def sparse_random_system(ring, number_of_polynomials, variables_per_polynomial, degree, random_seed=None):
"""
generates a system, which is sparse in the sense, that each polynomial
contains only a small subset of variables. In each variable that occurrs in a polynomial it is dense in the terms up to the given degree (every term occurs with probability 1/2).
The system will be satisfiable by at least one solution.
>>> from polybori import *
>>> r=Ring(10)
>>> s=sparse_random_system(r, number_of_polynomials = 20, variables_per_polynomial = 3, degree=2, random_seed=123)
>>> [p.deg() for p in s]
[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2]
>>> sorted(groebner_basis(s), reverse=True)
[x(0), x(1), x(2), x(3), x(4) + 1, x(5), x(6) + 1, x(7), x(8) + 1, x(9)]
"""
if random_seed is not None:
set_random_seed(random_seed)
random_generator = Random(random_seed)
solutions=[]
variables = [ring.variable(i) for i in xrange(ring.n_variables())]
for v in variables:
solutions.append(v+random_generator.randint(0,1))
solutions=ll_encode(solutions)
res = []
while len(res)<number_of_polynomials:
variables_as_monomial=Monomial(
random_generator.sample(
variables,
variables_per_polynomial)
)
p=Polynomial(random_set(variables_as_monomial, 2**(variables_per_polynomial-1)))
p=sum([p.graded_part(i) for i in xrange(degree+1)])
if p.deg()==degree:
res.append(p)
res=[p+ll_red_nf_redsb(p, solutions) for p in res]# evaluate it to guarantee a solution
return res
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 all_monomials_of_degree_d(d, variables):
variables = Monomial(variables)
variables = list(variables.variables())
if not variables:
assert d == 0
return BooleConstant(1)
ring = variables[0].ring()
if d > len(variables):
return Polynomial(0, ring)
if d < 0:
return Polynomial(1, ring)
deg_variables = variables[-d:]
#this ensures sorting by indices
res = Monomial(deg_variables)
for i in xrange(1, len(variables) - d + 1):
deg_variables = variables[-d - i:-i]
res = Polynomial(res)
nav = res.navigation()
navs = []
while not nav.constant():
navs.append(BooleSet(nav, ring))
nav = nav.then_branch()
acc = Polynomial(1, ring)
for (nav, v) in reversed(zip(navs, deg_variables)):
acc = if_then_else(v, acc, nav)
res = acc
return res.set()
def proofll(ifthen, reductors, redsb=True, prot=True):
if prot and (not ifthen.supposedToBeValid):
print "THIS THEOREM IS NOT SUPPOSED TO BE VALID"
ip_pre = ifthen.ifpart
ip = []
for p in ip_pre:
p = Polynomial(p)
if p.is_zero():
continue
li = list(p.lead().variables())
if len(li) == 1 and (not (li[0] in list(Polynomial(reductors).lead().
variables()))):
assert not Polynomial(reductors).is_zero()
lead_index = li[0]
if redsb:
p = ll_red_nf_redsb(p, reductors)
reductors = ll_red_nf_redsb(Polynomial(reductors), BooleSet(p.
