Hello,
during my experiments with python3, I am now stopped on a crash involving
hash of Complex interval fields.
The full log is attached. It ends with
TypeError: key = (Complex Interval Field with 53 bits of precision, ('x',),
False, None)
unhashable type: 'ComplexIntervalField_class_with_category'
This is strange, because CIF and type(CIF) are both hashable in the usual
sage with python2.
has anybody any idea of what is happening ?
Frederic
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***************************************************************************
IPython post-mortem report
{'commit_hash': '5c9c918',
'commit_source': 'installation',
'default_encoding': 'UTF-8',
'ipython_path':
'/home/chapoton/sage3/local/lib/python3.6/site-packages/IPython',
'ipython_version': '5.1.0',
'os_name': 'posix',
'platform': 'Linux-4.10.0-32-generic-x86_64-with-debian-stretch-sid',
'sys_executable': '/home/chapoton/sage3/local/bin/python3',
'sys_platform': 'linux',
'sys_version': '3.6.1 (default, May 25 2017, 08:13:20) \n[GCC 6.3.0 20170406]'}
***************************************************************************
***************************************************************************
Crash traceback:
---------------------------------------------------------------------------
---------------------------------------------------------------------------
TypeError Python 3.6.1: /home/chapoton/sage3/local/bin/python3
Sat Aug 26 08:37:09 2017
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.
/home/chapoton/sage3/local/lib/python3.6/site-packages/sage/rings/polynomial/polynomial_ring_constructor.py
in _get_from_cache(key=(Complex Interval Field with 53 bits of precision,
('x',), False, None))
603 try:
--> 604 return _cache[key]
global _cache = <WeakValueDictionary at 0x7fee50b01ac8>
key = (Complex Interval Field with 53 bits of precision, ('x',), False,
None)
605 except TypeError as msg:
/home/chapoton/sage3/src/sage/misc/weak_dict.pyx in
sage.misc.weak_dict.WeakValueDictionary.__getitem__
(/home/chapoton/sage3/src/build/cythonized/sage/misc/weak_dict.c:3507)()
TypeError: unhashable type: 'ComplexIntervalField_class_with_category'
During handling of the above exception, another exception occurred:
---------------------------------------------------------------------------
TypeError Python 3.6.1: /home/chapoton/sage3/local/bin/python3
Sat Aug 26 08:37:09 2017
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.
/home/chapoton/sage3/src/bin/sage-ipython in <module>()
1 #!/usr/bin/env python3
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 TerminalIPythonApp.initialize of
<sage.repl.interpreter.SageTerminalApp object at 0x7feeeb977630>>
11 app.start()
<decorator-gen-109> in initialize(self=<sage.repl.interpreter.SageTerminalApp
object>, argv=None)
/home/chapoton/sage3/local/lib/python3.6/site-packages/traitlets/config/application.py
in catch_config_error(method=<function TerminalIPythonApp.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 TerminalIPythonApp.initialize at 0x7feee4e55268>
app = <sage.repl.interpreter.SageTerminalApp object at 0x7feeeb977630>
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
/home/chapoton/sage3/local/lib/python3.6/site-packages/IPython/terminal/ipapp.py
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 0x7feeeb977630>>
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,
/home/chapoton/sage3/local/lib/python3.6/site-packages/sage/repl/interpreter.py
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 0x7feee4e6ee48>>
global SAGE_EXTENSION = 'sage'
763
764
/home/chapoton/sage3/local/lib/python3.6/site-packages/IPython/core/extensions.py
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 0x7feee4e6ee48>>
mod = <module 'sage' from
'/home/chapoton/sage3/local/lib/python3.6/site-packages/sage/__init__.py'>
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:
/home/chapoton/sage3/local/lib/python3.6/site-packages/IPython/core/extensions.py
in _call_load_ipython_extension(self=<IPython.core.extensions.ExtensionManager
object>, mod=<module 'sage' from
'/home/chapoton/sage3/local/lib/python3.6/site-packages/sage/__init__.py'>)
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
0x7feeea1160d0>
self.shell = <sage.repl.interpreter.SageTerminalInteractiveShell object
at 0x7feee4e6eeb8>
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.
