| ss | vx | vy | CAS used | integrate | time (sec) | memory (GB) | $\operatorname{ord}P$ | $\deg_tP$ | height of $P$ | length of $P$ | $\deg_tU$ | $\deg_uU$ | $\deg_vU$ | height of $U$ | length of $U$ | $\deg_tV$ | $\deg_uV$ | $\deg_vV$ | height of $V$ | length of $V$ | leading coefficient of $P$ |
|---|
| 01 |
0 | 0 | Maple | $v$, then $u$ | 1.23 | 0.0434 | 3 | 4 | 3 | 91 | 5 / 7 | 9 / 8 | 4 / 4 | 2 | 866 | 40 / 91 | 37 / 81 | 18 / 16 | 7 | 15537 | ${t}^{2} \left( 4\,t-1 \right) \left( 1+4\,t \right)
$ |
0 | 0 | Maple | $u$, then $v$ | 1.3 | 0.0434 | 3 | 4 | 3 | 91 | 7 / 9 | 7 / 6 | 15 / 15 | 4 | 3126 | 20 / 24 | 34 / 50 | 6 / 7 | 2 | 2542 | ${t}^{2} \left( 4\,t-1 \right) \left( 1+4\,t \right)
$ | 0 | 1 | Maple | $v$, then $u$ | 3.07 | 0.0959 | 4 | 6 | 4 | 216 | 7 / 7 | 12 / 12 | 3 / 4 | 4 | 2606 | 35 / 109 | 36 / 102 | 29 / 22 | 19 | 134187 | ${t}^{3} \left( 1+4\,t \right) \left( 4\,t+3 \right) \left( 4\,t-1
\right)
$ | 0 | 1 | Maple | $u$, then $v$ | 2.43 | 0.0446 | 4 | 6 | 4 | 216 | 31 / 17 | 17 / 19 | 34 / 30 | 6 | 116800 | 10 / 8 | 4 / 4 | 12 / 12 | 6 | 2777 | ${t}^{3} \left( 1+4\,t \right) \left( 4\,t+3 \right) \left( 4\,t-1
\right)
$ | 1 | 0 | Maple | $v$, then $u$ | 2.46 | 0.0446 | 4 | 6 | 4 | 216 | 7 / 8 | 10 / 12 | 4 / 4 | 3 | 2077 | 10 / 11 | 18 / 21 | 9 / 8 | 5 | 15076 | ${t}^{3} \left( 1+4\,t \right) \left( 4\,t+3 \right) \left( 4\,t-1
\right)
$ | 1 | 0 | Maple | $u$, then $v$ | 3.15 | 0.0996 | 4 | 6 | 4 | 216 | 12 / 12 | 7 / 8 | 22 / 22 | 6 | 18075 | 7 / 41 | 17 / 96 | 9 / 9 | 5 | 4274 | ${t}^{3} \left( 1+4\,t \right) \left( 4\,t+3 \right) \left( 4\,t-1
\right)
$ | 1 | 1 | Maple | $v$, then $u$ | 1.22 | 0.045 | 3 | 4 | 3 | 108 | 3 / 5 | 8 / 8 | 3 / 4 | 2 | 600 | 23 / 90 | 36 / 80 | 18 / 16 | 7 | 19516 | ${t}^{2} \left( 4\,t-1 \right) \left( 1+4\,t \right)
$ | 1 | 1 | Maple | $u$, then $v$ | 1.32 | 0.045 | 3 | 4 | 3 | 108 | 6 / 8 | 6 / 6 | 13 / 14 | 3 | 3032 | 3 / 22 | 3 / 50 | 8 / 6 | 2 | 602 | ${t}^{2} \left( 4\,t-1 \right) \left( 1+4\,t \right)
$ | 1 | 1 | Mathematica | $u$, then $v$ | 8.23 | n.a. | 3 | 4 | 3 | 108 | 4 / 5 | 5 / 5 | 5 / 4 | 3 | 1391 | 5 / 6 | 5 / 4 | 6 / 5 | 2 | 641 | ${t}^{2} \left( 4\,t-1 \right) \left( 1+4\,t \right)
$ | 1 | 1 | Mathematica | $v$, then $u$ | 1.71 | n.a. | 3 | 4 | 3 | 108 | 4 / 5 | 5 / 5 | 5 / 4 | 3 | 1391 | 5 / 6 | 5 / 4 | 6 / 5 | 2 | 641 | ${t}^{2} \left( 4\,t-1 \right) \left( 1+4\,t \right)
$ | x | 0 | Mathematica | $u$, then $v$ | 137 | n.a. | 5 | 10 | 6 | 2407 | 12 / 10 | 7 / 8 | 9 / 8 | 6 | 56561 | 13 / 11 | 6 / 8 | 10 / 10 | 6 | 47287 | ${t}^{3} \left( 4\,t-1 \right) \left( 1+4\,t \right) \left( t{x}^{2}-2
\,tx+t-x \right) \left( t{x}^{2}+2\,tx+t-x \right) \left( 16\,{t}^{3}
