x^7 + Mod(7*y - 7, y^2 - y - 1)*x^6 + Mod(-21*y + 28, y^2 - y - 1)*x^5 - 35*
x^4 + Mod(35*y - 49, y^2 - y - 1)*x^3 + Mod(-7*y + 84, y^2 - y - 1)*x^2 + Mo
d(-14*y + 21, y^2 - y - 1)*x + Mod(-y - 43, y^2 - y - 1)
x^8 + Mod(-5265231366756*y - 11544453645457, y^2 - y - 7)*x^7 + Mod(28411458
5416607426786*y + 622944640581258439174, y^2 - y - 7)*x^6 + Mod(-88698486784
831757442657946*y - 194478741347464554095950854, y^2 - y - 7)*x^5 + Mod(1457
861838374320941446687517087*y + 3196482213651741289611519839129, y^2 - y - 7
)*x^4 + Mod(-3466536016262523445329224834043387*y - 760066587058933027706659
6588522840, y^2 - y - 7)*x^3 + Mod(500059251848756466420835983321373618*y + 
1096421116344588264250099626740668170, y^2 - y - 7)*x^2 + Mod(-1916208944621
5341153510282273347908836*y - 42014460135353505823787366140454468112, y^2 - 
y - 7)*x + Mod(100691810991091652032034511974871062155*y + 22077509296238717
8747302102119022589688, y^2 - y - 7)
x^8 + Mod(-8*y + 1, y^2 - y - 7)*x^7 + Mod(21*y + 189, y^2 - y - 7)*x^6 + Mo
d(-385*y - 251, y^2 - y - 7)*x^5 + Mod(695*y + 2955, y^2 - y - 7)*x^4 + Mod(
-2451*y - 3350, y^2 - y - 7)*x^3 + Mod(2402*y + 6871, y^2 - y - 7)*x^2 + Mod
(-2050*y - 3861, y^2 - y - 7)*x + Mod(565*y + 1331, y^2 - y - 7)
x^8 + Mod(-8*y + 1, y^2 - y - 7)*x^7 + Mod(21*y + 189, y^2 - y - 7)*x^6 + Mo
d(-385*y - 251, y^2 - y - 7)*x^5 + Mod(695*y + 2955, y^2 - y - 7)*x^4 + Mod(
-2451*y - 3350, y^2 - y - 7)*x^3 + Mod(2402*y + 6871, y^2 - y - 7)*x^2 + Mod
(-2050*y - 3861, y^2 - y - 7)*x + Mod(565*y + 1331, y^2 - y - 7)
x^8 + Mod(-8*y + 1, y^2 - y - 7)*x^7 + Mod(21*y + 189, y^2 - y - 7)*x^6 + Mo
d(-385*y - 251, y^2 - y - 7)*x^5 + Mod(695*y + 2955, y^2 - y - 7)*x^4 + Mod(
-2451*y - 3350, y^2 - y - 7)*x^3 + Mod(2402*y + 6871, y^2 - y - 7)*x^2 + Mod
(-2050*y - 3861, y^2 - y - 7)*x + Mod(565*y + 1331, y^2 - y - 7)
x^8 + Mod(-8*y + 1, y^2 - y - 7)*x^7 + Mod(21*y + 189, y^2 - y - 7)*x^6 + Mo
d(-385*y - 251, y^2 - y - 7)*x^5 + Mod(695*y + 2955, y^2 - y - 7)*x^4 + Mod(
-2451*y - 3350, y^2 - y - 7)*x^3 + Mod(2402*y + 6871, y^2 - y - 7)*x^2 + Mod
(-2050*y - 3861, y^2 - y - 7)*x + Mod(565*y + 1331, y^2 - y - 7)
x^3 + Mod(y^2 - 2, y^3 - y - 1)*x^2 + Mod(-y + 1, y^3 - y - 1)*x + Mod(y - 1
, y^3 - y - 1)
x^9 - 4*x^8 + 8*x^7 - 9*x^6 + 7*x^5 - 3*x^4 - x^3 + 4*x^2 - 3*x + 1
Mod(0, x^3 + Mod(y^2 + y - 2, y^3 - y - 1)*x^2 + Mod(-y^2 + 3, y^3 - y - 1)*
x + Mod(y^2 - 1, y^3 - y - 1))
Mod(0, x^9 - 4*x^8 + 8*x^7 - 9*x^6 + 7*x^5 - 3*x^4 - x^3 + 4*x^2 - 3*x + 1)
Mod(0, x^9 - 4*x^8 + 8*x^7 - 9*x^6 + 7*x^5 - 3*x^4 - x^3 + 4*x^2 - 3*x + 1)
  *** nfinit: Warning: nonmonic polynomial. Result of the form [nf,c].
x^2 - 3646554366
304
x^4 + 1000000000000000000000*x^2 + 1
x^4 + 146077*x^2 + 2629386
[y^4 - 2*y^3 - 16*y^2 - 5*y + 4, Mod(-2/3*y^3 + 5/3*y^2 + 28/3*y + 2/3, y^4 
- 2*y^3 - 16*y^2 - 5*y + 4)]
x^9 - 4*x^7 - 3*x^6 + 9*x^5 + 8*x^4 - 6*x^3 - 9*x^2 - 4*x - 1
x^5 - 13*x^3 - 3*x^2 + 5*x + 1
x^6 + 21471450*x^2 + 71643071500
x^6 - 12*x^4 - 24*x^3 + 21651666*x^2 - 257657256*x + 71814482884
x^4 + 146077*x^2 + 10517544
x
[x, Mod(-1/2, x)]
  ***   at top-level: polred([x,[1]])
  ***                 ^---------------
  *** polred: domain error in gvaluation: p = 1
[x]
[x]

