def _sympysage_integral(self):
"""
EXAMPLES::
sage: from sympy import Symbol, Integral
sage: sx = Symbol('x')
sage: assert integral(x, x, hold=True)._sympy_() == Integral(sx, sx)
sage: assert integral(x, x, hold=True) == Integral(sx, sx)._sage_()
sage: assert integral(x, x, 0, 1, hold=True)._sympy_() == Integral(sx, (sx,0,1))
sage: assert integral(x, x, 0, 1, hold=True) == Integral(sx, (sx,0,1))._sage_()
"""
from sage.misc.functional import integral
f, limits = self.function._sage_(), list(self.limits)
for limit in limits:
if len(limit) == 1:
x = limit[0]
f = integral(f, x._sage_(), hold=True)
elif len(limit) == 2:
x, b = limit
f = integral(f, x._sage_(), b._sage_(), hold=True)
else:
x, a, b = limit
f = integral(f, (x._sage_(), a._sage_(), b._sage_()), hold=True)
return f
def _sympysage_integral(self):
"""
EXAMPLES::
sage: from sympy import Symbol, Integral
sage: sx = Symbol('x')
sage: assert integral(x, x, hold=True)._sympy_() == Integral(sx, sx)
sage: assert integral(x, x, hold=True) == Integral(sx, sx)._sage_()
sage: assert integral(x, x, 0, 1, hold=True)._sympy_() == Integral(sx, (sx,0,1))
sage: assert integral(x, x, 0, 1, hold=True) == Integral(sx, (sx,0,1))._sage_()
"""
from sage.misc.functional import integral
f, limits = self.function._sage_(), list(self.limits)
for limit in limits:
if len(limit) == 1:
x = limit[0]
f = integral(f, x._sage_(), hold=True)
elif len(limit) == 2:
x, b = limit
f = integral(f, x._sage_(), b._sage_(), hold=True)
else:
x, a, b = limit
f = integral(f, (x._sage_(), a._sage_(), b._sage_()), hold=True)
return f
