Thanks. The large S-unit generator is indeed produced by pari (but I'm not certain whether these are incorrect generators, or whether the initial bug comes from testing them for being S-units, and whether this also explains other inconsistencies between coecions between L and OLSstar and back in other examples):
L = bnfinit(x^6 - 68463*x^4 - 5120808*x^3 + 1250774892*x^2 + 192368273328*x + 7520491439712,1) S2 = idealprimedec(L,2) S2 = [S2[3],S2[2],S2[1]] S7 = idealprimedec(L,7) S13 = idealprimedec(L,13) S13 = [S13[1],S13[3],S13[2]] S5 = idealprimedec(L,5) S = concat([S2,S7,S13,S5]) #The order matters, this one is compatible with sage's S = L.primes_above(2*5*7*13) sfu = bnfsunit(L,S) In GP 2.11.2 (via Sage 9.0), the last two generators in sfu are indeed very large. In GP 2.9.4, it runs for a minute before raising a stack overflow. Running the same example with a different order of input primes raises another bug (perhaps they are related): S2 = idealprimedec(L,2) S2 = [S2[3],S2[2],S2[1]] S5 = idealprimedec(L,5) S7 = idealprimedec(L,7) S13 = idealprimedec(L,13) S13 = [S13[1],S13[3],S13[2]] S = concat([S2,S5,S7,S13]) #same order as what L.primes_above(2),...,L. primes_above(13) yields in sage. sfu = bnfsunit(L,S) In GP 2.11.2 (via Sage 9.0) this immediately raises an error: *** bnfsunit: impossible inverse in ZM_inv: [60, 40, 2, 0, 0, 0, 0, 54; 0, 20, 2, 0, 0, 0, 0, 0; 0, 0, 2, 0, 0, 0, 0, 0; 0, 0, 0, 6, 1, 2, 0, 0; 0, 0, 0, 0, 0, 6, 3, 0; 0, 0, 0, 0, 0, 0, 3, 0; 0, 0, 0, 0, 0, 0, 0, 42; 0, 0, 0, 0, 0, 0, 0, 0]. In GP 2.9.4 it again runs for a minute before raising a stack overflow. Benjamin On Friday, February 28, 2020 at 8:24:36 PM UTC-5, Justin Walker wrote: > > This isn’t an answer, but FWIW, I checked this on sage versions back to > 8.3, and get the same result. > > I also checked, on an older (“Yosemite”) system with sage 7.3, and that > worked as you expect. > > I don’t have time to dig into this, though. > > HTH, > > Justin > > PS: All these were on Macs. > > > On Feb 27, 2020, at 23:02 , 'Benjamin Matschke' via sage-nt < > [email protected] <javascript:>> wrote: > > > > Dear all, > > > > The following code raises a ValueError: [*some big element of L*] is not > an S-unit. > > > > L.<theta_L> = NumberField(x^6 - 68463*x^4 - 5120808*x^3 + 1250774892*x^2 > + 192368273328*x + 7520491439712) > > OLSstar = UnitGroup(L,proof=False,S=tuple(L.primes_above(2*5*7*13))) > > u = OLSstar.gen(11) > > print(u) # yields u11 > > print(L(u)) # yields some very large element of L > > print(OLSstar(L(u))) # raises a ValueError > > > > The last output should of course be u11 again. The above is the simplest > example that I could extract. I have other examples, where the composed > coersion from OLSstar to L and back to OLSstar is not the identity > (according to sage, sometimes a minus is falsely introduced), although it > should. I do not know where the error comes from. > > > > Sometimes UnitGroup() also raises a PariError, which comes from > bnfsunit() within UnitGroup.__init__(), which can be resolved by increasing > pari's precision. The above error however persists after increasing pari's > precision generously. > > > > This was run on Sage 9.0, Linux Mint 19.3. Any help is appreciated. > > > > Thanks, > > Benjamin > > > > -- > > You received this message because you are subscribed to the Google > Groups "sage-nt" group. > > To unsubscribe from this group and stop receiving emails from it, send > an email to [email protected] <javascript:>. > > To view this discussion on the web visit > https://groups.google.com/d/msgid/sage-nt/276bbea0-ca70-411b-b2f9-f8ced377c7c2%40googlegroups.com. > > > > -- > Justin C. Walker > Curmudgeon at Large > Director > Institute for the Enhancement of the Director's Income > -- > Build a man a fire and he'll be warm > for a night. > Set a man on fire and he'll be warm > for the rest of his life. > > > > -- You received this message because you are subscribed to the Google Groups "sage-nt" 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/sage-nt/bea704f1-8822-4239-ba77-94728ce95ef3%40googlegroups.com.
