def maxima_integrator(expression, v, a=None, b=None):
"""
Integration using Maxima
EXAMPLES::
sage: from sage.symbolic.integration.external import maxima_integrator
sage: maxima_integrator(sin(x), x)
-cos(x)
sage: maxima_integrator(cos(x), x)
sin(x)
sage: f(x) = function('f')(x)
sage: maxima_integrator(f(x), x)
integrate(f(x), x)
TESTS:
Check that :trac:`25817` is fixed::
sage: maxima_integrator(log(e^x*log(x)*sin(x))/x^2, x)
1/2*(x*(Ei(-log(x)) + conjugate(Ei(-log(x))))
- 2*x*integrate(sin(x)/(x*cos(x)^2 + x*sin(x)^2
+ 2*x*cos(x) + x), x) + 2*x*integrate(sin(x)/(x*cos(x)^2
+ x*sin(x)^2 - 2*x*cos(x) + x), x) + 2*x*log(x) + 2*log(2)
- log(cos(x)^2 + sin(x)^2 + 2*cos(x) + 1) - log(cos(x)^2
+ sin(x)^2 - 2*cos(x) + 1) - 2*log(log(x)))/x
"""
from sage.calculus.calculus import maxima
if not isinstance(expression, Expression):
expression = SR(expression)
if a is None:
result = maxima.sr_integral(expression, v)
else:
result = maxima.sr_integral(expression, v, a, b)
return result._sage_()
def maxima_integrator(expression, v, a=None, b=None):
"""
sage: from sage.symbolic.integration.external import maxima_integrator
sage: maxima_integrator(sin(x), x)
-cos(x)
sage: maxima_integrator(cos(x), x)
sin(x)
sage: f(x) = function('f')(x)
sage: maxima_integrator(f(x), x)
integrate(f(x), x)
"""
from sage.calculus.calculus import maxima
if not isinstance(expression, Expression):
expression = SR(expression)
if a is None:
result = maxima.sr_integral(expression, v)
else:
result = maxima.sr_integral(expression, v, a, b)
return result._sage_()
def maxima_integrator(expression, v, a=None, b=None):
"""
sage: from sage.symbolic.integration.external import maxima_integrator
sage: maxima_integrator(sin(x), x)
-cos(x)
sage: maxima_integrator(cos(x), x)
sin(x)
sage: f(x) = function('f', x)
sage: maxima_integrator(f(x), x)
integrate(f(x), x)
"""
from sage.calculus.calculus import maxima
if not isinstance(expression, Expression):
expression = SR(expression)
if a is None:
result = maxima.sr_integral(expression,v)
else:
result = maxima.sr_integral(expression, v, a, b)
return result._sage_()