cols = (L // B) * 2 + 1
M = []

# short mod n, so first column should contain a vector (n, 0, ..., 0)
M.append([n] + (cols - 1) * [0])

# require that |v_i| are short and add ti[i] * v to the short linear combination
# using a vector (ti[i], 0, ..., 0, 1, 0, ..., 0)
for i, v in enumerate(ti[1:]):
    M.append([v] + [0] * i + [1] + [0] * (cols - i - 2))

# add the final u term which should occure at most once
# to do this add (u*inv, 0, ..., 0, 2^8)
M.append([int(u * inv)] + [0] * (cols - 2) + [K])

# print the matrix for debugging
M = Matrix(M)
print(M)

# run LLL
row = M.LLL()[0]

# print solution
row[0] = -row[0]
print(row)

from lelele import *

le = LeLeLe()

q = le.var()
V = [le.short_var() for _ in range(len(ti))] # short variables (sugar for .is_short on a var)

# define short linear combination mod n
w = sum([t*v for (v, t) in zip(V, ti)]) + inv * u * q
w %= n
w.short()

# q should be taken at most once: require that q * <
   
    > is small
   
(q * 0x100).short()

# prints a description of the system
print(le)

# find a solution
le.solve()

# print values assigned in solution
print(-int(w), [int(v) for v in V])

from lelele import *

le = LeLeLe()

q = le.var()
V = [le.short_var() for _ in range(len(ti))] # short variables (sugar for .is_short on a var)

# define short linear combination mod n
w = sum([t*v for (v, t) in zip(V, ti)]) + inv * u * q
w %= n
w.short()

# q should be taken at most once: require that q * <
   
    > is small
   
(q * 0x100).short()

# export lattice, a list of lists of ints: [[int]]
M = le.system()