Changes between Version 3 and Version 4 of Ticket #10369


Ignore:
Timestamp:
12/10/10 20:31:02 (11 years ago)
Author:
jdemeyer
Comment:

Legend:

Unmodified
Added
Removed
Modified
  • Ticket #10369 – Description

    v3 v4  
    1 I have found several issues factoring polynomials over number fields. This time pari seems to work ok, so it is not related to #10279
     1I have found several issues factoring polynomials over number fields.
    22
    3 
     3'''First issue, fixed by #10430:'''
    44{{{
    55sage: N.<a>=NumberField(x^6+x^5+x^4+x^3+x^2+x+1)
     
    99}}}
    1010
    11 Depending on the execution I get two answers
    12 
    13 wrong answer:
    14 
     11Depending on the execution I get two answers.  A wrong answer
    1512{{{
    1613(-1/7*a^5 - 1/7*a^4 - 1/7*a^3 - 1/7*a^2 - 2/7*a - 1/7) * t^4 * (t^6 + (-19/7*a^5 - 17/7*a^4 - 15/7*a^3 - 13/7*a^2 - 11/7*a - 9/7)*t^5 + (2*a^5 - 10/7*a^4 - 16/7*a^3 + 10/7*a^2 - 2/7*a + 18/7)*t^4 + (-40/7*a^5 - 8/7*a^4 - 40/7*a^3 - 48/7*a^2 - 32/7)*t^3 + (26/7*a^5 - 6/7*a^4 + 26/7*a^3 - 6/7*a^2 - 4/7*a + 34/7)*t^2 + (-20/7*a^5 - 4/7*a^4 - 20/7*a^3 - 4/7*a^2 - 20/7*a - 16/7)*t + 2/7*a^5 - 2/7*a^4 + 2/7*a^3 - 2/7*a^2 + 2/7*a - 2/7)
    1714}}}
    18 
    19 solution that looks right:
    20 
     15or a correct answer:
    2116{{{
    2217(-1/7*a^5 - 1/7*a^4 - 1/7*a^3 - 1/7*a^2 - 2/7*a - 1/7) * t * (t - a^5 - a^4 - a^3 - a^2 - a - 1)^4 * (t^5 + (-12/7*a^5 - 10/7*a^4 - 8/7*a^3 - 6/7*a^2 - 4/7*a - 2/7)*t^4 + (12/7*a^5 - 8/7*a^3 + 16/7*a^2 + 2/7*a + 20/7)*t^3 + (-20/7*a^5 - 20/7*a^3 - 20/7*a^2 + 4/7*a - 2)*t^2 + (12/7*a^5 + 12/7*a^3 + 2/7*a + 16/7)*t - 4/7*a^5 - 4/7*a^3 - 4/7*a - 2/7)
    2318}}}
    2419
    25 With pari I only get the second answer, so it looks like a sage problem.
    26 
    27 Next example is different:
    28 
     20'''Second issue:'''
    2921{{{
    3022sage: l2 = (1/7*a^2 - 1/7*a)*t^10 + (4/7*a - 6/7)*t^9 + (102/49*a^5 + 99/49*a^4 + 96/49*a^3 + 93/49*a^2 + 90/49*a + 150/49)*t^8 + (-160/49*a^5 - 36/49*a^4 - 48/49*a^3 - 8/7*a^2 - 60/49*a - 60/49)*t^7 + (30/49*a^5 - 55/49*a^4 + 20/49*a^3 + 5/49*a^2)*t^6 + (6/49*a^4 - 12/49*a^3 + 6/49*a^2)*t^5
    3123}}}
    3224
    33 It is t**5 times an ireducible polynomial. With the Gp pari released with sage computes the factorization without problems, but trying to compute the factorization with sage the program starts to eat all available ram and you have to kill the program.
     25It is t**5 times an ireducible polynomial. GP released with Sage computes the factorization without problems, but trying to compute the factorization with Sage the program starts to eat all available RAM and you have to kill the program.  GP session:
     26{{{
     27  t; K = nfinit(a^6 + a^5 + a^4 + a^3 + a^2 + a + 1)
     28  l2 = (1/7*a^2 - 1/7*a)*t^10 + (4/7*a - 6/7)*t^9 + (102/49*a^5 + 99/49*a^4 + 96/49*a^3 + 93/49*a^2 + 90/49*a + 150/49)*t^8 + (-160/49*a^5 - 36/49*a^4 - 48/49*a^3 - 8/7*a^2 - 60/49*a - 60/49)*t^7 + (30/49*a^5 - 55/49*a^4 + 20/49*a^3 + 5/49*a^2)*t^6 + (6/49*a^4 - 12/49*a^3 + 6/49*a^2)*t^5
     29  nffactor(K, l2)
     30%3 =
     31[t 5]
     32
     33[t^5 + Mod(-40/7*a^5 - 38/7*a^4 - 36/7*a^3 - 34/7*a^2 - 32/7*a - 30/7, a^6 + a^5 + a^4 + a^3 + a^2 + a + 1)*t^4 + Mod(60/7*a^5 - 30/7*a^4 - 18/7*a^3 - 9/7*a^2 - 3/7*a, a^6 + a^5 + a^4 + a^3 + a^2 + a + 1)*t^3 + Mod(60/7*a^4 - 40/7*a^3 - 16/7*a^2 - 4/7*a, a^6 + a^5 + a^4 + a^3 + a^2 + a + 1)*t^2 + Mod(30/7*a^3 - 25/7*a^2 - 5/7*a, a^6 + a^5 + a^4 + a^3 + a^2 + a + 1)*t + Mod(6/7*a^2 - 6/7*a, a^6 + a^5 + a^4 + a^3 + a^2 + a + 1) 1]
     34}}}