{x}^{3}+2\,{t}^{2}{x}^{4}+16\,{t}^{3}x+28\,{t}^{2}{x}^{2}-9\,t{x}^{3}+2
\,{t}^{2}-9\,tx+6\,{x}^{2} \right)
$ | 0 | y | Mathematica | $u$, then $v$ | 144 | n.a. | 5 | 10 | 6 | 2407 | 14 / 12 | 9 / 10 | 9 / 8 | 8 | 90584 | 14 / 12 | 9 / 8 | 9 / 8 | 7 | 37949 | ${t}^{3} \left( 4\,t-1 \right) \left( 1+4\,t \right) \left( t{y}^{2}-2
\,ty+t-y \right) \left( t{y}^{2}+2\,ty+t-y \right) \left( 16\,{t}^{3}
{y}^{3}+2\,{t}^{2}{y}^{4}+16\,{t}^{3}y+28\,{t}^{2}{y}^{2}-9\,t{y}^{3}+2
\,{t}^{2}-9\,ty+6\,{y}^{2} \right)
$ | | ss | vx | vy | CAS used | integrate | time (sec) | memory (GB) | $\operatorname{ord}P$ | $\deg_tP$ | height of $P$ | length of $P$ | $\deg_tU$ | $\deg_uU$ | $\deg_vU$ | height of $U$ | length of $U$ | $\deg_tV$ | $\deg_uV$ | $\deg_vV$ | height of $V$ | length of $V$ | leading coefficient of $P$ |
|---|
| 02 |
0 | 0 | Maple | $v$, then $u$ | 1.03 | 0.0433 | 3 | 4 | 3 | 90 | 3 / 5 | 9 / 8 | 4 / 4 | 2 | 254 | 6 / 7 | 13 / 14 | 7 / 6 | 4 | 1879 | ${t}^{2} \left( 4\,t-1 \right) \left( 1+4\,t \right)
$ |
0 | 0 | Maple | $u$, then $v$ | 1.08 | 0.0433 | 3 | 4 | 3 | 90 | 6 / 7 | 7 / 6 | 13 / 14 | 4 | 1879 | 10 / 84 | 4 / 73 | 17 / 19 | 2 | 216 | ${t}^{2} \left( 4\,t-1 \right) \left( 1+4\,t \right)
$ | 0 | 1 | Maple | $v$, then $u$ | 1.97 | 0.0434 | 4 | 5 | 3 | 122 | 9 / 9 | 13 / 20 | 3 / 4 | 5 | 3356 | 9 / 126 | 20 / 91 | 8 / 59 | 7 | 9037 | ${t}^{3} \left( 4\,t-1 \right) \left( 1+4\,t \right)
$ | 0 | 1 | Maple | $u$, then $v$ | 2.25 | 0.0449 | 4 | 5 | 3 | 122 | 12 / 44 | 15 / 12 | 32 / 63 | 8 | 36302 | 5 / 165 | 4 / 142 | 12 / 36 | 3 | 381 | ${t}^{3} \left( 4\,t-1 \right) \left( 1+4\,t \right)
$ | 1 | 0 | Maple | $v$, then $u$ | 2.04 | 0.0449 | 4 | 5 | 3 | 122 | 6 / 8 | 12 / 12 | 4 / 4 | 3 | 416 | 11 / 12 | 18 / 20 | 9 / 8 | 7 | 11536 | ${t}^{3} \left( 4\,t-1 \right) \left( 1+4\,t \right)
$ | 1 | 0 | Maple | $u$, then $v$ | 2 | 0.0434 | 4 | 5 | 3 | 122 | 9 / 12 | 8 / 8 | 20 / 22 | 7 | 8968 | 7 / 8 | 3 / 4 | 12 / 12 | 5 | 1205 | ${t}^{3} \left( 4\,t-1 \right) \left( 1+4\,t \right)
$ | 1 | 1 | Maple | $v$, then $u$ | 1.38 | 0.0442 | 3 | 5 | 3 | 155 | 5 / 5 | 8 / 8 | 3 / 4 | 3 | 1001 | 14 / 99 | 15 / 60 | 19 / 59 | 7 | 18155 | ${t}^{2} \left( 1+4\,t \right) \left( 4\,t-1 \right) ^{2}
$ | 1 | 1 | Maple | $u$, then $v$ | 1.35 | 0.0442 | 3 | 5 | 3 | 155 | 39 / 30 | 8 / 8 | 34 / 40 | 5 | 13305 | 5 / 84 | 3 / 73 | 8 / 20 | 3 | 964 | ${t}^{2} \left( 1+4\,t \right) \left( 4\,t-1 \right) ^{2}
$ | 1 | 1 | Mathematica | $u$, then $v$ | 14.1 | n.a. | 3 | 5 | 3 | 155 | 4 / 3 | 6 / 5 | 5 / 4 | 3 | 1933 | 4 / 3 | 6 / 4 | 6 / 5 | 3 | 656 | ${t}^{2} \left( 1+4\,t \right) \left( 4\,t-1 \right) ^{2}
$ | 1 | 1 | Mathematica | $v$, then $u$ | 1.65 | n.a. | 3 | 5 | 3 | 155 | 4 / 3 | 6 / 5 | 5 / 4 | 3 | 1933 | 4 / 3 | 6 / 4 | 6 / 5 | 3 | 656 | ${t}^{2} \left( 1+4\,t \right) \left( 4\,t-1 \right) ^{2}
