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

# Copyright (C) 2005 William Stein <wstein@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/ 

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

  

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

# 

# ntl_mat_GF2E: Matrices over the GF(2**x) via NTL 

# 

# AUTHORS: 

# - Martin Albrecht <malb@informatik.uni-bremen.de> 

# 2006-01: initial version (based on code by William Stein) 

# 

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

from __future__ import absolute_import 

  

from cysignals.signals cimport sig_on, sig_off 

from sage.ext.cplusplus cimport ccrepr 

  

include 'misc.pxi' 

include 'decl.pxi' 

  

from cpython.object cimport Py_EQ, Py_NE 

from .ntl_GF2E cimport ntl_GF2E 

from .ntl_GF2EContext import ntl_GF2EContext 

from .ntl_GF2EContext cimport ntl_GF2EContext_class 

from sage.rings.integer cimport Integer 

from sage.misc.randstate cimport randstate, current_randstate 

  

from sage.libs.ntl.ntl_ZZ import unpickle_class_args 

  

cdef class ntl_mat_GF2E(object): 

r""" 

The \class{mat_GF2E} class implements arithmetic with matrices over $GF(2**x)$. 

""" 

def __init__(self, modulus = None, nrows=0, ncols=0, v=None): 

""" 

Constructs a matrix over ntl.GF2E. 

  

INPUT: 

modulus -- GF2E context 

nrows -- number of rows 

ncols -- number of columns 

v -- either a list or a matrix over GF(2^x) 

  

EXAMPLES:: 

  

sage: k.<a> = GF(2^4) 

sage: ctx = ntl.GF2EContext(k) 

sage: ntl.GF2XHexOutput(1) 

sage: ntl.mat_GF2E(ctx, 5,5, [0..24]) 

[[0x0 0x1 0x2 0x3 0x4] 

[0x5 0x6 0x7 0x8 0x9] 

[0xa 0xb 0xc 0xd 0xe] 

[0xf 0x3 0x2 0x1 0x0] 

[0x7 0x6 0x5 0x4 0xb] 

] 

sage: ntl.mat_GF2E(ctx, 5,5) 

[[0x0 0x0 0x0 0x0 0x0] 

[0x0 0x0 0x0 0x0 0x0] 

[0x0 0x0 0x0 0x0 0x0] 

[0x0 0x0 0x0 0x0 0x0] 

[0x0 0x0 0x0 0x0 0x0] 

] 

sage: A= matrix(k,5,5,[k.fetch_int(_%(2^4)) for _ in range(25)]) 

sage: ntl.mat_GF2E(ctx, A) 

[[0x0 0x1 0x2 0x3 0x4] 

[0x5 0x6 0x7 0x8 0x9] 

[0xa 0xb 0xc 0xd 0xe] 

[0xf 0x0 0x1 0x2 0x3] 

[0x4 0x5 0x6 0x7 0x8] 

] 

""" 

if modulus is None: 

raise ValueError("You must specify a modulus when creating a GF2E.") 

  

cdef unsigned long _nrows, _ncols 

cdef unsigned long i, j 

  

from sage.structure.element import is_Matrix 

if is_Matrix(nrows): 

_nrows = nrows.nrows() 

_ncols = nrows.ncols() 

v = nrows.list() 

else: 

_nrows = nrows 

_ncols = ncols 

  

self.x.SetDims(_nrows, _ncols) 

if v is not None: 

sig_on() 

for i from 0 <= i < _nrows: 

for j from 0 <= j < _ncols: 

elem = v[i*_ncols+j] 

if not isinstance(elem, ntl_GF2E): 

elem = ntl_GF2E(elem, modulus) 

mat_GF2E_setitem(&self.x, i, j, &(<ntl_GF2E>elem).x) 

sig_off() 

  

def __cinit__(self, modulus=None, nrows=0, ncols=0, v=None): 

#################### WARNING ################### 

## Before creating a GF2E, you must create a ## 

## GF2EContext, and restore it. In Python, ## 

## the error checking in __init__ will prevent## 

## you from constructing an ntl_GF2E ## 

## inappropriately. However, from Cython, you## 

## could do r = ntl_GF2E.__new__(ntl_GF2E) without 

## first restoring a GF2EContext, which could ## 

## have unfortunate consequences. See _new ## 

## defined below for an example of the right ## 

## way to short-circuit __init__ (or just call## 

## _new in your own code). ## 

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

if modulus is None: 

return 

if isinstance(modulus, ntl_GF2EContext_class): 

self.c = <ntl_GF2EContext_class>modulus 

self.c.restore_c() 

else: 

self.c = <ntl_GF2EContext_class>ntl_GF2EContext(modulus) 

self.c.restore_c() 

