On Tuesday, 20 July 2021 at 10:26:54 UTC-7 dim...@gmail.com wrote: > On Tue, Jul 20, 2021 at 11:23 AM 'Martin R' via sage-devel > <sage-...@googlegroups.com> wrote: > > > > So, do you have an alternative idea on how to translate these results > from FriCAS to sage? I guess the most interesting application is in > symbolic integration, where rootOf objects appear frequently. > > As far as integration goes, I only know about cases where one takes > the sum over the roots. > > I think that already gives problems. For instance if you have the roots r1=RootOf(x^5+x+1,x,index=1) r2=RootOf(x^5+x+1,x,index=2) r3=RootOf(x^5+x+1,x,index=3) r4=RootOf(x^5+x+1,x,index=4) r5=RootOf(x^5+x+1,x,index=5) then you know the roots are all pairwise distinct, so if they are roots in the same field, they must be *all* roots there, and thus r1+r2+r3+r4+r5=0 (and similarly, any symmetric function in the ri can be evaluated) However, if you're not tracking these indices, or if these rootofs are coming from unrelated source (and a translating interface may not know about the context in which the roots arose), then you cannot draw this conclusion It may well be that Axiom avoids this largely by whenever possible constructing nested rootofs to distinguish "second" roots of polynomials etc., but that means it would probably not be practically capable of computing the result above, because r4 would lie in some extension of absolute degree 120.
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