* [1, 1]
1
1
0
1
[1, 0]~
* [1, 2]
3/4
0
3
1
[0, 3]~
* [1, 3]
0.96774193548387096774193548387096774194
0
3
1
[0, 3]~
* [1, 4]
6
6
0
6
[6, 0]~
* [1, 5]
3/(x^2 + 1)
0
3
0
[0, 3]~
* [1, 6]
Mod(-3*x, x^2 + 1)
error("forbidden division t_INT \\ t_POLMOD.")
error("forbidden division t_INT % t_POLMOD.")
error("forbidden division t_INT \\ t_POLMOD.")
error("forbidden division t_INT \\ t_POLMOD.")
* [1, 7]
0
error("forbidden division t_INT \\ t_FFELT.")
error("forbidden division t_INT % t_FFELT.")
error("forbidden division t_INT \\ t_FFELT.")
error("forbidden division t_INT \\ t_FFELT.")
* [1, 8]
-3 + 3*w
1
3 - w
2
[1, 3 - w]~
* [1, 9]
-3/2*w
error("forbidden division t_INT \\ t_QUAD.")
error("forbidden division t_INT % t_QUAD.")
error("forbidden division t_INT \\ t_QUAD.")
error("forbidden division t_INT \\ t_QUAD.")
* [1, 10]
2*3 + 3^2 + 3^3 + O(3^4)
error("forbidden division t_INT \\ t_PADIC.")
error("forbidden division t_INT % t_PADIC.")
error("forbidden division t_INT \\ t_PADIC.")
error("forbidden division t_INT \\ t_PADIC.")
* [1, 11]
Mod(0, 3)
error("forbidden division t_INT \\ t_INTMOD.")
error("forbidden division t_INT % t_INTMOD.")
error("forbidden division t_INT \\ t_INTMOD.")
error("forbidden division t_INT \\ t_INTMOD.")
* [1, 12]
3/18446744073709551617
0
3
0
[0, 3]~
* [2, 1]
4/3
1
1
1
[1, 1]~
* [2, 2]
1
1
0
1
[1, 0]~
* [2, 3]
1.2903225806451612903225806451612903226
1
0.90000000000000000000000000000000000000
1
[1, 0.90000000000000000000000000000000000000]~
* [2, 4]
8
8
0
8
[8, 0]~
* [2, 5]
4/(x^2 + 1)
0
4
0
[0, 4]~
* [2, 6]
Mod(-4*x, x^2 + 1)
error("forbidden division t_INT \\ t_POLMOD.")
error("forbidden division t_INT % t_POLMOD.")
error("forbidden division t_INT \\ t_POLMOD.")
error("forbidden division t_INT \\ t_POLMOD.")
* [2, 7]
2*t^4 + 2*t^3 + t^2
error("forbidden division t_INT \\ t_FFELT.")
error("forbidden division t_INT % t_FFELT.")
error("forbidden division t_INT \\ t_FFELT.")
error("forbidden division t_INT \\ t_FFELT.")
* [2, 8]
-4 + 4*w
2
4 - 2*w
2
[2, 4 - 2*w]~
* [2, 9]
-2*w
error("forbidden division t_INT \\ t_QUAD.")
error("forbidden division t_INT % t_QUAD.")
error("forbidden division t_INT \\ t_QUAD.")
error("forbidden division t_INT \\ t_QUAD.")
* [2, 10]
2 + O(3^3)
error("forbidden division t_INT \\ t_PADIC.")
error("forbidden division t_INT % t_PADIC.")
error("forbidden division t_INT \\ t_PADIC.")
error("forbidden division t_INT \\ t_PADIC.")
* [2, 11]
Mod(2, 3)
error("forbidden division t_INT \\ t_INTMOD.")
error("forbidden division t_INT % t_INTMOD.")
error("forbidden division t_INT \\ t_INTMOD.")
error("forbidden division t_INT \\ t_INTMOD.")
* [2, 12]
4/18446744073709551617
0
4
0
[0, 4]~
* [3, 1]
1.0333333333333333333333333333333333333
1
0.099999999999999999999999999999999999995
1
[1, 0.099999999999999999999999999999999999995]~
* [3, 2]
0.77500000000000000000000000000000000000
0
3.1000000000000000000000000000000000000
1
[0, 3.1000000000000000000000000000000000000]~
* [3, 3]
1.0000000000000000000000000000000000000
1
0.E-37
1
[1, 0.E-37]~
* [3, 4]
6.2000000000000000000000000000000000000
6
0.099999999999999999999999999999999999995
6
[6, 0.099999999999999999999999999999999999995]~
* [3, 5]
3.1000000000000000000000000000000000000/(x^2 + 1)
0
3.1000000000000000000000000000000000000
0
[0, 3.1000000000000000000000000000000000000]~
* [3, 6]
Mod(-3.1000000000000000000000000000000000000*x, x^2 + 1)
error("forbidden division t_REAL \\ t_POLMOD.")
error("forbidden division t_REAL % t_POLMOD.")
error("forbidden division t_REAL \\ t_POLMOD.")
error("forbidden division t_REAL \\ t_POLMOD.")
* [3, 7]
error("forbidden division t_REAL / t_FFELT.")
error("forbidden division t_REAL \\ t_FFELT.")
error("forbidden division t_REAL % t_FFELT.")
error("forbidden division t_REAL \\ t_FFELT.")
error("forbidden division t_REAL \\ t_FFELT.")
