TESTS::¶
- sage.symbolic.integration.external.fricas_integrator(expression, v, a=None, b=None, noPole=True)[source]¶
Integration using FriCAS.
EXAMPLES:
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
>>> 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.symbolic.integration.external.giac_integrator(expression, v, a=None, b=None)[source]¶
Integration using Giac.
EXAMPLES:
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
>>> 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.symbolic.integration.external.libgiac_integrator(expression, v, a=None, b=None)[source]¶
Integration using libgiac.
EXAMPLES:
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
>>> 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.symbolic.integration.external.maxima_integrator(expression, v, a=None, b=None)[source]¶
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)
>>> 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.symbolic.integration.external.mma_free_integrator(expression, v, a=None, b=None)[source]¶
Integration using Mathematica’s online integrator.
EXAMPLES:
sage: from sage.symbolic.integration.external import mma_free_integrator sage: mma_free_integrator(sin(x), x) # optional - internet -cos(x)
>>> from sage.all import * >>> from sage.symbolic.integration.external import mma_free_integrator >>> mma_free_integrator(sin(x), x) # optional - internet -cos(x)
A definite integral:
sage: mma_free_integrator(e^(-x), x, a=0, b=oo) # optional - internet 1
>>> from sage.all import * >>> mma_free_integrator(e**(-x), x, a=Integer(0), b=oo) # optional - internet 1
- sage.symbolic.integration.external.sympy_integrator(expression, v, a=None, b=None)[source]¶
Integration using SymPy.
EXAMPLES:
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)
>>> 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)