  

cdef ntl_GF2E _new_element(self): 

cdef ntl_GF2E r 

self.c.restore_c() 

r = ntl_GF2E.__new__(ntl_GF2E) 

r.c = self.c 

return r 

  

cdef ntl_mat_GF2E _new(self): 

cdef ntl_mat_GF2E r 

self.c.restore_c() 

r = ntl_mat_GF2E.__new__(ntl_mat_GF2E) 

r.x.SetDims(self.x.NumRows(),self.x.NumCols()) 

r.c = self.c 

return r 

  

def modulus_context(self): 

""" 

Returns the structure that holds the underlying NTL GF2E modulus. 

  

EXAMPLES:: 

  

sage: ntl.GF2XHexOutput(0) 

sage: ctx = ntl.GF2EContext( ntl.GF2X([1,1,0,1,1,0,0,0,1]) ) 

sage: a = ntl.GF2E(ntl.ZZ_pX([1,1,3],2), ctx) 

sage: A= ntl.mat_GF2E(ctx, 1, 1, [a]) 

sage: cty = A.modulus_context(); cty 

NTL modulus [1 1 0 1 1 0 0 0 1] 

sage: ctx == cty 

True 

""" 

return self.c 

  

def __reduce__(self): 

""" 

EXAMPLES:: 

  

sage: k.<a> = GF(2^4) 

sage: ctx = ntl.GF2EContext(k) 

sage: A = ntl.mat_GF2E(ctx, 5,5, [0..24]) 

sage: A == loads(dumps(A)) 

True 

""" 

return unpickle_class_args, (ntl_mat_GF2E, (self.modulus_context(), self.x.NumRows(), self.x.NumCols(), self.list())) 

  

def __repr__(self): 

""" 

Return the string representation of self. 

  

EXAMPLES:: 

  

sage: ctx = ntl.GF2EContext([1,1,0,1,1,0,0,0,1]) 

sage: ntl.GF2XHexOutput(1) 

sage: ntl.mat_GF2E(ctx, 2,2,range(4)).__repr__() 

'[[0x0 0x1]\n[0x0 0x1]\n]' 

sage: ntl.GF2XHexOutput(0) 

sage: ntl.mat_GF2E(ctx, 2,2,range(4)).__repr__() 

'[[[] [1]]\n[[] [1]]\n]' 

""" 

self.c.restore_c() 

return ccrepr(self.x) 

  

def __mul__(ntl_mat_GF2E self, other): 

""" 

EXAMPLES:: 

  

sage: ctx = ntl.GF2EContext([1,1,0,1,1,0,0,0,1]) 

sage: ntl.GF2XHexOutput(1) 

sage: m = ntl.mat_GF2E(ctx, 5,5,[0..24]) 

sage: n = ntl.mat_GF2E(ctx, 5,5,[3..27]) 

sage: m*n ## indirect doctest 

[[0x87 0x04 0xc4 0xc7 0x87] 

[0x32 0x84 0x17 0x63 0x73] 

[0xa1 0x46 0x25 0xcd 0x2f] 

[0x1 0xcf 0xfb 0xd6 0x62] 

[0xcf 0x02 0x06 0xfd 0x79] 

] 

""" 

cdef ntl_mat_GF2E r = self._new() 

if not isinstance(other, ntl_mat_GF2E): 

other = ntl_mat_GF2E(other, self.c) 

if not self.c is (<ntl_mat_GF2E>other).c: 

raise ValueError("You can not perform arithmetic with matrices over different fields.") 

sig_on() 

mat_GF2E_mul(r.x, self.x, (<ntl_mat_GF2E>other).x) 

sig_off() 

return r 

  

def __sub__(ntl_mat_GF2E self, other): 

""" 

EXAMPLES:: 

  

sage: ctx = ntl.GF2EContext([1,1,0,1,1,0,0,0,1]) 

sage: m = ntl.mat_GF2E(ctx, 5,5,[0..24]) 

sage: n = ntl.mat_GF2E(ctx, 5,5,[3..27]) 

sage: ntl.GF2XHexOutput(0) 

sage: m-n ## indirect doctest 

[[[1 1] [1 0 1] [1 1 1] [1 0 1] [1 1]] 

