Paste #XpqSnolgiEfkYmPMv50v at spacepaste

***************************************************************************
IPython post-mortem report
{'commit_hash': u'c963f6b',
'commit_source': 'installation',
'default_encoding': 'UTF-8',
'ipython_path': '/usr/lib64/python2.7/site-packages/IPython',
'ipython_version': '4.2.0',
'os_name': 'posix',
'platform': 'Linux-4.7.5-gentoo-x86_64-Mobile_AMD_Sempron-tm-_Processor_3800+-with-gentoo-2.3',
'sys_executable': '/usr/bin/python2.7',
'sys_platform': 'linux2',
'sys_version': '2.7.12 (default, Sep 28 2016, 11:37:31) \n[GCC 5.4.0]'}
***************************************************************************
***************************************************************************
Crash traceback:
---------------------------------------------------------------------------
---------------------------------------------------------------------------
ImportError Python 2.7.12: /usr/bin/python2.7
Tue Oct 11 14:26:08 2016
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.
/usr/lib/python-exec/python2.7/sage-ipython in <module>()
1 #!/usr/bin/env python2.7
2 # -*- coding: utf-8 -*-
3 """
4 Sage IPython startup script.
5 """
6
7 # Install extra readline commands before IPython initialization
8 from sage.repl.readline_extra_commands import *
9
10 from sage.repl.interpreter import SageTerminalApp
11
12 app = SageTerminalApp.instance()
---> 13 app.initialize()
global app.initialize = <bound method SageTerminalApp.initialize of <sage.repl.interpreter.SageTerminalApp object at 0x7f2c139b62d0>>
14 app.start()
<decorator-gen-111> in initialize(self=<sage.repl.interpreter.SageTerminalApp object>, argv=None)
/usr/lib64/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 0x7f2c0c9c80c8>
app = <sage.repl.interpreter.SageTerminalApp object at 0x7f2c139b62d0>
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
/usr/lib64/python2.7/site-packages/IPython/terminal/ipapp.pyc in initialize(self=<sage.repl.interpreter.SageTerminalApp object>, argv=None)
290
291 return super(TerminalIPythonApp, self).parse_command_line(argv)
292
293 @catch_config_error
294 def initialize(self, argv=None):
295 """Do actions after construct, but before starting the app."""
296 super(TerminalIPythonApp, self).initialize(argv)
297 if self.subapp is not None:
298 # don't bother initializing further, starting subapp
299 return
300 # print self.extra_args
301 if self.extra_args and not self.something_to_run:
302 self.file_to_run = self.extra_args[0]
303 self.init_path()
304 # create the shell
--> 305 self.init_shell()
self.init_shell = <bound method SageTerminalApp.init_shell of <sage.repl.interpreter.SageTerminalApp object at 0x7f2c139b62d0>>
306 # and draw the banner
307 self.init_banner()
308 # Now a variety of things that happen after the banner is printed.
309 self.init_gui_pylab()
310 self.init_extensions()
311 self.init_code()
312
313 def init_shell(self):
314 """initialize the InteractiveShell instance"""
315 # Create an InteractiveShell instance.
316 # shell.display_banner should always be False for the terminal
317 # based app, because we call shell.show_banner() by hand below
318 # so the banner shows *before* all extension loading stuff.
319 self.shell = TerminalInteractiveShell.instance(parent=self,
320 display_banner=False, profile_dir=self.profile_dir,
/usr/lib64/python2.7/site-packages/sage/repl/interpreter.pyc in init_shell(self=<sage.repl.interpreter.SageTerminalApp object>)
783 self.shell.has_sage_extensions = SAGE_EXTENSION in self.extensions
784
785 # Load the %lprun extension if available
786 try:
787 import line_profiler
788 except ImportError:
789 pass
790 else:
791 self.extensions.append('line_profiler')
792
793 if self.shell.has_sage_extensions:
794 self.extensions.remove(SAGE_EXTENSION)
795
796 # load sage extension here to get a crash if
797 # something is wrong with the sage library
--> 798 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 0x7f2c0c0db050>>
global SAGE_EXTENSION = 'sage'
799
800
/usr/lib64/python2.7/site-packages/IPython/core/extensions.pyc in load_extension(self=<IPython.core.extensions.ExtensionManager object>, module_str='sage')
71
72 Returns the string "already loaded" if the extension is already loaded,
73 "no load function" if the module doesn't have a load_ipython_extension
74 function, or None if it succeeded.
