I'm running 5.11 (built from source-code). I went into the file
quadratic_form__local_field_invariants.py and added the line
from sage.rings.number_field.number_field import primes_above
Now when I try to run sage I get a crash message. I've attached the full
crash report. If I remove that line and rebuild sage it runs fine. Any
ideas why this would be? Outdated python or something? I appreciate any
help.
Thanks!
Anna
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***************************************************************************
IPython post-mortem report
{'commit_hash': '177894e',
'commit_source': 'installation',
'default_encoding': 'UTF-8',
'ipython_path':
'/Users/DrHanesch/sage-5.11/local/lib/python2.7/site-packages/IPython',
'ipython_version': '0.13.1',
'os_name': 'posix',
'platform': 'Darwin-12.5.0-x86_64-i386-64bit',
'sys_executable': '/Users/DrHanesch/sage-5.11/local/bin/python',
'sys_platform': 'darwin',
'sys_version': '2.7.5 (default, Aug 25 2013, 15:10:13) \n[GCC 4.7.3]'}
***************************************************************************
***************************************************************************
Crash traceback:
---------------------------------------------------------------------------
ImportError Python 2.7.5: /Users/DrHanesch/sage-5.11/local/bin/python
Thu Nov 14 15:23:11 2013
A problem occured executing Python code. Here is the sequence of function
calls leading up to the error, with the most recent (innermost) call last.
/Users/DrHanesch/sage-5.11/local/bin/sage-ipython in <module>()
2 # -*- coding: utf-8 -*-
3 """
4 Sage IPython startup script.
5 """
6 from sage.misc.interpreter import SageTerminalApp
7
8 # installs the extra readline commands before the IPython
initialization begins.
9 from sage.misc.readline_extra_commands import *
10
11 # Make sure we're using the Sage profile if one isn't specified.
12 import sys
13 if '--profile' not in sys.argv:
14 sys.argv.extend(['--profile', 'sage'])
15
16 app = SageTerminalApp.instance()
---> 17 app.initialize()
global app.initialize = <bound method SageTerminalApp.initialize of
<sage.misc.interpreter.SageTerminalApp object at 0x1087fc550>>
18 app.start()
/Users/DrHanesch/sage-5.11/local/lib/python2.7/site-packages/IPython/frontend/terminal/ipapp.pyc
in initialize(self=<sage.misc.interpreter.SageTerminalApp object>, argv=None)
/Users/DrHanesch/sage-5.11/local/lib/python2.7/site-packages/IPython/config/application.pyc
in catch_config_error(method=<function initialize>,
app=<sage.misc.interpreter.SageTerminalApp object>, *args=(None,), **kwargs={})
69
70
#-----------------------------------------------------------------------------
71 # Application class
72
#-----------------------------------------------------------------------------
73
74 @decorator
75 def catch_config_error(method, app, *args, **kwargs):
76 """Method decorator for catching invalid config
(Trait/ArgumentErrors) during init.
77
78 On a TraitError (generally caused by bad config), this will print
the trait's
79 message, and exit the app.
80
81 For use on init methods, to prevent invoking excepthook on invalid
input.
82 """
83 try:
---> 84 return method(app, *args, **kwargs)
method = <function initialize at 0x109b36140>
app = <sage.misc.interpreter.SageTerminalApp object at 0x1087fc550>
args = (None,)
kwargs = {}
85 except (TraitError, ArgumentError) as e:
86 app.print_description()
87 app.print_help()
88 app.print_examples()
89 app.log.fatal("Bad config encountered during initialization:")
90 app.log.fatal(str(e))
91 app.log.debug("Config at the time: %s", app.config)
92 app.exit(1)
93
94
95 class ApplicationError(Exception):
96 pass
97
98
99 class Application(SingletonConfigurable):
/Users/DrHanesch/sage-5.11/local/lib/python2.7/site-packages/IPython/frontend/terminal/ipapp.pyc
in initialize(self=<sage.misc.interpreter.SageTerminalApp object>, argv=None)
309
310 @catch_config_error
311 def initialize(self, argv=None):
312 """Do actions after construct, but before starting the app."""
