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 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 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 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):
"""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 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]