* [3, 8]
1.9159053651246740294342191865334781649
1
1.4819660112501051517954131656343618823
2
[1, 1.4819660112501051517954131656343618823]~
* [3, 9]
0.E-38 - 2.1920310216782973256426175225250320218*I
error("forbidden division t_REAL \\ t_QUAD.")
error("forbidden division t_REAL % t_QUAD.")
error("forbidden division t_REAL \\ t_QUAD.")
error("forbidden division t_REAL \\ t_QUAD.")
* [3, 10]
error("forbidden division t_REAL / t_PADIC.")
error("forbidden division t_REAL \\ t_PADIC.")
error("forbidden division t_REAL % t_PADIC.")
error("forbidden division t_REAL \\ t_PADIC.")
error("forbidden division t_REAL \\ t_PADIC.")
* [3, 11]
error("forbidden division t_REAL / t_INTMOD.")
error("forbidden division t_REAL \\ t_INTMOD.")
error("forbidden division t_REAL % t_INTMOD.")
error("forbidden division t_REAL \\ t_INTMOD.")
error("forbidden division t_REAL \\ t_INTMOD.")
* [3, 12]
1.6805133673525318726204510291596823708 E-19
0
3.1000000000000000000000000000000000000
0
[0, 3.1000000000000000000000000000000000000]~
* [4, 1]
1/6
0
2
0
[0, 1/2]~
* [4, 2]
1/8
0
error("impossible inverse in Fl_inv: Mod(2, 4).")
0
[0, 1/2]~
* [4, 3]
0.16129032258064516129032258064516129032
0
1/2
0
[0, 1/2]~
* [4, 4]
1
1
0
1
[1, 0]~
* [4, 5]
1/(2*x^2 + 2)
0
1/2
0
[0, 1/2]~
* [4, 6]
Mod(-1/2*x, x^2 + 1)
error("forbidden division t_FRAC \\ t_POLMOD.")
error("forbidden division t_FRAC % t_POLMOD.")
error("forbidden division t_FRAC \\ t_POLMOD.")
error("forbidden division t_FRAC \\ t_POLMOD.")
* [4, 7]
t^4 + t^3 + 2*t^2
error("forbidden division t_FRAC \\ t_FFELT.")
error("forbidden division t_FRAC % t_FFELT.")
error("forbidden division t_FRAC \\ t_FFELT.")
error("forbidden division t_FRAC \\ t_FFELT.")
* [4, 8]
-1/2 + 1/2*w
0
1/2
0
[0, 1/2]~
* [4, 9]
-1/4*w
error("forbidden division t_FRAC \\ t_QUAD.")
error("forbidden division t_FRAC % t_QUAD.")
error("forbidden division t_FRAC \\ t_QUAD.")
error("forbidden division t_FRAC \\ t_QUAD.")
* [4, 10]
1 + 2*3 + O(3^3)
error("forbidden division t_FRAC \\ t_PADIC.")
error("forbidden division t_FRAC % t_PADIC.")
error("forbidden division t_FRAC \\ t_PADIC.")
error("forbidden division t_FRAC \\ t_PADIC.")
* [4, 11]
Mod(1, 3)
error("forbidden division t_FRAC \\ t_INTMOD.")
error("forbidden division t_FRAC % t_INTMOD.")
error("forbidden division t_FRAC \\ t_INTMOD.")
error("forbidden division t_FRAC \\ t_INTMOD.")
* [4, 12]
1/36893488147419103234
0
9223372036854775809
0
[0, 1/2]~
* [5, 1]
1/3*x^2 + 1/3
1/3*x^2 + 1/3
0
1/3*x^2 + 1/3
[1/3*x^2 + 1/3, 0]~
* [5, 2]
1/4*x^2 + 1/4
1/4*x^2 + 1/4
0
1/4*x^2 + 1/4
[1/4*x^2 + 1/4, 0]~
* [5, 3]
0.32258064516129032258064516129032258065*x^2 + 0.322580645161290322580645161
29032258065
0.32258064516129032258064516129032258065*x^2 + 0.322580645161290322580645161
29032258065
0
0.32258064516129032258064516129032258065*x^2 + 0.322580645161290322580645161
29032258065
[0.32258064516129032258064516129032258065*x^2 + 0.32258064516129032258064516
129032258065, 0]~
* [5, 4]
2*x^2 + 2
2*x^2 + 2
0
2*x^2 + 2
[2*x^2 + 2, 0]~
* [5, 5]
1
1
0
1
[1, 0]~
* [5, 6]
Mod(0, x^2 + 1)
error("forbidden euclidean division t_POL , t_POLMOD.")
error("forbidden euclidean division t_POL , t_POLMOD.")
error("forbidden euclidean division t_POL , t_POLMOD.")
error("forbidden euclidean division t_POL , t_POLMOD.")
