Here is the first. Please note CAS integration tests uses sagemath for all
the tests
If you think this is sagemath bug, I can report it
>sage
┌────────────────────────────────────────────────────────────────────┐
│ SageMath version 9.8, Release Date: 2023-02-11 │
│ Using Python 3.11.1. Type "help()" for help. │
└────────────────────────────────────────────────────────────────────┘
sage: var('x')
x
sage: integrate(x*(1-x)^2014,x,algorithm="fricas")
Gives
File ~/TMP/sage-9.8/src/sage/interfaces/fricas.py:1313, in
FriCASElement._parse_and_eval(s, start)
1310 a += 1
1312 if s[a] == FriCASElement._LEFTBRACKET:
-> 1313 return FriCASElement._parse_list(s, start=a)
1314 elif s[a] == FriCASElement._STRINGMARKER:
1315 return FriCASElement._parse_string(s, start=a)
RecursionError: maximum recursion depth exceeded
---------------------------------------------
Here is the second one
sage: integrate(x*(1-x)^2020,x,algorithm="fricas")
gives
1310 a += 1
1312 if s[a] == FriCASElement._LEFTBRACKET:
-> 1313 return FriCASElement._parse_list(s, start=a)
1314 elif s[a] == FriCASElement._STRINGMARKER:
1315 return FriCASElement._parse_string(s, start=a)
RecursionError: maximum recursion depth exceeded
The third gives zero, due to a check in place which checks for this due to
earlier
problems with Fricas giving zero on integrals which it should not (may be
you remember this)
the test flagged this as failed. I can fix this.
The next one
sage: integrate(sin(101*x)*sin(x)^99,x,algorithm="fricas")
Failed due to timeout. I did not check the rest, but timeout must be the
same reason.
The tests have 3 minute timeout.
--Nasser
On Monday, March 6, 2023 at 12:08:19 PM UTC-6 Waldek Hebisch wrote:
> On Sat, Mar 04, 2023 at 12:34:25AM -0800, 'Nasser M. Abbasi' via FriCAS -
> computer algebra system wrote:
> >
> > Fyi;
> >
> > The following are the integrals from the MIT integration
> > problems which are not solved broken per CAS.
> >
> <snip>
> > Fricas:
> > -------
> > ln(x+1)/(x^2+1)
> > sin(101*x)*sin(x)^99
> > x*(1-x)^2014 Exception raised: RecursionError >> maximum recursion
> > depth exceeded
> > (2018*x^2017+2017*x^2016)/(x^4036+2*x^4035+x^4034+1) Timed out
> > cos(3*x)+sin(2*x)*(-sin(2019*x)+cos(3*x)) Timed out
> > x*(1-x)^2020 Exception raised: RecursionError >> maximum recursion depth
> > exceeded
> > (1-x)^3+(-x^2+x)^3+(x^2-1)^3-3*(1-x)*(-x^2+x)*(x^2-1)
> > (x+exp(1)+1)*x^exp(x)*exp(x)
> > (3*x^3+2*x^2+1)/(x^2+1)^(1/3)
> > (1/x*ln(1/x))^(1/2)
> > 2^(1/2)*ln(x)^(1/2)+1/2*2^(1/2)/ln(x)^(1/2)
>
> Hmm, AFACS FriCAS can do:
>
> x*(1-x)^2014
> x*(1-x)^2020
> (1-x)^3+(-x^2+x)^3+(x^2-1)^3-3*(1-x)*(-x^2+x)*(x^2-1)
>
> all 3 are polynomials so should be easy for computer. The first
> two give somewhat large result, but FriCAS is supposed to handle
> much larger polynomials. The third is 0.
>
> In principle FriCAS should do:
>
> sin(101*x)*sin(x)^99
> (2018*x^2017+2017*x^2016)/(x^4036+2*x^4035+x^4034+1)
> cos(3*x)+sin(2*x)*(-sin(2019*x)+cos(3*x))
>
> but first and third currently trigger costly transformations, that
> could be avoided. Second looks inherently heavy when done by
> general methods.
>
> --
> Waldek Hebisch
>
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