75 """
76 if module_str in self.loaded:
77 return "already loaded"
78
79 from IPython.utils.syspathcontext import prepended_to_syspath
80
81 with self.shell.builtin_trap:
82 if module_str not in sys.modules:
83 with prepended_to_syspath(self.ipython_extension_dir):
84 __import__(module_str)
85 mod = sys.modules[module_str]
---> 86 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 0x7f2c0c0db050>>
mod = <module 'sage' from '/usr/lib64/python2.7/site-packages/sage/__init__.pyc'>
87 self.loaded.add(module_str)
88 else:
89 return "no load function"
90
91 def unload_extension(self, module_str):
92 """Unload an IPython extension by its module name.
93
94 This function looks up the extension's name in ``sys.modules`` and
95 simply calls ``mod.unload_ipython_extension(self)``.
96
97 Returns the string "no unload function" if the extension doesn't define
98 a function to unload itself, "not loaded" if the extension isn't loaded,
99 otherwise None.
100 """
101 if module_str not in self.loaded:
/usr/lib64/python2.7/site-packages/IPython/core/extensions.pyc in _call_load_ipython_extension(self=<IPython.core.extensions.ExtensionManager object>, mod=<module 'sage' from '/usr/lib64/python2.7/site-packages/sage/__init__.pyc'>)
118 """
119 from IPython.utils.syspathcontext import prepended_to_syspath
120
121 if (module_str in self.loaded) and (module_str in sys.modules):
122 self.unload_extension(module_str)
123 mod = sys.modules[module_str]
124 with prepended_to_syspath(self.ipython_extension_dir):
125 reload(mod)
126 if self._call_load_ipython_extension(mod):
127 self.loaded.add(module_str)
128 else:
129 self.load_extension(module_str)
130
131 def _call_load_ipython_extension(self, mod):
132 if hasattr(mod, 'load_ipython_extension'):
--> 133 mod.load_ipython_extension(self.shell)
mod.load_ipython_extension = <function load_ipython_extension at 0x7f2c139a98c0>
self.shell = <sage.repl.interpreter.SageTerminalInteractiveShell object at 0x7f2c0c9d8510>
134 return True
135
136 def _call_unload_ipython_extension(self, mod):
137 if hasattr(mod, 'unload_ipython_extension'):
138 mod.unload_ipython_extension(self.shell)
139 return True
140
141 def install_extension(self, url, filename=None):
142 """Download and install an IPython extension.
143
144 If filename is given, the file will be so named (inside the extension
145 directory). Otherwise, the name from the URL will be used. The file must
146 have a .py or .zip extension; otherwise, a ValueError will be raised.
147
148 Returns the full path to the installed file.
/usr/lib64/python2.7/site-packages/sage/__init__.pyc in load_ipython_extension(*args=(<sage.repl.interpreter.SageTerminalInteractiveShell object>,))
1 __all__ = ['all']
2
3 # IPython calls this when starting up
4 def load_ipython_extension(*args):
5 import sage.repl.ipython_extension
----> 6 sage.repl.ipython_extension.load_ipython_extension(*args)
sage.repl.ipython_extension.load_ipython_extension = <function load_ipython_extension at 0x7f2c0c071b18>
args = (<sage.repl.interpreter.SageTerminalInteractiveShell object at 0x7f2c0c9d8510>,)
/usr/lib64/python2.7/site-packages/sage/repl/ipython_extension.pyc in wrapper(*args=(<sage.repl.interpreter.SageTerminalInteractiveShell object>,), **kwargs={})
459 ....: if work:
460 ....: return 'foo worked'
461 ....: raise RuntimeError("foo didn't work")
462 sage: foo(False)
463 Traceback (most recent call last):
464 ...
465 RuntimeError: foo didn't work
466 sage: foo(True)
467 'foo worked'
468 sage: foo(False)
469 sage: foo(True)
470 """
471 @wraps(func)
472 def wrapper(*args, **kwargs):
473 if not wrapper.has_run:
--> 474 result = func(*args, **kwargs)
result = undefined
global func = undefined
args = (<sage.repl.interpreter.SageTerminalInteractiveShell object at 0x7f2c0c9d8510>,)
kwargs = {}
475 wrapper.has_run = True
476 return result
477 wrapper.has_run = False
478 return wrapper
479
480
481 @run_once
482 def load_ipython_extension(ip):
483 """