* [5, 7]
(2*t^4 + 2*t^3 + t^2)*x^2 + (2*t^4 + 2*t^3 + t^2)
(2*t^4 + 2*t^3 + t^2)*x^2 + (2*t^4 + 2*t^3 + t^2)
0
(2*t^4 + 2*t^3 + t^2)*x^2 + (2*t^4 + 2*t^3 + t^2)
[(2*t^4 + 2*t^3 + t^2)*x^2 + (2*t^4 + 2*t^3 + t^2), 0]~
* [5, 8]
(-1 + w)*x^2 + (-1 + w)
(-1 + w)*x^2 + (-1 + w)
0
(-1 + w)*x^2 + (-1 + w)
[(-1 + w)*x^2 + (-1 + w), 0]~
* [5, 9]
-1/2*w*x^2 - 1/2*w
-1/2*w*x^2 - 1/2*w
0
-1/2*w*x^2 - 1/2*w
[-1/2*w*x^2 - 1/2*w, 0]~
* [5, 10]
(2 + 3 + 3^2 + O(3^3))*x^2 + (2 + 3 + 3^2 + O(3^3))
(2 + 3 + 3^2 + O(3^3))*x^2 + (2 + 3 + 3^2 + O(3^3))
0
(2 + 3 + 3^2 + O(3^3))*x^2 + (2 + 3 + 3^2 + O(3^3))
[(2 + 3 + 3^2 + O(3^3))*x^2 + (2 + 3 + 3^2 + O(3^3)), 0]~
* [5, 11]
Mod(2, 3)*x^2 + Mod(2, 3)
Mod(2, 3)*x^2 + Mod(2, 3)
Mod(0, 3)
Mod(2, 3)*x^2 + Mod(2, 3)
[Mod(2, 3)*x^2 + Mod(2, 3), Mod(0, 3)]~
* [5, 12]
1/18446744073709551617*x^2 + 1/18446744073709551617
1/18446744073709551617*x^2 + 1/18446744073709551617
0
1/18446744073709551617*x^2 + 1/18446744073709551617
[1/18446744073709551617*x^2 + 1/18446744073709551617, 0]~
* [6, 1]
Mod(1/3*x, x^2 + 1)
error("forbidden division t_POLMOD \\ t_INT.")
Mod(0, x^2 + 1)
error("forbidden division t_POLMOD \\ t_INT.")
error("forbidden division t_POLMOD \\ t_INT.")
* [6, 2]
Mod(1/4*x, x^2 + 1)
error("forbidden division t_POLMOD \\ t_INT.")
Mod(0, x^2 + 1)
error("forbidden division t_POLMOD \\ t_INT.")
error("forbidden division t_POLMOD \\ t_INT.")
* [6, 3]
Mod(0.32258064516129032258064516129032258065*x, x^2 + 1)
error("incorrect type in gfloor (t_POLMOD).")
error("forbidden division t_POLMOD % t_REAL.")
error("incorrect type in gfloor (t_POLMOD).")
error("incorrect type in gfloor (t_POLMOD).")
* [6, 4]
Mod(2*x, x^2 + 1)
error("incorrect type in gfloor (t_POLMOD).")
error("forbidden division t_POLMOD % t_FRAC.")
error("incorrect type in gfloor (t_POLMOD).")
error("incorrect type in gfloor (t_POLMOD).")
* [6, 5]
error("impossible inverse in QXQ_inv: Mod(0, x^2 + 1).")
error("forbidden euclidean division t_POLMOD , t_POL.")
Mod(x, x^2 + 1)
error("forbidden euclidean division t_POLMOD , t_POL.")
error("forbidden euclidean division t_POLMOD , t_POL.")
* [6, 6]
Mod(1, x^2 + 1)
error("forbidden division t_POLMOD \\ t_POLMOD.")
error("forbidden division t_POLMOD % t_POLMOD.")
error("forbidden division t_POLMOD \\ t_POLMOD.")
error("forbidden division t_POLMOD \\ t_POLMOD.")
* [6, 7]
Mod((2*t^4 + 2*t^3 + t^2)*x, x^2 + 1)
error("forbidden division t_POLMOD \\ t_FFELT.")
error("forbidden division t_POLMOD % t_FFELT.")
error("forbidden division t_POLMOD \\ t_FFELT.")
error("forbidden division t_POLMOD \\ t_FFELT.")
* [6, 8]
Mod((-1 + w)*x, x^2 + 1)
error("forbidden division t_POLMOD \\ t_QUAD.")
error("forbidden division t_POLMOD % t_QUAD.")
error("forbidden division t_POLMOD \\ t_QUAD.")
error("forbidden division t_POLMOD \\ t_QUAD.")
* [6, 9]
Mod(-1/2*w*x, x^2 + 1)
error("forbidden division t_POLMOD \\ t_QUAD.")
error("forbidden division t_POLMOD % t_QUAD.")
error("forbidden division t_POLMOD \\ t_QUAD.")
error("forbidden division t_POLMOD \\ t_QUAD.")
* [6, 10]
Mod((2 + 3 + 3^2 + O(3^3))*x, x^2 + 1)
error("forbidden division t_POLMOD \\ t_PADIC.")
error("forbidden division t_POLMOD % t_PADIC.")
error("forbidden division t_POLMOD \\ t_PADIC.")
error("forbidden division t_POLMOD \\ t_PADIC.")
* [6, 11]
Mod(Mod(2, 3)*x, x^2 + 1)
error("forbidden division t_POLMOD \\ t_INTMOD.")
error("forbidden division t_POLMOD % t_INTMOD.")
error("forbidden division t_POLMOD \\ t_INTMOD.")
error("forbidden division t_POLMOD \\ t_INTMOD.")
* [6, 12]
Mod(1/18446744073709551617*x, x^2 + 1)
error("forbidden division t_POLMOD \\ t_INT.")
error("forbidden division t_POLMOD % t_INT.")
error("forbidden division t_POLMOD \\ t_INT.")
error("forbidden division t_POLMOD \\ t_INT.")
