I have written following Lattice Reduction Algorithm. However, it does not
work properly (does not matche with the LLL algorithm
implemented in Sage). It will be great for me if any one check the program.
# LLL Algorithm
M=matrix(ZZ,4,4,
[1,57,67,75,
3,4,98,98,
34,23,267,111,
6,134,125,68
])
print M.LLL(),'Actual'
print '-----------------------------
-----------'
s=0
M1=matrix(QQ,4,4,
[0,0,0,0,
0,0,0,0,
0,0,0,0,
0,0,0,0])
M2=matrix(QQ,4,4,
[0,0,0,0,
0,0,0,0,
0,0,0,0,
0,0,0,0])
len=4
while(1):
M1=matrix(QQ,4,4,
[0,0,0,0,
0,0,0,0,
0,0,0,0,
0,0,0,0])
M1[0]=M[0]
#print 'ddddd',d
for i in range(1,len):
M11=matrix(QQ,4,4,
[0,0,0,0,
0,0,0,0,
0,0,0,0,
0,0,0,0])
for j in range(i):
y=(M[i]*M1[j])/(M1[j]*M1[j])
#print y
#M2[i,j]=y
#print y*M1[j]
#print M11
M11[0]=M11[0] + y*M1[j]
M1[i]=M[i]-M11[0]
#print M1[i]
for i in range(1,len):
j=i-1
while(j>=0):
M[i]=M[i]-round(M[i]*M1[j]/(M1[j]*M1[j]))*M[j]
j=j-1
#print '------------------------------'
#print M
#print '--------------------------------'
for i in range(0,len-1):
x=(3/4)*M1[i]*M1[i]
#print x
y=(M[i+1]*M1[i]/(M1[i]*M1[i]))*M1[i]+M1[i+1]
y=y*y
d=1
if(x > y):
c=M[i]
M[i]=M[i+1]
M[i+1]=c
d=0
break
#print 'YES',d
if(d==0):
continue
else:
break
print M
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