/home/chapoton/sage3/local/lib/python3.6/site-packages/sage/__init__.py 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 0x7feedfb99d08>
args = (<sage.repl.interpreter.SageTerminalInteractiveShell object at
0x7feee4e6eeb8>,)
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
/home/chapoton/sage3/local/lib/python3.6/site-packages/sage/repl/ipython_extension.py
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
0x7feee4e6eeb8>,)
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)
/home/chapoton/sage3/local/lib/python3.6/site-packages/sage/repl/ipython_extension.py
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
0x7feee4e6eeb8>
/home/chapoton/sage3/local/lib/python3.6/site-packages/sage/repl/ipython_extension.py
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)
/home/chapoton/sage3/local/lib/python3.6/site-packages/sage/all.py in <module>()
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 *
99 from sage.arith.all import *
100 from sage.matrix.all import *
101
--> 102 from sage.symbolic.all import *
global sage.symbolic.all = undefined
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 *
114 from sage.probability.all import *
115 from sage.interfaces.all import *
116
117 from sage.functions.all import *
/home/chapoton/sage3/local/lib/python3.6/site-packages/sage/symbolic/all.py in
<module>()
1 from __future__ import absolute_import
2
----> 3 from sage.libs.pynac.pynac import I
global sage.libs.pynac.pynac = undefined
global I = undefined
4 i = I
5
6 from .ring import SR
7 from .constants import (pi, e, NaN, golden_ratio, log2, euler_gamma,
catalan,
8 khinchin, twinprime, mertens, glaisher)
9 from .expression import Expression, solve_diophantine
10 from .callable import CallableSymbolicExpressionRing
11
12 from sage.symbolic.relation import solve, solve_mod, solve_ineq
13 from sage.symbolic.assumptions import assume, forget, assumptions
14
15 from .units import units
/home/chapoton/sage3/src/sage/libs/pynac/pynac.pyx in init
sage.libs.pynac.pynac()
2529 py_funcs.subs_args_to_PyTuple = &subs_args_to_PyTuple
2530 py_funcs.py_print_function = &py_print_function
2531 py_funcs.py_latex_function = &py_latex_function
2532 py_funcs.py_get_ginac_serial = &py_get_ginac_serial
2533 py_funcs.py_get_sfunction_from_serial =
&py_get_sfunction_from_serial
2534 py_funcs.py_get_serial_from_sfunction =
&py_get_serial_from_sfunction
2535 py_funcs.py_get_serial_for_new_sfunction =
&py_get_serial_for_new_sfunction
2536
2537 py_funcs.py_get_constant = &py_get_constant
2538 py_funcs.py_print_fderivative = &py_print_fderivative
2539 py_funcs.py_latex_fderivative = &py_latex_fderivative
2540 py_funcs.paramset_to_PyTuple = ¶mset_to_PyTuple
2541 py_funcs.py_rational_power_parts = &py_rational_power_parts
2542
2543 init_function_table()
-> 2544 init_pynac_I()
global init_pynac_I = <built-in function init_pynac_I>
2545
2546 set_ginac_fn_serial()
/home/chapoton/sage3/src/sage/libs/pynac/pynac.pyx in
sage.libs.pynac.pynac.init_pynac_I
(/home/chapoton/sage3/src/build/cythonized/sage/libs/pynac/pynac.cpp:28548)()
2415 <type
'sage.rings.number_field.number_field_element_quadratic.NumberFieldElement_quadratic'>
2416
2417 Check that :trac:`10064` is fixed::
2418
2419 sage: y = I*I*x / x # so y is the expression -1
2420 sage: y.is_positive()
2421 False
2422 sage: z = -x / x
2423 sage: z.is_positive()
2424 False
2425 sage: bool(z == y)
2426 True
2427 """
2428 global pynac_I, I
2429 from sage.rings.number_field.number_field import QuadraticField
-> 2430 K = QuadraticField(-1, 'I', embedding=CC.gen(), latex_name='i')
global K = undefined
global QuadraticField = undefined
global embedding = undefined
global CC.gen = <bound method ComplexField_class.gen of Complex Field
with 53 bits of precision>
global latex_name = undefined
2431 pynac_I = K.gen()
2432 ginac_pyinit_I(pynac_I)
2433 I = new_Expression_from_GEx(ring.SR, g_I)
2434
2435
2436 def init_function_table():
2437 """
2438 Initializes the function pointer table in Pynac. This must be
2439 called before Pynac is used; otherwise, there will be segfaults.
