setprecision!(f::CompletionMap)

[simonbrandhorst]

julia> K,toK = completion(F, 2*OF);

julia> F,_ = cyclotomic_field(3)
(Cyclotomic field of order 3, z_3)

julia> OF = maximal_order(F);

julia> K,toK = completion(F, 2*OF);

julia> setprecision!(toK,5)

it seems buggy also for the other methods in the same file

By the way, I found it surprising that the completion map can have a different precision than its codomain.

[joschmitt]

(That is also one of the questions I have in #1500.)

[simonbrandhorst]

For the record, another bug in the ramified case:

  Qx, x = QQ["x"];
  f = x^9 - 828*x^7 - 4371*x^6 + 226071*x^5 + 2371023*x^4 - 14243253*x^3 - 318645900*x^2 - 1637156439*x - 2754662093;

  K, a = number_field(f, "a");
  OK = maximal_order(K);
  p = 3;
  P = prime_ideals_over(OK, p)[1];
  C, mC = completion(K, P, 8);


  setprecision!(mC, 20)
  setprecision!(mC, 21)
  setprecision!(mC, 20) #throws

[joschmitt]

Looks like there is an assert that effectively prevents one from setting the precision back to an earlier value.
I also just realized that the field .precision of the map is never updated, although it is used in the setprecision! function.

@thofma These setprecision! methods need to be revised. I could try to understand what they are supposed to be doing. Or is this written down somewhere?

[thofma]

@fieker we forgot (did not have time) to discuss this. What is up with this @assert?

[simonbrandhorst]

#1821 fixes my personal problem. The second one persists and I noticed another one.

julia> Qx, x = QQ["x"];

julia> f = x^9 - 828*x^7 - 4371*x^6 + 226071*x^5 + 2371023*x^4 - 14243253*x^3 - 318645900*x^2 - 1637156439*x - 2754662093;

julia> K, a = number_field(f, "a");

julia> OK = maximal_order(K);

julia> p = 3;

julia> P = prime_ideals_over(OK, p)[1];

julia> C, mC = completion(K, P, 8);

julia> setprecision!(mC, 20)

julia> setprecision!(mC, 21)

julia> setprecision!(mC, 20) #throws
ERROR: AssertionError: !(new_prec in keys(Kp.def_poly_cache))

julia> a = mC(K(1//3))
3^-1 + O(3^12)

julia> preimage(mC, a) #throws independently of the above
Flint exception (General error):
    Exception (padic_get_fmpz).  Negative valuation.
ERROR: Problem in the FLINT-Subsystem

[simonbrandhorst]

And here is another one where small_lift does not yield the desired result. The example came from playing around. No real world input/motivation. I was just wondering however.

julia> Qx, x = QQ["x"];

julia> f = x^9 - 828*x^7 - 4371*x^6 + 226071*x^5 + 2371023*x^4 - 14243253*x^3 - 318645900*x^2 - 1637156439*x - 2754662093;

julia> K, a = number_field(f, "a");

julia> OK = maximal_order(K);

julia> p = 3;

julia> P = prime_ideals_over(OK, p)[1];

julia> C, mC = completion(K, P, 8);

julia> c = 1+a+23452*a^2+a^7
a^7 + 23452*a^2 + a + 1

julia> setprecision!(mC,101)

julia> preimage(mC,mC(c);small_lift=true)
3867197019993//45894251722978973525549278150*a^8 + 1011800160549344483095843//45894251722978973525549278150*a^7 + 46617534927776153614674762//22947125861489486762774639075*a^6 - 16770403710728089010971839//620192590851067209804719975*a^5 - 240512318922624346285934922//3278160837355640966110662725*a^4 + 13755872498317551516652483068//22947125861489486762774639075*a^3 + 36680519478293240230899114764//3278160837355640966110662725*a^2 - 64943879037445793216055192461//45894251722978973525549278150*a + 97293655997167134595110053563//45894251722978973525549278150

I would have expected that c gets reconstructed exactly here.Working with higher precision does not seem to help either.
Would you take a look @fieker ?

[fieker]

does not quite help, but the map is wrong..

g = minpoly(c)
g(mC(c))

has not enough precision....