313 super(TerminalIPythonApp, self).initialize(argv)
314 if self.subapp is not None:
315 # don't bother initializing further, starting subapp
316 return
317 if not self.ignore_old_config:
318 check_for_old_config(self.ipython_dir)
319 # print self.extra_args
320 if self.extra_args and not self.something_to_run:
321 self.file_to_run = self.extra_args[0]
322 self.init_path()
323 # create the shell
--> 324 self.init_shell()
self.init_shell = <bound method SageTerminalApp.init_shell of
<sage.misc.interpreter.SageTerminalApp object at 0x1087fc550>>
325 # and draw the banner
326 self.init_banner()
327 # Now a variety of things that happen after the banner is
printed.
328 self.init_gui_pylab()
329 self.init_extensions()
330 self.init_code()
331
332 def init_shell(self):
333 """initialize the InteractiveShell instance"""
334 # Create an InteractiveShell instance.
335 # shell.display_banner should always be False for the terminal
336 # based app, because we call shell.show_banner() by hand below
337 # so the banner shows *before* all extension loading stuff.
338 self.shell =
TerminalInteractiveShell.instance(config=self.config,
339 display_banner=False,
profile_dir=self.profile_dir,
/Users/DrHanesch/sage-5.11/local/lib/python2.7/site-packages/sage/misc/interpreter.pyc
in init_shell(self=<sage.misc.interpreter.SageTerminalApp object>)
720 sage: from sage.misc.interpreter import SageTerminalApp,
DEFAULT_SAGE_CONFIG
721 sage: app = SageTerminalApp(config=DEFAULT_SAGE_CONFIG)
722 sage: app.initialize(argv=[]) # indirect doctest
723 sage: app.shell
724 <sage.misc.interpreter.SageInteractiveShell object at 0x...>
725 """
726 # We need verbose crashes for the Sage crash handler. We set
it here
727 # so that we don't overwrite the traitlet attribute
728 self.verbose_crash = True
729
730 # Shell initialization
731 self.shell = SageInteractiveShell.instance(config=self.config,
732 display_banner=False,
profile_dir=self.profile_dir,
733 ipython_dir=self.ipython_dir)
734 self.shell.configurables.append(self)
--> 735
self.shell.extension_manager.load_extension('sage.misc.sage_extension')
self.shell.extension_manager.load_extension = <bound method
ExtensionManager.load_extension of <IPython.core.extensions.ExtensionManager
object at 0x109fd6710>>
/Users/DrHanesch/sage-5.11/local/lib/python2.7/site-packages/IPython/core/extensions.pyc
in load_extension(self=<IPython.core.extensions.ExtensionManager object>,
module_str='sage.misc.sage_extension')
75
76 def _on_ipython_dir_changed(self):
77 if not os.path.isdir(self.ipython_extension_dir):
78 os.makedirs(self.ipython_extension_dir, mode = 0777)
79
80 def load_extension(self, module_str):
81 """Load an IPython extension by its module name.
82
83 If :func:`load_ipython_extension` returns anything, this
function
84 will return that object.
85 """
86 from IPython.utils.syspathcontext import prepended_to_syspath
87
88 if module_str not in sys.modules:
89 with prepended_to_syspath(self.ipython_extension_dir):
---> 90 __import__(module_str)
global __import__ = undefined
module_str = 'sage.misc.sage_extension'
91 mod = sys.modules[module_str]
92 return self._call_load_ipython_extension(mod)
93
94 def unload_extension(self, module_str):
95 """Unload an IPython extension by its module name.
96
97 This function looks up the extension's name in ``sys.modules``
and
98 simply calls ``mod.unload_ipython_extension(self)``.
99 """
100 if module_str in sys.modules:
101 mod = sys.modules[module_str]
102 self._call_unload_ipython_extension(mod)
103
104 def reload_extension(self, module_str):
105 """Reload an IPython extension by calling reload.
