Timeline for Is there an algorithm for determining whether an expression involving nested radicals is rational?
Current License: CC BY-SA 4.0
8 events
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| Oct 24, 2019 at 14:30 | history | edited | François Brunault | CC BY-SA 4.0 |
Clarification: radicals --> real radicals
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| Oct 24, 2019 at 11:35 | comment | added | Ville Salo | Ok. Maybe I need to tone down my love for this package. | |
| Oct 24, 2019 at 11:34 | comment | added | François Brunault | I see -- that's good to know in any case. The doc gives the example of the computation of the regular 34-gon, and they say that comparing the two algebraic numbers "is currently infinitely long". I don't know whether this means that the algorithm fails in this case. | |
| Oct 24, 2019 at 11:33 | comment | added | Ville Salo | Let me retract that after reading "Algebraic numbers exist in one of the following forms". Any experts on CAS present? | |
| Oct 24, 2019 at 11:31 | comment | added | Ville Salo | My experience is that it is pretty much an implementation of algebraic reals in both a very correct, and a very practical sense. But I have not studied its theory or exact promises, and have only done simple things with it (computing exact trajectories for some toral automorphisms). (So the answer to your question would be "is", is my best guess.) | |
| Oct 24, 2019 at 11:27 | comment | added | François Brunault | @VilleSalo I didn't know this package. Do you know if this implementation allows to convert a nested expression into an absolute expression (meaning an irreducible polynomial plus a sufficiently precise approximation of the root)? Moreover, the doc says that conversion works only if the number is rational, and it's not clear to me whether they mean "is" or " is represented as". | |
| Oct 24, 2019 at 11:16 | comment | added | Ville Salo | To quote from doc.sagemath.org/html/en/reference/number_fields/sage/rings/… "minpoly() Compute the minimal polynomial of this algebraic number." so I guess AA implements this functionality. | |
| Oct 24, 2019 at 11:11 | history | answered | François Brunault | CC BY-SA 4.0 |