def __init__(self, c_value):
""" Give a positive constant here """
N = Nat()
N.belongs(c_value)
amap = MinusValueNatMap(c_value)
amap_dual = PlusValueNatMap(c_value)
WrapAMap.__init__(self, amap, amap_dual)
def __init__(self, c_value):
""" Give a positive constant here """
N = Nat()
N.belongs(c_value)
amap = MinusValueNatMap(c_value)
amap_dual = PlusValueNatMap(c_value)
WrapAMap.__init__(self, amap, amap_dual)
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 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 __init__(self, value):
N = Nat()
N.belongs(value)
amap = InvMultValueNatMap(value)
amap_dual = InvMultDualValueNatMap(value)
WrapAMap.__init__(self, amap, amap_dual)
def __init__(self, value):
N = Nat()
N.belongs(value)
amap = InvMultValueNatMap(value)
amap_dual = InvMultDualValueNatMap(value)
WrapAMap.__init__(self, amap, amap_dual)
class PlusValueNatMap(Map):
def __init__(self, value):
self.value = value
self.N = Nat()
self.N.belongs(value)
Map.__init__(self, dom=self.N, cod=self.N)
def _call(self, x):
return Nat_add(x, self.value)
def diagram_label(self):
return self.__str__()
def repr_map(self, letter):
return plusvaluemap_repr(letter, self.N, self.value)
def __str__(self):
return '+ %s' % self.N.format(self.value)
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)