/Users/DrHanesch/sage-5.11/local/lib/python2.7/site-packages/sage/misc/sage_extension.py
in <module>()
35 2
36
37 In contrast, input to the ``%time`` magic command is preparsed::
38
39 sage: shell.run_cell('%time 594.factor()')
40 CPU times: user ...
41 Wall time: ...
42 2 * 3^3 * 11
43 """
44
45 from IPython.core.hooks import TryNext
46 from IPython.core.magic import Magics, magics_class, line_magic
47 import os
48 import sys
49 import sage
---> 50 import sage.all
global sage.all = undefined
51 from sage.misc.interpreter import preparser
52 from sage.misc.preparser import preparse
53
54 @magics_class
55 class SageMagics(Magics):
56
57 @line_magic
58 def runfile(self, s):
59 r"""
60 Loads the code contained in the file ``s``. This is designed
61 to be used from the command line as ``%runfile /path/to/file``.
62
63 :param s: file to be loaded
64 :type s: string
65
/Users/DrHanesch/sage-5.11/local/lib/python2.7/site-packages/sage/all.py in
<module>()
84 from sage.misc.sh import sh
85
86 from sage.libs.all import *
87 from sage.doctest.all import *
88
89 from sage.rings.all import *
90 from sage.matrix.all import *
91
92 # This must come before Calculus -- it initializes the Pynac library.
93 import sage.symbolic.pynac
94
95 from sage.modules.all import *
96 from sage.monoids.all import *
97 from sage.algebras.all import *
98 from sage.modular.all import *
---> 99 from sage.schemes.all import *
global sage.schemes.all = undefined
100 from sage.graphs.all import *
101 from sage.groups.all import *
102 from sage.databases.all import *
103 from sage.structure.all import *
104 from sage.categories.all import *
105 from sage.sets.all import *
106 from sage.probability.all import *
107 from sage.interfaces.all import *
108
109 from sage.symbolic.all import *
110
111 from sage.functions.all import *
112 from sage.calculus.all import *
113
114 from sage.server.all import *
/Users/DrHanesch/sage-5.11/local/lib/python2.7/site-packages/sage/schemes/all.py
in <module>()
10 #
11 # Distributed under the terms of the GNU General Public License (GPL)
12 #
13 # This code is distributed in the hope that it will be useful,
14 # but WITHOUT ANY WARRANTY; without even the implied warranty of
15 # MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
16 # General Public License for more details.
17 #
18 # The full text of the GPL is available at:
19 #
20 # http://www.gnu.org/licenses/
21
#*****************************************************************************
22
23 from jacobians.all import *
24
---> 25 from hyperelliptic_curves.all import *
global hyperelliptic_curves.all = undefined
26
27 from plane_curves.all import *
28
29 from plane_conics.all import *
30
31 from elliptic_curves.all import *
32
33 from plane_quartics.all import *
34
35 from generic.all import *
36
37 from toric.all import *
38
39 from affine.all import *
40
/Users/DrHanesch/sage-5.11/local/lib/python2.7/site-packages/sage/schemes/hyperelliptic_curves/__init__.py
in <module>()
----> 1 import all
global all = undefined
/Users/DrHanesch/sage-5.11/local/lib/python2.7/site-packages/sage/schemes/hyperelliptic_curves/all.py
in <module>()
----> 1 from constructor import HyperellipticCurve
global constructor = undefined
global HyperellipticCurve = undefined
2 from hyperelliptic_generic import is_HyperellipticCurve
3 from kummer_surface import KummerSurface
4 from invariants import (igusa_clebsch_invariants,
5 absolute_igusa_invariants_kohel,
6 absolute_igusa_invariants_wamelen,
7 clebsch_invariants)
/Users/DrHanesch/sage-5.11/local/lib/python2.7/site-packages/sage/schemes/hyperelliptic_curves/constructor.py