* [7, 1]
error("impossible inverse in Fl_inv: Mod(0, 3).")
error("forbidden division t_FFELT \\ t_INT.")
error("forbidden division t_FFELT % t_INT.")
error("forbidden division t_FFELT \\ t_INT.")
error("forbidden division t_FFELT \\ t_INT.")
* [7, 2]
t
error("forbidden division t_FFELT \\ t_INT.")
error("forbidden division t_FFELT % t_INT.")
error("forbidden division t_FFELT \\ t_INT.")
error("forbidden division t_FFELT \\ t_INT.")
* [7, 3]
error("forbidden division t_FFELT / t_REAL.")
error("forbidden division t_FFELT / t_REAL.")
error("forbidden division t_FFELT % t_REAL.")
error("forbidden division t_FFELT / t_REAL.")
error("forbidden division t_FFELT / t_REAL.")
* [7, 4]
2*t
error("incorrect type in gfloor (t_FFELT).")
error("forbidden division t_FFELT % t_FRAC.")
error("incorrect type in gfloor (t_FFELT).")
error("incorrect type in gfloor (t_FFELT).")
* [7, 5]
t/(x^2 + 1)
0
t
0
[0, t]~
* [7, 6]
Mod(2*t*x, x^2 + 1)
error("forbidden division t_FFELT \\ t_POLMOD.")
error("forbidden division t_FFELT % t_POLMOD.")
error("forbidden division t_FFELT \\ t_POLMOD.")
error("forbidden division t_FFELT \\ t_POLMOD.")
* [7, 7]
1
error("forbidden division t_FFELT \\ t_FFELT.")
error("forbidden division t_FFELT % t_FFELT.")
error("forbidden division t_FFELT \\ t_FFELT.")
error("forbidden division t_FFELT \\ t_FFELT.")
* [7, 8]
error("forbidden division t_FFELT / t_QUAD.")
error("forbidden division t_FFELT \\ t_QUAD.")
error("forbidden division t_FFELT % t_QUAD.")
error("forbidden division t_FFELT \\ t_QUAD.")
error("forbidden division t_FFELT \\ t_QUAD.")
* [7, 9]
error("forbidden division t_FFELT / t_QUAD.")
error("forbidden division t_FFELT \\ t_QUAD.")
error("forbidden division t_FFELT % t_QUAD.")
error("forbidden division t_FFELT \\ t_QUAD.")
error("forbidden division t_FFELT \\ t_QUAD.")
* [7, 10]
error("forbidden division t_FFELT / t_PADIC.")
error("forbidden division t_FFELT \\ t_PADIC.")
error("forbidden division t_FFELT % t_PADIC.")
error("forbidden division t_FFELT \\ t_PADIC.")
error("forbidden division t_FFELT \\ t_PADIC.")
* [7, 11]
2*t
error("forbidden division t_FFELT \\ t_INTMOD.")
error("forbidden division t_FFELT % t_INTMOD.")
error("forbidden division t_FFELT \\ t_INTMOD.")
error("forbidden division t_FFELT \\ t_INTMOD.")
* [7, 12]
2*t
error("forbidden division t_FFELT \\ t_INT.")
error("forbidden division t_FFELT % t_INT.")
error("forbidden division t_FFELT \\ t_INT.")
error("forbidden division t_FFELT \\ t_INT.")
* [8, 1]
1/3*w
0
w
1
[0, w]~
* [8, 2]
1/4*w
0
w
0
[0, w]~
* [8, 3]
0.52194644798383704780793123689214132830
0
w
1
[0, w]~
* [8, 4]
2*w
3
-3/2 + w
3
[3, -3/2 + w]~
* [8, 5]
w/(x^2 + 1)
0
w
0
[0, w]~
* [8, 6]
Mod(-w*x, x^2 + 1)
error("forbidden division t_QUAD \\ t_POLMOD.")
error("forbidden division t_QUAD % t_POLMOD.")
error("forbidden division t_QUAD \\ t_POLMOD.")
error("forbidden division t_QUAD \\ t_POLMOD.")
* [8, 7]
error("forbidden division t_QUAD / t_FFELT.")
error("forbidden division t_QUAD \\ t_FFELT.")
error("forbidden division t_QUAD % t_FFELT.")
error("forbidden division t_QUAD \\ t_FFELT.")
error("forbidden division t_QUAD \\ t_FFELT.")
* [8, 8]
1
1
0
1
[1, 0]~
* [8, 9]
error("inconsistent division t_QUAD / t_QUAD.")
error("forbidden division t_QUAD \\ t_QUAD.")
error("forbidden division t_QUAD % t_QUAD.")
error("forbidden division t_QUAD \\ t_QUAD.")
error("forbidden division t_QUAD \\ t_QUAD.")
* [8, 10]
error("not an n-th power residue in Qp_sqrt: 5.")
error("forbidden division t_QUAD \\ t_PADIC.")
error("forbidden division t_QUAD % t_PADIC.")
error("forbidden division t_QUAD \\ t_PADIC.")
error("forbidden division t_QUAD \\ t_PADIC.")
* [8, 11]
Mod(0, 3) + Mod(2, 3)*w
error("forbidden division t_QUAD \\ t_INTMOD.")
error("forbidden division t_QUAD % t_INTMOD.")
error("forbidden division t_QUAD \\ t_INTMOD.")
error("forbidden division t_QUAD \\ t_INTMOD.")
