def Nat_mult_antichain_Max(m):
"""
Returns the set of elements of Nat so that their product is at most m:
Max { (a, b) | a * b <= m }
"""
# top -> [(top, top)]
P = Nat()
P.belongs(m)
top = P.get_top()
if is_top(P, m):
s = set([(top, top)])
return s
assert isinstance(m, int)
if m < 1:
return set([(0, 0)])
s = set()
for o1 in range(1, m + 1):
assert o1 >= 1
# We want the minimum x such that o1 * x >= f
# x >= f / o1
# x* = ceil(f / o1)
x = int(np.floor(m * 1.0 / o1))
assert x * o1 <= m # feasible
assert (x + 1) * o1 > m, (x + 1, o1, m) # and minimum
s.add((o1, x))
return s
def Nat_mult_antichain_Min(m):
"""
Returns the Minimal set of elements of Nat so that their product is at least m:
Min { (a, b) | a * b >= m }
"""
# (top, 1) or (1, top)
P = Nat()
P.belongs(m)
top = P.get_top()
if is_top(P, m):
s = set([(top, 1), (1, top)]) # XXX:
return s
assert isinstance(m, int)
if m == 0:
# any (r1,r2) is such that r1*r2 >= 0
return set([(0, 0)])
s = set()
for o1 in range(1, m + 1):
assert o1 >= 1
# We want the minimum x such that o1 * x >= f
# x >= f / o1
# x* = ceil(f / o1)
x = int(np.ceil(m * 1.0 / o1))
assert x * o1 >= m
assert (x - 1) * o1 < m
assert x >= 1
s.add((o1, x))
return s
def __init__(self, value):
N = Nat()
N.belongs(value)
amap = MultValueNatMap(value)
# if value = Top:
# f |-> f * Top
#
if is_top(N, value):
amap_dual = MultValueNatDPHelper2Map()
elif N.equal(0, value):
# r |-> Top
amap_dual = ConstantPosetMap(N, N, N.get_top())
else:
# f * c <= r
# f <= r / c
# r |-> floor(r/c)
amap_dual = MultValueNatDPhelper(value)
WrapAMap.__init__(self, amap, amap_dual)
def __init__(self, value):
N = Nat()
N.belongs(value)
amap = MultValueNatMap(value)
# if value = Top:
# f |-> f * Top
#
if is_top(N, value):
amap_dual = MultValueNatDPHelper2Map()
elif N.equal(0, value):
# r |-> Top
amap_dual = ConstantPosetMap(N, N, N.get_top())
else:
# f * c <= r
# f <= r / c
# r |-> floor(r/c)
amap_dual = MultValueNatDPhelper(value)
WrapAMap.__init__(self, amap, amap_dual)
def check_join_meet_1():
# test meet
# ⟨f₁, f₂⟩ ⟼ { min(f₁, f₂) }
# r ⟼ { ⟨r, ⊤⟩, ⟨⊤, r⟩ }
N = Nat()
dp = MeetNDP(2, N)
lf = dp.solve_r(5)
#print('lf: {}'.format(lf))
assert_belongs(lf, (10, 5))
assert_belongs(lf, (5, 10))
assert_does_not_belong(lf, (10, 10))
Rtop = N.get_top()
lf2 = dp.solve_r(Rtop)
#print('lf2: {}'.format(lf2))
assert_belongs(lf2, (10, 10))
assert_belongs(lf2, (Rtop, Rtop))
lf3 = dp.solve_r(0)
#print('lf3: {}'.format(lf3))
assert_belongs(lf3, (0, 0))
assert_does_not_belong(lf3, (0, 1))
assert_does_not_belong(lf3, (1, 0))
# Join ("max") of n variables.
# ⟨f₁, …, fₙ⟩ ⟼ { max(f₁, …, fₙ⟩ }
# r ⟼ ⟨r, …, r⟩
dp = JoinNDP(3, N)
ur = dp.solve((10, 3, 3))
assert_belongs(ur, 10)
assert_does_not_belong(ur, 9)
lf = dp.solve_r(10)
assert_does_not_belong(lf, (0, 11, 0))
assert_belongs(lf, (0, 10, 0))
assert_belongs(lf, (0, 9, 0))
def MinusValueNatDP2():
N = Nat()
v = N.get_top()
return MinusValueNatDP(v)
def MinusValueNatDP2():
N = Nat()
v = N.get_top()
return MinusValueNatDP(v)