484 Load the extension in IPython.
485 """
486 # this modifies ip
487 SageCustomizations(shell=ip)
/usr/lib64/python2.7/site-packages/sage/repl/ipython_extension.pyc in load_ipython_extension(ip=<sage.repl.interpreter.SageTerminalInteractiveShell object>)
472 def wrapper(*args, **kwargs):
473 if not wrapper.has_run:
474 result = func(*args, **kwargs)
475 wrapper.has_run = True
476 return result
477 wrapper.has_run = False
478 return wrapper
479
480
481 @run_once
482 def load_ipython_extension(ip):
483 """
484 Load the extension in IPython.
485 """
486 # this modifies ip
--> 487 SageCustomizations(shell=ip)
global SageCustomizations = <class 'sage.repl.ipython_extension.SageCustomizations'>
global shell = undefined
ip = <sage.repl.interpreter.SageTerminalInteractiveShell object at 0x7f2c0c9d8510>
/usr/lib64/python2.7/site-packages/sage/repl/ipython_extension.pyc in __init__(self=<sage.repl.ipython_extension.SageCustomizations object>, shell=<sage.repl.interpreter.SageTerminalInteractiveShell object>)
362 def __init__(self, shell=None):
363 """
364 Initialize the Sage plugin.
365 """
366 self.shell = shell
367
368 self.auto_magics = SageMagics(shell)
369 self.shell.register_magics(self.auto_magics)
370
371 import sage.misc.edit_module as edit_module
372 self.shell.set_hook('editor', edit_module.edit_devel)
373
374 self.init_inspector()
375 self.init_line_transforms()
376
--> 377 import sage.all # until sage's import hell is fixed
sage.all = undefined
378
379 self.shell.verbose_quit = True
380 self.set_quit_hook()
381
382 self.register_interface_magics()
383
384 if SAGE_IMPORTALL == 'yes':
385 self.init_environment()
386
387 def register_interface_magics(self):
388 """
389 Register magics for each of the Sage interfaces
390 """
391 from sage.repl.interface_magic import InterfaceMagic
392 InterfaceMagic.register_all(self.shell)
/usr/lib64/python2.7/site-packages/sage/all.py in <module>()
88
89 from time import sleep
90
91 import sage.misc.lazy_import
92 from sage.misc.all import * # takes a while
93 from sage.typeset.all import *
94 from sage.repl.all import *
95
96 from sage.misc.sh import sh
97
98 from sage.libs.all import *
99 from sage.data_structures.all import *
100 from sage.doctest.all import *
101
102 from sage.structure.all import *
--> 103 from sage.rings.all import *
global sage.rings.all = undefined
104 from sage.arith.all import *
105 from sage.matrix.all import *
106
107 # This must come before Calculus -- it initializes the Pynac library.
108 import sage.symbolic.pynac
109
110 from sage.modules.all import *
111 from sage.monoids.all import *
112 from sage.algebras.all import *
113 from sage.modular.all import *
114 from sage.sat.all import *
115 from sage.schemes.all import *
116 from sage.graphs.all import *
117 from sage.groups.all import *
118 from sage.databases.all import *
/usr/lib64/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
/usr/lib64/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)
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
/usr/lib64/python2.7/site-packages/sage/rings/number_field/totallyreal_data.pxd in init sage.rings.number_field.totallyreal (/var/tmp/portage/sci-mathematics/sage-7.3/work/sage-7.3/src-python2_7/build/cythonized/sage/rings/number_field/totallyreal.c:11602)()
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
/usr/lib64/python2.7/site-packages/sage/rings/number_field/totallyreal_data.pyx in init sage.rings.number_field.totallyreal_data (/var/tmp/portage/sci-mathematics/sage-7.3/work/sage-7.3/src-python2_7/build/cythonized/sage/rings/number_field/totallyreal_data.c:12297)()
24 #*****************************************************************************
25 from __future__ import print_function
26
27 include "sage/ext/cdefs.pxi"
28 include "cysignals/memory.pxi"
29
30 from sage.arith.all import binomial, gcd
31 from sage.rings.rational_field import RationalField
32 from sage.rings.polynomial.polynomial_ring_constructor import PolynomialRing
33 from sage.rings.real_mpfi import RealIntervalField
34 from sage.rings.real_mpfr import RealField
35 from sage.rings.integer_ring import ZZ
36 from sage.rings.integer cimport Integer
37
38 # Other global variables
---> 39 ZZx = PolynomialRing(ZZ, 'x')
global ZZx = undefined
global PolynomialRing = <function PolynomialRing at 0x7f2bc6ad3140>
global ZZ = Integer Ring
40
41 from libc.math cimport lrint, floor, ceil, fabs, round
42
43
44 #*********************************************************************
45 # Auxiliary routine
46 # Hermite constant, naive Newton-Raphson, and a specialized Lagrange
47 # multiplier solver.