set()))
p_nav = p.navigation()
reductors = recursively_insert(p_nav.else_branch(), p_nav.value(),
reductors)
else:
ip.append(p)
it = ifthen.thenpart
if prot:
print "proofing:", ifthen
ip = logicaland(ip)
for c in it:
if prot:
print "proofing part:", c
c = logicalor([BooleConstant(1) + ip, c])
if c.is_zero():
if prot:
print "TRUE (trivial)"
return True
else:
c_orig = c
if redsb:
c = ll_red_nf_redsb(c, reductors)
else:
c = ll_red_nf_noredsb(c, reductors)
if c.is_zero():
if prot:
print "TRUE"
return True
else:
if prot:
print "FAILED"
print "can construct COUNTER EXAMPLE with:", find_one(c)
return False
def add_simple_poly(p,i):
p=Polynomial(p)
if p.is_zero():
return
res_p=Polynomial(res.get(i, Polynomial(0, p.ring())))
res[i]=res_p+p
if res[i].is_zero():
del res[i]
inter=BooleSet(res_p).intersect(BooleSet(p))
add_simple_poly(inter, i+1)
return
def proofll(ifthen, reductors, redsb=True, prot=True):
if prot and (not ifthen.supposedToBeValid):
print "THIS THEOREM IS NOT SUPPOSED TO BE VALID"
ip_pre = ifthen.ifpart
ip = []
for p in ip_pre:
p = Polynomial(p)
if p.is_zero():
continue
li = list(p.lead().variables())
if len(li) == 1 and (not (li[0] in list(
Polynomial(reductors).lead().variables()))):
assert not Polynomial(reductors).is_zero()
lead_index = li[0]
if redsb:
p = ll_red_nf_redsb(p, reductors)
reductors = ll_red_nf_redsb(Polynomial(reductors),
BooleSet(p.set()))
p_nav = p.navigation()
reductors = recursively_insert(p_nav.else_branch(), p_nav.value(),
reductors)
else:
ip.append(p)
it = ifthen.thenpart
if prot:
print "proofing:", ifthen
ip = logicaland(ip)
for c in it:
if prot:
print "proofing part:", c
c = logicalor([BooleConstant(1) + ip, c])
if c.is_zero():
if prot:
print "TRUE (trivial)"
return True
else:
c_orig = c
if redsb:
c = ll_red_nf_redsb(c, reductors)
else:
c = ll_red_nf_noredsb(c, reductors)
if c.is_zero():
if prot:
print "TRUE"
return True
else:
if prot:
print "FAILED"
print "can construct COUNTER EXAMPLE with:", find_one(c)
return False
def interred(l, completely=False):
"""computes a new generating system (g1, ...,gn),
spanning the same ideal modulo field equations.
The system is interreduced: For i!=j:
gi.lead() does not divide any leading term of gj.
If completely is set to True, then also terms in the
tail are not reducible by other polynomials.
"""
l = [Polynomial(p) for p in l if not p == 0]
if not l:
return []
ring = l[0].ring()
l_old = None
l = tuple(l)
while l_old != l:
l_old = l
l = sorted(l, key=Polynomial.lead)
g = ReductionStrategy(ring)
if completely:
g.opt_red_tail = True
for p in l:
p = g.nf(p)
if not p.is_zero():
g.add_generator(p)
l = tuple([e.p for e in g])
return list(l)
def power_set(variables):
if not variables:
return BooleConstant(1)
variables = sorted(set(variables), reverse=True, key=top_index)
res = Polynomial(1, variables[0].ring()).set()
for v in variables:
res = if_then_else(v, res, res)
return res
def all_monomials_of_degree_d_old(d, variables):
if d == 0:
return BooleConstant(1)
if not variables:
return []
variables = sorted(set(variables), reverse=True, key=top_index)
m = variables[-1]
for v in variables[:-1]:
m = v + m
m = m.set()
i = 0
res = Polynomial(variables[0].ring().one()).set()
while (i < d):
i = i + 1
res = res.cartesian_product(m).diff(res)
return res
def all_monomials_of_degree_d_old(d,variables):
if d==0:
return BooleConstant(1)
if not variables:
return []
variables=sorted(set(variables),reverse=True,key=top_index)
m=variables[-1]
for v in variables[:-1]:
m=v+m
m=m.set()
i=0
res=Polynomial(variables[0].ring().one()).set()
while(i<d):
i=i+1
res=res.cartesian_product(m).diff(res)
return res
def gen_strat(polys):
polys = [Polynomial(p) for p in polys]
polys = [p for p in polys if not p.is_zero()]
assert len(set([p.lead() for p in polys])) == len(polys)
assert polys
strat = GroebnerStrategy(polys[0].ring())
for p in polys:
print "Adding"
strat.add_generator(p)
print "finished"
return strat
def gen_random_poly(ring, l,deg,vars_set,seed=123):
myrange=vars_set
r=Random(seed)
def helper(samples):
if samples==0:
return Polynomial(ring.zero())
if samples==1:
d=r.randint(0,deg)
variables=r.sample(myrange,d)
m=Monomial(ring)
for v in sorted(set(variables),reverse=True):
m=m*Variable(v, ring)
return Polynomial(m)
assert samples>=2
return helper(samples/2)+helper(samples-samples/2)
p=Polynomial(ring.zero())
while(len(p)<l):
p=Polynomial(p.set().union(helper(l-len(p)).set()))
return p
def vars_real_divisors(monomial, monomial_set):
"""
returns all elements of of monomial_set, which result multiplied by a variable in monomial.
