Coverage for local/lib/python2.7/site-packages/sage/databases/conway.py : 62%

""" 

Frank Luebeck's tables of Conway polynomials over finite fields 

""" 

#***************************************************************************** 

# 

# Sage: Copyright (C) 2005 William Stein <wstein@gmail.com> 

# Copyright (C) 2013 R. Andrew Ohana <andrew.ohana@gmail.com> 

# 

# Distributed under the terms of the GNU General Public License (GPL) 

# 

# This code is distributed in the hope that it will be useful, 

# but WITHOUT ANY WARRANTY; without even the implied warranty of 

# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU 

# General Public License for more details. 

# 

# The full text of the GPL is available at: 

# 

# http://www.gnu.org/licenses/ 

#***************************************************************************** 

from six import itervalues, iteritems 

from six.moves import cPickle as pickle 

import collections 

import os 

from sage.env import CONWAY_POLYNOMIALS_DATA_DIR 

_CONWAYDATA = os.path.join(CONWAY_POLYNOMIALS_DATA_DIR, 'conway_polynomials.p') 

_conwaydict = None 

class DictInMapping(collections.Mapping): 

def __init__(self, dict): 

""" 

Places dict into a non-mutable mapping. 

TESTS:: 

sage: from sage.databases.conway import DictInMapping 

sage: d = {} 

sage: m = DictInMapping(d); m 

{} 

sage: d[0] = 1; m 

{0: 1} 

sage: m[2] = 3 

Traceback (most recent call last): 

... 

TypeError: 'DictInMapping' object does not support item assignment 

""" 

self._store = dict 

def __getitem__(self, key): 

""" 

TESTS:: 

sage: from sage.databases.conway import DictInMapping 

sage: DictInMapping({'foo': 'bar'})['foo'] 

'bar' 

""" 

return self._store[key] 

def __len__(self): 

""" 

TESTS:: 

sage: from sage.databases.conway import DictInMapping 

sage: d = {} 

sage: m = DictInMapping(d); len(m) 

0 

sage: d['foo'] = 'bar'; len(m) 

1 

""" 

return len(self._store) 

def __iter__(self): 

""" 

TESTS:: 

sage: from sage.databases.conway import DictInMapping 

sage: next(iter(DictInMapping({'foo': 'bar'}))) 

'foo' 

""" 

return iter(self._store) 

def __repr__(self): 

""" 

TESTS:: 

sage: from sage.databases.conway import DictInMapping 

sage: DictInMapping({'foo': 'bar'}) 

{'foo': 'bar'} 

""" 

return repr(self._store) 

class ConwayPolynomials(collections.Mapping): 

def __init__(self): 

""" 

Initialize the database. 

TESTS:: 

sage: c = ConwayPolynomials() 

sage: c 

Frank Luebeck's database of Conway polynomials 

""" 

global _conwaydict 

if _conwaydict is None: 

if not os.path.exists(_CONWAYDATA): 

raise RuntimeError('In order to initialize the database, ' 

+ '%s must exist.' % _CONWAYDATA) 

with open(_CONWAYDATA, 'rb') as f: 

_conwaydict = pickle.load(f) 

self._store = _conwaydict 

def __repr__(self): 

""" 

Return a description of this database. 

TESTS:: 

sage: c = ConwayPolynomials() 

sage: c.__repr__() 

"Frank Luebeck's database of Conway polynomials" 

""" 

return "Frank Luebeck's database of Conway polynomials" 

def __getitem__(self, key): 

""" 

If key is a pair of integers ``p,n``, return the Conway 

polynomial of degree ``n`` over ``GF(p)``. 

If key is an integer ``p``, return a non-mutable mapping 

whose keys are the degrees of the polynomial values. 

TESTS:: 

sage: c = ConwayPolynomials() 

sage: c[60859] 

{1: (60856, 1), 2: (3, 60854, 1), 

3: (60856, 8, 0, 1), 4: (3, 32881, 3, 0, 1)} 

sage: c[60869, 3] 

(60867, 2, 0, 1) 

""" 

try: 

return DictInMapping(self._store[key]) 

except KeyError as err: 

try: 

if isinstance(key, (tuple, list)): 

if len(key) == 2: 

return self._store[key[0]][key[1]] 

except KeyError: 

pass 

raise err 

def __len__(self): 

""" 

Return the number of polynomials in this database. 

TESTS:: 

sage: c = ConwayPolynomials() 

sage: len(c) 

35352 

""" 

try: 

return self._len 

except AttributeError: 

pass 

self._len = sum(len(a) for a in itervalues(self._store)) 

return self._len 

def __iter__(self): 

""" 

Return an iterator over the keys of this database. 

TESTS:: 

sage: c = ConwayPolynomials() 

sage: itr = iter(c) 

sage: next(itr) 

(65537, 4) 

sage: next(itr) 

(2, 1) 

""" 

for a, b in iteritems(self._store): 

for c in b: 

yield a, c 

def polynomial(self, p, n): 

""" 

Return the Conway polynomial of degree ``n`` over ``GF(p)``, 

or raise a RuntimeError if this polynomial is not in the 

database. 

.. NOTE:: 

See also the global function ``conway_polynomial`` for 

a more user-friendly way of accessing the polynomial. 

INPUT: 

- ``p`` -- prime number 

- ``n`` -- positive integer 

OUTPUT: 

List of Python int's giving the coefficients of the corresponding 

Conway polynomial in ascending order of degree. 

EXAMPLES:: 

sage: c = ConwayPolynomials() 

sage: c.polynomial(3, 21) 

(1, 2, 0, 2, 0, 1, 2, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1) 

sage: c.polynomial(97, 128) 

Traceback (most recent call last): 

... 

RuntimeError: Conway polynomial over F_97 of degree 128 not in database. 

""" 

try: 

return self[p,n] 

except KeyError: 

raise RuntimeError("Conway polynomial over F_%s of degree %s not in database."%(p,n)) 

def has_polynomial(self, p, n): 

""" 

Return True if the database of Conway polynomials contains the 

polynomial of degree ``n`` over ``GF(p)``. 

INPUT: 

- ``p`` -- prime number 

- ``n`` -- positive integer 

EXAMPLES:: 

sage: c = ConwayPolynomials() 

sage: c.has_polynomial(97, 12) 

True 

sage: c.has_polynomial(60821, 5) 

False 

""" 

return (p,n) in self 

def primes(self): 

""" 

Return the list of prime numbers ``p`` for which the database of 

Conway polynomials contains polynomials over ``GF(p)``. 

EXAMPLES:: 

sage: c = ConwayPolynomials() 

sage: P = c.primes() 

sage: 2 in P 

True 

sage: next_prime(10^7) in P 

False 

""" 

return self._store.keys() 

def degrees(self, p): 

""" 

Return the list of integers ``n`` for which the database of Conway 

polynomials contains the polynomial of degree ``n`` over ``GF(p)``. 

EXAMPLES:: 

sage: c = ConwayPolynomials() 

sage: c.degrees(60821) 

[1, 2, 3, 4] 

sage: c.degrees(next_prime(10^7)) 

[] 

""" 

if p not in self._store: 

return [] 

return self._store[p].keys() 

def __reduce__(self): 

""" 

TESTS:: 

sage: c = ConwayPolynomials() 

sage: loads(dumps(c)) == c 

True 

""" 

return (ConwayPolynomials, ())