in <module>()
1 """
2 Hyperelliptic curve constructor
3 """
4
5
#*****************************************************************************
6 # Copyright (C) 2006 David Kohel <ko...@maths.usyd.edu>
7 # Distributed under the terms of the GNU General Public License (GPL)
8 # http://www.gnu.org/licenses/
9
#*****************************************************************************
10
11 from sage.schemes.projective.projective_space import ProjectiveSpace
12
---> 13 from hyperelliptic_generic import HyperellipticCurve_generic
global hyperelliptic_generic = undefined
global HyperellipticCurve_generic = undefined
14 from hyperelliptic_finite_field import HyperellipticCurve_finite_field
15 from hyperelliptic_rational_field import
HyperellipticCurve_rational_field
16 from hyperelliptic_padic_field import HyperellipticCurve_padic_field
17 from hyperelliptic_g2_generic import HyperellipticCurve_g2_generic
18 from hyperelliptic_g2_finite_field import
HyperellipticCurve_g2_finite_field
19 from hyperelliptic_g2_rational_field import
HyperellipticCurve_g2_rational_field
20 from hyperelliptic_g2_padic_field import
HyperellipticCurve_g2_padic_field
21
22 from sage.rings.all import is_FiniteField, is_RationalField,
is_Polynomial, is_pAdicField
23
24 def HyperellipticCurve(f, h=None, names=None, PP=None,
check_squarefree=True):
25 r"""
26 Returns the hyperelliptic curve `y^2 + h y = f`, for
27 univariate polynomials `h` and `f`. If `h`
28 is not given, then it defaults to 0.
29
30 INPUT:
31
/Users/DrHanesch/sage-5.11/local/lib/python2.7/site-packages/sage/schemes/hyperelliptic_curves/hyperelliptic_generic.py
in <module>()
19
20 sage: D = C.affine_patch(0)
21 sage: D.defining_polynomials()[0].parent()
22 Multivariate Polynomial Ring in x0, x1 over Rational Field
23 """
24
25
#*****************************************************************************
26 # Copyright (C) 2006 David Kohel <ko...@maths.usyd.edu>
27 # Distributed under the terms of the GNU General Public License (GPL)
28 # http://www.gnu.org/licenses/
29
#*****************************************************************************
30
31 from sage.rings.all import PolynomialRing, RR, PowerSeriesRing,
LaurentSeriesRing, O
32 from sage.functions.all import log
33
---> 34 import sage.schemes.plane_curves.projective_curve as plane_curve
global sage.schemes.plane_curves.projective_curve = undefined
global plane_curve = undefined
35
36 def is_HyperellipticCurve(C):
37 """
38 EXAMPLES::
39
40 sage: R.<x> = QQ[]; C = HyperellipticCurve(x^3 + x - 1); C
41 Hyperelliptic Curve over Rational Field defined by y^2 = x^3 +
x - 1
42 sage:
sage.schemes.hyperelliptic_curves.hyperelliptic_generic.is_HyperellipticCurve(C)
43 True
44 """
45 return isinstance(C,HyperellipticCurve_generic)
46
47 class HyperellipticCurve_generic(plane_curve.ProjectiveCurve_generic):
48 def __init__(self, PP, f, h=None, names=None, genus=None):
49 x, y, z = PP.gens()
/Users/DrHanesch/sage-5.11/local/lib/python2.7/site-packages/sage/schemes/plane_curves/__init__.py
in <module>()
----> 1 import all
global all = undefined
/Users/DrHanesch/sage-5.11/local/lib/python2.7/site-packages/sage/schemes/plane_curves/all.py
in <module>()
8 #
9 # Copyright (C) 2005 William Stein <w...@math.harvard.edu>
10 #
11 # Distributed under the terms of the GNU General Public License (GPL)
12 #
13 # This code is distributed in the hope that it will be useful,
14 # but WITHOUT ANY WARRANTY; without even the implied warranty of
15 # MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
16 # General Public License for more details.