>>> from polybori.PyPolyBoRi import OrderCode
>>> dp_asc = OrderCode.dp_asc
>>> from polybori.PyPolyBoRi import Ring
>>> r=Ring(1000)
>>> x = r.variable
>>> b=BooleSet([x(1)*x(2),x(2)])
>>> vars_real_divisors(x(1)*x(2)*x(3),b)
{{x(1),x(2)}}
"""
return BooleSet(Polynomial(monomial_set.divisors_of(monomial)). \
graded_part(monomial.deg() - 1))
def dense_system(I):
I = (Polynomial(p) for p in I)
I = (p for p in I if not p.is_zero())
for p in I:
d = p.deg()
if p.deg() == 1:
continue
else:
try:
if len(p) > 2**d + 5:
return True
except OverflowError:
return True
return False
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 __coerce__(self, other):
#TODO handle long
if isinstance(other, int) and other >= 0:
i = 0
res = []
while 2**i <= other:
and_ = 2**i & other
if and_:
res.append(i)
return (self,
IntegerPolynomial(
dict([(i, BooleConstant(1)) for i in res])))
if not isinstance(other, IntegerPolynomial):
other = Polynomial(other)
return (self, IntegerPolynomial(dict([(0, other)])))
def gauss_on_linear(I):
I = (Polynomial(p) for p in I)
linear = []
non_linear = []
for p in I:
if p.is_zero():
continue
if p.deg() <= 1:
linear.append(p)
else:
non_linear.append(p)
if len(linear) == 0:
return non_linear
linear = list(gauss_on_polys(linear))
return linear + non_linear
def add_simple_poly(p, i):
p = Polynomial(p)
if p.is_zero():
return
res_p = Polynomial(res.get(i, Polynomial(0, p.ring())))
res[i] = res_p + p
if res[i].is_zero():
del res[i]
inter = BooleSet(res_p).intersect(BooleSet(p))
add_simple_poly(inter, i + 1)
return
def register(self, start, context):
super(AdderBlock, self).register(start, context)
a = context[self.input1]
b = context[self.input2]
self.s = shift(context[self.sums], self.start_index)
self.c = shift(context[self.carries], self.start_index)
a = shift(a, self.start_index)
b = shift(b, self.start_index)
carries = [Polynomial(a(0).ring().zero())]
for i in xrange(self.adder_bits):
#print i, ":"
c = 1 + (1 + a(i) * b(i)) * (1 + carries[-1] * a(i)) * (
1 + carries[-1] * b(i))
carries.append(c)
self.add_results = [
a(i) + b(i) + carries[i] for i in xrange(self.adder_bits)
]
self.carries_polys = carries[1:]
def from_fast_pickable(l, r):
"""from_fast_pickable(l, ring) undoes the operation to_fast_pickable. The first argument is an object created by to_fast_pickable.
For the specified format, see the documentation of to_fast_pickable.
The second argument is ring, in which this polynomial should be created.