[  0       x]

[2*x x^2 + 1]

x + 1
[x + 1, Mod(-1/2, x + 1)]
[x^2 + 1, Mod(1/2*x, x^2 + 1)]
[2*x + 1]
[x, x^2 + 1]
[x^8 - 4*x^7 + 24*x^6 - 58*x^5 + 126*x^4 - 160*x^3 + 160*x^2 - 89*x + 26, Mo
d(-68/135*x^7 + 208/135*x^6 - 1378/135*x^5 + 56/3*x^4 - 194/5*x^3 + 4976/135
*x^2 - 4492/135*x + 1856/135, x^8 - 4*x^7 + 24*x^6 - 58*x^5 + 126*x^4 - 160*
x^3 + 160*x^2 - 89*x + 26)]
x^16 - 4*x^15 - 334*x^14 + 264*x^13 + 32231*x^12 + 57392*x^11 - 1031422*x^10
 - 3628868*x^9 + 7185297*x^8 + 42417784*x^7 + 11283472*x^6 - 137773504*x^5 -
 127243504*x^4 + 69059728*x^3 + 56307944*x^2 - 6264432*x + 6436
  ***   Warning: new stack size = 25165824 (24.000 Mbytes).
x^5 + 5*x - 1
[x^12 - 2*x^11 - 11*x^9 + 13*x^8 + 5, Mod(0, x^12 - 2*x^11 - 11*x^9 + 13*x^8
 + 5)]
x^15 - 15*x^13 - 2*x^12 + 78*x^11 - 10*x^10 - 393*x^9 + 81*x^8 + 939*x^7 - 3
73*x^6 - 822*x^5 + 723*x^4 - 1588*x^3 - 57*x^2 + 127*x - 13
1
x^4 + Mod(-1/24*z^3 - 1/8*z^2 - 59/24*z - 27/8, z^4 + 50*z^2 + 45)*x^3 + Mod
(1/12*z^3 + 41/12*z + 5/2, z^4 + 50*z^2 + 45)*x^2 + Mod(-1/24*z^3 - 1/8*z^2 
- 59/24*z - 27/8, z^4 + 50*z^2 + 45)*x + 1
x^4 + Mod(-1/24*z^3 - 1/8*z^2 - 59/24*z - 27/8, z^4 + 50*z^2 + 45)*x^3 + Mod
(1/12*z^3 + 41/12*z + 5/2, z^4 + 50*z^2 + 45)*x^2 + Mod(-1/24*z^3 - 1/8*z^2 
- 59/24*z - 27/8, z^4 + 50*z^2 + 45)*x + 1
y^2 + Mod(t^3, t^4 + t^3 + t^2 + t + 1)*y + Mod(8*t^2 - 46*t + 8, t^4 + t^3 
+ t^2 + t + 1)
[x^6 - 2*x^3 + 2, Mod(-1/2*x^4 + x, x^6 - 2*x^3 + 2)]
  ***   at top-level: polredbest(x^6+30*x^5+133*x^4-2340*x^3-12284*x
  ***                 ^----------------------------------------------
  *** polredbest: not an irreducible polynomial in set_LLL_basis: x^6 + 30*x^5 + 133*x^4 - 2340*x^3 - 12284*x^2 + 29519*x - 3856.
Total time spent: 4994
