Thank you for your advice, I tried to reinstall python3 from Homebrew, but
it still doesn't work. After I reinstall/upgrade python 3 and gsl from
Homebrew, my working directory sage 9.6 crashed. My laptop is MacBook Pro
with M1 chip with MacOS Big
Sur version11.4. Thanks for any suggestion and help!
Sincerely,
Yueqi
On Sunday, July 17, 2022 at 5:57:55 AM UTC-4 [email protected] wrote:
> I recommend that you do as recommended in the
> output of ./configure, and install python3 from Homebrew
>
> On Sun, 17 Jul 2022, 08:59 Yueqi Li, <[email protected]> wrote:
>
>> Dear Prof. Koeppe,
>>
>> Thank you so much for your help! After I run "brew install gsl," I was
>> not able to run any doctes. Then I try to run ./configure and make to fix
>> it. But it dosen't work, and I had error while I make it. I attached the
>> configure information, make error and doctest error with this massage.
>>
>> Thank you for any help you may have!
>>
>> Sincerely,
>> Yueqi
>>
>> --
>> You received this message because you are subscribed to the Google Groups
>> "sage-devel" group.
>> To unsubscribe from this group and stop receiving emails from it, send an
>> email to [email protected].
>> To view this discussion on the web visit
>> https://groups.google.com/d/msgid/sage-devel/c407887f-201a-43d5-908b-44af013781c6n%40googlegroups.com
>>
>> <https://groups.google.com/d/msgid/sage-devel/c407887f-201a-43d5-908b-44af013781c6n%40googlegroups.com?utm_medium=email&utm_source=footer>
>> .
>>
>
--
You received this message because you are subscribed to the Google Groups
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***************************************************************************
IPython post-mortem report
{'commit_hash': 'bf6aeb906d',
'commit_source': 'installation',
'default_encoding': 'utf-8',
'ipython_path':
'/Users/yueqili/sage-9.5/local/var/lib/sage/venv-python3.10.3/lib/python3.10/site-packages/IPython',
'ipython_version': '7.29.0',
'os_name': 'posix',
'platform': 'macOS-11.4-arm64-arm-64bit',
'sys_executable':
'/Users/yueqili/sage-9.5/local/var/lib/sage/venv-python3.10.3/bin/python3',
'sys_platform': 'darwin',
'sys_version': '3.10.3 (main, Jun 29 2022, 02:14:46) [Clang 13.0.0 '
'(clang-1300.0.29.30)]'}
***************************************************************************
***************************************************************************
Crash traceback:
---------------------------------------------------------------------------
---------------------------------------------------------------------------
ImportErrorPython 3.10.3:
/Users/yueqili/sage-9.5/local/var/lib/sage/venv-python3.10.3/bin/python3
Mon Jul 18 01:30:42 2022
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.
~/sage-9.5/src/bin/sage-ipython in <module>
1 #!/usr/bin/env sage-python
2 # -*- coding: utf-8 -*-
3 """
4 Sage IPython startup script.
5 """
6
7 # Display startup banner. Do this before anything else to give the user
8 # early feedback that Sage is starting.
9 from sage.misc.banner import banner
10 banner()
11
12 from sage.repl.interpreter import SageTerminalApp
13
14 app = SageTerminalApp.instance()
---> 15 app.initialize()
global app.initialize = <bound method TerminalIPythonApp.initialize of
<sage.repl.interpreter.SageTerminalApp object at 0x104747130>>
16 app.start()
~/sage-9.5/local/var/lib/sage/venv-python3.10.3/lib/python3.10/site-packages/traitlets/config/application.py
in inner(app=<sage.repl.interpreter.SageTerminalApp object>, *args=(),
**kwargs={})
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 def catch_config_error(method):
78 """Method decorator for catching invalid config
(Trait/ArgumentErrors) during init.
79
80 On a TraitError (generally caused by bad config), this will print
the trait's
81 message, and exit the app.
82
83 For use on init methods, to prevent invoking excepthook on invalid
input.