INPUT:
see OUTPUT of to_fast_pickable
OUTPUT:
a list of Boolean polynomials
EXAMPLES:
>>> from polybori.PyPolyBoRi import Ring
>>> r=Ring(1000)
>>> x = r.variable
>>> from_fast_pickable([[1], []], r)
[1]
>>> from_fast_pickable([[0], []], r)
[0]
>>> from_fast_pickable([[2], [(0, 1, 0)]], r)
[x(0)]
>>> from_fast_pickable([[2], [(1, 1, 0)]], r)
[x(1)]
>>> from_fast_pickable([[2], [(0, 1, 1)]], r)
[x(0) + 1]
>>> from_fast_pickable([[2], [(0, 3, 0), (1, 1, 0)]], r)
[x(0)*x(1)]
>>> from_fast_pickable([[2], [(0, 3, 3), (1, 1, 0)]], r)
[x(0)*x(1) + x(1)]
>>> from_fast_pickable([[2], [(0, 3, 4), (1, 1, 0), (2, 1, 0)]], r)
[x(0)*x(1) + x(2)]
>>> from_fast_pickable([[2, 0, 1, 4], [(0, 3, 0), (1, 1, 0), (3, 1, 0)]], r)
[x(0)*x(1), 0, 1, x(3)]
"""
i2poly = {0: r.zero(), 1: r.one()}
(indices, terms) = l
for i in reversed(xrange(len(terms))):
(v, t, e) = terms[i]
t = i2poly[t]
e = i2poly[e]
terms[i] = if_then_else(v, t, e)
i2poly[i + 2] = terms[i]
return [Polynomial(i2poly[i]) for i in indices]
def add_bits(bits):
"""Adds n bit variables, by Lucas theorem
>>> from polybori import *
>>> r=Ring(10)
>>> add_bits([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([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), x(0)*x(1)*x(2)*x(3)]
>>> add_bits([r.variable(0)])
[x(0)]
"""
bits = list(bits)
if len(bits) < 2:
return bits
n = len(bits)
bits_expr = [] # [sum(bits)]
step = 0
while n >= 2**step:
bits_expr.append(Polynomial(all_monomials_of_degree_d(2**step, bits)))
step = step + 1
return bits_expr
print list(all_monomials_of_degree_d(3, [Variable(i) for i in range(4)]))
print list(all_monomials_of_degree_d(4, [Variable(i) for i in range(4)]))
print list(all_monomials_of_degree_d(0, []))
print list(all_monomials_of_degree_d(1, []))
print list(power_set([Variable(i) for i in range(2)]))
print list(power_set([Variable(i) for i in range(4)]))
print list(power_set([]))
#every monomial in the first 8 var, which is at most linear in the first 5
print list(
mod_mon_set(
power_set([Variable(i) for i in range(8)]),
all_monomials_of_degree_d(2, [Variable(i) for i in range(5)])))
#specialized normal form computation
print Polynomial(
mod_mon_set(
(x(1) * x(2) + x(1) + 1).set(),
all_monomials_of_degree_d(2, [Variable(i) for i in range(1000)])))
print list(
mod_mon_set(
power_set([Variable(i) for i in range(50)]),
all_monomials_of_degree_d(2, [Variable(i) for i in range(1000)])))
def monomial_from_indices(ring, indices):
l = sorted(indices, reverse=True)
res = Monomial(ring)
for i in l:
res = res * ring.variable(i)
return res
def plot(p,
filename,
colored=True,
format="png",
highlight_monomial=None,
fontsize=14,
template_engine='jinja',
landscape=False):
"""plots ZDD structure to <filename> in format <format>
EXAMPLES:
>>> r=Ring(1000)
>>> x = r.variable
>>> plot(x(1)+x(0),"/dev/null", colored=True)
>>> plot(x(1)+x(0),"/dev/null", colored=False)
"""
THICK_PEN = 5
highlight_path = dict()
if highlight_monomial:
highlight_path = monomial_path_in_zdd(highlight_monomial, p)
def display_monomial(m):
return unicode(m).replace("*", u"⋅")
def penwidth_else(n):
if n in highlight_path and highlight_path[n] == ELSE:
return THICK_PEN
return 1
def penwidth_then(n):
if n in highlight_path and highlight_path[n] == THEN:
return THICK_PEN
return 1
if not colored:
color_then = "black"
color_else = "black"
else:
color_then = "red"
color_else = "blue"
def find_navs(nav):
if not nav in nodes:
nodes.add(nav)
if not nav.constant():
find_navs(nav.then_branch())
find_navs(nav.else_branch())
p = Polynomial(p)
nodes = set()
nav = p.navigation()
find_navs(nav)
non_constant_nodes = [n for n in nodes if not n.constant()]
