Thank you very much for the quick reply. Does this mean that we will not be able to find the integration involving the differential using sagemath ??
I am trying to find the solution for the following integral, provided with p(x) and p(y), expecting the solution in terms of "f" <https://lh3.googleusercontent.com/-0k08-cd20Tk/VbXcDaeOQfI/AAAAAAAAAGA/gkTo3EtmO4U/s1600/CodeCogsEqn2.gif> <https://lh3.googleusercontent.com/-2v4buhYDQww/VbXb55K_ZhI/AAAAAAAAAF4/3SqJyjPXP0Y/s1600/CodeCogsEqn1.gif> Can you please suggest me the best way to get around with the solution of the integral. Thank you once again, Regards, sairam On Monday, July 27, 2015 at 11:49:12 AM UTC+5:30, David Joyner wrote: > > > > On Mon, Jul 27, 2015 at 1:09 AM, sairam <sairam.t...@gmail.com > <javascript:>> wrote: > >> Thank you very much for the reply. In the integration specified, f is a >> function of y >> >> When I use the following as suggested by you, >> >> x, y, a= var('x,y,a') >> f = function("f", y) >> integrate(integrate((diff(f,y))*(exp(-a*x^2)*cos(y)^2*sin(x)^3), x, 0, >> pi), y, -pi, pi) >> >> Sagemath is dumping an error. I would appreciate if you can helping me >> sorting out the problem in evaluating the integral. >> >> > A simpler way to get this error (since your double integral is obviously a > product of 2 integrals) is below. I don't understand this error either. > > sage: f = function("f", x) > sage: integrate(diff(f,x)*cos(x)^2, x, -pi, pi) > #0: > signum_int(q=cos(2*_SAGE_VAR_x)*'diff('realpart(f(_SAGE_VAR_x)),_SAGE_VAR_x,1)+sin(2*_SAGE_VAR_x)*'diff('imagpart...,x=_SAGE_VAR_x) > #1: > extra_integrate(q=cos(2*_SAGE_VAR_x)*'diff('realpart(f(_SAGE_VAR_x)),_SAGE_VAR_x,1)+sin(2*_SAGE_VAR_x)*'diff('imagpart...,x=_SAGE_VAR_x) > --------------------------------------------------------------------------- > RuntimeError Traceback (most recent call last) > <ipython-input-17-9166435d0d62> in <module>() > ----> 1 integrate(diff(f,x)*cos(x)**Integer(2), x, -pi, pi) > > /Volumes/Bay3/sagefiles2/sage-6.4.1/local/lib/python2.7/site-packages/sage/misc/functional.pyc > > in integral(x, *args, **kwds) > 800 """ > 801 if hasattr(x, 'integral'): > --> 802 return x.integral(*args, **kwds) > 803 else: > 804 from sage.symbolic.ring import SR > > /Volumes/Bay3/sagefiles2/sage-6.4.1/local/lib/python2.7/site-packages/sage/symbolic/expression.so > > in sage.symbolic.expression.Expression.integral > (build/cythonized/sage/symbolic/expression.cpp:50961)() > > /Volumes/Bay3/sagefiles2/sage-6.4.1/local/lib/python2.7/site-packages/sage/symbolic/integration/integral.pyc > > in integrate(expression, v, a, b, algorithm, hold) > 710 return indefinite_integral(expression, v, hold=hold) > 711 else: > --> 712 return definite_integral(expression, v, a, b, hold=hold) > 713 > 714 integral = integrate > > /Volumes/Bay3/sagefiles2/sage-6.4.1/local/lib/python2.7/site-packages/sage/symbolic/function.so > > in sage.symbolic.function.BuiltinFunction.__call__ > (build/cythonized/sage/symbolic/function.cpp:9269)() > > /Volumes/Bay3/sagefiles2/sage-6.4.1/local/lib/python2.7/site-packages/sage/symbolic/function.so > > in sage.symbolic.function.Function.