* [8, 12]
1/18446744073709551617*w
0
w
0
[0, w]~
* [9, 1]
1/3*w
error("forbidden division t_QUAD \\ t_INT.")
error("forbidden division t_QUAD % t_INT.")
error("forbidden division t_QUAD \\ t_INT.")
error("forbidden division t_QUAD \\ t_INT.")
* [9, 2]
1/4*w
error("forbidden division t_QUAD \\ t_INT.")
error("forbidden division t_QUAD % t_INT.")
error("forbidden division t_QUAD \\ t_INT.")
error("forbidden division t_QUAD \\ t_INT.")
* [9, 3]
0.E-38 + 0.45619792334615969316183507232570905760*I
error("incorrect type in gfloor (t_COMPLEX).")
error("forbidden division t_QUAD % t_REAL.")
error("incorrect type in gfloor (t_COMPLEX).")
error("incorrect type in gfloor (t_COMPLEX).")
* [9, 4]
2*w
error("incorrect type in gfloor (t_QUAD).")
error("forbidden division t_QUAD % t_FRAC.")
error("incorrect type in gfloor (t_QUAD).")
error("incorrect type in gfloor (t_QUAD).")
* [9, 5]
w/(x^2 + 1)
0
w
0
[0, w]~
* [9, 6]
Mod(-w*x, x^2 + 1)
error("forbidden division t_QUAD \\ t_POLMOD.")
error("forbidden division t_QUAD % t_POLMOD.")
error("forbidden division t_QUAD \\ t_POLMOD.")
error("forbidden division t_QUAD \\ t_POLMOD.")
* [9, 7]
error("forbidden division t_QUAD / t_FFELT.")
error("forbidden division t_QUAD \\ t_FFELT.")
error("forbidden division t_QUAD % t_FFELT.")
error("forbidden division t_QUAD \\ t_FFELT.")
error("forbidden division t_QUAD \\ t_FFELT.")
* [9, 8]
error("inconsistent division t_QUAD / t_QUAD.")
error("forbidden division t_QUAD \\ t_QUAD.")
error("forbidden division t_QUAD % t_QUAD.")
error("forbidden division t_QUAD \\ t_QUAD.")
error("forbidden division t_QUAD \\ t_QUAD.")
* [9, 9]
1
error("forbidden division t_QUAD \\ t_QUAD.")
error("forbidden division t_QUAD % t_QUAD.")
error("forbidden division t_QUAD \\ t_QUAD.")
error("forbidden division t_QUAD \\ t_QUAD.")
* [9, 10]
1 + 2*3 + 3^2 + O(3^3)
error("forbidden division t_QUAD \\ t_PADIC.")
error("forbidden division t_QUAD % t_PADIC.")
error("forbidden division t_QUAD \\ t_PADIC.")
error("forbidden division t_QUAD \\ t_PADIC.")
* [9, 11]
Mod(0, 3) + Mod(2, 3)*w
error("forbidden division t_QUAD \\ t_INTMOD.")
error("forbidden division t_QUAD % t_INTMOD.")
error("forbidden division t_QUAD \\ t_INTMOD.")
error("forbidden division t_QUAD \\ t_INTMOD.")
* [9, 12]
1/18446744073709551617*w
error("forbidden division t_QUAD \\ t_INT.")
error("forbidden division t_QUAD % t_INT.")
error("forbidden division t_QUAD \\ t_INT.")
error("forbidden division t_QUAD \\ t_INT.")
* [10, 1]
2*3^-1 + O(3^2)
error("forbidden division t_PADIC \\ t_INT.")
2
error("forbidden division t_PADIC \\ t_INT.")
error("forbidden division t_PADIC \\ t_INT.")
* [10, 2]
2 + 3 + 3^2 + O(3^3)
error("forbidden division t_PADIC \\ t_INT.")
error("inconsistent  t_PADIC , t_INTMOD.")
error("forbidden division t_PADIC \\ t_INT.")
error("forbidden division t_PADIC \\ t_INT.")
* [10, 3]
error("forbidden division t_PADIC / t_REAL.")
error("forbidden division t_PADIC / t_REAL.")
error("forbidden division t_PADIC % t_REAL.")
error("forbidden division t_PADIC / t_REAL.")
error("forbidden division t_PADIC / t_REAL.")
* [10, 4]
1 + 3 + O(3^3)
error("incorrect type in gfloor (t_PADIC).")
error("forbidden division t_PADIC % t_FRAC.")
error("incorrect type in gfloor (t_PADIC).")
error("incorrect type in gfloor (t_PADIC).")
* [10, 5]
(2 + O(3^3))/(x^2 + 1)
0
2 + O(3^3)
0
[0, 2 + O(3^3)]~
* [10, 6]
Mod((1 + 2*3 + 2*3^2 + O(3^3))*x, x^2 + 1)
error("forbidden division t_PADIC \\ t_POLMOD.")
error("forbidden division t_PADIC % t_POLMOD.")
error("forbidden division t_PADIC \\ t_POLMOD.")
error("forbidden division t_PADIC \\ t_POLMOD.")
* [10, 7]
error("forbidden division t_PADIC / t_FFELT.")
error("forbidden division t_PADIC \\ t_FFELT.")
error("forbidden division t_PADIC % t_FFELT.")
error("forbidden division t_PADIC \\ t_FFELT.")
error("forbidden division t_PADIC \\ t_FFELT.")
