This is a bug in PARI, rather than in Sage, apparently:
GP/PARI CALCULATOR Version 2.9.4 (released)
amd64 running linux (x86-64/GMP-6.1.0 kernel) 64-bit version
[...]
? nffactor(y^8 - y^6 + y^4 - y^2 + 1, x^4 + 1) \\ works
%1 =
[x^2 + Mod(-y^5, y^8 - y^6 + y^4 - y^2 + 1) 1]
[ x^2 + Mod(y^5, y^8 - y^6 + y^4 - y^2 + 1) 1]
? nffactor(y^8 - y^6 + y^4 - y^2 + 1, x^4 - 1) \\ boom
*** at top-level: nffactor(y^8-y^6+y^4
*** ^--------------------
*** nffactor: inconsistent concatenation t_VEC (2 elts) , t_COL (2 elts).
*** Break loop: type 'break' to go back to GP prompt
On 16 February 2018 at 16:54, <[email protected]> wrote:
> The following code crashes (in Sage 8.1 and on CoCalc):
>
> sage: K=CyclotomicField(20)
> sage: R.<x>=PolynomialRing(K)
> sage: (x^4-1).factor()
> ------------------------------------------------------------
> ---------------
> PariError Traceback (most
> recent call last)
> <ipython-input-3-12edfe8f4001> in <module>()
> ----> 1 (x**Integer(4)-Integer(1)).factor()
>
> /ext/sage/sage-8.1/src/sage/rings/polynomial/polynomial_element.pyx in
> sage.rings.polynomial.polynomial_element.Polynomial.factor (build/
> cythonized/sage/rings/polynomi
> al/polynomial_element.c:39428)()
> 4127 # polynomial instead.
> 4128 Rpari = R.pari_polynomial("y")
> -> 4129 G = list(Rpari.nffactor(f))
> 4130 # PARI's nffactor() ignores the unit, _
> factor_pari_helper()
> 4131 # adds back the unit of the factorization.
>
> cypari2/auto_gen.pxi in cypari2.gen.Gen_auto.nffactor()
>
> cypari2/handle_error.pyx in cypari2.handle_error._pari_err_handle()
>
> PariError: inconsistent concatenation t_VEC (2 elts) , t_COL (2 elts)
>
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