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minor details in piecewise functions #38876

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Merged
vbraun merged 1 commit into from
Nov 3, 2024
Merged

minor details in piecewise functions #38876

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43 changes: 22 additions & 21 deletions src/sage/functions/piecewise.py
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Original file line number Diff line number Diff line change
Expand Up @@ -673,39 +673,40 @@ def piecewise_add(self, parameters, variable, other):
funcs = []
contains_lower = False
contains_upper = False
for i in range(len(points)-1):
for i in range(len(points) - 1):
a, b = points[i], points[i + 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]))
contains_lower = (self.domain().contains(a) or
other.domain().contains(a)) and not contains_upper
contains_upper = (self.domain().contains(b) or
other.domain().contains(b))
if contains_lower:
if contains_upper:
rs = RealSet.closed(points[i], points[i+1])
rs = RealSet.closed(a, b)
else:
rs = RealSet.closed_open(points[i], points[i+1])
rs = RealSet.closed_open(a, b)
else:
if contains_upper:
rs = RealSet.open_closed(points[i], points[i+1])
rs = RealSet.open_closed(a, b)
else:
rs = RealSet.open(points[i], points[i+1])
point = (points[i+1] + points[i])/2
rs = RealSet.open(a, b)
point = (b + a) / 2
except ValueError:
if points[i] == minus_infinity and points[i+1] == infinity:
if a == minus_infinity and b == infinity:
rs = RealSet.open(minus_infinity, infinity)
point = 0
elif points[i] == minus_infinity:
elif a == minus_infinity:
if contains_lower:
rs = RealSet.unbounded_below_closed(points[i+1])
rs = RealSet.unbounded_below_closed(b)
else:
rs = RealSet.unbounded_below_open(points[i+1])
point = points[i+1]-1
elif points[i+1] == infinity:
rs = RealSet.unbounded_below_open(b)
point = b - 1
elif b == infinity:
if contains_upper:
rs = RealSet.unbounded_above_closed(points[i])
rs = RealSet.unbounded_above_closed(a)
else:
rs = RealSet.unbounded_above_open(points[i])
point = points[i]+1
rs = RealSet.unbounded_above_open(a)
point = a + 1
else:
raise
try:
Expand Down Expand Up @@ -1160,17 +1161,17 @@ def laplace(self, parameters, variable, x='x', s='t'):
(s + 1)*e^(-s)/s^2 + 2*e^(-s)/s - 1/s^2
"""
from sage.symbolic.assumptions import assume, forget
from sage.functions.log import exp

x = SR.var(x)
s = SR.var(s)
assume(s > 0)
exp_sx = (-s * x).exp()
result = 0
for domain, f in parameters:
for interval in domain:
a = interval.lower()
b = interval.upper()
result += (SR(f)*exp(-s*x)).integral(x, a, b)
result += (SR(f) * exp_sx).integral(x, a, b)
forget(s > 0)
return result

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