def generate_matrix(q, number_processes = 35):
field = Field(q)
two_powers = [2 ** (q - i) for i in xrange(q + 1)]
with Manager() as manager:
A = manager.dict() # where we store the row integers
amount = lambda : len(A) # I use this to print out how many rows we have generated periodically
def append(x):
if x in A:
return 0
A[x] = True
return 1
#append = lambda x : A.__setitem__(x, True)
is_new = lambda x : not A.__contains__(x) # to avoid duplicate entries
# we don't need the a = 0, b = q - 1 case because it requires setting the 0th column (0 * (q-1)) which has already been chosen
a = q - 1
# generate all the numerators quickly
numerators = [[field.add(field.multiply(a, t), c) for t in field.trace()] for c in field]
bs = range(q - 3) + [q - 1] # all the b values we need
_distribute(lambda bs : _make_and_start_process(bs, a, field, numerators, append, is_new, two_powers, amount), bs, number_processes)
# start all the processes and then wait for them to finish
# the keys of the dictionary represent the row integers for the problem
return A.keys()
