[Maxima-discuss] How can I catch this error? "errcatch" doesn't do the trick.

[Aleksas D. <ale...@gm...>]

David Scherfgen <d.scherfgen@go...> - 2015-09-08 11:14:22   wrote:


Dear Richard,
>
> thank you for your very detailed response and your patience with me! :-)
>
> integrate_use_rootsof is indeed interesting, thanks for pointing it out to
> me.
>
> However, I think that it doesn't quite work in the way it is intended to.
> For example, take the function 1/(x^(1/3)+x+1). When we integrate it with
> integrate_use_rootsof enabled, we get an answer that contains
> rootsof(x+x^(1/3)+1). Doesn't the use of rootsof in an integral only make
> sense for polynomials, since only they can be factored into factors of (x -
> root_n)? Note that Wolfram Alpha gives an answer that is very similar to
> Maxima's, but it involves the roots of the polynomial x^3+x+1.
>
> Maxima's answer is wrong, there seems to be a bug in the part that uses
> integrate_use_rootsof. I think this is what happens: integrate performs the
> substitution u=x^(1/3), which results in 3*integrate(u^2/(u^3+u+1),u). Here
> we have that polynomial u^3+u+1 (from Wolfram Alpha's answer) in the
> denominator. But instead of outputting rootsof(u^3+u+1), Maxima substitutes
> u=x^(1/3) back and outputs rootsof(x^(1/3)+x+1). It should not perform this
> back-substitution. Unless you tell me that I'm wrong, I will file a bug
> report about that ...
>
>


Output is removed.

(%i1) integrate(1/(x+x^(1/3)+1),x);
(%i2) S:changevar(%, y^3=x, y, x);
(%i3) solve(y^3+y+1)$
(%i4) sols:map(rhs,%);
(%i5) tr:(sqrt(31)/(2*3^(3/2))-1/2)^(1/3)=omega;
(%i6) float(%), numer;
(%i7) assume(omega>0)$
(%i8) spr:subst(tr,sols);
(%i9) y^3+y+1=expand((y-spr[1])*(y-spr[2]))*(y-spr[3]);
(%i10) subst(%,S);
(%i11) ev(%, nouns);
(%i12) solution:subst([y=(x)^(1/3),reverse(tr)],%);

 Test of integration:
(%i15) diff(solution,x),radcan;
(%o15) 1/(x+x^(1/3)+1)

 If x>0 solution is real function
(%i14) wxplot2d([solution], [x,0,5])$

best

Aleksas Domarkas