* [10, 8]
1 + 2*3 + 2*3^2 + O(3^3) + (2 + O(3^3))*w
error("forbidden division t_PADIC \\ t_QUAD.")
error("forbidden division t_PADIC % t_QUAD.")
error("forbidden division t_PADIC \\ t_QUAD.")
error("forbidden division t_PADIC \\ t_QUAD.")
* [10, 9]
1 + 3 + 2*3^2 + O(3^3)
error("forbidden division t_PADIC \\ t_QUAD.")
error("forbidden division t_PADIC % t_QUAD.")
error("forbidden division t_PADIC \\ t_QUAD.")
error("forbidden division t_PADIC \\ t_QUAD.")
* [10, 10]
1 + O(3^3)
error("forbidden division t_PADIC \\ t_PADIC.")
error("forbidden division t_PADIC % t_PADIC.")
error("forbidden division t_PADIC \\ t_PADIC.")
error("forbidden division t_PADIC \\ t_PADIC.")
* [10, 11]
Mod(1, 3)
error("forbidden division t_PADIC \\ t_INTMOD.")
error("forbidden division t_PADIC % t_INTMOD.")
error("forbidden division t_PADIC \\ t_INTMOD.")
error("forbidden division t_PADIC \\ t_INTMOD.")
* [10, 12]
1 + 2*3 + 2*3^2 + O(3^3)
error("forbidden division t_PADIC \\ t_INT.")
error("inconsistent  t_PADIC , t_INTMOD.")
error("forbidden division t_PADIC \\ t_INT.")
error("forbidden division t_PADIC \\ t_INT.")
* [11, 1]
error("impossible inverse in Fl_inv: Mod(0, 3).")
error("forbidden division t_INTMOD \\ t_INT.")
Mod(2, 3)
error("forbidden division t_INTMOD \\ t_INT.")
error("forbidden division t_INTMOD \\ t_INT.")
* [11, 2]
Mod(2, 3)
error("forbidden division t_INTMOD \\ t_INT.")
Mod(0, 1)
error("forbidden division t_INTMOD \\ t_INT.")
error("forbidden division t_INTMOD \\ t_INT.")
* [11, 3]
error("forbidden division t_INTMOD / t_REAL.")
error("forbidden division t_INTMOD / t_REAL.")
error("forbidden division t_INTMOD % t_REAL.")
error("forbidden division t_INTMOD / t_REAL.")
error("forbidden division t_INTMOD / t_REAL.")
* [11, 4]
Mod(1, 3)
error("incorrect type in gfloor (t_INTMOD).")
error("forbidden division t_INTMOD % t_FRAC.")
error("incorrect type in gfloor (t_INTMOD).")
error("incorrect type in gfloor (t_INTMOD).")
* [11, 5]
Mod(2, 3)/(Mod(1, 3)*x^2 + Mod(1, 3))
0
Mod(2, 3)
0
[0, Mod(2, 3)]~
* [11, 6]
Mod(Mod(1, 3)*x, x^2 + 1)
error("forbidden division t_INTMOD \\ t_POLMOD.")
error("forbidden division t_INTMOD % t_POLMOD.")
error("forbidden division t_INTMOD \\ t_POLMOD.")
error("forbidden division t_INTMOD \\ t_POLMOD.")
* [11, 7]
t^4 + t^3 + 2*t^2
error("forbidden division t_INTMOD \\ t_FFELT.")
error("forbidden division t_INTMOD % t_FFELT.")
error("forbidden division t_INTMOD \\ t_FFELT.")
error("forbidden division t_INTMOD \\ t_FFELT.")
* [11, 8]
Mod(1, 3) + Mod(2, 3)*w
error("forbidden division t_INTMOD \\ t_QUAD.")
error("forbidden division t_INTMOD % t_QUAD.")
error("forbidden division t_INTMOD \\ t_QUAD.")
error("forbidden division t_INTMOD \\ t_QUAD.")
* [11, 9]
Mod(0, 3) + Mod(2, 3)*w
error("forbidden division t_INTMOD \\ t_QUAD.")
error("forbidden division t_INTMOD % t_QUAD.")
error("forbidden division t_INTMOD \\ t_QUAD.")
error("forbidden division t_INTMOD \\ t_QUAD.")
* [11, 10]
Mod(1, 3)
error("forbidden division t_INTMOD \\ t_PADIC.")
error("forbidden division t_INTMOD % t_PADIC.")
error("forbidden division t_INTMOD \\ t_PADIC.")
error("forbidden division t_INTMOD \\ t_PADIC.")
* [11, 11]
Mod(1, 3)
error("forbidden division t_INTMOD \\ t_INTMOD.")
error("forbidden division t_INTMOD % t_INTMOD.")
error("forbidden division t_INTMOD \\ t_INTMOD.")
error("forbidden division t_INTMOD \\ t_INTMOD.")
* [11, 12]
Mod(1, 3)
error("forbidden division t_INTMOD \\ t_INT.")
Mod(0, 1)
error("forbidden division t_INTMOD \\ t_INT.")
error("forbidden division t_INTMOD \\ t_INT.")
