"As I wrote large size/timeout on such integrals is artifact of
Sage interface. You can see answer on FriCAS command line."
But it hangs using Fricas directly. When I tried it above I was not using
sagemath at all.
=========================
(1) -> setSimplifyDenomsFlag(true)
(1) false
Type:
Boolean
(2) -> ii:=integrate(cos(d*x+c)^4/(a+b*sin(d*x+c)^3)^2,x);
===========================
The above hangs on my computer. I am using 1.3.8. I waited for more than
30
minutes and had to stop it. But this below completes in about 1 minute:
=============================
1) -> setSimplifyDenomsFlag(false)
(1) false
Type:
Boolean
(2) -> ii:=integrate(cos(d*x+c)^4/(a+b*sin(d*x+c)^3)^2,x);
==============================
I am using
======================
FRICAS="/usr/local/lib/fricas/target/x86_64-linux-gnu"
spad-lib="/usr/local/lib/fricas/target/x86_64-linux-gnu/lib/libspad.so"
FriCAS Computer Algebra System
Version: FriCAS 1.3.8
=====================
On Linux Manjaro.
If this is not what you are also seeing, then I wonder why then it hangs on
my system.
I am running Linux inside a virtual box. But this should not have anything
to do with it.
"Yes, RootSum (and rootof) are considered elementary functions."
Ah, I see. For some reason I thought these are not considered elementary
functions.
This is good to know.
I will email Albert links to these integrals you showed.
But in addition, all such integrals that are solved but marked as
non-integrable in
the Rubi input files, are already tagged as such in the reports generated
by CAS integration
test to make it easy for anyone to view them.
These integrals are listed as bold letters in the main page, chapter 2
"links to individual test reports"
<https://12000.org/my_notes/CAS_integration_tests/reports/summer_2022/indexchapter2.htm>
"The list of numbers in the curly brackets after that (if any) is the list
of the integrals
in that specific test which were solved by any CAS which are known not to
have antiderivative.
This makes it easier to find these integrals and do more investigation into
them."
It will be up to Albert Rich to decide to update his Rubi input files based
on this finding. But
I will let him know as well.
Regards
--Nasser
On Saturday, September 24, 2022 at 5:01:17 PM UTC-5 Waldek Hebisch wrote:
> On Sat, Sep 24, 2022 at 08:46:35AM -0700, 'Nasser M. Abbasi' via FriCAS -
> computer algebra system wrote:
> > " BTW: I am not sure how you maintain "has_known_anti". The following
> > 9 have has_known_anti = 0, but belong to well-known class having
> > elementary integrals:"
> >
> > Hello;
> >
> > I myself do not edit or modify the input files. The Rubi input files are
> > maintained by Albert Rich.
> > This way there is only only source. If I modify or edit these files,
> then
> > things will get out of sync.
> >
> > I will forward these integrals you found to Albert Rich and let him know
> > that these have known
> > anti-derivatives so he can update the files on his end for next release.
> > But first I would
> > need to know the list of the known antiderivatives for these to send
> them
> > as well.
> >
> > For example the first integral in your list is integral number 399 in
> file
> > 4_Trig_functions/4.1_Sine/4.1.7-d_trig-^m-a+b-c_sin-^n-^p.txt
> >
> > And the Rubi input file says
> >
> > {Cos[c + d*x]^4/(a + b*Sin[c + d*x]^3)^2, x, 0, Unintegrable[Cos[c +
> > d*x]^4/(a + b*Sin[c + d*x]^3)^2, x]}
> >
> > It is the 4th field above which says it is not integrable. Otherwise it
> > will have the optimal
> > antiderivative there.
> >
> > Mathematica gives solution but in terms of rootsof
> >
> > In[2]:= Integrate[Cos[c+d*x]^4/(a+b*Sin[c+d*x]^3)^2,x]
> > Out[2]= (1/(18 a b d))(-I RootSum[-I b+3 I b #1^2+8 a #1^3-3 I b #1^4+I
> b
> > #1^6&,(2 b ArcTan[Sin[c+d x]/(Cos[c+d x]-#1)]-I b Log[1-2 Cos[c+d x]
> > #1+#1^2]+4 I a ArcTan[Sin[c+d x]/(Cos[c+d x]-#1)] #1+2 a Log[1-2 Cos[c+d
> x]
> > #1+#1^2] #1+12 b ArcTan[Sin[c+d x]/(Cos[c+d x]-#1)] #1^2-6 I b Log[1-2
> > Cos[c+d x] #1+#1^2] #1^2-4 I a ArcTan[Sin[c+d x]/(Cos[c+d x]-#1)] #1^3-2
> a
> > Log[1-2 Cos[c+d x] #1+#1^2] #1^3+2 b ArcTan[Sin[c+d x]/(Cos[c+d x]-#1)]
> > #1^4-I b Log[1-2 Cos[c+d x] #1+#1^2] #1^4)/(b #1-4 I a #1^2-2 b #1^3+b
> > #1^5)&]+(24 Cos[c+d x] (a+b Sin[c+d x]))/(4 a+3 b Sin[c+d x]-b Sin[3
> (c+d
> > x)]))
> >
> > And Rubi does not solve it
> >
> > In[4]:= Int[Cos[c+d*x]^4/(a+b*Sin[c+d*x]^3)^2,x]
> > Out[4]= Int[Cos[c+d x]^4/(a+b Sin[c+d x]^3)^2,x]
>
> Well, that is known weakness of Rubi.
>
> > Maple gives solution is also in terms of rootof
> >
> <snip>
> >
> > Looking at Fricas I see it timed out on this:
> >
> > sqlite> select fricas_anti from main where rowid=37649;
> > Timed out
>
> As I wrote large size/timeout on such integrals is artifact of
> Sage interface. You can see answer on FriCAS command line.
>
> > But this must be because of the use of the flag set to true.
> > When I tried it now without setting the flag:
> >
> > ii:=integrate(cos(d*x+c)^4/(a+b*sin(d*x+c)^3)^2,x);
> >
> > Fricas gave a very large output also using Root object. But you said
> > antiderivative is
> > in terms of elementary functions?
>
> Yes, RootSum (and rootof) are considered elementary functions.
> And results of integration look exactly as they should.
> Here (in all 9 examples) in fact implicit roots are only used
> to provide constants.
>
> --
> 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/c0e56d63-b47b-4180-bbfc-174d71fd8bean%40googlegroups.com.
