinIntegers
8
----> 9 from .totallyreal import enumerate_totallyreal_fields_prim
global totallyreal = undefined
global enumerate_totallyreal_fields_prim = undefined
10 from .totallyreal_data import hermite_constant
11 from .totallyreal_rel import enumerate_totallyreal_fields_all,
enumerate_totallyreal_fields_rel
12
13 from .unit_group import UnitGroup
/opt/sage-8.1/local/lib/python2.7/site-packages/sage/rings/number_field/totallyreal_data.pxd
in init sage.rings.number_field.totallyreal()
1 cdef double eval_seq_as_poly(int *f, int n, double x)
2 cdef double newton(int *f, int *df, int n, double x0, double eps)
3 cdef void newton_in_intervals(int *f, int *df, int n, double *beta,
double eps, double *rts)
4 cpdef lagrange_degree_3(int n, int an1, int an2, int an3)
5
6 cimport sage.rings.integer
7
8 cdef int eval_seq_as_poly_int(int *f, int n, int x)
9
10 cdef int easy_is_irreducible(int *a, int n)
11
---> 12 cdef class tr_data:
global cdef = undefined
global tr_data = undefined
13
14 cdef int n, k
15 cdef double B
16 cdef double b_lower, b_upper, gamma
17
18 cdef int *a
19 cdef int *amax
20 cdef double *beta
21 cdef int *gnk
22
23 cdef int *df
24
25 cdef void incr(self, int *f_out, int verbose, int haltk, int phc)
26
/opt/sage-8.1/src/sage/rings/number_field/totallyreal_data.pyx in init
sage.rings.number_field.totallyreal_data()
26 from __future__ import absolute_import, print_function
27
28 from libc.math cimport sqrt
29 from cysignals.memory cimport sig_malloc, sig_free
30
31 from sage.arith.all import binomial, gcd
32 from sage.libs.gmp.mpz cimport *
33 from sage.rings.rational_field import RationalField
34 from sage.rings.polynomial.polynomial_ring_constructor import
PolynomialRing
35 from sage.rings.real_mpfi import RealIntervalField
36 from sage.rings.real_mpfr import RealField
37 from sage.rings.integer_ring import ZZ
38 from sage.rings.integer cimport Integer
39
40 # Other global variables
---> 41 ZZx = PolynomialRing(ZZ, 'x')
global ZZx = undefined
global PolynomialRing = <function PolynomialRing at 0x7fef981d5aa0>
global ZZ = Integer Ring
42
43 from libc.math cimport lrint, floor, ceil, fabs, round
44
45
46 #*********************************************************************
47 # Auxiliary routine
48 # Hermite constant, naive Newton-Raphson, and a specialized Lagrange
49 # multiplier solver.
50 #*********************************************************************
51
52 def hermite_constant(n):
53 r"""
54 This function returns the nth Hermite constant
55
56 The nth Hermite constant (typically denoted `\gamma_n`), is defined
/opt/sage-8.1/local/lib/python2.7/site-packages/sage/rings/polynomial/polynomial_ring_constructor.pyc
in PolynomialRing(base_ring=Integer Ring, *args=('x',), **kwds={})
570 # At this point, we have only handled the "names" keyword if it was
571 # needed. Since we know the variable names, it would logically be
572 # an error to specify an additional "names" keyword. However,
573 # people often abuse the preparser with
574 # R.<x> = PolynomialRing(QQ, 'x')
575 # and we allow this for historical reasons. However, the names
576 # must be consistent!
577 if "names" in kwds:
578 kwnames = kwds.pop("names")
579 if kwnames != names:
580 raise TypeError("variable names specified twice
inconsistently: %r and %r" % (names, kwnames))
581
582 if multivariate or len(names) != 1:
583 return _multi_variate(base_ring, names, **kwds)
584 else:
--> 585 return _single_variate(base_ring, names, **kwds)
global _single_variate = <function _single_variate at 0x7fef96ca7668>
base_ring = Integer Ring
names = ('x',)
kwds = {}
586
587
588 def unpickle_PolynomialRing(base_ring, arg1=None, arg2=None,
sparse=False):
589 """
590 Custom unpickling function for polynomial rings.
591
592 This has the same positional arguments as the old
593 ``PolynomialRing`` constructor before :trac:`23338`.
