Given an authorative answer, it should not be hard to add that translation to the sagemath-fricas interface. Just let me know.
Martin On Wednesday 10 April 2024 at 09:16:15 UTC+2 Nasser M. Abbasi wrote: > > " 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/9a8b71d0-e07c-4a41-ab86-597e0f74051cn%40googlegroups.com.