$ | x | 0 | Mathematica | $u$, then $v$ | 234 | n.a. | 5 | 8 | 5 | 557 | 12 / 8 | 9 / 8 | 7 / 8 | 8 | 42685 | 13 / 9 | 9 / 8 | 10 / 10 | 8 | 35668 | ${t}^{4} \left( 4\,t-1 \right) \left( 1+4\,t \right) \left( 2\,t{x}^{2
}+2\,t+x \right) \left( 2\,t{x}^{2}+2\,t-x \right)
$ | 0 | y | Mathematica | $u$, then $v$ | 172 | n.a. | 5 | 8 | 5 | 557 | 8 / 6 | 10 / 10 | 9 / 8 | 7 | 24466 | 6 / 5 | 3 / 8 | 9 / 8 | 5 | 4284 | ${t}^{4} \left( 4\,t-1 \right) \left( 1+4\,t \right) \left( 2\,t{y}^{2
}+2\,t+y \right) \left( 2\,t{y}^{2}+2\,t-y \right)
$ | | ss | vx | vy | CAS used | integrate | time (sec) | memory (GB) | $\operatorname{ord}P$ | $\deg_tP$ | height of $P$ | length of $P$ | $\deg_tU$ | $\deg_uU$ | $\deg_vU$ | height of $U$ | length of $U$ | $\deg_tV$ | $\deg_uV$ | $\deg_vV$ | height of $V$ | length of $V$ | leading coefficient of $P$ |
|---|
| 03 |
0 | 0 | Maple | $v$, then $u$ | 2.36 | 0.0437 | 4 | 9 | 5 | 242 | 9 / 7 | 12 / 12 | 4 / 4 | 6 | 2673 | 13 / 10 | 20 / 21 | 9 / 8 | 9 | 18865 | ${t}^{3} \left( 6\,t-1 \right) \left( 1+2\,t \right) \left( 2\,t-1
\right) \left( 6\,t+1 \right) \left( 12\,{t}^{2}-1 \right)
$ |
0 | 0 | Maple | $u$, then $v$ | 2.5 | 0.0437 | 4 | 9 | 5 | 242 | 14 / 13 | 9 / 8 | 24 / 26 | 9 | 26367 | 10 / 7 | 4 / 4 | 12 / 12 | 6 | 3111 | ${t}^{3} \left( 6\,t-1 \right) \left( 1+2\,t \right) \left( 2\,t-1
\right) \left( 6\,t+1 \right) \left( 12\,{t}^{2}-1 \right)
$ | 0 | 1 | Maple | $v$, then $u$ | 3.02 | 0.0443 | 4 | 10 | 6 | 459 | 11 / 7 | 12 / 12 | 3 / 4 | 7 | 4865 | 13 / 11 | 20 / 22 | 8 / 8 | 9 | 26372 | ${t}^{3} \left( 6\,t-1 \right) \left( 1+2\,t \right) \left( 2\,t-1
\right) \left( 6\,t+1 \right) \left( 72\,{t}^{3}-36\,{t}^{2}-6\,t+1
\right)
$ | 0 | 1 | Maple | $u$, then $v$ | 2.98 | 0.0448 | 4 | 10 | 6 | 459 | 13 / 11 | 9 / 8 | 19 / 22 | 9 | 34652 | 11 / 7 | 4 / 4 | 12 / 12 | 6 | 5885 | ${t}^{3} \left( 6\,t-1 \right) \left( 1+2\,t \right) \left( 2\,t-1
\right) \left( 6\,t+1 \right) \left( 72\,{t}^{3}-36\,{t}^{2}-6\,t+1
\right)
$ | 1 | 0 | Maple | $v$, then $u$ | 2.09 | 0.0436 | 4 | 7 | 4 | 179 | 6 / 6 | 12 / 12 | 4 / 4 | 4 | 590 | 13 / 66 | 19 / 80 | 9 / 29 | 9 | 18983 | ${t}^{3} \left( 6\,t-1 \right) \left( 1+2\,t \right) \left( 2\,t-1
\right) \left( 6\,t+1 \right)
$ | 1 | 0 | Maple | $u$, then $v$ | 2.61 | 0.0435 | 4 | 7 | 4 | 179 | 15 / 15 | 8 / 8 | 24 / 26 | 8 | 22684 | 10 / 9 | 3 / 4 | 12 / 12 | 5 | 2698 | ${t}^{3} \left( 6\,t-1 \right) \left( 1+2\,t \right) \left( 2\,t-1
\right) \left( 6\,t+1 \right)
$ | 1 | 1 | Maple | $v$, then $u$ | 1.53 | 0.0442 | 3 | 8 | 5 | 247 | 8 / 5 | 8 / 8 | 3 / 4 | 5 | 2205 | 10 / 36 | 14 / 52 | 6 / 20 | 7 | 9206 | ${t}^{2} \left( 6\,t-1 \right) \left( 1+2\,t \right) \left( 2\,t-1