84 """
85 @functools.wraps(method)
86 def inner(app, *args, **kwargs):
87 try:
---> 88 return method(app, *args, **kwargs)
global method = undefined
app = <sage.repl.interpreter.SageTerminalApp object at 0x104747130>
args = ()
kwargs = {}
89 except (TraitError, ArgumentError) as e:
90 app.log.fatal("Bad config encountered during
initialization: %s", e)
91 app.log.debug("Config at the time: %s", app.config)
92 app.exit(1)
93
94 return inner
95
96 class ApplicationError(Exception):
97 pass
98
99
100 class LevelFormatter(logging.Formatter):
101 """Formatter with additional `highlevel` record
102
103 This field is empty if log level is less than highlevel_limit,
~/sage-9.5/local/var/lib/sage/venv-python3.10.3/lib/python3.10/site-packages/IPython/terminal/ipapp.py
in initialize(self=<sage.repl.interpreter.SageTerminalApp object>, argv=None)
302
303 return super(TerminalIPythonApp, self).parse_command_line(argv)
304
305 @catch_config_error
306 def initialize(self, argv=None):
307 """Do actions after construct, but before starting the app."""
308 super(TerminalIPythonApp, self).initialize(argv)
309 if self.subapp is not None:
310 # don't bother initializing further, starting subapp
311 return
312 # print self.extra_args
313 if self.extra_args and not self.something_to_run:
314 self.file_to_run = self.extra_args[0]
315 self.init_path()
316 # create the shell
--> 317 self.init_shell()
self.init_shell = <bound method SageTerminalApp.init_shell of
<sage.repl.interpreter.SageTerminalApp object at 0x104747130>>
318 # and draw the banner
319 self.init_banner()
320 # Now a variety of things that happen after the banner is
printed.
321 self.init_gui_pylab()
322 self.init_extensions()
323 self.init_code()
324
325 def init_shell(self):
326 """initialize the InteractiveShell instance"""
327 # Create an InteractiveShell instance.
328 # shell.display_banner should always be False for the terminal
329 # based app, because we call shell.show_banner() by hand below
330 # so the banner shows *before* all extension loading stuff.
331 self.shell = self.interactive_shell_class.instance(parent=self,
332 profile_dir=self.profile_dir,
~/sage-9.5/local/var/lib/sage/venv-python3.10.3/lib/python3.10/site-packages/sage/repl/interpreter.py
in init_shell(self=<sage.repl.interpreter.SageTerminalApp object>)
772
773 # Load the %lprun extension if available
774 try:
775 import line_profiler
776 assert line_profiler # silence pyflakes
777 except ImportError:
778 pass
779 else:
780 self.extensions.append('line_profiler')
781
782 if self.shell.has_sage_extensions:
783 self.extensions.remove(SAGE_EXTENSION)
784
785 # load sage extension here to get a crash if
786 # something is wrong with the sage library
--> 787 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 0x107e276d0>>
global SAGE_EXTENSION = 'sage'
~/sage-9.5/local/var/lib/sage/venv-python3.10.3/lib/python3.10/site-packages/IPython/core/extensions.py
in load_extension(self=<IPython.core.extensions.ExtensionManager object>,
module_str='sage')
72 if module_str in self.loaded:
73 return "already loaded"
74
75 from IPython.utils.syspathcontext import prepended_to_syspath
76
77 with self.shell.builtin_trap:
78 if module_str not in sys.modules:
79 with prepended_to_syspath(self.ipython_extension_dir):
80 mod = import_module(module_str)
81 if
mod.__file__.startswith(self.ipython_extension_dir):
82 print(("Loading extensions from {dir} is
deprecated. "
83 "We recommend managing extensions like
any "
84 "other Python packages, in
site-packages.").format(
85
dir=compress_user(self.ipython_extension_dir)))
86 mod = sys.modules[module_str]
---> 87 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 0x107e276d0>>
mod = <module 'sage' from
'/Users/yueqili/sage-9.5/local/var/lib/sage/venv-python3.10.3/lib/python3.10/site-packages/sage/__init__.py'>
88 self.loaded.add(module_str)
89 else:
90 return "no load function"
91
92 def unload_extension(self, module_str):
93 """Unload an IPython extension by its module name.
94
95 This function looks up the extension's name in ``sys.modules``
and
96 simply calls ``mod.unload_ipython_extension(self)``.
97
98 Returns the string "no unload function" if the extension
doesn't define
99 a function to unload itself, "not loaded" if the extension
isn't loaded,
100 otherwise None.