__call__ > (build/cythonized/sage/symbolic/function.cpp:5911)() > > /Volumes/Bay3/sagefiles2/sage-6.4.1/local/lib/python2.7/site-packages/sage/symbolic/integration/integral.pyc > > in _eval_(self, f, x, a, b) > 173 for integrator in self.integrators: > 174 try: > --> 175 return integrator(*args) > 176 except NotImplementedError: > 177 pass > > /Volumes/Bay3/sagefiles2/sage-6.4.1/local/lib/python2.7/site-packages/sage/symbolic/integration/external.pyc > > in maxima_integrator(expression, v, a, b) > 19 result = maxima.sr_integral(expression,v) > 20 else: > ---> 21 result = maxima.sr_integral(expression, v, a, b) > 22 return result._sage_() > 23 > > /Volumes/Bay3/sagefiles2/sage-6.4.1/local/lib/python2.7/site-packages/sage/interfaces/maxima_lib.pyc > > in sr_integral(self, *args) > 774 """ > 775 try: > --> 776 return > max_to_sr(maxima_eval(([max_integrate],[sr_to_max(SR(a)) for a in args]))) > 777 except RuntimeError as error: > 778 s = str(error) > > /Volumes/Bay3/sagefiles2/sage-6.4.1/local/lib/python2.7/site-packages/sage/libs/ecl.so > > in sage.libs.ecl.EclObject.__call__ > (build/cythonized/sage/libs/ecl.c:6877)() > > /Volumes/Bay3/sagefiles2/sage-6.4.1/local/lib/python2.7/site-packages/sage/libs/ecl.so > > in sage.libs.ecl.ecl_safe_apply (build/cythonized/sage/libs/ecl.c:4734)() > > RuntimeError: ECL says: Error executing code in Maxima: > > Thank you once again, >> >> Regards, >> sairam >> >> On Sunday, July 26, 2015 at 4:38:59 PM UTC+5:30, David Joyner wrote: >>> >>> In the integrand below, is f simply a function of y or does it also >>> depend on x? >>> >>> >>> On Jul 26, 2015, at 04:25, sairam <sairam.t...@gmail.com> wrote: >>>> >>>> >>>> <https://lh3.googleusercontent.com/-HGLRuiudDNI/VbRfkfqbiNI/AAAAAAAAAFk/gVw9Ejc6pyo/s1600/CodeCogsEqn.gif> >>>> >>>> Hi >>>> >>>> I am new bie to sagemath and trying to find the analytical integration >>>> for the above. >>>> >>>> I have used the following expressions in sagemath >>>> >>>> x, y, a, f = var('x,y,a,f') >>>> >>>> >>> >>> f = function("f", x) >>> or >>> f = function("f",x,y) >>> >>> integrate(integrate((diff(f))*(exp(-a*x^2)*cos(y)^2*sin(x)^3), x, 0, >>>> pi), y, -pi, pi) >>>> >>>> >>> In the first case, you want >>> >>> >>> x, y, a= var('x,y,a') >>> f = function("f", x) >>> integrate(integrate((diff(f,x))*(exp(-a*x^2)*cos(y)^2*sin(x)^3), x, 0, >>> pi), y, -pi, pi) >>> >>> which will give you the partially evaluated integral. >>> >>> The sagemath tutorials have more examples. >>> http://doc.sagemath.org/html/en/tutorial/index.html >>> >>> >>> >>> >>>> Though it gives output for the above expression, it does not consider >>>> the term differential of f, can you please let me know how to include the >>>> differential in the integration. >>>> >>>> If I use the following, which includes differential with respect to y, >>>> it does not run but dumps an error >>>> >>>> integrate(integrate((diff(f), y)*(exp(-a*x^2)*cos(y)^2*sin(x)^3), x, 0, >>>> pi), y, -pi, pi) >>>> >>>> Any help for solving the above integration will be highly appreciated. >>>> >>>> Thanks in advance, >>>> >>>> Regards, >>>> sairam >>>> >>>> >>>> > -- You received this message because you are subscribed to the Google Groups "sage-edu" group. 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