from sage.symbolic.relation import solve
from sage.symbolic.ring import SR
pair_keep = staticmethod(lambda i, j: (i, j))
pair_swap = staticmethod(lambda i, j: (j, i))
CHECK_LEVELS = 4
INTERVAL = {
(True, True): RealSet.closed,
(True, False): RealSet.closed_open,
(True, None): lambda l, u: RealSet.unbounded_above_closed(l),
(False, True): RealSet.open_closed,
(False, False): RealSet.open,
(False, None): lambda l, u: RealSet.unbounded_above_open(l),
(None, True): lambda l, u: RealSet.unbounded_below_closed(u),
(None, False): lambda l, u: RealSet.unbounded_below_open(u),
(None, None): lambda l, u: RealSet().complement()
}
def checklist(checks, inherit=None):
"""
Initialize the list of feasibility checking functions
and return a decorator for the functions.
"""
if inherit is None:
for i in range(CHECK_LEVELS):
checks.append([])
else:
for lvl in inherit:
def piecewise_add(cls, self, parameters, variable, other):
"""
Return a new piecewise function with domain the union
of the original domains and functions summed. Undefined
intervals in the union domain get function value `0`.
EXAMPLES::
sage: f = piecewise([([0,1], 1), ((2,3), x)])
sage: g = piecewise([((1/2, 2), x)])
sage: f.piecewise_add(g).unextend_zero()
piecewise(x|-->1 on (0, 1/2], x|-->x + 1 on (1/2, 1], x|-->x on (1, 2) + (2, 3); x)
"""
points = ([minus_infinity] +
sorted(set(self.end_points() + other.end_points())) +
[infinity])
domain = []
funcs = []
contains_lower = False
contains_upper = False
for i in range(len(points)-1):
try:
contains_lower = (self.domain().contains(points[i]) or
other.domain().contains(points[i])) and not contains_upper
contains_upper = (self.domain().contains(points[i+1]) or
other.domain().contains(points[i+1]))
if contains_lower:
if contains_upper:
rs = RealSet.closed(points[i],points[i+1])
else:
rs = RealSet.closed_open(points[i],points[i+1])
else:
if contains_upper:
rs = RealSet.open_closed(points[i],points[i+1])
else:
rs = RealSet.open(points[i],points[i+1])
point = (points[i+1] + points[i])/2
except ValueError:
if points[i] == minus_infinity and points[i+1] == infinity:
rs = RealSet.open(minus_infinity, infinity)
point = 0
elif points[i] == minus_infinity:
if contains_lower:
rs = RealSet.unbounded_below_closed(points[i+1])
else:
rs = RealSet.unbounded_below_open(points[i+1])
point = points[i+1]-1
elif points[i+1] == infinity:
if contains_upper:
rs = RealSet.unbounded_above_closed(points[i])
else:
rs = RealSet.unbounded_above_open(points[i])
point = points[i]+1
else:
raise
try:
ex1 = self.expression_at(point)
except ValueError:
ex1 = 0
try:
ex2 = other.expression_at(point)
except ValueError:
ex2 = 0
ex = ex1 + ex2
if i>0 and funcs[-1] == ex:
# extend the previous domain
rs += domain[-1]
domain[-1] = rs
else:
domain += rs
funcs.append(ex)
return piecewise(zip(domain, funcs))
def piecewise_add(cls, self, parameters, variable, other):
"""
Return a new piecewise function with domain the union
of the original domains and functions summed. Undefined
intervals in the union domain get function value `0`.
EXAMPLES::
sage: f = piecewise([([0,1], 1), ((2,3), x)])
sage: g = piecewise([((1/2, 2), x)])
sage: f.piecewise_add(g).unextend_zero()
piecewise(x|-->1 on (0, 1/2], x|-->x + 1 on (1/2, 1], x|-->x on (1, 2) + (2, 3); x)
"""
points = ([minus_infinity] +
sorted(set(self.end_points() + other.end_points())) +
[infinity])
domain = []
funcs = []
contains_lower = False
contains_upper = False
for i in range(len(points) - 1):
try:
contains_lower = (self.domain().contains(points[i])
or other.domain().contains(
points[i])) and not contains_upper
contains_upper = (self.domain().contains(points[i + 1]) or
other.domain().contains(points[i + 1]))
if contains_lower:
if contains_upper:
rs = RealSet.closed(points[i], points[i + 1])
else:
rs = RealSet.closed_open(points[i], points[i + 1])
else:
if contains_upper:
rs = RealSet.open_closed(points[i], points[i + 1])
else:
rs = RealSet.open(points[i], points[i + 1])
point = (points[i + 1] + points[i]) / 2
except ValueError:
if points[i] == minus_infinity and points[i +
1] == infinity:
rs = RealSet.open(minus_infinity, infinity)
point = 0
elif points[i] == minus_infinity:
if contains_lower:
rs = RealSet.unbounded_below_closed(points[i + 1])
else:
rs = RealSet.unbounded_below_open(points[i + 1])
point = points[i + 1] - 1
elif points[i + 1] == infinity:
if contains_upper:
rs = RealSet.unbounded_above_closed(points[i])
else:
rs = RealSet.unbounded_above_open(points[i])
point = points[i] + 1
else:
raise
try:
ex1 = self.expression_at(point)
except ValueError:
ex1 = 0
try:
ex2 = other.expression_at(point)
except ValueError:
ex2 = 0
ex = ex1 + ex2
if i > 0 and funcs[-1] == ex:
# extend the previous domain
rs += domain[-1]
domain[-1] = rs
else:
domain += rs
funcs.append(ex)
return piecewise(zip(domain, funcs))
