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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