\right) \left( 6\,t+1 \right) \left( 12\,{t}^{2}-1 \right)
$ | 1 | 1 | Maple | $u$, then $v$ | 1.79 | 0.0444 | 3 | 8 | 5 | 247 | 11 / 9 | 6 / 6 | 15 / 18 | 7 | 15199 | 10 / 5 | 3 / 4 | 16 / 9 | 5 | 4954 | ${t}^{2} \left( 6\,t-1 \right) \left( 1+2\,t \right) \left( 2\,t-1
\right) \left( 6\,t+1 \right) \left( 12\,{t}^{2}-1 \right)
$ | 1 | 1 | Mathematica | $u$, then $v$ | 15.7 | n.a. | 3 | 8 | 5 | 247 | 7 / 3 | 6 / 5 | 5 / 4 | 5 | 4467 | 7 / 3 | 5 / 4 | 6 / 5 | 4 | 1317 | ${t}^{2} \left( 6\,t-1 \right) \left( 1+2\,t \right) \left( 2\,t-1
\right) \left( 6\,t+1 \right) \left( 12\,{t}^{2}-1 \right)
$ | 1 | 1 | Mathematica | $v$, then $u$ | 1.94 | n.a. | 3 | 8 | 5 | 247 | 7 / 3 | 6 / 5 | 5 / 4 | 5 | 4467 | 7 / 3 | 5 / 4 | 6 / 5 | 4 | 1317 | ${t}^{2} \left( 6\,t-1 \right) \left( 1+2\,t \right) \left( 2\,t-1
\right) \left( 6\,t+1 \right) \left( 12\,{t}^{2}-1 \right)
$ | x | 0 | Mathematica | $u$, then $v$ | 313 | n.a. | 5 | 14 | 9 | 4791 | 16 / 6 | 9 / 8 | 7 / 8 | 11 | 194231 | 17 / 7 | 9 / 8 | 10 / 10 | 12 | 154153 | ${t}^{4} \left( 6\,t-1 \right) \left( 1+2\,t \right) \left( 2\,t-1
\right) \left( 6\,t+1 \right) \left( 2\,t{x}^{2}+2\,tx+2\,t+x
\right) \left( 2\,t{x}^{2}+2\,tx+2\,t-x \right) \left( 384\,{t}^{4}{
x}^{4}+192\,{t}^{4}{x}^{3}+576\,{t}^{4}{x}^{2}-28\,{t}^{2}{x}^{4}+192\,
{t}^{4}x+8\,{t}^{2}{x}^{3}+384\,{t}^{4}-8\,{t}^{2}{x}^{2}+{x}^{4}+8\,{t
}^{2}x+2\,{x}^{3}-28\,{t}^{2}+2\,{x}^{2}+2\,x+1 \right)
$ | 0 | y | Mathematica | $u$, then $v$ | 264 | n.a. | 5 | 15 | 10 | 5112 | 16 / 7 | 10 / 10 | 9 / 8 | 11 | 202357 | 15 / 6 | 3 / 8 | 9 / 8 | 10 | 40759 | ${t}^{3} \left( 6\,t-1 \right) \left( 1+2\,t \right) \left( 2\,t-1
\right) \left( 6\,t+1 \right) \left( t{y}^{2}+t+y \right) \left(
3456\,{t}^{6}{y}^{4}+6912\,{t}^{6}{y}^{2}-2160\,{t}^{5}{y}^{3}-252\,{t}
^{4}{y}^{4}+3456\,{t}^{6}-2160\,{t}^{5}y-504\,{t}^{4}{y}^{2}+312\,{t}^{
3}{y}^{3}+9\,{t}^{2}{y}^{4}-252\,{t}^{4}+312\,{t}^{3}y+30\,{t}^{2}{y}^{
2}-3\,t{y}^{3}+9\,{t}^{2}-3\,ty-{y}^{2} \right) \left( 3\,t{y}^{2}+3\,
t-y \right)
$ | | ss | vx | vy | CAS used | integrate | time (sec) | memory (GB) | $\operatorname{ord}P$ | $\deg_tP$ | height of $P$ | length of $P$ | $\deg_tU$ | $\deg_uU$ | $\deg_vU$ | height of $U$ | length of $U$ | $\deg_tV$ | $\deg_uV$ | $\deg_vV$ | height of $V$ | length of $V$ | leading coefficient of $P$ |
|---|
| 04 |
0 | 0 | Maple | $v$, then $u$ | 4.04 | 0.053 | 4 | 7 | 4 | 260 | 8 / 9 | 12 / 12 | 4 / 4 | 5 | 3989 | 15 / 139 | 30 / 119 | 9 / 41 | 11 | 64950 | ${t}^{3} \left( 1+4\,t \right) \left( 8\,t-1 \right) \left( 2\,t-1
\right) \left( t+1 \right)
$ |