2440 """
2441
2442 py_funcs.py_binomial_int = &py_binomial_int
2443 py_funcs.py_binomial = &py_binomial
2444 py_funcs.py_gcd = &py_gcd
2445 py_funcs.py_lcm = &py_lcm
/home/chapoton/sage3/local/lib/python3.6/site-packages/sage/rings/number_field/number_field.py
in QuadraticField(D=b'-1', name='I', check=True,
embedding=b.'100000000000000'*I, latex_name='i', **args={})
912 False
913 """
914 D = QQ(D)
915 if check:
916 if D.is_square():
917 raise ValueError("D must not be a perfect square.")
918 R = QQ['x']
919 f = R([-D, 0, 1])
920 if embedding is True:
921 if D > 0:
922 embedding = RLF(D).sqrt()
923 else:
924 embedding = CLF(D).sqrt()
925 if latex_name == 'sqrt':
926 latex_name = r'\sqrt{%s}' % D
--> 927 return NumberField(f, name, check=False, embedding=embedding,
latex_name=latex_name, **args)
global NumberField = <function NumberField at 0x7fee4c817840>
f = b'1'*x^2 + b'1'
name = 'I'
check = True
embedding = b.'100000000000000'*I
latex_name = 'i'
args = {}
928
929 def is_AbsoluteNumberField(x):
930 """
931 Return True if x is an absolute number field.
932
933 EXAMPLES::
934
935 sage: from sage.rings.number_field.number_field import
is_AbsoluteNumberField
936 sage: is_AbsoluteNumberField(NumberField(x^2+1,'a'))
937 True
938 sage: is_AbsoluteNumberField(NumberField([x^3 + 17, x^2+1],'a'))
939 False
940
941 The rationals are a number field, but they're not of the absolute
942 number field class.
/home/chapoton/sage3/local/lib/python3.6/site-packages/sage/rings/number_field/number_field.py
in NumberField(polynomial=b'1'*x^2 + b'1', name='I', check=False, names=None,
embedding=b.'100000000000000'*I, latex_name='i', assume_disc_small=False,
maximize_at_primes=None, structure=None)
514 (2,)
515
516 It is an error not to specify the generator::
517
518 sage: K = NumberField(x^2-2)
519 Traceback (most recent call last):
520 ...
521 TypeError: You must specify the name of the generator.
522
523 """
524 if names is not None:
525 name = names
526 if isinstance(polynomial, (list,tuple)):
527 return NumberFieldTower(polynomial, names=name, check=check,
embeddings=embedding, latex_names=latex_name,
assume_disc_small=assume_disc_small, maximize_at_primes=maximize_at_primes,
structures=structure)
528
--> 529 return NumberField_version2(polynomial=polynomial, name=name,
check=check, embedding=embedding, latex_name=latex_name,
assume_disc_small=assume_disc_small, maximize_at_primes=maximize_at_primes,
structure=structure)
global NumberField_version2 = <class
'sage.rings.number_field.number_field.NumberFieldFactory'>
polynomial = b'1'*x^2 + b'1'
name = 'I'
check = False
embedding = b.'100000000000000'*I
latex_name = 'i'
assume_disc_small = False
maximize_at_primes = None
structure = None
530
531 class NumberFieldFactory(UniqueFactory):
532 r"""
533 Factory for number fields.
534
535 This should usually not be called directly, use :meth:`NumberField`
536 instead.
537
538 INPUT:
539
540 - ``polynomial`` - a polynomial over `\QQ` or a number field.