* [12, 1]
18446744073709551617/3
6148914691236517205
2
6148914691236517206
[6148914691236517205, 2]~
* [12, 2]
18446744073709551617/4
4611686018427387904
1
4611686018427387904
[4611686018427387904, 1]~
* [12, 3]
5950562604422436005.4838709677419354839
5950562604422436005
1.5000000000000000001
5950562604422436005
[5950562604422436005, 1.5000000000000000001]~
* [12, 4]
36893488147419103234
36893488147419103234
0
36893488147419103234
[36893488147419103234, 0]~
* [12, 5]
18446744073709551617/(x^2 + 1)
0
18446744073709551617
0
[0, 18446744073709551617]~
* [12, 6]
Mod(-18446744073709551617*x, x^2 + 1)
error("forbidden division t_INT \\ t_POLMOD.")
error("forbidden division t_INT % t_POLMOD.")
error("forbidden division t_INT \\ t_POLMOD.")
error("forbidden division t_INT \\ t_POLMOD.")
* [12, 7]
t^4 + t^3 + 2*t^2
error("forbidden division t_INT \\ t_FFELT.")
error("forbidden division t_INT % t_FFELT.")
error("forbidden division t_INT \\ t_FFELT.")
error("forbidden division t_INT \\ t_FFELT.")
* [12, 8]
-18446744073709551617 + 18446744073709551617*w
11400714819323198486
18446744073709551617 - 11400714819323198486*w
11400714819323198487
[11400714819323198486, 18446744073709551617 - 11400714819323198486*w]~
* [12, 9]
-18446744073709551617/2*w
error("forbidden division t_INT \\ t_QUAD.")
error("forbidden division t_INT % t_QUAD.")
error("forbidden division t_INT \\ t_QUAD.")
error("forbidden division t_INT \\ t_QUAD.")
* [12, 10]
1 + 3 + 3^2 + O(3^3)
error("forbidden division t_INT \\ t_PADIC.")
error("forbidden division t_INT % t_PADIC.")
error("forbidden division t_INT \\ t_PADIC.")
error("forbidden division t_INT \\ t_PADIC.")
* [12, 11]
Mod(1, 3)
error("forbidden division t_INT \\ t_INTMOD.")
error("forbidden division t_INT % t_INTMOD.")
error("forbidden division t_INT \\ t_INTMOD.")
error("forbidden division t_INT \\ t_INTMOD.")
* [12, 12]
1
1
0
1
[1, 0]~
* [1, 1]
1/3*x + O(x^2)
error("forbidden division t_SER \\ t_INT.")
error("forbidden division t_SER % t_INT.")
error("forbidden division t_SER \\ t_INT.")
* [1, 2]
1/4*x + O(x^2)
error("forbidden division t_SER \\ t_INT.")
error("forbidden division t_SER % t_INT.")
error("forbidden division t_SER \\ t_INT.")
* [1, 3]
0.32258064516129032258064516129032258065*x + O(x^2)
error("incorrect type in gfloor (t_SER).")
error("forbidden division t_SER % t_REAL.")
error("incorrect type in gfloor (t_SER).")
* [1, 4]
2*x + O(x^2)
error("incorrect type in gfloor (t_SER).")
error("forbidden division t_SER % t_FRAC.")
error("incorrect type in gfloor (t_SER).")
* [1, 5]
x + O(x^2)
error("forbidden euclidean division t_SER , t_POL.")
error("forbidden division t_SER % t_POL.")
error("forbidden euclidean division t_SER , t_POL.")
* [1, 6]
error("forbidden division t_SER % t_POL.")
error("forbidden division t_SER \\ t_POLMOD.")
error("forbidden division t_SER % t_POLMOD.")
error("forbidden division t_SER \\ t_POLMOD.")
* [1, 7]
(2*t^4 + 2*t^3 + t^2)*x + O(x^2)
error("forbidden division t_SER \\ t_FFELT.")
error("forbidden division t_SER % t_FFELT.")
error("forbidden division t_SER \\ t_FFELT.")
* [1, 8]
(-1 + w)*x + O(x^2)
error("forbidden division t_SER \\ t_QUAD.")
error("forbidden division t_SER % t_QUAD.")
error("forbidden division t_SER \\ t_QUAD.")
* [1, 9]
-1/2*w*x + O(x^2)
error("forbidden division t_SER \\ t_QUAD.")
error("forbidden division t_SER % t_QUAD.")
error("forbidden division t_SER \\ t_QUAD.")
* [1, 10]
(2 + 3 + 3^2 + O(3^3))*x + O(x^2)
error("forbidden division t_SER \\ t_PADIC.")
error("forbidden division t_SER % t_PADIC.")
error("forbidden division t_SER \\ t_PADIC.")
* [1, 11]
Mod(2, 3)*x + O(x^2)
error("forbidden division t_SER \\ t_INTMOD.")
error("forbidden division t_SER % t_INTMOD.")
error("forbidden division t_SER \\ t_INTMOD.")
* [1, 12]
1/18446744073709551617*x + O(x^2)
error("forbidden division t_SER \\ t_INT.")
error("forbidden division t_SER % t_INT.")
error("forbidden division t_SER \\ t_INT.")