0 | 0 | Maple | $u$, then $v$ | 4.06 | 0.053 | 4 | 7 | 4 | 260 | 15 / 16 | 9 / 8 | 30 / 32 | 11 | 64814 | 8 / 13 | 4 / 4 | 17 / 22 | 5 | 5785 | ${t}^{3} \left( 1+4\,t \right) \left( 8\,t-1 \right) \left( 2\,t-1
\right) \left( t+1 \right)
$ | 0 | 1 | Maple | $v$, then $u$ | 3.64 | 0.047 | 4 | 8 | 5 | 331 | 9 / 9 | 12 / 12 | 3 / 4 | 6 | 4360 | 44 / 162 | 46 / 107 | 29 / 68 | 19 | 261681 | ${t}^{3} \left( 1+4\,t \right) \left( t+1 \right) ^{2} \left( 8\,t-1
\right) ^{2}
$ | 0 | 1 | Maple | $u$, then $v$ | 4.27 | 0.0906 | 4 | 8 | 5 | 331 | 17 / 17 | 9 / 8 | 30 / 32 | 12 | 81666 | 18 / 13 | 4 / 4 | 17 / 22 | 6 | 10964 | ${t}^{3} \left( 1+4\,t \right) \left( t+1 \right) ^{2} \left( 8\,t-1
\right) ^{2}
$ | 1 | 0 | Maple | $v$, then $u$ | 4.32 | 0.0906 | 4 | 8 | 5 | 331 | 9 / 9 | 12 / 12 | 4 / 4 | 6 | 4731 | 17 / 17 | 30 / 32 | 9 / 8 | 12 | 81666 | ${t}^{3} \left( 1+4\,t \right) \left( t+1 \right) ^{2} \left( 8\,t-1
\right) ^{2}
$ | 1 | 0 | Maple | $u$, then $v$ | 3.59 | 0.047 | 4 | 8 | 5 | 331 | 12 / 12 | 8 / 8 | 20 / 22 | 9 | 24037 | 9 / 9 | 3 / 4 | 12 / 12 | 6 | 4360 | ${t}^{3} \left( 1+4\,t \right) \left( t+1 \right) ^{2} \left( 8\,t-1
\right) ^{2}
$ | 1 | 1 | Maple | $v$, then $u$ | 1.88 | 0.0472 | 3 | 6 | 4 | 195 | 8 / 38 | 12 / 6 | 3 / 81 | 5 | 4482 | 9 / 11 | 16 / 8 | 5 / 17 | 6 | 10848 | ${t}^{2} \left( 1+4\,t \right) \left( 8\,t-1 \right) \left( 2\,t-1
\right) \left( t+1 \right)
$ | 1 | 1 | Maple | $u$, then $v$ | 1.93 | 0.0472 | 3 | 6 | 4 | 195 | 9 / 9 | 5 / 6 | 16 / 18 | 6 | 10848 | 6 / 6 | 3 / 4 | 8 / 8 | 3 | 1843 | ${t}^{2} \left( 1+4\,t \right) \left( 8\,t-1 \right) \left( 2\,t-1
\right) \left( t+1 \right)
$ | 1 | 1 | Mathematica | $u$, then $v$ | 15.5 | n.a. | 3 | 6 | 4 | 195 | 5 / 4 | 6 / 5 | 5 / 4 | 4 | 3167 | 5 / 4 | 5 / 4 | 6 / 5 | 4 | 1449 | ${t}^{2} \left( 1+4\,t \right) \left( 8\,t-1 \right) \left( 2\,t-1
\right) \left( t+1 \right)
$ | 1 | 1 | Mathematica | $v$, then $u$ | 2.29 | n.a. | 3 | 6 | 4 | 195 | 5 / 4 | 6 / 5 | 5 / 4 | 4 | 3167 | 5 / 4 | 5 / 4 | 6 / 5 | 4 | 1449 | ${t}^{2} \left( 1+4\,t \right) \left( 8\,t-1 \right) \left( 2\,t-1
\right) \left( t+1 \right)
$ | x | 0 | Mathematica | $u$, then $v$ | 475 | n.a. | 5 | 13 | 9 | 7579 | 17 / 13 | 9 / 8 | 7 / 8 | 12 | 401880 | 18 / 14 | 9 / 8 | 10 / 10 | 13 | 346626 | ${t}^{3} \left( 1+4\,t \right) \left( 8\,t-1 \right) \left( t+1
\right) \left( t{x}^{2}+2\,tx+t+x \right) \left( 3\,t{x}^{2}+2\,tx+3
\,t-x \right) \left( 360\,{t}^{5}{x}^{4}+576\,{t}^{5}{x}^{3}+54\,{t}^{
4}{x}^{4}+944\,{t}^{5}{x}^{2}+168\,{t}^{4}{x}^{3}-54\,{t}^{3}{x}^{4}+
576\,{t}^{5}x+244\,{t}^{4}{x}^{2}+117\,{t}^{3}{x}^{3}+9\,{t}^{2}{x}^{4}
+360\,{t}^{5}+168\,{t}^{4}x+80\,{t}^{3}{x}^{2}+36\,{t}^{2}{x}^{3}+54\,{
t}^{4}+117\,{t}^{3}x+44\,{t}^{2}{x}^{2}-3\,t{x}^{3}-54\,{t}^{3}+36\,{t}