[[1 0 1 1] [1 1 1 1] [1 0 1 1] [1 1] [1 0 1]] 

[[1 1 1] [1 0 1] [1 1] [1 0 1 1 1] [1 1 1 1 1]] 

[[1 0 1 1 1] [1 1] [1 0 1] [1 1 1] [1 0 1]] 

[[1 1] [1 0 1 1] [1 1 1 1] [1 0 1 1] [1 1]] 

] 

""" 

cdef ntl_mat_GF2E r = self._new() 

if not isinstance(other, ntl_mat_GF2E): 

other = ntl_mat_GF2E(other, self.c) 

if not self.c is (<ntl_mat_GF2E>other).c: 

raise ValueError("You can not perform arithmetic with matrices over different fields.") 

sig_on() 

mat_GF2E_sub(r.x, self.x, (<ntl_mat_GF2E>other).x) 

sig_off() 

return r 

  

def __add__(ntl_mat_GF2E self, other): 

""" 

EXAMPLES:: 

  

sage: ctx = ntl.GF2EContext([1,1,0,1,1,0,0,0,1]) 

sage: m = ntl.mat_GF2E(ctx, 5,5,[0..24]) 

sage: n = ntl.mat_GF2E(ctx, 5,5,[3..27]) 

sage: m+n ## indirect doctest 

[[[1 1] [1 0 1] [1 1 1] [1 0 1] [1 1]] 

[[1 0 1 1] [1 1 1 1] [1 0 1 1] [1 1] [1 0 1]] 

[[1 1 1] [1 0 1] [1 1] [1 0 1 1 1] [1 1 1 1 1]] 

[[1 0 1 1 1] [1 1] [1 0 1] [1 1 1] [1 0 1]] 

[[1 1] [1 0 1 1] [1 1 1 1] [1 0 1 1] [1 1]] 

] 

""" 

cdef ntl_mat_GF2E r = self._new() 

if not isinstance(other, ntl_mat_GF2E): 

other = ntl_mat_GF2E(other, self.c) 

if not self.c is (<ntl_mat_GF2E>other).c: 

raise ValueError("You can not perform arithmetic with matrices over different fields.") 

sig_on() 

mat_GF2E_add(r.x, self.x, (<ntl_mat_GF2E>other).x) 

sig_off() 

return r 

  

def __neg__(ntl_mat_GF2E self): 

""" 

EXAMPLES:: 

  

sage: ctx = ntl.GF2EContext([1,1,0,1,1,0,0,0,1]) 

sage: m = ntl.mat_GF2E(ctx, 5,5,[0..24]) 

sage: -m == m ## indirect doctest 

True 

""" 

cdef ntl_mat_GF2E r = self._new() 

sig_on() 

mat_GF2E_negate(r.x, self.x) 

sig_off() 

return r 

  

def __pow__(ntl_mat_GF2E self, long e, ignored): 

""" 

EXAMPLES:: 

  

sage: ctx = ntl.GF2EContext([1,1,0,1,1,0,0,0,1]) 

sage: m = ntl.mat_GF2E(ctx, 5,5,[0..24]) 

sage: m**2 == m*m ## indirect doctest 

True 

""" 

cdef ntl_mat_GF2E r = self._new() 

sig_on() 

mat_GF2E_power(r.x, self.x, e) 

sig_off() 

return r 

  

def __richcmp__(ntl_mat_GF2E self, other, int op): 

""" 

Compare self to other. 

  

EXAMPLES:: 

  

sage: ctx = ntl.GF2EContext([1,1,0,1,1,0,0,0,1]) 

sage: m = ntl.mat_GF2E(ctx, 5,5,[0..24]) 

sage: n = ntl.mat_GF2E(ctx, 5,5,[3..27]) 

sage: m == n 

False 

sage: m == m 

True 

sage: m == [] 

False 

""" 

self.c.restore_c() 

  

if op != Py_EQ and op != Py_NE: 

raise TypeError("matrices over GF(2^e) are not ordered") 

  

cdef ntl_mat_GF2E b 

try: 

b = <ntl_mat_GF2E?>other 

except TypeError: 

return NotImplemented 

  

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

  

def NumRows(self): 

""" 

Return the number of rows in self. 

  

EXAMPLES:: 

  

sage: ctx = ntl.GF2EContext([1,1,0,1,1,0,0,0,1]) 

sage: m = ntl.mat_GF2E(ctx, 5,5,[0..24]) ; m.NumRows() 

5 

""" 

return int(self.x.NumRows()) 

  

def NumCols(self): 

""" 

Return the number of columns in self. 