17 #
18 # The full text of the GPL is available at:
19 #
20 # http://www.gnu.org/licenses/
21
#*****************************************************************************
22
---> 23 from constructor import Curve
global constructor = undefined
global Curve = undefined
24
25 from projective_curve import Hasse_bounds
26
/Users/DrHanesch/sage-5.11/local/lib/python2.7/site-packages/sage/schemes/plane_curves/constructor.py
in <module>()
32 from sage.schemes.affine.all import AffineSpace
33
34 from sage.schemes.projective.all import ProjectiveSpace
35
36
37 from projective_curve import (ProjectiveCurve_generic,
38 ProjectiveSpaceCurve_generic,
39 ProjectiveCurve_finite_field,
40 ProjectiveCurve_prime_finite_field)
41
42 from affine_curve import (AffineCurve_generic,
43 AffineSpaceCurve_generic,
44 AffineCurve_finite_field,
45 AffineCurve_prime_finite_field)
46
---> 47 from sage.schemes.plane_conics.constructor import Conic
global sage.schemes.plane_conics.constructor = undefined
global Conic = undefined
48
49 def Curve(F):
50 """
51 Return the plane or space curve defined by `F`, where
52 `F` can be either a multivariate polynomial, a list or
53 tuple of polynomials, or an algebraic scheme.
54
55 If `F` is in two variables the curve is affine, and if it
56 is homogenous in `3` variables, then the curve is
57 projective.
58
59 EXAMPLE: A projective plane curve
60
61 ::
62
/Users/DrHanesch/sage-5.11/local/lib/python2.7/site-packages/sage/schemes/plane_conics/__init__.py
in <module>()
----> 1 import all
global all = undefined
/Users/DrHanesch/sage-5.11/local/lib/python2.7/site-packages/sage/schemes/plane_conics/all.py
in <module>()
8 #
9 # Copyright (C) 2005 William Stein <w...@math.harvard.edu>
10 #
11 # Distributed under the terms of the GNU General Public License (GPL)
12 #
13 # This code is distributed in the hope that it will be useful,
14 # but WITHOUT ANY WARRANTY; without even the implied warranty of
15 # MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
16 # General Public License for more details.
17 #
18 # The full text of the GPL is available at:
19 #
20 # http://www.gnu.org/licenses/
21
#*****************************************************************************
22
---> 23 from constructor import Conic
global constructor = undefined
global Conic = undefined
24
25
/Users/DrHanesch/sage-5.11/local/lib/python2.7/site-packages/sage/schemes/plane_conics/constructor.py
in <module>()
14 #
15 # Distributed under the terms of the GNU General Public License (GPL)
16 #
17 # This code is distributed in the hope that it will be useful,
18 # but WITHOUT ANY WARRANTY; without even the implied warranty of
19 # MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
20 # General Public License for more details.
21 #
22 # The full text of the GPL is available at:
23 #
24 # http://www.gnu.org/licenses/
25
#*****************************************************************************
26
27 from sage.matrix.constructor import Matrix
28 from sage.modules.free_module_element import vector
---> 29 from sage.quadratic_forms.all import is_QuadraticForm
global sage.quadratic_forms.all = undefined
global is_QuadraticForm = undefined
30 from sage.rings.all import (is_MPolynomial, PolynomialRing,
31 is_IntegralDomain, is_FiniteField,
32 is_PrimeFiniteField,
33 is_RationalField)
34 from sage.rings.number_field.number_field import is_NumberField
35 from sage.schemes.projective.projective_space import ProjectiveSpace
36 from sage.schemes.projective.projective_point import
SchemeMorphism_point_projective_field
37 from sage.schemes.affine.affine_point import SchemeMorphism_point_affine
38 from sage.structure.all import Sequence
39 from sage.structure.element import is_Matrix
40
41 from con_field import ProjectiveConic_field