^{2}x-8\,t{x}^{2}+9\,{t}^{2}-3\,tx-{x}^{2} \right)
$ | 0 | y | Mathematica | $u$, then $v$ | 382 | n.a. | 5 | 13 | 9 | 7579 | 15 / 11 | 10 / 10 | 9 / 8 | 11 | 274166 | 14 / 10 | 9 / 8 | 9 / 8 | 10 | 107444 | ${t}^{3} \left( 1+4\,t \right) \left( 8\,t-1 \right) \left( t+1
\right) \left( t{y}^{2}+2\,ty+t+y \right) \left( 3\,t{y}^{2}+2\,ty+3
\,t-y \right) \left( 360\,{t}^{5}{y}^{4}+576\,{t}^{5}{y}^{3}+54\,{t}^{
4}{y}^{4}+944\,{t}^{5}{y}^{2}+168\,{t}^{4}{y}^{3}-54\,{t}^{3}{y}^{4}+
576\,{t}^{5}y+244\,{t}^{4}{y}^{2}+117\,{t}^{3}{y}^{3}+9\,{t}^{2}{y}^{4}
+360\,{t}^{5}+168\,{t}^{4}y+80\,{t}^{3}{y}^{2}+36\,{t}^{2}{y}^{3}+54\,{
t}^{4}+117\,{t}^{3}y+44\,{t}^{2}{y}^{2}-3\,t{y}^{3}-54\,{t}^{3}+36\,{t}
^{2}y-8\,t{y}^{2}+9\,{t}^{2}-3\,ty-{y}^{2} \right)
$ | | ss | vx | vy | CAS used | integrate | time (sec) | memory (GB) | $\operatorname{ord}P$ | $\deg_tP$ | height of $P$ | length of $P$ | $\deg_tU$ | $\deg_uU$ | $\deg_vU$ | height of $U$ | length of $U$ | $\deg_tV$ | $\deg_uV$ | $\deg_vV$ | height of $V$ | length of $V$ | leading coefficient of $P$ |
|---|
| 05 |
0 | 0 | Maple | $v$, then $u$ | 0.961 | 0.0436 | 3 | 6 | 4 | 97 | 4 / 5 | 9 / 8 | 4 / 4 | 2 | 356 | 12 / 84 | 6 / 144 | 19 / 81 | 7 | 9419 | ${t}^{2} \left( 8\,{t}^{2}-1 \right) \left( 8\,{t}^{2}+1 \right)
$ |
0 | 0 | Maple | $u$, then $v$ | 2.49 | 0.0433 | 3 | 6 | 4 | 97 | 9 / 10 | 7 / 6 | 15 / 16 | 5 | 2803 | 7 / 6 | 6 / 6 | 10 / 9 | 3 | 1675 | ${t}^{2} \left( 8\,{t}^{2}-1 \right) \left( 8\,{t}^{2}+1 \right)
$ | 0 | 1 | Maple | $v$, then $u$ | 66.4 | 0.643 | 6 | 18 | 11 | 1591 | 26 / 100 | 28 / 44 | 32 / 17 | 13 | 123359 | 52 / 161 | 101 / 325 | 30 / 144 | 21 | 1676397 | ${t}^{3} \left( t-1 \right) \left( 3\,t-1 \right) \left( t+1 \right)
\left( 8\,{t}^{2}-1 \right) \left( 8\,{t}^{2}+1 \right) \left( 30976
\,{t}^{8}-15696\,{t}^{7}-4464\,{t}^{6}+9864\,{t}^{5}-5124\,{t}^{4}-480
\,{t}^{3}+101\,{t}^{2}+12\,t-6 \right)
$ | 0 | 1 | Maple | $u$, then $v$ | 54 | 0.412 | 6 | 18 | 11 | 1591 | 29 / 24 | 13 / 12 | 33 / 38 | 14 | 190000 | 23 / 18 | 6 / 6 | 22 / 24 | 12 | 49829 | ${t}^{3} \left( t-1 \right) \left( 3\,t-1 \right) \left( t+1 \right)
\left( 8\,{t}^{2}-1 \right) \left( 8\,{t}^{2}+1 \right) \left( 30976
\,{t}^{8}-15696\,{t}^{7}-4464\,{t}^{6}+9864\,{t}^{5}-5124\,{t}^{4}-480
\,{t}^{3}+101\,{t}^{2}+12\,t-6 \right)
$ | 1 | 0 | Maple | $v$, then $u$ | 1.18 | 0.0446 | 3 | 6 | 4 | 119 | 4 / 5 | 8 / 8 | 4 / 4 | 2 | 422 | 9 / 107 | 16 / 92 | 9 / 42 | 5 | 4633 | ${t}^{2} \left( 8\,{t}^{2}-1 \right) \left( 8\,{t}^{2}+1 \right)
$ | 1 | 0 | Maple | $u$, then $v$ | 2.59 | 0.0441 | 3 | 6 | 4 | 119 | 9 / 10 | 6 / 6 | 14 / 16 | 4 | 2888 | 16 / 96 | 5 / 79 | 18 / 24 | 4 | 8236 | ${t}^{2} \left( 8\,{t}^{2}-1 \right) \left( 8\,{t}^{2}+1 \right)