node_to_int = dict([(n, i) for (i, n) in enumerate(nodes)])
r = p.ring()
def identifier(n):
return "n" + str(node_to_int[n])
def label(n):
if n.constant():
if n.terminal_one():
return "1"
else:
return "0"
else:
return str(r.variable(n.value()))
def shape(n):
if n.constant():
return "box"
else:
return "ellipse"
renderers = dict(genshi=render_genshi, jinja=render_jinja)
dot_input = renderers[template_engine](locals())
if isinstance(dot_input, unicode):
dot_input = dot_input.encode('utf-8')
process = Popen(["dot", "-T" + format, "-o", filename],
stdin=PIPE,
stdout=PIPE)
process.stdin.write(dot_input)
process.stdin.close()
process.wait()
def zero_blocks(self, f):
"""divides the zero set of f into blocks
>>> from polybori import *
>>> r = declare_ring(["x", "y", "z"], dict())
>>> e = CNFEncoder(r)
>>> e.zero_blocks(r.variable(0)*r.variable(1)*r.variable(2))
[{y: 0}, {z: 0}, {x: 0}]
"""
f=Polynomial(f)
variables = f.vars_as_monomial()
space = variables.divisors()
variables = list(variables.variables())
zeros = f.zeros_in(space)
rest = zeros
res = list()
def choose_old(s):
return iter(rest).next()# somewhat
#inefficient compared to polynomials lex_lead
def choose(s):
indices = []
assert not s.empty()
nav = s.navigation()
while not nav.constant():
e = nav.else_branch()
t = nav.then_branch()
if e.constant() and not e.terminal_one():
indices.append(nav.value())
nav = t
else:
if self.random_generator.randint(0,1):
indices.append(nav.value())
nav = t
else:
nav = e
assert nav.terminal_one()
res = self.one_set
for i in reversed(indices):
res = ite(i, res, self.empty_set)
return iter(res).next()
while not rest.empty():
l = choose(rest)
l_variables = set(l.variables())
def get_val(var):
if var in l_variables:
return 1
return 0
block_dict = dict([(v, get_val(v)) for v in variables])
l = l.set()
self.random_generator.shuffle(variables)
for v in variables:
candidate = l.change(v.index())
if candidate.diff(zeros).empty():
l = l.union(candidate)
del block_dict[v]
rest = rest.diff(l)
res.append(block_dict)
return res
def preprocess(I, prot=True):
def min_gb(I):
strat = symmGB_F2_C(I,
opt_lazy=False,
opt_exchange=False,
prot=prot,
selection_size=10000,
opt_red_tail=True)
return list(strat.minimalize_and_tail_reduce())
I = [Polynomial(p) for p in I]
lin = [p for p in I if p.deg() == 1]
# lin_strat=symmGB_F2_C(lin, opt_lazy=False,opt_exchange=False,prot=prot,sele
# ction_size=10000,opt_red_tail=True)
lin = min_gb(lin) # list(lin_strat.minimalize_and_tail_reduce())
for m in sorted([p.lead() for p in lin]):
print m
lin_ll = ll_encode(lin)
square = [p.lead() for p in I if p.deg() == 2 and len(p) == 1]
assert (len(lin) + len(square) == len(I))
res = list(lin)
counter = OccCounter()
def unique_index(s):
for idx in s:
if counter[idx] == 1:
return idx
never_come_here = False
assert never_come_here
for m in square:
for idx in m:
counter.increase(idx)
systems = dict(((idx, []) for idx in counter.uniques()))
for m in square:
u_index = unique_index(m)
systems[u_index].append(ll_red_nf(m / Variable(u_index), lin_ll))
rewritings = dict()
u_var = Variable(u)
u_im = ll_red_nf(u_var, lin_ll)
if not u_im.isConstant():
if u_im != u_var:
r = u_im.navigation().value()
else:
pass
for u in counter.uniques():
#print u
u_var = Variable(u)
u_im = ll_red_nf(u_var, lin_ll)
if not u_im.isConstant():
if u_im != u_var:
r = u_im.navigation().value()
else:
pass
for u in systems.keys():
u_var = Variable(u)
u_im = ll_red_nf(u_var, lin_ll)
res.extend([u_im * p for p in min_gb(systems[u])])
#print [u_im*p for p in min_gb(systems[u])]
print "lin:", len(lin), "res:", len(res), "square:", len(square)
res = [p for p in (Polynomial(p) for p in res) if not p.is_zero()]
