" Maple page says: Ei(a, z) = z^(a-1)*GAMMA(1-a, z)
In FriCAS that would be Ei(a, z) == z^(a-1)*Gamma(1 - a, z) I am not sure if Maple is right, example above leads to Gamma(0, x) which is undefined." But the help page https://www.maplesoft.com/support/help/maple/view.aspx?path=Ei says "with the exception of the point 0 in the case of Ei1(z)." Ok, so the bottom line is that Fricas does not have a builtin function for the two argument version for exponential integral function that sagemath can translate the call to. In this case, for now, I will remove these problems (135 in total from this particular Rubi test file), because now Fricas fails all of them since sagemath is assuming Fricas has the two argument version. --Nasser On Tuesday, April 9, 2024 at 11:30:13 PM UTC-5 Waldek Hebisch wrote: > On Tue, Apr 09, 2024 at 08:24:35PM -0700, 'Nasser M. Abbasi' via FriCAS - > computer algebra system wrote: > > I found problem integrating many problems using sagemath calling Fricas > to > > do the integration when using exponential integral function. These are > > problems from Rubi test files. > > > > It works OK with other CAS systems supported by sagemath (Maxima and > GIAC) > > but sagemath 10.3 does not seem to correctly translate the call to > Fricas. > > > > I am having hard time finding what the exponential integral function is > > called before I ask at sagemath forum. I looked at the Fricas book and > do > > not see anything,. I tried Ei but this does not work. (i.e. does not > give > > same answer as other cas systems). > > Well, 'Ei' is "true exponential integral". Other systems ofer you > variants, in FriCAS it is just 'Ei'. Some variants are equivalent > to incomplete gamma function, in such case FriCAS gives you > incomplete gamma. > > > First here is a link to the special function I am taking about > > > > https://reference.wolfram.com/language/ref/ExpIntegralE.html > > > > https://www.maplesoft.com/support/help/maple/view.aspx?path=Ei > > > > Here is a test to what values it should give for some random input. In > > Mathematica it gives > > > > ExpIntegralE[3, 5.0] > > .000877801 > > > > In Maple > > > > Ei(3,5.0) > > 0.0008778008928 > > > > IN sagemath 10.3 > > > > sage: exp_integral_e(3,5.0) > > 0.000877800892770638 > > > > But I tried Ei(3,5.0) in Fricas and it gives error. > > 'Ei' takes a single argument. If you need relations between various > functions look into Abramowitz and Stegun, FriCAS Ei is exactly as > defined in Abramowitz and Stegun. > > > > > Here is an example, using sagemath trying to integrate. It works OK with > > maxima and giac but gives error with Fricas. I am using > > > > >fricas --version > > FriCAS 1.3.10 > > based on sbcl 2.3.11 > > > > with sagemath > > >sage --version > > SageMath version 10.3, Release Date: 2024-03-19 > > > > Starting sagemath and typing: > > > > sage: var('x a b') > > (x, a, b) > > > > sage: integrate(exp_integral_e(1,b*x),x,algorithm="giac") > > integrate(exp_integral_e(1, b*x), x) > > > > sage: integrate(exp_integral_e(1,b*x),x,algorithm="maxima") > > -exp_integral_e(2, b*x)/b > > > > sage: integrate(exp_integral_e(1,b*x),x,algorithm="fricas") > > RuntimeError Traceback (most recent call last) > > TypeError: An error occurred when FriCAS evaluated > > 'exp_integral_e(((1)::EXPR INT),(b)*(x))': > > There are no library operations named exp_integral_e > > > > So clearly sagemath did not translate the exp_integral_e to Fricas > > correctly. > > > > What should the translation look like? > > Maple page says: > > Ei(a, z) = z^(a-1)*GAMMA(1-a, z) > > In FriCAS that would be > > Ei(a, z) == z^(a-1)*Gamma(1 - a, z) > > I am not sure if Maple is right, example above leads to Gamma(0, x) > which is undefined. > > -- > Waldek Hebisch > -- You received this message because you are subscribed to the Google Groups "FriCAS - computer algebra system" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To view this discussion on the web visit https://groups.google.com/d/msgid/fricas-devel/e461b761-03fc-4a35-8317-f53672edebd9n%40googlegroups.com.