541 - ``name`` - a string (default: ``'a'``), the name of the
generator
542 - ``check`` - a boolean (default: ``True``); do type checking
and
543 irreducibility checking.
544 - ``embedding`` - ``None`` or an element, the images of the
generator
/home/chapoton/sage3/src/sage/structure/factory.pyx in
sage.structure.factory.UniqueFactory.__call__
(/home/chapoton/sage3/src/build/cythonized/sage/structure/factory.c:1882)()
/home/chapoton/sage3/src/sage/structure/factory.pyx in
sage.structure.factory.UniqueFactory.get_object
(/home/chapoton/sage3/src/build/cythonized/sage/structure/factory.c:2116)()
/home/chapoton/sage3/src/sage/misc/cachefunc.pyx in
sage.misc.cachefunc.cache_key
(/home/chapoton/sage3/src/build/cythonized/sage/misc/cachefunc.c:3097)()
/home/chapoton/sage3/src/sage/misc/cachefunc.pyx in
sage.misc.cachefunc.cache_key_unhashable
(/home/chapoton/sage3/src/build/cythonized/sage/misc/cachefunc.c:3411)()
/home/chapoton/sage3/src/sage/misc/cachefunc.pyx in genexpr
(/home/chapoton/sage3/src/build/cythonized/sage/misc/cachefunc.c:3308)()
/home/chapoton/sage3/src/sage/misc/cachefunc.pyx in
sage.misc.cachefunc.cache_key
(/home/chapoton/sage3/src/build/cythonized/sage/misc/cachefunc.c:3097)()
/home/chapoton/sage3/src/sage/misc/cachefunc.pyx in
sage.misc.cachefunc.cache_key_unhashable
(/home/chapoton/sage3/src/build/cythonized/sage/misc/cachefunc.c:3411)()
/home/chapoton/sage3/src/sage/misc/cachefunc.pyx in genexpr
(/home/chapoton/sage3/src/build/cythonized/sage/misc/cachefunc.c:3308)()
/home/chapoton/sage3/src/sage/misc/cachefunc.pyx in
sage.misc.cachefunc.cache_key
(/home/chapoton/sage3/src/build/cythonized/sage/misc/cachefunc.c:3097)()
/home/chapoton/sage3/src/sage/misc/cachefunc.pyx in
sage.misc.cachefunc.cache_key_unhashable
(/home/chapoton/sage3/src/build/cythonized/sage/misc/cachefunc.c:3466)()
/home/chapoton/sage3/src/sage/structure/element.pyx in
sage.structure.element.Element._cache_key
(/home/chapoton/sage3/src/build/cythonized/sage/structure/element.c:9862)()
/home/chapoton/sage3/src/sage/structure/sage_object.pyx in
sage.structure.sage_object.SageObject.__repr__
(/home/chapoton/sage3/src/build/cythonized/sage/structure/sage_object.c:2705)()
/home/chapoton/sage3/src/sage/rings/real_lazy.pyx in
sage.rings.real_lazy.LazyFieldElement._repr_
(/home/chapoton/sage3/src/build/cythonized/sage/rings/real_lazy.c:9675)()
/home/chapoton/sage3/src/sage/rings/real_lazy.pyx in
sage.rings.real_lazy.LazyFieldElement.approx
(/home/chapoton/sage3/src/build/cythonized/sage/rings/real_lazy.c:9770)()
/home/chapoton/sage3/src/sage/rings/real_lazy.pyx in
sage.rings.real_lazy.LazyAlgebraic.eval
(/home/chapoton/sage3/src/build/cythonized/sage/rings/real_lazy.c:18752)()
/home/chapoton/sage3/src/sage/rings/polynomial/polynomial_element.pyx in
sage.rings.polynomial.polynomial_element.Polynomial.roots
(/home/chapoton/sage3/src/build/cythonized/sage/rings/polynomial/polynomial_element.c:68682)()
/home/chapoton/sage3/local/lib/python3.6/site-packages/sage/rings/polynomial/complex_roots.py
in complex_roots(p=b'1'*x^2 + b'1', skip_squarefree=False, retval='algebraic',
min_prec=0)
252
253 all_rts = []
254 ok = True
255
256 for (factor, exp) in factors:
257 cfac = CCX(factor)
258 rts = cfac.roots(multiplicities=False)
259 # Make sure the number of roots we found is the degree. If
260 # we don't find that many roots, it's because the
261 # precision isn't big enough and though the (possibly
262 # exact) polynomial "factor" is squarefree, it is not
263 # squarefree as an element of CCX.