594 """
595 args = [arg for arg in (arg1, arg2) if arg is not None]
596 return PolynomialRing(base_ring, *args, sparse=sparse)
597
598 from sage.structure.sage_object import register_unpickle_override
599
register_unpickle_override('sage.rings.polynomial.polynomial_ring_constructor',
'PolynomialRing', unpickle_PolynomialRing)
600
/opt/sage-8.1/local/lib/python2.7/site-packages/sage/rings/polynomial/polynomial_ring_constructor.pyc
in _single_variate(base_ring=Integer Ring, name=('x',), sparse=False,
implementation=None, order=None)
650 R =
m.PolynomialRing_dense_padic_ring_capped_absolute(base_ring, name)
651
652 elif isinstance(base_ring, padic_base_leaves.pAdicRingFixedMod):
653 R = m.PolynomialRing_dense_padic_ring_fixed_mod(base_ring,
name)
654
655 elif base_ring in _CompleteDiscreteValuationRings:
656 R = m.PolynomialRing_cdvr(base_ring, name, sparse)
657
658 elif base_ring in _CompleteDiscreteValuationFields:
659 R = m.PolynomialRing_cdvf(base_ring, name, sparse)
660
661 elif base_ring.is_field(proof = False):
662 R = m.PolynomialRing_field(base_ring, name, sparse)
663
664 elif base_ring.is_integral_domain(proof = False):
--> 665 R = m.PolynomialRing_integral_domain(base_ring, name,
sparse, implementation)
R = None
m.PolynomialRing_integral_domain = <class
'sage.rings.polynomial.polynomial_ring.PolynomialRing_integral_domain'>
base_ring = Integer Ring
name = ('x',)
sparse = False
implementation = None
666 else:
667 R = m.PolynomialRing_commutative(base_ring, name, sparse)
668 else:
669 R = m.PolynomialRing_general(base_ring, name, sparse)
670
671 if hasattr(R, '_implementation_names'):
672 for name in R._implementation_names:
673 real_key = key[0:3] + (name,)
674 _save_in_cache(real_key, R)
675 else:
676 _save_in_cache(key, R)
677 return R
678
679 def _multi_variate(base_ring, names, sparse=None, order="degrevlex",
implementation=None):
680 # if not sparse:
/opt/sage-8.1/local/lib/python2.7/site-packages/sage/rings/polynomial/polynomial_ring.pyc
in __init__(self=Univariate Polynomial Ring in x over Integer Ring,
base_ring=Integer Ring, name=('x',), sparse=False, implementation=None,
element_class=<type
'sage.rings.polynomial.polynomial_integer_dense_flint.Polynomial_integer_dense_flint'>,
category=None)
1585 if is_IntegerRing(base_ring) and not sparse:
1586 if implementation == 'NTL':
1587 from
sage.rings.polynomial.polynomial_integer_dense_ntl \
1588 import Polynomial_integer_dense_ntl
1589 element_class = Polynomial_integer_dense_ntl
1590 self._implementation_names = ('NTL',)
1591 self._implementation_repr = ' (using NTL)'
1592 elif implementation == 'FLINT' or implementation is
None:
1593 from
sage.rings.polynomial.polynomial_integer_dense_flint \
1594 import Polynomial_integer_dense_flint
1595 element_class = Polynomial_integer_dense_flint
1596 self._implementation_names = (None, 'FLINT')
1597 else:
1598 raise ValueError("unknown implementation %r for
ZZ[%r]" % (implementation, name[0]))
1599 PolynomialRing_commutative.__init__(self, base_ring, name=name,
-> 1600 sparse=sparse, element_class=element_class,
category=category)
sparse = False
element_class = <type
'sage.rings.polynomial.polynomial_integer_dense_flint.Polynomial_integer_dense_flint'>
category = None
1601
1602 def _repr_(self):
1603 """
1604 TESTS::
1605
1606 sage: from sage.rings.polynomial.polynomial_ring import
PolynomialRing_integral_domain as PRing
1607 sage: R = PRing(ZZ, 'x', implementation='NTL'); R
1608 Univariate Polynomial Ring in x over Integer Ring (using
NTL)
1609 """
1610 s = PolynomialRing_commutative._repr_(self)
1611 return s + self._implementation_repr
1612
1613
1614 class PolynomialRing_field(PolynomialRing_integral_domain,
1615 PolynomialRing_singular_repr,
/opt/sage-8.1/local/lib/python2.7/site-packages/sage/rings/polynomial/polynomial_ring.pyc
in __init__(self=Univariate Polynomial Ring in x over Integer Ring,
base_ring=Integer Ring, name=('x',), sparse=False, element_class=<type
'sage.rings.polynomial.polynomial_integer_dense_flint.Polynomial_integer_dense_flint'>,
category=Join of Category of unique factorization domains...s and infinite
enumerated sets and metric spaces))
1456 if max_degree is not None and of_degree is None:
1457 return self._monics_max( max_degree )
1458 raise ValueError("you should pass exactly one of of_degree and
max_degree")
1459
1460 class PolynomialRing_commutative(PolynomialRing_general,
commutative_algebra.CommutativeAlgebra):
1461 """
