Changes between Version 3 and Version 4 of Ticket #10369
 Timestamp:
 12/10/10 20:31:02 (11 years ago)
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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 #102791 I have found several issues factoring polynomials over number fields. 2 2 3 3 '''First issue, fixed by #10430:''' 4 4 {{{ 5 5 sage: N.<a>=NumberField(x^6+x^5+x^4+x^3+x^2+x+1) … … 9 9 }}} 10 10 11 Depending on the execution I get two answers 12 13 wrong answer: 14 11 Depending on the execution I get two answers. A wrong answer 15 12 {{{ 16 13 (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) 17 14 }}} 18 19 solution that looks right: 20 15 or a correct answer: 21 16 {{{ 22 17 (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) 23 18 }}} 24 19 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:''' 29 21 {{{ 30 22 sage: 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 31 23 }}} 32 24 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. 25 It 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 }}}