Vectors with elements in \(\GF{2}\)#

AUTHOR:

Martin Albrecht (2009-12): initial implementation
Thomas Feulner (2012-11): added Vector_mod2_dense.hamming_weight()

EXAMPLES:

Sage

sage: VS = GF(2)^3
sage: e = VS.random_element()
sage: e.parent() is VS
True
sage: S = set(vector(v, immutable=True) for v in VS)
sage: S1 = set()
sage: while S != S1:
....:     S1.add(vector(VS.random_element(), immutable=True))

Python

>>> from sage.all import *
>>> VS = GF(Integer(2))**Integer(3)
>>> e = VS.random_element()
>>> e.parent() is VS
True
>>> S = set(vector(v, immutable=True) for v in VS)
>>> S1 = set()
>>> while S != S1:
...     S1.add(vector(VS.random_element(), immutable=True))

class sage.modules.vector_mod2_dense.Vector_mod2_dense[source]#

Bases: FreeModuleElement

EXAMPLES:

Sage

sage: VS = VectorSpace(GF(2),3)
sage: VS((0,0,1/3))
(0, 0, 1)
sage: type(_)
<class 'sage.modules.vector_mod2_dense.Vector_mod2_dense'>
sage: VS((0,0,int(3)))
(0, 0, 1)
sage: VS((0,0,3))
(0, 0, 1)
sage: VS((0,0,GF(2)(1)))
(0, 0, 1)

Python

>>> from sage.all import *
>>> VS = VectorSpace(GF(Integer(2)),Integer(3))
>>> VS((Integer(0),Integer(0),Integer(1)/Integer(3)))
(0, 0, 1)
>>> type(_)
<class 'sage.modules.vector_mod2_dense.Vector_mod2_dense'>
>>> VS((Integer(0),Integer(0),int(Integer(3))))
(0, 0, 1)
>>> VS((Integer(0),Integer(0),Integer(3)))
(0, 0, 1)
>>> VS((Integer(0),Integer(0),GF(Integer(2))(Integer(1))))
(0, 0, 1)

hamming_weight()[source]#

Return the number of positions i such that self[i] != 0.

EXAMPLES:

Sage

sage: vector(GF(2), [1,1,0]).hamming_weight()
2

Python

>>> from sage.all import *
>>> vector(GF(Integer(2)), [Integer(1),Integer(1),Integer(0)]).hamming_weight()
2

list(copy=True)[source]#

Return a list of entries in self.

INPUT:

copy – always True

EXAMPLES:

Sage

sage: VS = VectorSpace(GF(2), 10)
sage: entries = [GF(2).random_element() for _ in range(10)]
sage: e = VS(entries)
sage: e.list() == entries
True

Python

>>> from sage.all import *
>>> VS = VectorSpace(GF(Integer(2)), Integer(10))
>>> entries = [GF(Integer(2)).random_element() for _ in range(Integer(10))]
>>> e = VS(entries)
>>> e.list() == entries
True

sage.modules.vector_mod2_dense.unpickle_v0(parent, entries, degree, is_immutable)[source]#

EXAMPLES:

Sage

sage: from sage.modules.vector_mod2_dense import unpickle_v0
sage: VS = VectorSpace(GF(2),10)
sage: unpickle_v0(VS, [0,1,2,3,4,5,6,7,8,9], 10, 0)
(0, 1, 0, 1, 0, 1, 0, 1, 0, 1)

Python

>>> from sage.all import *
>>> from sage.modules.vector_mod2_dense import unpickle_v0
>>> VS = VectorSpace(GF(Integer(2)),Integer(10))
>>> unpickle_v0(VS, [Integer(0),Integer(1),Integer(2),Integer(3),Integer(4),Integer(5),Integer(6),Integer(7),Integer(8),Integer(9)], Integer(10), Integer(0))
(0, 1, 0, 1, 0, 1, 0, 1, 0, 1)