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My attepts to tackle computing the norm of an ideal in the 5th cyclotomic field, (denoted K5) polcyclo(5) the polynomial defining the field were successful in PARI/GP. I was also able to find its principal generators and compute more (the command on the third and fourth lines).

(09:24) gp > J = idealhnf(bnfinit(polcyclo(5)),11,x-3);
(09:24) gp > idealnorm(bnfinit(polcyclo(5)),J)
%16 = 11
(09:24) gp > Jp = bnfisprincipal(bnfinit(polcyclo(5)),J)
%17 = [[]~, [1, -1, -1, 0]~]
(09:24) gp > u = nfbasistoalg(bnfinit(polcyclo(5)),Jp[2])
%18 = Mod(-x^2 - x + 1, x^4 + x^3 + x^2 + x + 1)
(09:24) gp >

I would like to perform the same task at the same pace for K179, but this is not working. What is wrong with PARI/GP? Do I need another program to do this?

(09:25) gp > J = idealhnf(bnfinit(polcyclo(179)),359,x-2);
  ***   at top-level: J=idealhnf(bnfinit(polcyclo(179
  ***                            ^--------------------
  *** bnfinit: the PARI stack overflows !
  current stack size: 16000000 (15.259 Mbytes)
  [hint] you can increase GP stack with allocatemem()

(09:26) gp > idealnorm(bnfinit(polcyclo(179)),J)
  ***   at top-level: idealnorm(bnfinit(polcyclo(179
  ***                           ^--------------------
  *** bnfinit: the PARI stack overflows !
  current stack size: 16000000 (15.259 Mbytes)
  [hint] you can increase GP stack with allocatemem()

(09:27) gp > Jp = bnfisprincipal(bnfinit(polcyclo(179)),J)
  ***   at top-level: Jp=bnfisprincipal(bnfinit(polcyclo(179
  ***                                   ^--------------------
  *** bnfinit: the PARI stack overflows !
  current stack size: 16000000 (15.259 Mbytes)
  [hint] you can increase GP stack with allocatemem()

(09:28) gp > u = nfbasistoalg(bnfinit(polcyclo(179)),Jp[2])
  ***   at top-level: u=nfbasistoalg(bnfinit(polcyclo(179
  ***                                ^--------------------
  *** bnfinit: the PARI stack overflows !
  current stack size: 16000000 (15.259 Mbytes)
  [hint] you can increase GP stack with allocatemem()

(09:29) gp >

I also increased the stack size to 1024000000 (the maximum) and it still gives the same overflow error. Does anyone know what I should do to perform all four computations correctly? Thanks in advance.

Paul Roub
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J. Linne
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  • According to `?bnfinit` message, it works "if parameters are not too large". Unfortunately, it seems that `179` is large. I recommend you to ask PARI/GP contributors at mailing list about any work-around. – Piotr Semenov Nov 20 '17 at 13:46
  • I believe you are using a 32-bit build of PARI/GP. You can download a 64-bit build at [https://pari.math.u-bordeaux.fr/download.html](https://pari.math.u-bordeaux.fr/download.html). I have a stack size of 6 giga (`6*10^9`). I do not get the stack size problem with your first function call. However, I get another error: `bnfinit: overflow in t_REAL->double conversion.` – Jeppe Stig Nielsen Dec 11 '17 at 13:59

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