$ | 1 | 1 | Maple | $v$, then $u$ | 21.7 | 0.379 | 5 | 16 | 9 | 1036 | 18 / 13 | 16 / 16 | 4 / 5 | 9 | 21234 | 35 / 189 | 45 / 166 | 17 / 53 | 20 | 493526 | ${t}^{4} \left( t-1 \right) \left( 3\,t-1 \right) \left( t+1 \right)
\left( 8\,{t}^{2}-1 \right) \left( 896\,{t}^{5}-512\,{t}^{4}+832\,{t}
^{3}-127\,{t}^{2}-6\,t-12 \right) \left( 8\,{t}^{2}+1 \right)
$ | 1 | 1 | Maple | $u$, then $v$ | 33.4 | 0.682 | 5 | 16 | 9 | 1036 | 39 / 82 | 23 / 49 | 38 / 78 | 13 | 335714 | 18 / 142 | 5 / 125 | 20 / 34 | 9 | 31034 | ${t}^{4} \left( t-1 \right) \left( 3\,t-1 \right) \left( t+1 \right)
\left( 8\,{t}^{2}-1 \right) \left( 896\,{t}^{5}-512\,{t}^{4}+832\,{t}
^{3}-127\,{t}^{2}-6\,t-12 \right) \left( 8\,{t}^{2}+1 \right)
$ | 1 | 1 | Mathematica | $u$, then $v$ | 494 | n.a. | 5 | 16 | 9 | 1036 | 28 / 21 | 11 / 11 | 9 / 10 | 20 | 84001 | 28 / 21 | 11 / 8 | 9 / 8 | 18 | 38974 | ${t}^{4} \left( t-1 \right) \left( 3\,t-1 \right) \left( t+1 \right)
\left( 8\,{t}^{2}-1 \right) \left( 896\,{t}^{5}-512\,{t}^{4}+832\,{t}
^{3}-127\,{t}^{2}-6\,t-12 \right) \left( 8\,{t}^{2}+1 \right)
$ | 1 | 1 | Mathematica | $v$, then $u$ | 32.2 | n.a. | 5 | 16 | 9 | 1036 | 28 / 21 | 11 / 11 | 9 / 10 | 20 | 84001 | 28 / 21 | 11 / 8 | 9 / 8 | 18 | 38974 | ${t}^{4} \left( t-1 \right) \left( 3\,t-1 \right) \left( t+1 \right)
\left( 8\,{t}^{2}-1 \right) \left( 896\,{t}^{5}-512\,{t}^{4}+832\,{t}
^{3}-127\,{t}^{2}-6\,t-12 \right) \left( 8\,{t}^{2}+1 \right)
$ | x | 0 | Mathematica | $u$, then $v$ | 191 | n.a. | 4 | 9 | 5 | 372 | 10 / 8 | 8 / 8 | 6 / 6 | 5 | 7834 | 12 / 10 | 8 / 8 | 9 / 8 | 5 | 13056 | ${t}^{3} \left( 8\,{t}^{2}-1 \right) \left( 8\,{t}^{2}+1 \right)
\left( 4\,{t}^{2}{x}^{2}+4\,{t}^{2}-x \right)
$ | 0 | y | Mathematica | $u$, then $v$ | 854 | n.a. | 6 | 18 | 11 | 6555 | 40 / 33 | 13 / 14 | 11 / 12 | 29 | 1352111 | 40 / 33 | 13 / 10 | 11 / 10 | 27 | 521652 | ${t}^{3} \left( 8\,{t}^{2}-1 \right) \left( 8\,{t}^{2}+1 \right)
\left( 2\,t{y}^{2}+t-y \right) \left( 2\,t{y}^{2}-t+y \right)
\left( -y+t \right) \left( 29696\,{t}^{8}{y}^{7}-11520\,{t}^{7}{y}^{8
}-7680\,{t}^{6}{y}^{9}-1280\,{t}^{5}{y}^{10}+1280\,{t}^{8}{y}^{3}-4224
\,{t}^{7}{y}^{4}+3648\,{t}^{6}{y}^{5}+9696\,{t}^{5}{y}^{6}-3312\,{t}^{4
}{y}^{7}-960\,{t}^{3}{y}^{8}+48\,{t}^{7}-432\,{t}^{6}y+1448\,{t}^{5}{y}
^{2}-1812\,{t}^{4}{y}^{3}+480\,{t}^{3}{y}^{4}+106\,{t}^{2}{y}^{5}-5\,{t
}^{2}y+12\,t{y}^{2}-6\,{y}^{3} \right)
$ | | ss | vx | vy | CAS used | integrate | time (sec) | memory (GB) | $\operatorname{ord}P$ | $\deg_tP$ | height of $P$ | length of $P$ | $\deg_tU$ | $\deg_uU$ | $\deg_vU$ | height of $U$ | length of $U$ | $\deg_tV$ | $\deg_uV$ | $\deg_vV$ | height of $V$ | length of $V$ | leading coefficient of $P$ |
|---|
| 06 |