48 #*********************************************************************
49
50 def hermite_constant(n):
51 r"""
52 This function returns the nth Hermite constant
53
54 The nth Hermite constant (typically denoted `\gamma_n`), is defined
/usr/lib64/python2.7/site-packages/sage/rings/polynomial/polynomial_ring_constructor.pyc in PolynomialRing(base_ring=Integer Ring, arg1='x', arg2=None, sparse=False, order='degrevlex', names=None, name='x', var_array=None, implementation=None)
446 arg2 = [str(x) for x in arg2]
447 if isinstance(arg2, (int, long, Integer)):
448 # 3. PolynomialRing(base_ring, names, n, order='degrevlex'):
449 if not isinstance(arg1, (list, tuple, str)):
450 raise TypeError("You *must* specify the names of the variables.")
451 n = int(arg2)
452 names = arg1
453 R = _multi_variate(base_ring, names, n, sparse, order, implementation)
454
455 elif isinstance(arg1, str) or (isinstance(arg1, (list,tuple)) and len(arg1) == 1):
456 if not ',' in arg1:
457 # 1. PolynomialRing(base_ring, name, sparse=False):
458 if not arg2 is None:
459 raise TypeError("if second arguments is a string with no commas, then there must be no other non-optional arguments")
460 name = arg1
--> 461 R = _single_variate(base_ring, name, sparse, implementation)
R = None
global _single_variate = <function _single_variate at 0x7f2bc6ad3398>
base_ring = Integer Ring
name = 'x'
sparse = False
implementation = None
462 else:
463 # 2-4. PolynomialRing(base_ring, names, order='degrevlex'):
464 if not arg2 is None:
465 raise TypeError("invalid input to PolynomialRing function; please see the docstring for that function")
466 names = arg1.split(',')
467 R = _multi_variate(base_ring, names, -1, sparse, order, implementation)
468 elif isinstance(arg1, (list, tuple)):
469 # PolynomialRing(base_ring, names (list or tuple), order='degrevlex'):
470 names = arg1
471 R = _multi_variate(base_ring, names, -1, sparse, order, implementation)
472
473 if arg1 is None and arg2 is None:
474 raise TypeError("you *must* specify the indeterminates (as not None).")
475 if R is None:
476 raise TypeError("invalid input (%s, %s, %s) to PolynomialRing function; please see the docstring for that function"%(
/usr/lib64/python2.7/site-packages/sage/rings/polynomial/polynomial_ring_constructor.pyc in _single_variate(base_ring=Integer Ring, name=('x',), sparse=False, implementation=None)
524 R = m.PolynomialRing_dense_padic_ring_capped_absolute(base_ring, name)
525
526 elif isinstance(base_ring, padic_base_leaves.pAdicRingFixedMod):
527 R = m.PolynomialRing_dense_padic_ring_fixed_mod(base_ring, name)
528
529 elif base_ring in _CompleteDiscreteValuationRings:
530 R = m.PolynomialRing_cdvr(base_ring, name, sparse)
531
532 elif base_ring in _CompleteDiscreteValuationFields:
533 R = m.PolynomialRing_cdvf(base_ring, name, sparse)
534
535 elif base_ring.is_field(proof = False):
536 R = m.PolynomialRing_field(base_ring, name, sparse)
537
538 elif base_ring.is_integral_domain(proof = False):
--> 539 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
540 else:
541 R = m.PolynomialRing_commutative(base_ring, name, sparse)
542 else:
543 R = m.PolynomialRing_general(base_ring, name, sparse)
544
545 if hasattr(R, '_implementation_names'):
546 for name in R._implementation_names:
547 real_key = key[0:3] + (name,)
548 _save_in_cache(real_key, R)
549 else:
550 _save_in_cache(key, R)
551 return R
552
553 def _multi_variate(base_ring, names, n, sparse, order, implementation):
554 # if not sparse:
/usr/lib64/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)
1518 if is_IntegerRing(base_ring) and not sparse:
1519 if implementation == 'NTL':
1520 from sage.rings.polynomial.polynomial_integer_dense_ntl \
1521 import Polynomial_integer_dense_ntl
1522 element_class = Polynomial_integer_dense_ntl
1523 self._implementation_names = ('NTL',)
1524 self._implementation_repr = ' (using NTL)'
