Behind the scene, Sage uses pynac (a clone of ginac) for its handling of symbolics. Implicit roots are supported. Docs say:
-------- "By default, all the roots are required to be explicit rather than implicit. To get implicit roots, pass explicit_solutions=False to .roots() ------ I am not sure how well fricas interface is handling these, though. Dima On Tue, 23 Aug 2022, 15:22 Waldek Hebisch, <[email protected]> wrote: > On Tue, Aug 23, 2022 at 05:55:29AM -0700, 'Martin R' via FriCAS - computer > algebra system wrote: > > If I understand correctly, FriCAS' result of integrate(1/(b*x^5+a), x) > > contains some algebraic numbers with placeholders like %%G0. To convert > > the result into a sage expression, these are substituted back. > > Unfortunately, these expressions may be extremely large, and this effect > > multiplies when the constants appear multiple times. > > Those are not placeholders, they are roots of polynomials in > implict form. MMas call them RootOf. > > > If you have any suggestions on how to improve the situation, I'd be > happy > > to hear it. Leaving them out is not really an option, because one may > want > > to do further computations with the integral. > > Represent them faithfully as implicit roots. AFAICS Sage expands > them to explicit form and this is _much_ larger than necessary. > Worse, explicit form is problematic for later computations. > > BTW: Could you try the the attached patch? The patch is not > ready to be included now, but once problems are worked out > many integrals will produce result like below. In this example > with the patch I get: > > (1) -> integrate(1/(b*x^5+a), x) > > --+ > (1) > %E log(x + 5 %E a) > --+ > 4 5 > 3125 a b %E - 1 = 0 > Type: > Union(Expression(Integer),...) > (2) -> %::EXPR(INT)::InputForm > > (2) > (%root_sum (* %E (log (+ x (* (* 5 %E) a)))) %E > (/ (+ (* (* (* 3125 (^ %E 5)) (^ a 4)) b) - 1) (* (* 3125 (^ a 4)) b))) > Type: > InputForm > > > -- > 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/20220823142241.GA29641%40fricas.math.uni.wroc.pl > . > -- 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/CAAWYfq0x6eimq6GDw%3DnjvTo4zFV5-STcj_7_fSkYe1dkn%3DtNzQ%40mail.gmail.com.
