TESTS::

sage.symbolic.integration.external.fricas_integrator(expression, v, a=None, b=None, noPole=True)

Integration using FriCAS.

EXAMPLES:

Sage

sage: # optional - fricas
sage: from sage.symbolic.integration.external import fricas_integrator
sage: fricas_integrator(sin(x), x)
-cos(x)
sage: fricas_integrator(cos(x), x)
sin(x)
sage: fricas_integrator(1/(x^2-2), x, 0, 1)
-1/8*sqrt(2)*(log(2) - log(-24*sqrt(2) + 34))
sage: fricas_integrator(1/(x^2+6), x, -oo, oo)
1/6*sqrt(6)*pi

Python

>>> from sage.all import *
>>> # optional - fricas
>>> from sage.symbolic.integration.external import fricas_integrator
>>> fricas_integrator(sin(x), x)
-cos(x)
>>> fricas_integrator(cos(x), x)
sin(x)
>>> fricas_integrator(Integer(1)/(x**Integer(2)-Integer(2)), x, Integer(0), Integer(1))
-1/8*sqrt(2)*(log(2) - log(-24*sqrt(2) + 34))
>>> fricas_integrator(Integer(1)/(x**Integer(2)+Integer(6)), x, -oo, oo)
1/6*sqrt(6)*pi

Sage Live

# optional - fricas
from sage.symbolic.integration.external import fricas_integrator
fricas_integrator(sin(x), x)
fricas_integrator(cos(x), x)
fricas_integrator(1/(x^2-2), x, 0, 1)
fricas_integrator(1/(x^2+6), x, -oo, oo)

sage.symbolic.integration.external.giac_integrator(expression, v, a=None, b=None)

Integration using Giac.

EXAMPLES:

Sage

sage: from sage.symbolic.integration.external import giac_integrator
sage: giac_integrator(sin(x), x)
-cos(x)
sage: giac_integrator(1/(x^2+6), x, -oo, oo)
1/6*sqrt(6)*pi

Python

>>> from sage.all import *
>>> from sage.symbolic.integration.external import giac_integrator
>>> giac_integrator(sin(x), x)
-cos(x)
>>> giac_integrator(Integer(1)/(x**Integer(2)+Integer(6)), x, -oo, oo)
1/6*sqrt(6)*pi

Sage Live

from sage.symbolic.integration.external import giac_integrator
giac_integrator(sin(x), x)
giac_integrator(1/(x^2+6), x, -oo, oo)

sage.symbolic.integration.external.libgiac_integrator(expression, v, a=None, b=None)

Integration using libgiac.

EXAMPLES:

Sage

sage: import sage.libs.giac
...
sage: from sage.symbolic.integration.external import libgiac_integrator
sage: libgiac_integrator(sin(x), x)
-cos(x)
sage: libgiac_integrator(1/(x^2+6), x, -oo, oo)
No checks were made for singular points of antiderivative...
1/6*sqrt(6)*pi

Python

>>> from sage.all import *
>>> import sage.libs.giac
...
>>> from sage.symbolic.integration.external import libgiac_integrator
>>> libgiac_integrator(sin(x), x)
-cos(x)
>>> libgiac_integrator(Integer(1)/(x**Integer(2)+Integer(6)), x, -oo, oo)
No checks were made for singular points of antiderivative...
1/6*sqrt(6)*pi

Sage Live

import sage.libs.giac
from sage.symbolic.integration.external import libgiac_integrator
libgiac_integrator(sin(x), x)
libgiac_integrator(1/(x^2+6), x, -oo, oo)

sage.symbolic.integration.external.maxima_integrator(expression, v, a=None, b=None)

Integration using Maxima.

EXAMPLES:

Sage

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)

Python

>>> from sage.all import *
>>> from sage.symbolic.integration.external import maxima_integrator
>>> maxima_integrator(sin(x), x)
-cos(x)
>>> maxima_integrator(cos(x), x)
sin(x)
>>> __tmp__=var("x"); f = symbolic_expression(function('f')(x)).function(x)
>>> maxima_integrator(f(x), x)
integrate(f(x), x)

Sage Live

from sage.symbolic.integration.external import maxima_integrator
maxima_integrator(sin(x), x)
maxima_integrator(cos(x), x)
f(x) = function('f')(x)
maxima_integrator(f(x), x)

sage.symbolic.integration.external.mma_free_integrator(expression, v, a=None, b=None)

Integration using Mathematica’s online integrator.

EXAMPLES:

Sage

sage: from sage.symbolic.integration.external import mma_free_integrator
sage: mma_free_integrator(sin(x), x) # optional - internet
-cos(x)

Python

>>> from sage.all import *
>>> from sage.symbolic.integration.external import mma_free_integrator
>>> mma_free_integrator(sin(x), x) # optional - internet
-cos(x)

Sage Live

from sage.symbolic.integration.external import mma_free_integrator
mma_free_integrator(sin(x), x) # optional - internet

A definite integral:

Sage

sage: mma_free_integrator(e^(-x), x, a=0, b=oo) # optional - internet
1

Python

>>> from sage.all import *
>>> mma_free_integrator(e**(-x), x, a=Integer(0), b=oo) # optional - internet
1

Sage Live

mma_free_integrator(e^(-x), x, a=0, b=oo) # optional - internet

sage.symbolic.integration.external.sympy_integrator(expression, v, a=None, b=None)

Integration using SymPy.

EXAMPLES:

Sage

sage: from sage.symbolic.integration.external import sympy_integrator
sage: sympy_integrator(sin(x), x)                                               # needs sympy
-cos(x)
sage: sympy_integrator(cos(x), x)                                               # needs sympy
sin(x)

Python

>>> from sage.all import *
>>> from sage.symbolic.integration.external import sympy_integrator
>>> sympy_integrator(sin(x), x)                                               # needs sympy
-cos(x)
>>> sympy_integrator(cos(x), x)                                               # needs sympy
sin(x)

Sage Live

from sage.symbolic.integration.external import sympy_integrator
sympy_integrator(sin(x), x)                                               # needs sympy
sympy_integrator(cos(x), x)                                               # needs sympy

Make live