  

EXAMPLES:: 

  

sage: ctx = ntl.GF2EContext([1,1,0,1,1,0,0,0,1]) 

sage: m = ntl.mat_GF2E(ctx, 5,5,[0..24]) ; m.NumCols() 

5 

""" 

return int(self.x.NumCols()) 

  

def __setitem__(self, ij, x): 

""" 

EXAMPLES:: 

  

sage: ctx = ntl.GF2EContext([1,1,0,1,1,0,0,0,1]) 

sage: m = ntl.mat_GF2E(ctx, 5,5,[0..24]) 

sage: ntl.GF2XHexOutput(0) 

sage: m[0,0] 

[] 

sage: m[0,0] = 1 

sage: m[0,0] 

[1] 

""" 

cdef int i, j 

if not isinstance(x, ntl_GF2E): 

x = ntl_GF2E(x, self.c) 

  

if isinstance(ij, tuple) and len(ij) == 2: 

i, j = ij 

elif self.x.NumCols()==1 and (isinstance(ij, Integer) or isinstance(ij, int)): 

i = ij 

j = 0 

elif self.x.NumRows()==1 and (isinstance(ij, Integer) or isinstance(ij, int)): 

i = 0 

j = ij 

else: 

raise TypeError('ij is not a matrix index') 

  

if i < 0 or i >= self.x.NumRows() or j < 0 or j >= self.x.NumCols(): 

raise IndexError("array index out of range") 

  

if not (<ntl_GF2E>x).c is self.c: 

raise ValueError("You can not assign elements from different fields.") 

  

self.c.restore_c() 

  

mat_GF2E_setitem(&self.x, i, j, &(<ntl_GF2E>x).x) 

  

def __getitem__(self, ij): 

""" 

EXAMPLES:: 

  

sage: ctx = ntl.GF2EContext([1,1,0,1,1,0,0,0,1]) 

sage: m = ntl.mat_GF2E(ctx, 5,5,[0..24]) 

sage: m[0,1] 

[1] 

sage: m[0,0] = 0 

sage: m[0,0] 

[] 

""" 

cdef int i, j 

if isinstance(ij, tuple) and len(ij) == 2: 

i, j = ij 

elif self.x.NumCols() == 1 and (isinstance(ij, Integer) or isinstance(ij, int)): 

i = ij 

j = 0 

elif self.x.NumRows() == 1 and (isinstance(ij, Integer) or isinstance(ij, int)): 

i = 0 

j = ij 

else: 

raise TypeError('ij is not a matrix index') 

  

if i < 0 or i >= self.x.NumRows() or j < 0 or j >= self.x.NumCols(): 

raise IndexError("array index out of range") 

  

cdef ntl_GF2E e = self._new_element() 

e.x = self.x.get( i+1, j+1 ) 

return e 

  

def determinant(self): 

""" 

Returns the determinant. 

  

EXAMPLES:: 

  

sage: ctx = ntl.GF2EContext([1,1,0,1,1,0,0,0,1]) 

sage: ntl.GF2XHexOutput(0) 

sage: ntl.mat_GF2E(ctx, 5,5,[0..24]).determinant() 

[0 1 0 1 1 1 1] 

sage: ntl.mat_GF2E(ctx, 5,5,[3..27]).determinant() 

[0 1 1 0 0 1] 

""" 

cdef ntl_GF2E r = self._new_element() 

sig_on() 

r.x = mat_GF2E_determinant(self.x) 

sig_off() 

return r 

  

def gauss(self,ncols=-1): 

""" 

Performs unitary row operations so as to bring this matrix 

into row echelon form. If the optional argument \code{ncols} 

is supplied, stops when first ncols columns are in echelon 

form. The return value is the rank (or the rank of the first 

ncols columns). 