101 """
102 if module_str not in self.loaded:
~/sage-9.5/local/var/lib/sage/venv-python3.10.3/lib/python3.10/site-packages/IPython/core/extensions.py
in _call_load_ipython_extension(self=<IPython.core.extensions.ExtensionManager
object>, mod=<module 'sage' from
'/Users/yueqili/sage-9.5/loc...3/lib/python3.10/site-packages/sage/__init__.py'>)
119 """
120 from IPython.utils.syspathcontext import prepended_to_syspath
121
122 if (module_str in self.loaded) and (module_str in sys.modules):
123 self.unload_extension(module_str)
124 mod = sys.modules[module_str]
125 with prepended_to_syspath(self.ipython_extension_dir):
126 reload(mod)
127 if self._call_load_ipython_extension(mod):
128 self.loaded.add(module_str)
129 else:
130 self.load_extension(module_str)
131
132 def _call_load_ipython_extension(self, mod):
133 if hasattr(mod, 'load_ipython_extension'):
--> 134 mod.load_ipython_extension(self.shell)
mod.load_ipython_extension = <function load_ipython_extension at
0x104947eb0>
self.shell = <sage.repl.interpreter.SageTerminalInteractiveShell object
at 0x1063c21d0>
135 return True
136
137 def _call_unload_ipython_extension(self, mod):
138 if hasattr(mod, 'unload_ipython_extension'):
139 mod.unload_ipython_extension(self.shell)
140 return True
141
142 @undoc
143 def install_extension(self, url, filename=None):
144 """
145 Deprecated.
146 """
147 # Ensure the extension directory exists
148 raise DeprecationWarning(
149 '`install_extension` and the `install_ext` magic have been
deprecated since IPython 4.0'
~/sage-9.5/local/var/lib/sage/venv-python3.10.3/lib/python3.10/site-packages/sage/repl/__init__.py
in
load_ipython_extension(*args=(<sage.repl.interpreter.SageTerminalInteractiveShell
object>,))
1 # IPython calls this when "%load_ext sage.repl" is used.
2 # The Sage application loads it when starting up.
3 def load_ipython_extension(*args):
4 import sage.repl.ipython_extension
----> 5 sage.repl.ipython_extension.load_ipython_extension(*args)
sage.repl.ipython_extension.load_ipython_extension = <function
load_ipython_extension at 0x1080364d0>
args = (<sage.repl.interpreter.SageTerminalInteractiveShell object at
0x1063c21d0>,)
6
7
8 # The above used to be in sage.__init__, allowing users to use
"%load_ext sage".
9 # But we are clearing out the __init__.py file as a preparation for
10 # making sage a native namespace package.
11 #
12 # So we make "%load_ext sage" work by monkey-patching the function
13 # into the sage package upon importing sage.repl.
14 import sage
15 sage.load_ipython_extension = load_ipython_extension
~/sage-9.5/local/var/lib/sage/venv-python3.10.3/lib/python3.10/site-packages/sage/repl/ipython_extension.py
in wrapper(*args=(<sage.repl.interpreter.SageTerminalInteractiveShell
object>,), **kwargs={})
591 ....: if work:
592 ....: return 'foo worked'
593 ....: raise RuntimeError("foo didn't work")
594 sage: foo(False)
595 Traceback (most recent call last):
596 ...
597 RuntimeError: foo didn't work
598 sage: foo(True)
599 'foo worked'
600 sage: foo(False)
601 sage: foo(True)
602 """
603 @wraps(func)
604 def wrapper(*args, **kwargs):
605 if not wrapper.has_run:
--> 606 result = func(*args, **kwargs)
result = undefined
global func = undefined
args = (<sage.repl.interpreter.SageTerminalInteractiveShell object at
0x1063c21d0>,)
kwargs = {}
607 wrapper.has_run = True
608 return result
609 wrapper.has_run = False
610 return wrapper
611
612
613 @run_once
614 def load_ipython_extension(ip):
615 """