264 if len(rts) < factor.degree():
265 ok = False
266 break
--> 267 irts = interval_roots(factor, rts, max(prec, min_prec))
irts = undefined
global interval_roots = <function interval_roots at 0x7fee39a0d7b8>
factor = b'1'*x^2 + b'1'
rts = [b.'-100000000000000'*I, b.'100000000000000'*I]
global max = undefined
prec = 53
min_prec = 0
268 if irts is None:
269 ok = False
270 break
271 if retval != 'interval':
272 factor = QQbar.common_polynomial(factor)
273 for irt in irts:
274 all_rts.append((irt, factor, exp))
275
276 if ok and intervals_disjoint([rt for (rt, fac, mult) in
all_rts]):
277 all_rts = sort_complex_numbers_for_display(all_rts)
278 if retval == 'interval':
279 return [(rt, mult) for (rt, fac, mult) in all_rts]
280 elif retval == 'algebraic':
281 return [(QQbar.polynomial_root(fac, rt), mult) for (rt,
fac, mult) in all_rts]
282 elif retval == 'algebraic_real':
/home/chapoton/sage3/local/lib/python3.6/site-packages/sage/rings/polynomial/complex_roots.py
in interval_roots(p=b'1'*x^2 + b'1', rts=[b.'-100000000000000'*I,
b.'100000000000000'*I], prec=53)
55 fail, we return None.
56
57 EXAMPLES::
58
59 sage: x = polygen(ZZ)
60 sage: p = x^3 - 1
61 sage: rts = [CC.zeta(3)^i for i in range(0, 3)]
62 sage: from sage.rings.polynomial.complex_roots import
interval_roots
63 sage: interval_roots(p, rts, 53)
64 [1, -0.500000000000000? + 0.866025403784439?*I,
-0.500000000000000? - 0.866025403784439?*I]
65 sage: interval_roots(p, rts, 200)
66 [1,
-0.500000000000000000000000000000000000000000000000000000000000? +
0.866025403784438646763723170752936183471402626905190314027904?*I,
-0.500000000000000000000000000000000000000000000000000000000000? -
0.866025403784438646763723170752936183471402626905190314027904?*I]
67 """
68
69 CIF = ComplexIntervalField(prec)
---> 70 CIFX = CIF['x']
CIFX = undefined
CIF = Complex Interval Field with 53 bits of precision
71
72 ip = CIFX(p)
73 ipd = CIFX(p.derivative())
74
75 irts = []
76
77 for rt in rts:
78 irt = refine_root(ip, ipd, CIF(rt), CIF)
79 if irt is None:
80 return None
81 irts.append(irt)
82
83 return irts
84
85 def intervals_disjoint(intvs):
/home/chapoton/sage3/src/sage/structure/parent.pyx in
sage.structure.parent.Parent.__getitem__
(/home/chapoton/sage3/src/build/cythonized/sage/structure/parent.c:11975)()
/home/chapoton/sage3/local/lib/python3.6/site-packages/sage/categories/rings.py
in __getitem__(self=Complex Interval Field with 53 bits of precision, arg='x')
1067 and
elt.imag().is_zero()):
1068 emb = RLF(elt)
1069 else:
1070 emb = CLF(elt)
1071 return self.extension(minpolys[0], names[0],
embedding=emb)
1072 try:
1073 # Doing the extension all at once is best, if
possible...
