def all_monomials_of_degree_d(d, variables):
"""
Return monomials of degree d in the given 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 range(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 combine(reductors, p, reduce=None):
p_nav = p.navigation()
assert p_nav.value() < reductors.navigation().value()
p_else = BooleSet(p_nav.else_branch(), p.ring())
if reduce:
p_else = reduce(p_else, reductors)
return if_then_else(p_nav.value(), reductors, p_else)
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 from_fast_pickable(l, r):
r"""
Undo the operation :func:`to_fast_pickable`.
The first argument is an object created by :func:`to_fast_pickable`.
For the specified format, see the documentation of :func:`to_fast_pickable`.
The second argument is ring, in which this polynomial should be created.
INPUT:
See OUTPUT of :func:`to_fast_pickable`
OUTPUT:
a list of Boolean polynomials
EXAMPLES::
sage: from sage.rings.polynomial.pbori import Ring
sage: from sage.rings.polynomial.pbori.parallel import from_fast_pickable
sage: r = Ring(1000)
sage: x = r.variable
sage: from_fast_pickable([[1], []], r)
[1]
sage: from_fast_pickable([[0], []], r)
[0]
sage: from_fast_pickable([[2], [(0, 1, 0)]], r)
[x(0)]
sage: from_fast_pickable([[2], [(1, 1, 0)]], r)
[x(1)]
sage: from_fast_pickable([[2], [(0, 1, 1)]], r)
[x(0) + 1]
sage: from_fast_pickable([[2], [(0, 3, 0), (1, 1, 0)]], r)
[x(0)*x(1)]
sage: from_fast_pickable([[2], [(0, 3, 3), (1, 1, 0)]], r)
[x(0)*x(1) + x(1)]
sage: from_fast_pickable([[2], [(0, 3, 4), (1, 1, 0), (2, 1, 0)]], r)
[x(0)*x(1) + x(2)]
sage: 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(range(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]