616 Load the extension in IPython.
617 """
618 # this modifies ip
619 SageCustomizations(shell=ip)
~/sage-9.5/local/var/lib/sage/venv-python3.10.3/lib/python3.10/site-packages/sage/repl/ipython_extension.py
in
load_ipython_extension(ip=<sage.repl.interpreter.SageTerminalInteractiveShell
object>)
604 def wrapper(*args, **kwargs):
605 if not wrapper.has_run:
606 result = func(*args, **kwargs)
607 wrapper.has_run = True
608 return result
609 wrapper.has_run = False
610 return wrapper
611
612
613 @run_once
614 def load_ipython_extension(ip):
615 """
616 Load the extension in IPython.
617 """
618 # this modifies ip
--> 619 SageCustomizations(shell=ip)
global SageCustomizations = <class
'sage.repl.ipython_extension.SageCustomizations'>
global shell = undefined
ip = <sage.repl.interpreter.SageTerminalInteractiveShell object at
0x1063c21d0>
~/sage-9.5/local/var/lib/sage/venv-python3.10.3/lib/python3.10/site-packages/sage/repl/ipython_extension.py
in __init__(self=<sage.repl.ipython_extension.SageCustomizations object>,
shell=<sage.repl.interpreter.SageTerminalInteractiveShell object>)
419 def __init__(self, shell=None):
420 """
421 Initialize the Sage plugin.
422 """
423 self.shell = shell
424
425 self.auto_magics = SageMagics(shell)
426 self.shell.register_magics(self.auto_magics)
427
428 import sage.misc.edit_module as edit_module
429 self.shell.set_hook('editor', edit_module.edit_devel)
430
431 self.init_inspector()
432 self.init_line_transforms()
433
--> 434 import sage.all # until sage's import hell is fixed
sage.all = undefined
435
436 self.shell.verbose_quit = True
437
438 self.register_interface_magics()
439
440 if SAGE_IMPORTALL == 'yes':
441 self.init_environment()
442
443 def register_interface_magics(self):
444 """
445 Register magics for each of the Sage interfaces
446 """
447 from sage.repl.interface_magic import InterfaceMagic
448 InterfaceMagic.register_all(self.shell)
449
~/sage-9.5/local/var/lib/sage/venv-python3.10.3/lib/python3.10/site-packages/sage/all.py
in <module>
123
124 from sage.misc.sh import sh
125
126 from sage.libs.all import *
127 from sage.data_structures.all import *
128 from sage.doctest.all import *
129
130 from sage.structure.all import *
131 from sage.rings.all import *
132 from sage.arith.all import *
133 from sage.matrix.all import *
134
135 from sage.symbolic.all import *
136 from sage.modules.all import *
137 from sage.monoids.all import *
--> 138 from sage.algebras.all import *
global sage.algebras.all = undefined
139 from sage.modular.all import *
140 from sage.sat.all import *
141 from sage.schemes.all import *
142 from sage.graphs.all import *
143 from sage.groups.all import *
144 from sage.arith.power import generic_power as power
145 from sage.databases.all import *
146 from sage.categories.all import *
147 from sage.sets.all import *
148 from sage.probability.all import *
149 from sage.interfaces.all import *
150
151 from sage.functions.all import *
152 from sage.calculus.all import *
153
~/sage-9.5/local/var/lib/sage/venv-python3.10.3/lib/python3.10/site-packages/sage/algebras/all.py
in <module>
6 # Copyright (C) 2005 William Stein <[email protected]>
7 #
8 # Distributed under the terms of the GNU General Public License (GPL)
9 #
10 # This code is distributed in the hope that it will be useful,
11 # but WITHOUT ANY WARRANTY; without even the implied warranty of
12 # MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
13 # General Public License for more details.
