/usr/lib/python2.7/dist-packages/brial/specialsets.py is in python-brial 0.8.5-4.
This file is owned by root:root, with mode 0o644.
The actual contents of the file can be viewed below.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 | from .PyPolyBoRi import (BooleSet, Polynomial, mod_mon_set,
if_then_else, Monomial, top_index, BooleConstant)
#def all_monomials_of_degree_d(d,variables):
# res=all_monomials_of_degree_d_new(d, variables)
# ref=all_monomials_of_degree_d_old(d, variables)
# assert res==ref, (d, variables)
# 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(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 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 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
if __name__ == '__main__':
from .blocks import declare_ring, Block
r = declare_ring([Block("x", 10000)], globals())
print(list(all_monomials_of_degree_d(0, [Variable(i) for i in range(100)])))
print(list(all_monomials_of_degree_d(1, [Variable(i) for i in range(10)])))
print(list(all_monomials_of_degree_d(2, [Variable(i) for i in range(4)])))
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
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