def critical_points(cls, self, parameters, variable):
"""
Return the critical points of this piecewise function.
EXAMPLES::
sage: R.<x> = QQ[]
sage: f1 = x^0
sage: f2 = 10*x - x^2
sage: f3 = 3*x^4 - 156*x^3 + 3036*x^2 - 26208*x
sage: f = piecewise([[(0,3),f1],[(3,10),f2],[(10,20),f3]])
sage: expected = [5, 12, 13, 14]
sage: all(abs(e-a) < 0.001 for e,a in zip(expected, f.critical_points()))
True
TESTS:
Use variables other than x (:trac:`13836`)::
sage: R.<y> = QQ[]
sage: f1 = y^0
sage: f2 = 10*y - y^2
sage: f3 = 3*y^4 - 156*y^3 + 3036*y^2 - 26208*y
sage: f = piecewise([[(0,3),f1],[(3,10),f2],[(10,20),f3]])
sage: expected = [5, 12, 13, 14]
sage: all(abs(e-a) < 0.001 for e,a in zip(expected, f.critical_points()))
True
"""
from sage.calculus.calculus import maxima
x = QQ[self.default_variable()].gen()
crit_pts = []
for domain, f in parameters:
for interval in domain:
a = interval.lower()
b = interval.upper()
for root in maxima.allroots(SR(f).diff(x)==0):
root = float(root.rhs())
if a < root < b:
crit_pts.append(root)
return crit_pts
def critical_points(cls, self, parameters, variable):
"""
Return the critical points of this piecewise function.
EXAMPLES::
sage: R.<x> = QQ[]
sage: f1 = x^0
sage: f2 = 10*x - x^2
sage: f3 = 3*x^4 - 156*x^3 + 3036*x^2 - 26208*x
sage: f = piecewise([[(0,3),f1],[(3,10),f2],[(10,20),f3]])
sage: expected = [5, 12, 13, 14]
sage: all(abs(e-a) < 0.001 for e,a in zip(expected, f.critical_points()))
True
TESTS:
Use variables other than x (:trac:`13836`)::
sage: R.<y> = QQ[]
sage: f1 = y^0
sage: f2 = 10*y - y^2
sage: f3 = 3*y^4 - 156*y^3 + 3036*y^2 - 26208*y
sage: f = piecewise([[(0,3),f1],[(3,10),f2],[(10,20),f3]])
sage: expected = [5, 12, 13, 14]
sage: all(abs(e-a) < 0.001 for e,a in zip(expected, f.critical_points()))
True
"""
from sage.calculus.calculus import maxima
x = QQ[self.default_variable()].gen()
crit_pts = []
for domain, f in parameters:
for interval in domain:
a = interval.lower()
b = interval.upper()
for root in maxima.allroots(SR(f).diff(x) == 0):
root = float(root.rhs())
if a < root < b:
crit_pts.append(root)
return crit_pts