14 #
15 # The full text of the GPL is available at:
16 #
17 # http://www.gnu.org/licenses/
18
#*****************************************************************************
19 from sage.misc.lazy_import import lazy_import
20
---> 21 import sage.algebras.catalog as algebras
global sage.algebras.catalog = undefined
global algebras = undefined
22
23 from .quantum_groups.all import *
24 from .quatalg.all import *
25
26 # Algebra base classes
27 from .algebra import Algebra
28 from .free_algebra import FreeAlgebra
29 from .free_algebra_quotient import FreeAlgebraQuotient
30
31 from .steenrod.all import *
32 from .lie_algebras.all import *
33 from .quantum_groups.all import *
34 from .lie_conformal_algebras.all import *
35
36 from .finite_dimensional_algebras.all import FiniteDimensionalAlgebra
~/sage-9.5/local/var/lib/sage/venv-python3.10.3/lib/python3.10/site-packages/sage/algebras/catalog.py
in <module>
69 - :class:`algebras.Steenrod
70 <sage.algebras.steenrod.steenrod_algebra.SteenrodAlgebra>`
71 - :class:`algebras.TemperleyLieb
<sage.combinat.diagram_algebras.TemperleyLiebAlgebra>`
72 - :class:`algebras.WQSym
<sage.combinat.chas.wqsym.WordQuasiSymmetricFunctions>`
73 - :class:`algebras.Yangian <sage.algebras.yangian.Yangian>`
74 - :class:`algebras.YokonumaHecke
75 <sage.algebras.yokonuma_hecke_algebra.YokonumaHeckeAlgebra>`
76 - :class:`algebras.Tensor <sage.algebras.tensor_algebra.TensorAlgebra>`
77 """
78
79 from sage.algebras.free_algebra import FreeAlgebra as Free
80 from sage.algebras.quatalg.quaternion_algebra import QuaternionAlgebra
as Quaternion
81 from sage.algebras.steenrod.steenrod_algebra import SteenrodAlgebra as
Steenrod
82 from
sage.algebras.finite_dimensional_algebras.finite_dimensional_algebra import
FiniteDimensionalAlgebra as FiniteDimensional
83 from sage.algebras.group_algebra import GroupAlgebra as Group
---> 84 from sage.algebras.clifford_algebra import CliffordAlgebra as Clifford
global sage.algebras.clifford_algebra = undefined
global CliffordAlgebra = undefined
global Clifford = undefined
85 from sage.algebras.clifford_algebra import ExteriorAlgebra as Exterior
86 from sage.algebras.weyl_algebra import DifferentialWeylAlgebra as
DifferentialWeyl
87 from sage.algebras.lie_algebras.lie_algebra import LieAlgebra as Lie
88
89 from sage.misc.lazy_import import lazy_import
90 lazy_import('sage.algebras.iwahori_hecke_algebra',
'IwahoriHeckeAlgebra', 'IwahoriHecke')
91 lazy_import('sage.algebras.nil_coxeter_algebra', 'NilCoxeterAlgebra',
'NilCoxeter')
92 lazy_import('sage.algebras.free_zinbiel_algebra', 'FreeZinbielAlgebra',
'FreeZinbiel')
93 lazy_import('sage.algebras.askey_wilson', 'AskeyWilsonAlgebra',
'AskeyWilson')
94 lazy_import('sage.algebras.hall_algebra', 'HallAlgebra', 'Hall')
95 lazy_import('sage.algebras.jordan_algebra', 'JordanAlgebra', 'Jordan')
96 lazy_import('sage.algebras.orlik_solomon', 'OrlikSolomonAlgebra',
'OrlikSolomon')
97 lazy_import('sage.algebras.orlik_terao', 'OrlikTeraoAlgebra',
'OrlikTerao')
98 lazy_import('sage.algebras.shuffle_algebra', 'ShuffleAlgebra',
'Shuffle')
99 lazy_import('sage.algebras.schur_algebra', 'SchurAlgebra', 'Schur')
~/sage-9.5/local/var/lib/sage/venv-python3.10.3/lib/python3.10/site-packages/sage/algebras/clifford_algebra.py
in <module>
20 from sage.misc.cachefunc import cached_method
21 from sage.structure.unique_representation import UniqueRepresentation
22 from copy import copy
23
24 from sage.categories.algebras_with_basis import AlgebrasWithBasis
25 from sage.categories.hopf_algebras_with_basis import
HopfAlgebrasWithBasis
26 from sage.modules.with_basis.morphism import ModuleMorphismByLinearity
27 from sage.categories.poor_man_map import PoorManMap
28 from sage.rings.integer_ring import ZZ
29 from sage.modules.free_module import FreeModule, FreeModule_generic
30 from sage.matrix.constructor import Matrix
31 from sage.matrix.args import MatrixArgs
32 from sage.sets.family import Family
33 from sage.combinat.free_module import CombinatorialFreeModule
34 from sage.combinat.subset import SubsetsSorted
---> 35 from sage.quadratic_forms.quadratic_form import QuadraticForm
global sage.quadratic_forms.quadratic_form = undefined
global QuadraticForm = undefined
36 from sage.algebras.weyl_algebra import repr_from_monomials
37 from sage.misc.inherit_comparison import
InheritComparisonClasscallMetaclass
38 from sage.typeset.ascii_art import ascii_art
39 from sage.typeset.unicode_art import unicode_art
40 import unicodedata
41
42
43 class CliffordAlgebraElement(CombinatorialFreeModule.Element):
44 """
