Igor Schein on Wed, 3 Feb 1999 14:57:21 -0500 |
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Re: polgalois() |
On Thu, Jan 28, 1999 at 02:22:39PM -0500, Igor Schein wrote: > On Tue, Jan 26, 1999 at 11:55:39AM -0500, Igor Schein wrote: > > Hi, > > > > polgalois(x^11+2) runs forever. I haven't had patience to see if it'd > > ever finish. Is it expectable? > > > > Thanks > > > > Igor > > Looks like it might finish after a very long time ( at least 2 > Ultra-60 CPU days, according to a very rough estimate ). > > Indeed, here's the loop: > > galois.c:862: for (nocos=1; nocos<=nbcos; nocos++) > > For 11-degree polynomial nbcos is 11!, which is ~400M. > > So it's one loooong loop. > > polgalois() never gets inside this loop of all other polynomials I > tried, including degree-8,9,10 and degree-11 polynomials. So it's > either a bug or bad coding. For comparison, I tried an equivalent > of polgalois() in GAP software, and it came back with an answer in a > short time. > > Igor I thought I should follow up on this one. There're a total of 8 Galois groups for degree-11 polynomials. Juergen Klueren provided me with representatives for each of them. If you exclude A_11 and S_11, there're 6 remaining. 4 of them are EVEN groups. For those, the loop above goes to nocos=2500, so the answer takes less than 20s on Ultra-60. The other 2 are the ones where PARI fails to give an answer in reasonable time. One has representatives of form x^11+k, where abs(k)>1. This is my original observation. The other one is represented by p=x^11 - x^10 + 5*x^9 - 4*x^8 + 10*x^7 - 6*x^6 + 11*x^5 - 7*x^4 +\ 9*x^3 - 4*x^2 + 2*x + 1; nocos goes way beyond 2500. It might not go all the way to 11!, like I originally thought, but still... Any ideas why PARI stumbles on ODD groups in particular? Igor