42 from con_finite_field import ProjectiveConic_finite_field
43 from con_prime_finite_field import ProjectiveConic_prime_finite_field
44 from con_number_field import ProjectiveConic_number_field
/Users/DrHanesch/sage-5.11/local/lib/python2.7/site-packages/sage/quadratic_forms/__init__.py
in <module>()
----> 1 import all
global all = undefined
/Users/DrHanesch/sage-5.11/local/lib/python2.7/site-packages/sage/quadratic_forms/all.py
in <module>()
1 from binary_qf import BinaryQF, BinaryQF_reduced_representatives
2
----> 3 from ternary_qf import TernaryQF, find_all_ternary_qf_by_level_disc,
find_a_ternary_qf_by_level_disc
global ternary_qf = undefined
global TernaryQF = undefined
global find_all_ternary_qf_by_level_disc = undefined
global find_a_ternary_qf_by_level_disc = undefined
4
5 from quadratic_form import QuadraticForm, DiagonalQuadraticForm,
is_QuadraticForm
6
7 from random_quadraticform import random_quadraticform,
random_quadraticform_with_conditions, random_ternaryqf,
random_ternaryqf_with_conditions
8
9 from extras import least_quadratic_nonresidue, extend_to_primitive,
is_triangular_number
10
11 from special_values import gamma__exact, zeta__exact,
QuadraticBernoulliNumber, \
12 quadratic_L_function__exact, quadratic_L_function__numerical
13
14 from genera.genus import is_GlobalGenus, is_2_adic_genus
15 #is_trivial_symbol
16
17 from constructions import BezoutianQuadraticForm,
HyperbolicPlane_quadratic_form
18
/Users/DrHanesch/sage-5.11/local/lib/python2.7/site-packages/sage/quadratic_forms/ternary_qf.py
in <module>()
18 #
19 # This code is distributed in the hope that it will be useful,
20 # but WITHOUT ANY WARRANTY; without even the implied warranty of
21 # MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
22 # General Public License for more details.
23 #
24 # The full text of the GPL is available at:
25 #
26 # http://www.gnu.org/licenses/
27
#*****************************************************************************
28
29
30 from sage.structure.sage_object import SageObject
31 from sage.rings.all import ZZ
32 from sage.rings.arith import gcd, inverse_mod, kronecker_symbol
---> 33 from sage.quadratic_forms.quadratic_form import QuadraticForm
global sage.quadratic_forms.quadratic_form = undefined
global QuadraticForm = undefined
34 from sage.matrix.constructor import matrix, identity_matrix
35 from sage.matrix.matrix import Matrix, is_Matrix
36 from sage.structure.element import is_Vector
37 from sage.quadratic_forms.ternary import
_reduced_ternary_form_eisenstein_with_matrix
38 from sage.quadratic_forms.ternary import
_reduced_ternary_form_eisenstein_without_matrix, _find_zeros_mod_p_odd,
_find_zeros_mod_p_2, _find_p_neighbor_from_vec, _basic_lemma
39 from sage.quadratic_forms.ternary import
_find_all_ternary_qf_by_level_disc, _find_a_ternary_qf_by_level_disc
40 from sage.misc.prandom import randint
41 from sage.rings.finite_rings.integer_mod import mod
42 from sage.modules.free_module_element import vector
43 from sage.rings.ring import is_Ring
44 from sage.rings.rational_field import QQ
45 from sage.rings.polynomial.polynomial_ring import polygen, polygens
46
47 class TernaryQF(SageObject):
48 """
/Users/DrHanesch/sage-5.11/local/lib/python2.7/site-packages/sage/quadratic_forms/quadratic_form.py
in <module>()
68 Determines if the object Q is an element of the QuadraticForm class.
69
70 EXAMPLES::
71
72 sage: Q = QuadraticForm(ZZ, 2, [1,2,3])
73 sage: is_QuadraticForm(Q) ##random -- deprecated
74 True
75 sage: is_QuadraticForm(2) ##random -- deprecated
76 False
77
78 """
79 return isinstance(Q, QuadraticForm)
80
81
82
---> 83 class QuadraticForm(SageObject):
global QuadraticForm = undefined
global SageObject = None
84 r"""
85 The ``QuadraticForm`` class represents a quadratic form in n
variables with
86 coefficients in the ring R.