  

INPUT: 

  

- ``ncols`` - number of columns to process (default: all) 

  

EXAMPLES:: 

  

sage: m = ctx = ntl.GF2EContext(ntl.GF2X([1,1,0,1,1,0,0,0,1])) 

sage: ntl.mat_GF2E(ctx, 5,5,[3..27]).gauss() 

5 

sage: ntl.mat_GF2E(ctx, 5,5).gauss() 

0 

sage: ntl.mat_GF2E(ctx, 5,5,[3..27]).gauss(3) 

3 

""" 

if ncols == -1: 

ncols = self.x.NumCols() 

return int(mat_GF2E_gauss(self.x, int(ncols))) 

  

def list(self): 

""" 

Returns a list of the entries in this matrix 

  

EXAMPLES:: 

  

sage: ctx = ntl.GF2EContext([1,1,0,1,1,0,0,0,1]) 

sage: m = ntl.mat_GF2E(ctx, 2,2,[ntl.GF2E_random(ctx) for x in range(2*2)]) 

sage: ntl.GF2XHexOutput(0) 

sage: m.list() 

[[1 1 0 0 1 0 1 1], [1 1 1 0 1 1 1], [0 1 1 1 1 0 0 1], [0 1 0 1 1 1]] 

""" 

return [self[i,j] for i in range(self.NumRows()) for j in range(self.x.NumCols())] 

  

def IsZero(self): 

""" 

Return True if self is zero, and false otherwise. 

  

EXAMPLES:: 

  

sage: ctx = ntl.GF2EContext([1,1,0,1,1,0,0,0,1]) 

sage: m = ntl.mat_GF2E(ctx, 5,5,[0..24]) 

sage: n = ntl.mat_GF2E(ctx, 5,5) 

sage: m.IsZero() 

False 

sage: n.IsZero() 

True 

""" 

cdef long isZero 

sig_on() 

isZero = mat_GF2E_IsZero(self.x) 

sig_off() 

return bool(isZero) 

  

def _sage_(ntl_mat_GF2E self, k=None): 

""" 

Returns a ``Matrix`` over a ``FiniteField`` representation 

of this element. 

  

INPUT: 

  

- ``k`` - optional GF(2**deg) 

  

OUTPUT: 

Matrix over k 

  

EXAMPLES:: 

  

sage: ctx = ntl.GF2EContext([1,1,0,1]) 

sage: m = ntl.mat_GF2E(ctx, 2,2,[3..6]) 

sage: ntl.GF2XHexOutput(0) 

sage: m 

[[[1 1] [0 0 1]] 

[[1 0 1] [0 1 1]] 

] 

sage: m._sage_() 

[ a + 1 a^2] 

[a^2 + 1 a^2 + a] 

""" 

if k is None: 

from sage.rings.finite_rings.finite_field_constructor import FiniteField 

f = self.c.m._sage_() 

e = GF2E_degree() 

k = FiniteField(2**e, name='a', modulus=f) 

  

l = [e._sage_(k) for e in self.list()] # we actually can do faster than this 

  

from sage.matrix.constructor import Matrix 

return Matrix(k,self.x.NumRows(),self.x.NumCols(),l) 

  

def transpose(ntl_mat_GF2E self): 

""" 

Returns the transposed matrix of self. 

  

OUTPUT: 

transposed Matrix 

  

EXAMPLES:: 

  

sage: ctx = ntl.GF2EContext([1,1,0,1,1,0,0,0,1]) 

sage: m = ntl.mat_GF2E(ctx, 5,5,[0..24]) 

sage: n = m.transpose() 

sage: n == m 

False 

sage: n.transpose() == m 

True 

""" 

cdef ntl_mat_GF2E r = self._new() 

sig_on() 

mat_GF2E_transpose(r.x, self.x) 

sig_off() 

return r 

  

def __invert__(self): 

""" 

Return $X = A^{-1}$; an error is raised if A is singular. 

  

EXAMPLES:: 

  

sage: ctx = ntl.GF2EContext([1,1,0,1,1,0,0,0,1]) 

sage: m = ntl.mat_GF2E(ctx, 5,5,[0..24]) 

sage: n = ~m 

sage: o = n*m 

sage: o.IsIdent() 

True 

""" 

cdef ntl_mat_GF2E r = self._new() 

sig_on() 

mat_GF2E_inv(r.x, self.x) 

sig_off() 

return r 

  

def IsIdent(self, n = -1): 

""" 

test if A is the n x n identity matrix 

  

EXAMPLES:: 

  

sage: ctx = ntl.GF2EContext([1,1,0,1,1,0,0,0,1]) 

sage: m = ntl.mat_GF2E(ctx, 5,5,[0..24]) 

sage: n = ~m 

sage: o = n*m 

sage: o.IsIdent() 

True 

""" 

if n < 0: 

n = self.NumRows() 

return bool(mat_GF2E_IsIdent(self.x, n)) 

  

def IsDiag(self, long n, ntl_GF2E d): 

""" 

Test if X is an n x n diagonal matrix with d on diagonal. 