1525 elif implementation == 'FLINT' or implementation is None:
1526 from sage.rings.polynomial.polynomial_integer_dense_flint \
1527 import Polynomial_integer_dense_flint
1528 element_class = Polynomial_integer_dense_flint
1529 self._implementation_names = (None, 'FLINT')
1530 else:
1531 raise ValueError("Unknown implementation %s for ZZ[x]"%implementation)
1532 PolynomialRing_commutative.__init__(self, base_ring, name=name,
-> 1533 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
1534
1535 def _repr_(self):
1536 """
1537 TESTS::
1538
1539 sage: from sage.rings.polynomial.polynomial_ring import PolynomialRing_integral_domain as PRing
1540 sage: R = PRing(ZZ, 'x', implementation='NTL'); R
1541 Univariate Polynomial Ring in x over Integer Ring (using NTL)
1542 """
1543 s = PolynomialRing_commutative._repr_(self)
1544 return s + self._implementation_repr
1545
1546
1547 class PolynomialRing_field(PolynomialRing_integral_domain,
1548 PolynomialRing_singular_repr,
/usr/lib64/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))
1425 if max_degree is not None and of_degree is None:
1426 return self._monics_max( max_degree )
1427 raise ValueError("you should pass exactly one of of_degree and max_degree")
1428
1429 class PolynomialRing_commutative(PolynomialRing_general, commutative_algebra.CommutativeAlgebra):
1430 """
1431 Univariate polynomial ring over a commutative ring.
1432 """
1433 def __init__(self, base_ring, name=None, sparse=False, element_class=None, category=None):
1434 if base_ring not in _CommutativeRings:
1435 raise TypeError("Base ring %s must be a commutative ring."%repr(base_ring))
1436 # We trust that, if a category is given, that it is useful.
1437 if category is None:
1438 category = polynomial_default_category(base_ring.category(),False)
1439 PolynomialRing_general.__init__(self, base_ring, name=name,
-> 1440 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)
1441
1442 def quotient_by_principal_ideal(self, f, names=None):
1443 """
1444 Return the quotient of this polynomial ring by the principal
1445 ideal (generated by) `f`.
1446
1447 INPUT:
1448
1449 - ``f`` - either a polynomial in ``self``, or a principal
1450 ideal of ``self``.
1451
1452 EXAMPLES::
1453
1454 sage: R.<x> = QQ[]
1455 sage: I = (x^2-1)*R
/usr/lib64/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))
274 self._has_singular = False
275 # Algebra.__init__ also calls __init_extra__ of Algebras(...).parent_class, which
276 # tries to provide a conversion from the base ring, if it does not exist.
277 # This is for algebras that only do the generic stuff in their initialisation.
278 # But the attribute _no_generic_basering_coercion prevents that from happening,
279 # since we want to use PolynomialBaseringInjection.
280 sage.algebras.algebra.Algebra.__init__(self, base_ring, names=name, normalize=True, category=category)
281 self.__generator = self.element_class(self, [0,1], is_gen=True)
282 self._populate_coercion_lists_(
283 #coerce_list = [base_inject],
284 #convert_list = [list, base_inject],
285 convert_method_name = '_polynomial_')
286 if is_PolynomialRing(base_ring):
287 self._Karatsuba_threshold = 0
288 else:
--> 289 from sage.matrix.matrix_space import is_MatrixSpace
global sage.matrix.matrix_space = undefined
is_MatrixSpace = undefined
290 if is_MatrixSpace(base_ring):
291 self._Karatsuba_threshold = 0
292 else:
293 self._Karatsuba_threshold = 8
294
295 def __reduce__(self):
296 import sage.rings.polynomial.polynomial_ring_constructor
297 return (sage.rings.polynomial.polynomial_ring_constructor.PolynomialRing,
298 (self.base_ring(), self.variable_name(), None, self.is_sparse()))
299
300
301 def _element_constructor_(self, x=None, check=True, is_gen = False, construct=False, **kwds):
302 r"""
303 Convert ``x`` into this univariate polynomial ring,
304 possibly non-canonically.
