Mod(0, 3) Mod(0, 3) Mod(0, 3)
Mod(0, 3)*y^15 + O(y^16) Mod(0, 3)*x^15 + O(x^16) Mod(0, 3)*x^4 + O(x^5)
y x x
y + O(y^17) y + O(x^16) y + O(x^5)
0 0 0
y^-1 + O(y^15) 1/y + O(x^16) 1/y + O(x^5)
y x x
y^-1 + y + O(y^15) ((y^2 + 1)/y) + O(x^16) ((y^2 + 1)/y) + O(x^5)
y^2 + 2*y + 3 x^2 + 2*x + 3 3*x^2 + 2*x + 1
1 + 2*y + 3*y^2 + O(y^3) 1 + 2*x + 3*x^2 + O(x^3) 1 + 2*x + 3*x^2 + O(x^5)
y^2 + 2*y x^2 + 2*x 2*x + 1
1 + 2*y + O(y^3) 1 + 2*x + O(x^3) 1 + 2*x + O(x^5)
y^2 + 2*y + 4 x^2 + 2*x + 4 4*x^2 + 2*x + 1
1 + 2*y + 4*y^2 + O(y^3) 1 + 2*x + 4*x^2 + O(x^3) 1 + 2*x + 4*x^2 + O(x^5)
y^2 + 2*y - 4 x^2 + 2*x - 4 -4*x^2 + 2*x + 1
1 + 2*y - 4*y^2 + O(y^3) 1 + 2*x - 4*x^2 + O(x^3) 1 + 2*x - 4*x^2 + O(x^5)
2*y^2 + y 2*x^2 + x 2*x^2 + x
y + 2*y^2 + O(y^4) (y + 2*y^2 + O(y^4)) + O(x^16) (y + 2*y^2 + O(y^4)) + O(x
^5)
2 2 3
y + 2 y + 2 2 + x + O(x^2)
1 1 x + 2
1
z
y
x^2 + x + 1
-x^3 - 2*x^2 - x + 1
[4, 0, 0, 0, -2]~
x^2 - 2
[x^2 - 2, 6]
x^2 + 1
[x^2 + 1, 1/2]
1
x^2 + 1
1
1
1
2
0
0
0

[0 -1/2]

[1    0]