* [2, 1]
[2/3, 1]
[0, 1]
[2, 0]
[1, 1]
* [2, 2]
[1/2, 3/4]
[0, 0]
[2, 3]
[1, 1]
* [2, 3]
[0.64516129032258064516129032258064516129, 0.9677419354838709677419354838709
6774194]
[0, 0]
[2, 3]
[1, 1]
* [2, 4]
[4, 6]
[4, 6]
[0, 0]
[4, 6]
* [2, 5]
[2/(x^2 + 1), 3/(x^2 + 1)]
[0, 0]
[2, 3]
[0, 0]
* [2, 6]
[Mod(-2*x, x^2 + 1), Mod(-3*x, x^2 + 1)]
error("forbidden division t_INT \\ t_POLMOD.")
error("forbidden division t_INT % t_POLMOD.")
error("forbidden division t_INT \\ t_POLMOD.")
* [2, 7]
[t^4 + t^3 + 2*t^2, 0]
error("forbidden division t_INT \\ t_FFELT.")
error("forbidden division t_INT % t_FFELT.")
error("forbidden division t_INT \\ t_FFELT.")
* [2, 8]
[-2 + 2*w, -3 + 3*w]
[1, 1]
[2 - w, 3 - w]
[1, 2]
* [2, 9]
[-w, -3/2*w]
error("forbidden division t_INT \\ t_QUAD.")
error("forbidden division t_INT % t_QUAD.")
error("forbidden division t_INT \\ t_QUAD.")
* [2, 10]
[1 + O(3^3), 2*3 + 3^2 + 3^3 + O(3^4)]
error("forbidden division t_INT \\ t_PADIC.")
error("forbidden division t_INT % t_PADIC.")
error("forbidden division t_INT \\ t_PADIC.")
* [2, 11]
[Mod(1, 3), Mod(0, 3)]
error("forbidden division t_INT \\ t_INTMOD.")
error("forbidden division t_INT % t_INTMOD.")
error("forbidden division t_INT \\ t_INTMOD.")
* [2, 12]
[2/18446744073709551617, 3/18446744073709551617]
[0, 0]
[2, 3]
[0, 0]
* [3, 1]
Mat(2/3)
Mat(0)
Mat(2)
Mat(1)
* [3, 2]
Mat(1/2)
Mat(0)
Mat(2)
Mat(1)
* [3, 3]
Mat(0.64516129032258064516129032258064516129)
Mat(0)
Mat(2)
Mat(1)
* [3, 4]
Mat(4)
Mat(4)
Mat(0)
Mat(4)
* [3, 5]
Mat(2/(x^2 + 1))
Mat(0)
Mat(2)
Mat(0)
* [3, 6]
Mat(Mod(-2*x, x^2 + 1))
error("forbidden division t_INT \\ t_POLMOD.")
error("forbidden division t_INT % t_POLMOD.")
error("forbidden division t_INT \\ t_POLMOD.")
* [3, 7]
Mat(t^4 + t^3 + 2*t^2)
error("forbidden division t_INT \\ t_FFELT.")
error("forbidden division t_INT % t_FFELT.")
error("forbidden division t_INT \\ t_FFELT.")
* [3, 8]
Mat(-2 + 2*w)
Mat(1)
Mat(2 - w)
Mat(1)
* [3, 9]
Mat(-w)
error("forbidden division t_INT \\ t_QUAD.")
error("forbidden division t_INT % t_QUAD.")
error("forbidden division t_INT \\ t_QUAD.")
* [3, 10]
Mat(1 + O(3^3))
error("forbidden division t_INT \\ t_PADIC.")
error("forbidden division t_INT % t_PADIC.")
error("forbidden division t_INT \\ t_PADIC.")
* [3, 11]
Mat(Mod(1, 3))
error("forbidden division t_INT \\ t_INTMOD.")
error("forbidden division t_INT % t_INTMOD.")
error("forbidden division t_INT \\ t_INTMOD.")
* [3, 12]
Mat(2/18446744073709551617)
Mat(0)
Mat(2)
Mat(0)
[0, 1]
Mat(0)
[1, 1]
Mat(1)
[-x + y, x^2 + x]~
[[1, 1]~, [2, 1]~]
[0, 1]~
[1, 0]~
  ***   at top-level: divrem(1,"a")
  ***                 ^-------------
  *** divrem: forbidden division t_INT \ t_STR.
2
x
-1/(y*x - 1)
1/(y*x - 1)

[ 53/29 20/29 -32/29]

[193/29 40/29 -93/29]

[]
[]~
[;]
  ***   at top-level: [1]/0
  ***                    ^--
  *** _/_: impossible inverse in gdiv: 0.
Mod(Mod(2, 3)*a + Mod(1, 3), Mod(1, 3)*a^3 + Mod(2, 3)*a + Mod(2, 3))*x^4 + 
Mod(Mod(2, 3)*a^2 + Mod(2, 3), Mod(1, 3)*a^3 + Mod(2, 3)*a + Mod(2, 3))*x^3 
+ Mod(Mod(2, 3)*a, Mod(1, 3)*a^3 + Mod(2, 3)*a + Mod(2, 3))*x^2 + Mod(Mod(1,
 3)*a^2 + Mod(2, 3), Mod(1, 3)*a^3 + Mod(2, 3)*a + Mod(2, 3))*x + Mod(Mod(1,
 3)*a, Mod(1, 3)*a^3 + Mod(2, 3)*a + Mod(2, 3))
Mod(1, 2)*x^3 + Mod(1, 2)*x
Mod(1, 2)
Mod(1, 2) + O(x^2)
Mod(1, 2)*x + Mod(1, 2)
Mod(1, 2)*x
Total time spent: 0