1462 Univariate polynomial ring over a commutative ring.
1463 """
1464 def __init__(self, base_ring, name=None, sparse=False,
element_class=None, category=None):
1465 if base_ring not in _CommutativeRings:
1466 raise TypeError("Base ring %s must be a commutative
ring."%repr(base_ring))
1467 # We trust that, if a category is given, that it is useful.
1468 if category is None:
1469 category =
polynomial_default_category(base_ring.category(),False)
1470 PolynomialRing_general.__init__(self, base_ring, name=name,
-> 1471 sparse=sparse, element_class=element_class,
category=category)
sparse = False
element_class = <type
'sage.rings.polynomial.polynomial_integer_dense_flint.Polynomial_integer_dense_flint'>
category = Join of Category of unique factorization domains and
Category of commutative algebras over (euclidean domains and infinite
enumerated sets and metric spaces)
1472
1473 def quotient_by_principal_ideal(self, f, names=None):
1474 """
1475 Return the quotient of this polynomial ring by the principal
1476 ideal (generated by) `f`.
1477
1478 INPUT:
1479
1480 - ``f`` - either a polynomial in ``self``, or a principal
1481 ideal of ``self``.
1482
1483 EXAMPLES::
1484
1485 sage: R.<x> = QQ[]
1486 sage: I = (x^2-1)*R
/opt/sage-8.1/local/lib/python2.7/site-packages/sage/rings/polynomial/polynomial_ring.pyc
in __init__(self=Univariate Polynomial Ring in x over Integer Ring,
base_ring=Integer Ring, name=('x',), sparse=False, element_class=<type
'sage.rings.polynomial.polynomial_integer_dense_flint.Polynomial_integer_dense_flint'>,
category=Join of Category of unique factorization domains...s and infinite
enumerated sets and metric spaces))
273 self._has_singular = False
274 # Algebra.__init__ also calls __init_extra__ of
Algebras(...).parent_class, which
275 # tries to provide a conversion from the base ring, if it does
not exist.
276 # This is for algebras that only do the generic stuff in their
initialisation.
277 # But the attribute _no_generic_basering_coercion prevents that
from happening,
278 # since we want to use PolynomialBaseringInjection.
279 sage.algebras.algebra.Algebra.__init__(self, base_ring,
names=name, normalize=True, category=category)
280 self.__generator = self.element_class(self, [0,1], is_gen=True)
281 self._populate_coercion_lists_(
282 #coerce_list = [base_inject],
283 #convert_list = [list, base_inject],
284 convert_method_name = '_polynomial_')
285 if is_PolynomialRing(base_ring):
286 self._Karatsuba_threshold = 0
287 else:
--> 288 from sage.matrix.matrix_space import MatrixSpace
global sage.matrix.matrix_space = undefined
MatrixSpace = undefined
289 if isinstance(base_ring, MatrixSpace):
290 self._Karatsuba_threshold = 0
291 else:
292 self._Karatsuba_threshold = 8
293
294 def __reduce__(self):
295 from sage.rings.polynomial.polynomial_ring_constructor import
unpickle_PolynomialRing
296 args = (self.base_ring(), self.variable_names(), None,
self.is_sparse())
297 return unpickle_PolynomialRing, args
298
299 def _element_constructor_(self, x=None, check=True, is_gen=False,
300 construct=False, **kwds):
301 r"""
302 Convert ``x`` into this univariate polynomial ring,
303 possibly non-canonically.
