def add_bits_old(bits):
"""Adds n bits
>>> from polybori import *
>>> r=Ring(10)
>>> add_bits_old([r.variable(i) for i in xrange(3)])
[x(0) + x(1) + x(2), x(0)*x(1) + x(0)*x(2) + x(1)*x(2)]
>>> add_bits_old([r.variable(i) for i in xrange(4)])
[x(0) + x(1) + x(2) + x(3), x(0)*x(1) + x(0)*x(2) + x(0)*x(3) + x(1)*x(2) + x(1)*x(3) + x(2)*x(3)]
"""
bits = list(bits)
n = len(bits)
deg_d_monomials = [
Polynomial(all_monomials_of_degree_d(i, bits)) for i in xrange(n + 1)
]
full = power_set(bits)
bits_expr = [] # [sum(bits)]
step = 0
while n > 2**step:
to_one = sum(
[deg_d_monomials[i] for i in xrange(n + 1) if i & 2**step])
to_one = Polynomial(to_one)
fun = PartialFunction(ones=to_one, zeros=full.diff(to_one))
poly = fun.interpolate_smallest_lex()
bits_expr.append(poly)
step = step + 1
return bits_expr
def add_bits_old(bits):
"""Adds n bits
>>> from polybori import *
>>> r=Ring(10)
>>> add_bits_old([r.variable(i) for i in xrange(3)])
[x(0) + x(1) + x(2), x(0)*x(1) + x(0)*x(2) + x(1)*x(2)]
>>> add_bits_old([r.variable(i) for i in xrange(4)])
[x(0) + x(1) + x(2) + x(3), x(0)*x(1) + x(0)*x(2) + x(0)*x(3) + x(1)*x(2) + x(1)*x(3) + x(2)*x(3)]
"""
bits = list(bits)
n = len(bits)
deg_d_monomials = [Polynomial(all_monomials_of_degree_d(i, bits)) for i in
xrange(n + 1)]
full = power_set(bits)
bits_expr = [] # [sum(bits)]
step = 0
while n > 2 ** step:
to_one = sum([deg_d_monomials[i] for i in xrange(n + 1) if i & 2 **
step])
to_one = Polynomial(to_one)
fun = PartialFunction(ones=to_one, zeros=full.diff(to_one))
poly = fun.interpolate_smallest_lex()
bits_expr.append(poly)
step = step + 1
return bits_expr
def main():
r = Ring(1000)
x = Variable = VariableFactory(r)
from os import system
from polybori.specialsets import all_monomials_of_degree_d, power_set
full_set = list(power_set([Variable(i) for i in xrange(15)]))
from random import Random
generator = Random(123)
random_set = sum(generator.sample(full_set, 30))
full_polynomial = list(all_monomials_of_degree_d(3, [Variable(i) for i in
xrange(30)]))
random_poly = sum(generator.sample(full_polynomial, 30))
polynomials = [
x(1) * x(2) + x(3),
(x(1) + 1) * (x(2) + x(3)),
(x(1) + 1) * (x(2) + 1) * (x(3) + 1),
x(1) * x(2) + x(2) * x(3) + x(1) * x(3) + x(1),
x(0) + x(1) + x(2) + x(3) + x(4) + x(5),
all_monomials_of_degree_d(3, [x(i) for i in xrange(10)]),
power_set([x(i) for i in xrange(10)]),
random_poly,
random_set,
Polynomial(all_monomials_of_degree_d(3, [x(i) for i in xrange(10)])) +
Polynomial(power_set([x(i) for i in xrange(10)])),
Polynomial(power_set([x(i) for i in xrange(10)])) + 1
]
for colored in [True, False]:
if colored:
colored_suffix = "_colored"
else:
colored_suffix = ""
for format in ["png", "svg"]:
for (i, p) in enumerate(polynomials):
#dot_file=str(i) +colored_suffix+".dot"
#f=open(dot_file, "w")
#f.write(dot)
#f.close()
out_file = str(i) + colored_suffix + "." + format
plot(p, out_file, colored=colored, format=format)
def main():
r = Ring(1000)
x = Variable = VariableFactory(r)
from os import system
from polybori.specialsets import all_monomials_of_degree_d, power_set
full_set = list(power_set([Variable(i) for i in xrange(15)]))
from random import Random
generator = Random(123)
random_set = sum(generator.sample(full_set, 30))
full_polynomial = list(
all_monomials_of_degree_d(3, [Variable(i) for i in xrange(30)]))
random_poly = sum(generator.sample(full_polynomial, 30))
polynomials = [
x(1) * x(2) + x(3), (x(1) + 1) * (x(2) + x(3)),
(x(1) + 1) * (x(2) + 1) * (x(3) + 1),
x(1) * x(2) + x(2) * x(3) + x(1) * x(3) + x(1),
x(0) + x(1) + x(2) + x(3) + x(4) + x(5),
all_monomials_of_degree_d(3, [x(i) for i in xrange(10)]),
power_set([x(i) for i in xrange(10)]), random_poly, random_set,
Polynomial(all_monomials_of_degree_d(3, [x(i) for i in xrange(10)])) +
Polynomial(power_set([x(i) for i in xrange(10)])),
Polynomial(power_set([x(i) for i in xrange(10)])) + 1
]
for colored in [True, False]:
if colored:
colored_suffix = "_colored"
else:
colored_suffix = ""
for format in ["png", "svg"]:
for (i, p) in enumerate(polynomials):
#dot_file=str(i) +colored_suffix+".dot"
#f=open(dot_file, "w")
#f.write(dot)
#f.close()
out_file = str(i) + colored_suffix + "." + format
plot(p, out_file, colored=colored, format=format)