return res
def zero_blocks(self, f):
"""divides the zero set of f into blocks
>>> from polybori import *
>>> r = declare_ring(["x", "y", "z"], dict())
>>> e = CNFEncoder(r)
>>> e.zero_blocks(r.variable(0)*r.variable(1)*r.variable(2))
[{y: 0}, {z: 0}, {x: 0}]
"""
f = Polynomial(f)
variables = f.vars_as_monomial()
space = variables.divisors()
variables = list(variables.variables())
zeros = f.zeros_in(space)
rest = zeros
res = list()
def choose_old(s):
return iter(rest).next() # somewhat
#inefficient compared to polynomials lex_lead
def choose(s):
indices = []
assert not s.empty()
nav = s.navigation()
while not nav.constant():
e = nav.else_branch()
t = nav.then_branch()
if e.constant() and not e.terminal_one():
indices.append(nav.value())
nav = t
else:
if self.random_generator.randint(0, 1):
indices.append(nav.value())
nav = t
else:
nav = e
assert nav.terminal_one()
res = self.one_set
for i in reversed(indices):
res = ite(i, res, self.empty_set)
return iter(res).next()
while not rest.empty():
l = choose(rest)
l_variables = set(l.variables())
def get_val(var):
if var in l_variables:
return 1
return 0
block_dict = dict([(v, get_val(v)) for v in variables])
l = l.set()
self.random_generator.shuffle(variables)
for v in variables:
candidate = l.change(v.index())
if candidate.diff(zeros).empty():
l = l.union(candidate)
del block_dict[v]
rest = rest.diff(l)
res.append(block_dict)
return res
def __init__(self, boolean_polys):
super(IntegerPolynomial, self).__init__()
if not isinstance(boolean_polys, dict):
boolean_polys = dict([(0, Polynomial(boolean_polys))])
self.boolean_polys = boolean_polys
def pickle_bset(self):
return (BooleSet, (Polynomial(self), ))
def plot(p, filename, colored=True, format="png",
highlight_monomial=None, fontsize=14,
template_engine='jinja', landscape=False
):
"""plots ZDD structure to <filename> in format <format>
EXAMPLES:
>>> r=Ring(1000)
>>> x = r.variable
>>> plot(x(1)+x(0),"/dev/null", colored=True)
>>> plot(x(1)+x(0),"/dev/null", colored=False)
"""
THICK_PEN = 5
highlight_path = dict()
if highlight_monomial:
highlight_path = monomial_path_in_zdd(highlight_monomial, p)
def display_monomial(m):
return unicode(m).replace("*", u"⋅")
def penwidth_else(n):
if n in highlight_path and highlight_path[n] == ELSE:
return THICK_PEN
return 1
def penwidth_then(n):
if n in highlight_path and highlight_path[n] == THEN:
return THICK_PEN
return 1
if not colored:
color_then = "black"
color_else = "black"
else:
color_then = "red"
color_else = "blue"
def find_navs(nav):
if not nav in nodes:
nodes.add(nav)
if not nav.constant():
find_navs(nav.then_branch())
find_navs(nav.else_branch())
p = Polynomial(p)
nodes = set()
nav = p.navigation()
find_navs(nav)
non_constant_nodes = [n for n in nodes if not n.constant()]
node_to_int = dict([(n, i) for (i, n) in enumerate(nodes)])
r = p.ring()
def identifier(n):
return "n" + str(node_to_int[n])
def label(n):
if n.constant():
if n.terminal_one():
return "1"
else:
return "0"
else:
return str(r.variable(n.value()))
def shape(n):
if n.constant():
return "box"
else:
return "ellipse"
renderers = dict(genshi=render_genshi, jinja=render_jinja)
dot_input = renderers[template_engine](locals())
if isinstance(dot_input, unicode):
dot_input = dot_input.encode('utf-8')
process = Popen(["dot", "-T" + format, "-o", filename], stdin=PIPE,
stdout=PIPE)
process.stdin.write(dot_input)
process.stdin.close()
process.wait()
def __init__(self, ifpart, thenpart, supposed_to_be_valid=True):
self.ifpart = [Polynomial(p) for p in ifpart]
self.thenpart = [Polynomial(p) for p in thenpart]
self.supposedToBeValid = supposed_to_be_valid