87
88 INPUT:
89
90 The constructor may be called in any of the following ways.
91
92 #. ``QuadraticForm(R, n, entries)``, where
93
94 - `R` -- ring for which the quadratic form is defined
95 - `n` -- an integer >= 0
96 - ``entries`` -- a list of `n(n+1)/2` coefficients of the
quadratic form
97 in `R` (given lexographically, or equivalently, by rows of the
matrix)
98
/Users/DrHanesch/sage-5.11/local/lib/python2.7/site-packages/sage/quadratic_forms/quadratic_form.py
in QuadraticForm()
198 local_normal_form, \
199 jordan_blocks_by_scale_and_unimodular, \
200 jordan_blocks_in_unimodular_list_by_scale_power
201
202 ## Routines to perform elementary variable substitutions
203 from sage.quadratic_forms.quadratic_form__variable_substitutions
import \
204 swap_variables, \
205 multiply_variable, \
206 divide_variable, \
207 scale_by_factor, \
208 extract_variables, \
209 elementary_substitution, \
210 add_symmetric
211
212 ## Routines to compute p-adic field invariants
--> 213 from sage.quadratic_forms.quadratic_form__local_field_invariants
import \
global sage.quadratic_forms.quadratic_form__local_field_invariants =
undefined
global rational_diagonal_form = undefined
global signature_vector = undefined
global signature = undefined
global hasse_invariant = undefined
global hasse_invariant__OMeara = undefined
global hasse_invariant__numfield = undefined
global is_hyperbolic = undefined
global is_anisotropic = undefined
global is_isotropic = undefined
global anisotropic_primes = undefined
global compute_definiteness = undefined
global compute_definiteness_string_by_determinants = undefined
global is_positive_definite = undefined
global is_negative_definite = undefined
global is_indefinite = undefined
global is_definite = undefined
214 rational_diagonal_form, \
215 signature_vector, \
216 signature, \
217 hasse_invariant, \
218 hasse_invariant__OMeara, \
219 hasse_invariant__numfield, \
220 is_hyperbolic, \
221 is_anisotropic, \
222 is_isotropic, \
223 anisotropic_primes, \
224 compute_definiteness, \
225 compute_definiteness_string_by_determinants, \
226 is_positive_definite, \
227 is_negative_definite, \
228 is_indefinite, \
/Users/DrHanesch/sage-5.11/local/lib/python2.7/site-packages/sage/quadratic_forms/quadratic_form__local_field_invariants.py
in <module>()
16 # http://www.gnu.org/licenses/
17
#*****************************************************************************
18
19
20
###########################################################################
21 ## TO DO: Add routines for hasse invariants at all places, anisotropic
22 ## places, is_semi_definite, and support for number fields.
23
###########################################################################
24
25
26 import copy
27
28 from sage.rings.integer_ring import ZZ
29 from sage.rings.rational_field import QQ
30 from sage.rings.real_mpfr import RR
---> 31 from sage.rings.number_field.number_field import primes_above
global sage.rings.number_field.number_field = undefined
global primes_above = undefined
32 from sage.rings.arith import prime_divisors, hilbert_symbol
33 from sage.functions.all import sgn
34 from sage.rings.fraction_field import FractionField
35 from sage.matrix.matrix_space import MatrixSpace
36
37
38 ## Routines to compute local (p-adic) invariants of a quadratic form Q:
39 ## (Note: Here Q is the matrix so that Q(x) = x^t * Q * x.)
40 ## --------------------------------------------------------------------
41
42 def rational_diagonal_form(self, return_matrix=False):
43 """
44 Returns a diagonal form equivalent to Q over the fraction field of
45 its defining ring. If the return_matrix is True, then we return
46 the transformation matrix performing the diagonalization as the
ImportError: cannot import name primes_above
***************************************************************************
History of session input:
*** Last line of input (may not be in above history):
