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.libgiac_integrator(expression, v, a=None, b=None)[source]¶
- Integration using libgiac. - EXAMPLES: - sage: # needs sage.libs.giac 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) 1/6*sqrt(6)*pi - >>> from sage.all import * >>> # needs sage.libs.giac >>> 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) 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)