  

EXAMPLES:: 

  

sage: ctx = ntl.GF2EContext([1,1,0,1,1,0,0,0,1]) 

sage: m = ntl.mat_GF2E(ctx, 3,3,[[0,1],0,0, 0,[0,1],0, 0,0,[0,1]]) 

sage: m.IsDiag(2, ntl.GF2E([0,1],ctx)) 

False 

sage: m.IsDiag(3, ntl.GF2E([0,1],ctx)) 

True 

""" 

return bool(mat_GF2E_IsDiag(self.x, n, d.x)) 

  

def image(self): 

""" 

The rows of X are computed as basis of A's row space. X is 

row echelon form. 

  

EXAMPLES:: 

  

sage: ctx = ntl.GF2EContext([1,1,0,1,1,0,0,0,1]) 

sage: m = ntl.mat_GF2E(ctx, 3,3,[0..24]) 

sage: ntl.GF2XHexOutput(1) 

sage: m.image() 

[[0x3 0x4 0x5] 

[0x0 0x1 0x2] 

[0x0 0x0 0xc1] 

] 

""" 

cdef ntl_mat_GF2E X = self._new() 

sig_on() 

mat_GF2E_image(X.x, self.x) 

sig_off() 

return X 

  

def kernel(self): 

""" 

Computes a basis for the kernel of the map ``x -> x*A``, where 

``x`` is a row vector. 

  

EXAMPLES:: 

  

sage: ctx = ntl.GF2EContext([1,1,0,1,1,0,0,0,1]) 

sage: m = ntl.mat_GF2E(ctx, 3,3,[0..24]) 

sage: ntl.GF2XHexOutput(1) 

sage: m.kernel() 

[] 

""" 

cdef ntl_mat_GF2E X = self._new() 

sig_on() 

mat_GF2E_kernel(X.x, self.x) 

sig_off() 

return X 

  

def randomize(self, density=1, nonzero=False): 

""" 

Randomize ``density`` proportion of the entries of this matrix, 

leaving the rest unchanged. 

  

INPUT: 

  

- ``density`` - float; proportion (roughly) to be considered for 

changes 

- ``nonzero`` - Bool (default: ``False``); whether the new entries 

are forced to be non-zero 

  

EXAMPLES:: 

  

sage: k.<a> = GF(2^4) 

sage: ctx = ntl.GF2EContext(k) 

sage: ntl.GF2XHexOutput(1) 

sage: A = ntl.mat_GF2E(ctx, 100,100) 

sage: A.randomize() 

sage: len([e for e in A.list() if e!=0]) 

9346 

  

sage: A = ntl.mat_GF2E(ctx, 100,100) 

sage: A.randomize(nonzero=True) 

sage: len([e for e in A.list() if e!=0]) 

10000 

  

sage: A = ntl.mat_GF2E(ctx, 100,100) 

sage: A.randomize(nonzero=True, density=0.1) 

sage: len([e for e in A.list() if e!=0]) 

994 

  

""" 

cdef long i,j 

cdef GF2E_c tmp 

  

cdef float _density = density 

cdef randstate rstate = current_randstate() 

  

if _density <= 0: 

return 

if _density > 1: 

_density = 1.0 

  

if not nonzero: 

if _density == 1.0: 

for i in xrange(self.x.NumRows()): 

for j in xrange(self.x.NumCols()): 

tmp = GF2E_random() 

mat_GF2E_setitem(&self.x, i, j, &tmp) 

else: 

for i in xrange(self.x.NumRows()): 

for j in xrange(self.x.NumCols()): 

if rstate.c_rand_double() <= _density: 

tmp = GF2E_random() 

mat_GF2E_setitem(&self.x, i, j, &tmp) 

else: 

if _density == 1.0: 

for i in xrange(self.x.NumRows()): 

for j in xrange(self.x.NumCols()): 

tmp = GF2E_random() 

while GF2E_IsZero(tmp): 

tmp = GF2E_random() 

mat_GF2E_setitem(&self.x, i, j, &tmp) 

else: 

for i in xrange(self.x.NumRows()): 

for j in xrange(self.x.NumCols()): 

if rstate.c_rand_double() <= _density: 

tmp = GF2E_random() 

while GF2E_IsZero(tmp): 

tmp = GF2E_random() 

mat_GF2E_setitem(&self.x, i, j, &tmp)