/usr/lib64/python2.7/site-packages/sage/matrix/matrix_space.pyc in <module>()
32 # http://www.gnu.org/licenses/
33 #*****************************************************************************
34 from __future__ import print_function
35 from __future__ import absolute_import
36
37 # System imports
38 import sys
39 import types
40 import operator
41
42 # Sage matrix imports
43 from . import matrix
44 from . import matrix_generic_dense
45 from . import matrix_generic_sparse
46
---> 47 from . import matrix_modn_sparse
global matrix_modn_sparse = undefined
48
49 from . import matrix_mod2_dense
50 from . import matrix_gf2e_dense
51
52 from . import matrix_integer_dense
53 from . import matrix_integer_sparse
54
55 from . import matrix_rational_dense
56 from . import matrix_rational_sparse
57
58 from . import matrix_mpolynomial_dense
59
60 # Sage imports
61 from sage.misc.superseded import deprecation
62 import sage.structure.coerce
/usr/lib64/python2.7/site-packages/sage/matrix/matrix_integer_dense.pxd in init sage.matrix.matrix_modn_sparse (/var/tmp/portage/sci-mathematics/sage-7.3/work/sage-7.3/src-python2_7/build/cythonized/sage/matrix/matrix_modn_sparse.c:19852)()
1 from sage.libs.gmp.types cimport *
2 from sage.libs.flint.fmpz cimport *
3 from sage.libs.flint.fmpz_mat cimport *
4
5 from .matrix_dense cimport Matrix_dense
6 from sage.rings.integer cimport Integer
7 from sage.ext.mod_int cimport *
8
9 ctypedef long* GEN
10
---> 11 cdef class Matrix_integer_dense(Matrix_dense):
global cdef = undefined
global Matrix_integer_dense = undefined
global Matrix_dense = undefined
12 cdef fmpz_mat_t _matrix # Always initialized in __cinit__
13 cdef bint _initialized_mpz
14 cdef mpz_t * _entries # Only used if _initialized_mpz
15 cdef mpz_t ** _rows # Only used if _initialized_mpz
16 cdef object _pivots
17 cdef int mpz_height(self, mpz_t height) except -1
18 cdef _mod_int_c(self, mod_int modulus)
19 cdef _mod_two(self)
20 cdef _pickle_version0(self)
21 cdef _unpickle_version0(self, data)
22 cpdef _export_as_string(self, int base=?)
23 cdef inline int _init_mpz(self) except -1
24 cdef int _init_mpz_impl(self) except -1
25 cdef inline int _init_linbox(self) except -1
26 cdef void _dealloc_mpz(self)
27 cdef void set_unsafe_mpz(self, Py_ssize_t i, Py_ssize_t j, const mpz_t value)
28 cdef void set_unsafe_si(self, Py_ssize_t i, Py_ssize_t j, long value)
29 cdef void set_unsafe_double(self, Py_ssize_t i, Py_ssize_t j, double value)
30 cdef inline void get_unsafe_mpz(self, Py_ssize_t i, Py_ssize_t j, mpz_t value)
31 cdef inline double get_unsafe_double(self, Py_ssize_t i, Py_ssize_t j)
/usr/lib64/python2.7/site-packages/sage/matrix/matrix_modn_dense_template_header.pxi in init sage.matrix.matrix_integer_dense (/var/tmp/portage/sci-mathematics/sage-7.3/work/sage-7.3/src-python2_7/build/cythonized/sage/matrix/matrix_integer_dense.cpp:53038)()
1 """
2 Dense Matrix Template for C/C++ Library Interfaces
3 """
4
5 from sage.ext.mod_int cimport *
6 from sage.matrix.matrix_dense cimport Matrix_dense
7
----> 8 cdef class Matrix_modn_dense_template(Matrix_dense):
global cdef = undefined
global Matrix_modn_dense_template = undefined
global Matrix_dense = undefined
9 cdef celement **_matrix
10 cdef celement *_entries
11 cdef mod_int p
12 cdef xgcd_eliminate (self, celement * row1, celement* row2, Py_ssize_t start_col)
13 cdef set_unsafe_int(self, Py_ssize_t i, Py_ssize_t j, int value)
14 cpdef _export_as_string(self)
15 cdef int _copy_row_to_mod_int_array(self, mod_int *to, Py_ssize_t i)
ImportError: /usr/lib64/python2.7/site-packages/sage/matrix/matrix_modn_dense_float.so: undefined symbol: cblas_dger
***************************************************************************
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