/opt/sage-8.1/local/lib/python2.7/site-packages/sage/matrix/matrix_space.pyc in
<module>()
33
#*****************************************************************************
34 from __future__ import print_function, absolute_import
35 from six.moves import range
36 from six import iteritems, integer_types
37
38 # System imports
39 import sys
40 import types
41 import operator
42
43 # Sage matrix imports
44 from . import matrix
45 from . import matrix_generic_dense
46 from . import matrix_generic_sparse
47
---> 48 from . import matrix_modn_sparse
global matrix_modn_sparse = undefined
49
50 from . import matrix_mod2_dense
51 from . import matrix_gf2e_dense
52
53 from . import matrix_integer_dense
54 from . import matrix_integer_sparse
55
56 from . import matrix_rational_dense
57 from . import matrix_rational_sparse
58
59 from . import matrix_polynomial_dense
60 from . import matrix_mpolynomial_dense
61
62 # Sage imports
63 from sage.misc.superseded import deprecation
/opt/sage-8.1/local/lib/python2.7/site-packages/sage/matrix/matrix_integer_dense.pxd
in init sage.matrix.matrix_modn_sparse()
1 from sage.libs.gmp.types cimport *
2 from sage.libs.flint.types cimport fmpz_mat_t
3
4 from .matrix_dense cimport Matrix_dense
5 from sage.rings.integer cimport Integer
6 from sage.ext.mod_int cimport *
7
8 ctypedef long* GEN
9
---> 10 cdef class Matrix_integer_dense(Matrix_dense):
global cdef = undefined
global Matrix_integer_dense = undefined
global Matrix_dense = undefined
11 cdef fmpz_mat_t _matrix
12 cdef object _pivots
13 cdef int mpz_height(self, mpz_t height) except -1
14 cdef _mod_int_c(self, mod_int modulus)
15 cdef _mod_two(self)
16 cdef _pickle_version0(self)
17 cdef _unpickle_version0(self, data)
18 cpdef _export_as_string(self, int base=?)
19 cdef void set_unsafe_mpz(self, Py_ssize_t i, Py_ssize_t j, const
mpz_t value)
20 cdef void set_unsafe_si(self, Py_ssize_t i, Py_ssize_t j, long
value)
21 cdef void set_unsafe_double(self, Py_ssize_t i, Py_ssize_t j,
double value)
22 cdef inline void get_unsafe_mpz(self, Py_ssize_t i, Py_ssize_t j,
mpz_t value)
23 cdef inline double get_unsafe_double(self, Py_ssize_t i, Py_ssize_t
j)
24
25 # HNF Modn
26 cdef int _hnf_modn(Matrix_integer_dense self, Matrix_integer_dense
res,
27 unsigned int det) except -1
28 cdef int* _hnf_modn_impl(Matrix_integer_dense self, unsigned int
det,
29 Py_ssize_t nrows, Py_ssize_t ncols) except NULL
30
31 cdef Matrix_integer_dense _new(self, Py_ssize_t nrows, Py_ssize_t
ncols)
/opt/sage-8.1/local/lib/python2.7/site-packages/sage/matrix/matrix_mod2_dense.pxd
in init sage.matrix.matrix_integer_dense()
1 from .matrix_dense cimport Matrix_dense
2 from sage.libs.m4ri cimport *
3
----> 4 cdef class Matrix_mod2_dense(Matrix_dense):
global cdef = undefined
global Matrix_mod2_dense = undefined
global Matrix_dense = undefined
5 cdef mzd_t *_entries
6 cdef object _one
7 cdef object _zero
8
9 cdef set_unsafe_int(self, Py_ssize_t i, Py_ssize_t j, int value)
10
11 cpdef Matrix_mod2_dense _multiply_m4rm(Matrix_mod2_dense self,
Matrix_mod2_dense right, int k)
12 cpdef Matrix_mod2_dense _multiply_strassen(Matrix_mod2_dense self,
Matrix_mod2_dense right, int cutoff)
13
14 # For conversion to other systems
15 cpdef _export_as_string(self)
ImportError: libvpx.so.4: cannot open shared object file: No such file or
directory
***************************************************************************
History of session input:
*** Last line of input (may not be in above history):
