Coverage for local/lib/python2.7/site-packages/sage/libs/ntl/ntl_GF2.pyx : 69%

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

# Copyright (C) 2007 Martin Albrecht <malb@informatik.uni-bremen.de> 

# 

# 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 __future__ import division 

from cysignals.signals cimport sig_on, sig_off 

from sage.ext.cplusplus cimport ccrepr, ccreadstr 

include 'misc.pxi' 

include 'decl.pxi' 

from cpython.object cimport Py_EQ, Py_NE 

from sage.rings.integer cimport Integer 

from sage.rings.integer_ring cimport IntegerRing_class 

############################################################################## 

# GF2: Bits 

############################################################################## 

cdef class ntl_GF2(object): 

r""" 

The \class{GF2} represents the field GF(2). Computationally 

speaking, it is not a particularly useful class. Its main use is 

to make the interfaces to the various finite field classes as 

uniform as possible. 

""" 

def __init__(self, v=None): 

r""" 

Initializes a NTL bit. 

EXAMPLES: 

sage: ntl.GF2(1) 

1 

sage: ntl.GF2(int(2)) 

0 

sage: ntl.GF2('1') 

1 

""" 

if isinstance(v, ntl_GF2): 

self.x = (<ntl_GF2>v).x 

elif isinstance(v, int) or isinstance(v, long) or isinstance(v, Integer): 

GF2_conv_long(self.x, int(v) % 2) 

elif v is not None: 

ccreadstr(self.x, str(v)) 

def __repr__(self): 

""" 

Return the string representation of self. 

EXAMPLES: 

sage: str(ntl.GF2(1)) # indirect doctest 

'1' 

""" 

return ccrepr(self.x) 

def __reduce__(self): 

""" 

Serializes self. 

EXAMPLES: 

sage: a = ntl.GF2(1) 

sage: loads(dumps(a)) 

1 

""" 

return unpickle_class_value, (ntl_GF2, int(self)) 

def __richcmp__(ntl_GF2 self, other, int op): 

""" 

Compare self to other. 

EXAMPLES:: 

sage: a = ntl.GF2(1) 

sage: b = ntl.GF2(0) 

sage: a == a 

True 

sage: a == b 

False 

sage: a == 1 

True 

sage: a < b 

Traceback (most recent call last): 

... 

TypeError: elements of GF(2) are not ordered 

""" 

if op != Py_EQ and op != Py_NE: 

raise TypeError("elements of GF(2) are not ordered") 

cdef ntl_GF2 b 

try: 

b = <ntl_GF2?>other 

except TypeError: 

b = ntl_GF2(other) 

return (op == Py_EQ) == (self.x == b.x) 

def __mul__(self, other): 

""" 

sage: o = ntl.GF2(1) 

sage: z = ntl.GF2(0) 

sage: o*o 

1 

sage: o*z 

0 

sage: z*o 

0 

sage: z*z 

0 

""" 

cdef ntl_GF2 r = ntl_GF2.__new__(ntl_GF2) 

if not isinstance(self, ntl_GF2): 

self = ntl_GF2(self) 

if not isinstance(other, ntl_GF2): 

other = ntl_GF2(other) 

GF2_mul(r.x, (<ntl_GF2>self).x, (<ntl_GF2>other).x) 

return r 

def __truediv__(self, other): 

""" 

sage: o = ntl.GF2(1) 

sage: z = ntl.GF2(0) 

sage: o/o 

1 

sage: o/z 

Traceback (most recent call last): 

... 

ZeroDivisionError 

""" 

cdef ntl_GF2 r 

if not isinstance(self, ntl_GF2): 

self = ntl_GF2(self) 

if not isinstance(other, ntl_GF2): 

other = ntl_GF2(other) 

if GF2_IsZero((<ntl_GF2>other).x): 

raise ZeroDivisionError 

r = ntl_GF2.__new__(ntl_GF2) 

GF2_div(r.x, (<ntl_GF2>self).x, (<ntl_GF2>other).x) 

return r 

def __div__(self, other): 

return self / other 

def __sub__(self, other): 

""" 

sage: o = ntl.GF2(1) 

sage: z = ntl.GF2(0) 

sage: o-o 

0 

sage: o-z 

1 

sage: z-o 

1 

sage: z-z 

0 

""" 

cdef ntl_GF2 r = ntl_GF2.__new__(ntl_GF2) 

if not isinstance(self, ntl_GF2): 

self = ntl_GF2(self) 

if not isinstance(other, ntl_GF2): 

other = ntl_GF2(other) 

GF2_sub(r.x, (<ntl_GF2>self).x, (<ntl_GF2>other).x) 

return r 

def __add__(self, other): 

""" 

sage: o = ntl.GF2(1) 

sage: z = ntl.GF2(0) 

sage: o+o 

0 

sage: o+z 

1 

sage: z+o 

1 

sage: z+z 

0 

""" 

cdef ntl_GF2 r = ntl_GF2.__new__(ntl_GF2) 

if not isinstance(self, ntl_GF2): 

self = ntl_GF2(self) 

if not isinstance(other, ntl_GF2): 

other = ntl_GF2(other) 

GF2_add(r.x, (<ntl_GF2>self).x, (<ntl_GF2>other).x) 

return r 

def __neg__(ntl_GF2 self): 

""" 

sage: o = ntl.GF2(1) 

sage: z = ntl.GF2(0) 

sage: -z 

0 

sage: -o 

1 

""" 

cdef ntl_GF2 r = ntl_GF2.__new__(ntl_GF2) 

GF2_negate(r.x, self.x) 

return r 

def __pow__(ntl_GF2 self, long e, ignored): 

""" 

sage: o = ntl.GF2(1) 

sage: z = ntl.GF2(0) 

sage: z^2 

0 

sage: o^2 

1 

""" 

cdef ntl_GF2 r = ntl_GF2() 

GF2_power(r.x, self.x, e) 

return r 

def __int__(self): 

""" 

Return self as an int. 

EXAMPLES: 

sage: o = ntl.GF2(1) 

sage: z = ntl.GF2(0) 

sage: int(z) 

0 

sage: int(o) 

1 

""" 

cdef long l = GF2_conv_to_long(self.x) 

return int(l) 

def unpickle_class_value(cls, x): 

""" 

Here for unpickling. 

EXAMPLES: 

sage: sage.libs.ntl.ntl_GF2.unpickle_class_value(ntl.GF2,1) 

1 

sage: type(sage.libs.ntl.ntl_GF2.unpickle_class_value(ntl.GF2,1)) 

<type 'sage.libs.ntl.ntl_GF2.ntl_GF2'> 

""" 

return cls(x) 

def unpickle_class_args(cls, x): 

""" 

Here for unpickling. 

EXAMPLES: 

sage: sage.libs.ntl.ntl_GF2.unpickle_class_args(ntl.GF2,[1]) 

1 

sage: type(sage.libs.ntl.ntl_GF2.unpickle_class_args(ntl.GF2,[1])) 

<type 'sage.libs.ntl.ntl_GF2.ntl_GF2'> 

""" 

return cls(*x)