45 An element in a Clifford algebra.
46
47 TESTS::
48
49 sage: Q = QuadraticForm(ZZ, 3, [1, 2, 3, 4, 5, 6])
50 sage: Cl.<x,y,z> = CliffordAlgebra(Q)
~/sage-9.5/local/var/lib/sage/venv-python3.10.3/lib/python3.10/site-packages/sage/quadratic_forms/quadratic_form.py
in <module>
177 S += [-1]
178 a = QQ.hilbert_symbol_negative_at_S(S,-d)
179 a = ZZ(a)
180 P = ([p for p in P if hilbert_symbol(a, -d, p) == 1]
181 +[p for p in (2*a*d).prime_divisors()
182 if hilbert_symbol(a, -d, p)==-1 and p not in P])
183 sminus = max(0, sminus-1)
184 rk = rk - 1
185 d = a*d
186 D.append(a.squarefree_part())
187 d = d.squarefree_part()
188 D.append(d)
189 return DiagonalQuadraticForm(QQ,D)
190
191
--> 192 class QuadraticForm(SageObject):
global QuadraticForm = undefined
global SageObject = <class 'sage.structure.sage_object.SageObject'>
193 r"""
194 The ``QuadraticForm`` class represents a quadratic form in n
variables with
195 coefficients in the ring R.
196
197 INPUT:
198
199 The constructor may be called in any of the following ways.
200
201 #. ``QuadraticForm(R, n, entries)``, where
202
203 - `R` -- ring for which the quadratic form is defined
204 - `n` -- an integer >= 0
205 - ``entries`` -- a list of `n(n+1)/2` coefficients of the
quadratic form
206 in `R` (given lexicographically, or equivalently, by rows of
the
207 matrix)
~/sage-9.5/local/var/lib/sage/venv-python3.10.3/lib/python3.10/site-packages/sage/quadratic_forms/quadratic_form.py
in QuadraticForm()
308 local_normal_form, \
309 jordan_blocks_by_scale_and_unimodular, \
310 jordan_blocks_in_unimodular_list_by_scale_power
311
312 ## Routines to perform elementary variable substitutions
313 from sage.quadratic_forms.quadratic_form__variable_substitutions
import \
314 swap_variables, \
315 multiply_variable, \
316 divide_variable, \
317 scale_by_factor, \
318 extract_variables, \
319 elementary_substitution, \
320 add_symmetric
321
322 ## Routines to compute p-adic field invariants
--> 323 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 _rational_diagonal_form_and_transformation = undefined
global signature_vector = undefined
global signature = undefined
global hasse_invariant = undefined
global hasse_invariant__OMeara = 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
324 rational_diagonal_form, \
325 _rational_diagonal_form_and_transformation, \
326 signature_vector, \
327 signature, \
328 hasse_invariant, \
329 hasse_invariant__OMeara, \
330 is_hyperbolic, \
331 is_anisotropic, \
332 is_isotropic, \
333 anisotropic_primes, \
334 compute_definiteness, \
335 compute_definiteness_string_by_determinants, \
336 is_positive_definite, \
337 is_negative_definite, \
338 is_indefinite, \
~/sage-9.5/local/var/lib/sage/venv-python3.10.3/lib/python3.10/site-packages/sage/quadratic_forms/quadratic_form__local_field_invariants.py
in <module>
15 # (at your option) any later version.
16 # http://www.gnu.org/licenses/
17
#*****************************************************************************
18
19
###########################################################################
20 ## TO DO: Add routines for hasse invariants at all places, anisotropic
21 ## places, is_semi_definite, and support for number fields.