2*x^2 + x + 1
6*x^3 + 2*x^2
1
1:x^8 + 14*x^7 + 49*x^6 + 24*x^5 + 178*x^4 + 70*x^3 + 144*x^2 + 120*x + 25
2:x^8 + 7*x^7 + 49/4*x^6 + 24/7*x^5 + 29/2*x^4 + 35/4*x^3 + 144/49*x^2 + 30/
7*x + 25/16
3:Mod(1, 11)*x^8 + Mod(3, 11)*x^7 + Mod(5, 11)*x^6 + Mod(2, 11)*x^5 + Mod(2,
 11)*x^4 + Mod(4, 11)*x^3 + Mod(1, 11)*x^2 + Mod(10, 11)*x + Mod(3, 11)
4:x^8 + (8*a + 3)*x^7 + (6*a^2 + 10*a + 5)*x^6 + (a^3 + 8*a^2 + 8*a + 2)*x^5
 + (4*a^4 + 6*a^3 + 9*a^2 + 10*a + 2)*x^4 + (5*a^4 + 2*a^3 + 8*a^2 + 7*a + 1
0)*x^3 + (2*a^4 + 5*a^3 + 4*a^2 + 2*a + 2)*x^2 + (a^4 + a^3 + 6)*x + (4*a^4 
+ 3*a^3 + 10*a^2 + 2*a + 8)
5:x^8 + x^6 + b^2*x^4 + b^4*x^2 + (b^8 + b^6 + 1)
6:Mod(1, y^3 - y - 1)*x^8 + Mod(8*y + 14, y^3 - y - 1)*x^7 + Mod(28*y^2 + 98
*y + 49, y^3 - y - 1)*x^6 + Mod(294*y^2 + 350*y + 80, y^3 - y - 1)*x^5 + Mod
(805*y^2 + 680*y + 668, y^3 - y - 1)*x^4 + Mod(786*y^2 + 2238*y + 1106, y^3 
- y - 1)*x^3 + Mod(2125*y^2 + 1535*y + 706, y^3 - y - 1)*x^2 + Mod(738*y^2 +
 1626*y + 1232, y^3 - y - 1)*x + Mod(425*y^2 + 521*y + 184, y^3 - y - 1)
7:Mod(1, 7*y^3 - y - 1)*x^8 + Mod(8*y + 14, 7*y^3 - y - 1)*x^7 + Mod(28*y^2 
+ 98*y + 49, 7*y^3 - y - 1)*x^6 + Mod(294*y^2 + 302*y + 32, 7*y^3 - y - 1)*x
^5 + Mod(745*y^2 + 200*y + 248, 7*y^3 - y - 1)*x^4 + Mod(318*y^2 + 6462/7*y 
+ 1478/7, 7*y^3 - y - 1)*x^3 + Mod(8509/7*y^2 + 2495/7*y + 1294/7, 7*y^3 - y
 - 1)*x^2 + Mod(13302/49*y^2 + 143046/343*y + 78800/343, 7*y^3 - y - 1)*x + 
Mod(59837/343*y^2 + 54281/343*y + 12532/343, 7*y^3 - y - 1)
8:Mod(1, y^3 - y - 1)*x^8 + Mod(8/3*y + 14, y^3 - y - 1)*x^7 + Mod(28/9*y^2 
+ 98/3*y + 49, y^3 - y - 1)*x^6 + Mod(98/3*y^2 + 2702/27*y + 704/27, y^3 - y
 - 1)*x^5 + Mod(6685/81*y^2 + 4780/81*y + 5296/27, y^3 - y - 1)*x^4 + Mod(80
06/243*y^2 + 68018/243*y + 25886/243, y^3 - y - 1)*x^3 + Mod(94033/729*y^2 +
 65063/729*y + 112366/729, y^3 - y - 1)*x^2 + Mod(57226/2187*y^2 + 274114/21
87*y + 323060/2187, y^3 - y - 1)*x + Mod(120569/6561*y^2 + 98495/2187*y + 18
2168/6561, y^3 - y - 1)
9:Mod(1, 7*y^3 - y - 1)*x^8 + Mod(8/3*y + 14, 7*y^3 - y - 1)*x^7 + Mod(28/9*
y^2 + 98/3*y + 49, 7*y^3 - y - 1)*x^6 + Mod(98/3*y^2 + 2654/27*y + 656/27, 7
*y^3 - y - 1)*x^5 + Mod(6625/81*y^2 + 3460/81*y + 4876/27, 7*y^3 - y - 1)*x^
4 + Mod(6698/243*y^2 + 414002/1701*y + 127898/1701, 7*y^3 - y - 1)*x^3 + Mod
(613057/5103*y^2 + 370439/5103*y + 741442/5103, 7*y^3 - y - 1)*x^2 + Mod(254
1982/107163*y^2 + 75020926/750141*y + 92863436/750141, 7*y^3 - y - 1)*x + Mo
d(36748685/2250423*y^2 + 30522647/750141*y + 57101732/2250423, 7*y^3 - y - 1
)
10:Mod(Mod(1, 11), Mod(7, 11)*y^3 + Mod(10, 11)*y + Mod(10, 11))*x^8 + Mod(M
od(8, 11)*y + Mod(3, 11), Mod(7, 11)*y^3 + Mod(10, 11)*y + Mod(10, 11))*x^7 
+ Mod(Mod(6, 11)*y^2 + Mod(10, 11)*y + Mod(5, 11), Mod(7, 11)*y^3 + Mod(10, 
11)*y + Mod(10, 11))*x^6 + Mod(Mod(8, 11)*y^2 + Mod(5, 11)*y + Mod(10, 11), 
Mod(7, 11)*y^3 + Mod(10, 11)*y + Mod(10, 11))*x^5 + Mod(Mod(8, 11)*y^2 + Mod
(2, 11)*y + Mod(6, 11), Mod(7, 11)*y^3 + Mod(10, 11)*y + Mod(10, 11))*x^4 + 
Mod(Mod(10, 11)*y^2 + Mod(7, 11)*y + Mod(10, 11), Mod(7, 11)*y^3 + Mod(10, 1
1)*y + Mod(10, 11))*x^3 + Mod(Mod(4, 11)*y^2 + Mod(6, 11)*y + Mod(1, 11), Mo
d(7, 11)*y^3 + Mod(10, 11)*y + Mod(10, 11))*x^2 + Mod(Mod(5, 11)*y^2 + Mod(1
, 11)*y + Mod(9, 11), Mod(7, 11)*y^3 + Mod(10, 11)*y + Mod(10, 11))*x + Mod(
Mod(4, 11)*y^2 + Mod(9, 11)*y + Mod(7, 11), Mod(7, 11)*y^3 + Mod(10, 11)*y +
 Mod(10, 11))
done
Mod(-6, y^2 - 2)*x^2 + Mod(48*z, y^2 - 2)*x + Mod(480*z + 600, y^2 - 2)
1.4284266449676411750
1.4142277045794296914
"t_INT"
[1.6967749516455178867147127964496742725 E-78 + 6.27680359220261705581969849
48534498009 E-40*I, 1.5000000000000000000000000000000000000 + 1.593167581732
6095290002105566876736750 E39*I]~
130
0
[0.E-38 + 0.E-38*I, 0.E-38 + 0.E-38*I, 0.E-38 + 0.E-38*I, 0.E-38 + 0.E-38*I,
 -0.50000000000000000000000000000000000000 - 6.30476010645924576561431291726
65561499*I, -0.50000000000000000000000000000000000000 + 6.304760106459245765
6143129172665561499*I]~
0
  ***   at top-level: polrootsbound(Pol(0))
  ***                 ^---------------------
  *** polrootsbound: zero polynomial in roots.
  ***   at top-level: polrootsbound(1)
  ***                 ^----------------
  *** polrootsbound: incorrect type in polrootsbound (t_INT).
  ***   at top-level: Pol("")
  ***                 ^-------
  *** Pol: incorrect type in gtopoly (t_STR).
  ***   at top-level: (1/x)%x
  ***                      ^--
  *** _%_: impossible inverse in QXQ_inv: Mod(0, x).
  ***   at top-level: poltomonic(Pol(0))
  ***                 ^------------------
  *** poltomonic: zero polynomial in poltomonic.
Total time spent: 12