1074 return self.extension(minpolys, names)
1075 except (TypeError, ValueError):
1076 # ...but we can also construct it iteratively
1077 return reduce(lambda R, ext: R.extension(*ext),
zip(minpolys, names), self)
1078
1079 # 2. Otherwise, try to return a polynomial ring
1080
1081 from sage.rings.polynomial.polynomial_ring_constructor
import PolynomialRing
-> 1082 return PolynomialRing(self, elts)
PolynomialRing = <function PolynomialRing at 0x7fee50f9c840>
self = Complex Interval Field with 53 bits of precision
elts = ('x',)
1083
1084 class ElementMethods:
1085 def is_unit(self):
1086 r"""
1087 Return whether this element is a unit in the ring.
1088
1089 .. NOTE::
1090
1091 This is a generic implementation for (non-commutative)
rings
1092 which only works for the one element, its additive
inverse, and
1093 the zero element. Most rings should provide a more
specialized
1094 implementation.
1095
1096 EXAMPLES::
1097
/home/chapoton/sage3/local/lib/python3.6/site-packages/sage/rings/polynomial/polynomial_ring_constructor.py
in PolynomialRing(base_ring=Complex Interval Field with 53 bits of precision,
*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 0x7fee4f870d08>
base_ring = Complex Interval Field with 53 bits of precision
global names = undefined
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
/home/chapoton/sage3/local/lib/python3.6/site-packages/sage/rings/polynomial/polynomial_ring_constructor.py
in _single_variate(base_ring=Complex Interval Field with 53 bits of precision,
name=('x',), sparse=False, implementation=None, order=None)
610 def _save_in_cache(key, R):
611 try:
612 _cache[key] = R
613 except TypeError as msg:
614 raise TypeError('key = %s\n%s'%(key,msg))
615
616
617 def _single_variate(base_ring, name, sparse=None, implementation=None,
order=None):
618 # The "order" argument is unused, but we allow it (and ignore it)
619 # for consistency with the multi-variate case.
620 sparse = bool(sparse)
621 if sparse:
622 implementation = None
623
624 key = (base_ring, name, sparse, implementation)
--> 625 R = _get_from_cache(key)
R = undefined
global _get_from_cache = <function _get_from_cache at 0x7fee4f870bf8>
key = (Complex Interval Field with 53 bits of precision, ('x',), False,
None)
626 if R is not None:
627 return R
628
629 import sage.rings.polynomial.polynomial_ring as m
630 if isinstance(base_ring, ring.CommutativeRing):
631 if is_IntegerModRing(base_ring) and not sparse:
632 n = base_ring.order()
633 if n.is_prime():
634 R = m.PolynomialRing_dense_mod_p(base_ring, name,
implementation=implementation)
635 elif n > 1:
636 R = m.PolynomialRing_dense_mod_n(base_ring, name,
implementation=implementation)
637 else: # n == 1!
638 R = m.PolynomialRing_integral_domain(base_ring, name)
# specialized code breaks in this case.
639
640 elif is_FiniteField(base_ring) and not sparse:
/home/chapoton/sage3/local/lib/python3.6/site-packages/sage/rings/polynomial/polynomial_ring_constructor.py
in _get_from_cache(key=(Complex Interval Field with 53 bits of precision,
('x',), False, None))
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
601
602 def _get_from_cache(key):
603 try:
604 return _cache[key]
605 except TypeError as msg:
--> 606 raise TypeError('key = %s\n%s'%(key,msg))
global TypeError = undefined
key = (Complex Interval Field with 53 bits of precision, ('x',), False,
None)
msg = undefined
607 except KeyError:
608 return None
609
610 def _save_in_cache(key, R):
611 try:
612 _cache[key] = R
613 except TypeError as msg:
614 raise TypeError('key = %s\n%s'%(key,msg))
615
616
617 def _single_variate(base_ring, name, sparse=None, implementation=None,
order=None):
618 # The "order" argument is unused, but we allow it (and ignore it)
619 # for consistency with the multi-variate case.
620 sparse = bool(sparse)
621 if sparse:
TypeError: key = (Complex Interval Field with 53 bits of precision, ('x',),
False, None)
unhashable type: 'ComplexIntervalField_class_with_category'
***************************************************************************
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