22
###########################################################################
23
24
25 from copy import deepcopy
26 from sage.rings.integer_ring import ZZ
27 from sage.rings.rational_field import QQ
28 from sage.rings.real_mpfr import RR
29 from sage.arith.all import prime_divisors, hilbert_symbol
---> 30 from sage.functions.all import sgn
global sage.functions.all = undefined
global sgn = undefined
31 from sage.matrix.matrix_space import MatrixSpace
32 from sage.misc.cachefunc import cached_method
33
34
35 def rational_diagonal_form(self, return_matrix=False):
36 """
37 Return a diagonal form equivalent to the given quadratic from
38 over the fraction field of its defining ring.
39
40 INPUT:
41
42 - ``return_matrix`` -- (boolean, default: False) also return the
43 transformation matrix
44
45 OUTPUT: either ``D`` (if ``return_matrix`` is false) or ``(D,T)``
~/sage-9.5/local/var/lib/sage/venv-python3.10.3/lib/python3.10/site-packages/sage/functions/all.py
in <module>
53 gen_legendre_P,
54 gen_legendre_Q,
55 hermite,
56 jacobi_P,
57 laguerre,
58 legendre_P,
59 legendre_Q,
60 ultraspherical,
61 gegenbauer,
62 krawtchouk,
63 meixner,
64 hahn)
65
66 from .spike_function import spike_function
67
---> 68 from .prime_pi import legendre_phi, partial_sieve_function, prime_pi
global prime_pi = undefined
global legendre_phi = undefined
global partial_sieve_function = undefined
69
70 from .wigner import (wigner_3j, clebsch_gordan, racah, wigner_6j,
71 wigner_9j, gaunt)
72
73 from .generalized import (dirac_delta, heaviside, unit_step, sgn, sign,
74 kronecker_delta)
75
76 from .min_max import max_symbolic, min_symbolic
77
78 from .airy import airy_ai, airy_ai_prime, airy_bi, airy_bi_prime
79
80 from .exp_integral import (exp_integral_e, exp_integral_e1,
log_integral, li, Li,
81 log_integral_offset,
82 sin_integral, cos_integral, Si, Ci,
83 sinh_integral, cosh_integral, Shi, Chi,
~/sage-9.5/local/var/lib/sage/venv-python3.10.3/lib/python3.10/site-packages/sage/functions/prime_pi.pyx
in init sage.functions.prime_pi
(build/cythonized/sage/functions/prime_pi.c:5928)()
22 True
23 """
24
25 #
****************************************************************************
26 # Copyright (C) 2009,2011 R. Andrew Ohana <[email protected]>
27 # Copyright (C) 2009 William Stein <[email protected]>
28 #
29 # Distributed under the terms of the GNU General Public License (GPL)
30 # as published by the Free Software Foundation; either version 2 of
31 # the License, or (at your option) any later version.
32 # https://www.gnu.org/licenses/
33 #
****************************************************************************
34
35 from sage.rings.integer cimport Integer
36 from sage.symbolic.function cimport BuiltinFunction
---> 37 from primecountpy.primecount import prime_pi as _prime_pi
global primecountpy.primecount = undefined
global prime_pi = undefined
global _prime_pi = undefined
38 from primecountpy.primecount import phi as _phi
39
40 cdef class PrimePi(BuiltinFunction):
41 def __init__(self):
42 r"""
43 The prime counting function, which counts the number of primes
less
44 than or equal to a given value.
45
46 INPUT:
47
48 - ``x`` - a real number
49 - ``prime_bound`` - (default 0) a real number < 2^32,
``prime_pi`` will
50 make sure to use all the primes up to ``prime_bound``
(although,
51 possibly more) in computing ``prime_pi``, this can potentially
52 speedup the time of computation, at a cost to memory usage.
~/sage-9.5/local/var/lib/sage/venv-python3.10.3/lib/python3.10/site-packages/primecountpy/__init__.py
in <module>
----> 1 from .primecount import *
global primecount = undefined
ImportError:
dlopen(/Users/yueqili/sage-9.5/local/var/lib/sage/venv-python3.10.3/lib/python3.10/site-packages/primecountpy/primecount.cpython-310-darwin.so,
2): Library not loaded: /opt/homebrew/opt/primesieve/lib/libprimesieve.9.dylib
Referenced from:
/Users/yueqili/sage-9.5/local/var/lib/sage/venv-python3.10.3/lib/python3.10/site-packages/primecountpy/primecount.cpython-310-darwin.so
Reason: image not found
***************************************************************************
History of session input:
*** Last line of input (may not be in above history):