0 | 0 | Maple | $v$, then $u$ | 5.16 | 0.374 | 4 | 10 | 5 | 447 | 11 / 16 | 14 / 10 | 19 / 22 | 4 | 9332 | 14 / 127 | 26 / 234 | 11 / 57 | 7 | 41238 | ${t}^{3} \left( t+1 \right) \left( 4\,{t}^{2}+4\,t+3 \right) \left( 12
\,{t}^{2}+4\,t+1 \right) \left( 4\,{t}^{2}+4\,t-1 \right)
$ |
0 | 0 | Maple | $u$, then $v$ | 19.5 | 0.472 | 4 | 10 | 5 | 447 | 16 / 15 | 9 / 8 | 21 / 24 | 8 | 41849 | 12 / 11 | 6 / 6 | 13 / 14 | 6 | 12645 | ${t}^{3} \left( t+1 \right) \left( 4\,{t}^{2}+4\,t+3 \right) \left( 12
\,{t}^{2}+4\,t+1 \right) \left( 4\,{t}^{2}+4\,t-1 \right)
$ | 0 | 1 | Maple | $v$, then $u$ | 14900 | 14.4 | 6 | 22 | 14 | 2290 | 29 / 20 | 28 / 28 | 4 / 5 | 16 | 82520 | 36 / 27 | 42 / 44 | 12 / 12 | 21 | 347577 | ${t}^{3} \left( t-1 \right) \left( 5\,t-1 \right) \left( 3\,t+1
\right) \left( t+1 \right) \left( 4\,{t}^{2}+4\,t-1 \right) \left(
12\,{t}^{2}+4\,t+1 \right) \left( 751104\,{t}^{11}+1393344\,{t}^{10}+
1298352\,{t}^{9}+208592\,{t}^{8}-234112\,{t}^{7}-9804\,{t}^{6}-37199\,{
t}^{5}-19403\,{t}^{4}-5352\,{t}^{3}-172\,{t}^{2}-13\,t-9 \right)
$ | 0 | 1 | Maple | $u$, then $v$ | 113 | 0.57 | 6 | 22 | 14 | 2290 | 33 / 24 | 13 / 12 | 36 / 39 | 19 | 313832 | 27 / 100 | 95 / 492 | 15 / 32 | 17 | 267949 | ${t}^{3} \left( t-1 \right) \left( 5\,t-1 \right) \left( 3\,t+1
\right) \left( t+1 \right) \left( 4\,{t}^{2}+4\,t-1 \right) \left(
12\,{t}^{2}+4\,t+1 \right) \left( 751104\,{t}^{11}+1393344\,{t}^{10}+
1298352\,{t}^{9}+208592\,{t}^{8}-234112\,{t}^{7}-9804\,{t}^{6}-37199\,{
t}^{5}-19403\,{t}^{4}-5352\,{t}^{3}-172\,{t}^{2}-13\,t-9 \right)
$ | 1 | 0 | Maple | $v$, then $u$ | 4.64 | 0.08 | 4 | 11 | 6 | 506 | 10 / 8 | 14 / 14 | 4 / 4 | 5 | 4627 | 15 / 13 | 24 / 25 | 9 / 8 | 8 | 47961 | ${t}^{3} \left( 1+2\,t \right) \left( t+1 \right) \left( 4\,{t}^{2}+4
\,t-1 \right) \left( 12\,{t}^{2}+4\,t+1 \right) \left( 4\,{t}^{2}+2\,
t+1 \right)
$ | 1 | 0 | Maple | $u$, then $v$ | 22.8 | 0.472 | 4 | 11 | 6 | 506 | 20 / 17 | 7 / 8 | 25 / 25 | 10 | 62320 | 17 / 67 | 5 / 282 | 21 / 31 | 9 | 40044 | ${t}^{3} \left( 1+2\,t \right) \left( t+1 \right) \left( 4\,{t}^{2}+4
\,t-1 \right) \left( 12\,{t}^{2}+4\,t+1 \right) \left( 4\,{t}^{2}+2\,
t+1 \right)
$ | 1 | 1 | Maple | $v$, then $u$ | 55.5 | 0.539 | 5 | 20 | 11 | 1685 | 25 / 16 | 22 / 22 | 4 / 5 | 14 | 52878 | 36 / 132 | 99 / 317 | 30 / 49 | 20 | 1177085 | ${t}^{2} \left( t-1 \right) \left( 5\,t-1 \right) \left( 3\,t+1
\right) \left( t+1 \right) \left( 4\,{t}^{2}+4\,t-1 \right) \left(
12\,{t}^{2}+4\,t+1 \right) \left( 22656\,{t}^{10}+29504\,{t}^{9}+36608
\,{t}^{8}+36240\,{t}^{7}+23436\,{t}^{6}+12592\,{t}^{5}+3913\,{t}^{4}+
1378\,{t}^{3}+248\,{t}^{2}+22\,t+3 \right)
$ | 1 | 1 | Maple | $u$, then $v$ | 857 | 4.3 | 5 | 20 | 11 | 1685 | 30 / 21 | 9 / 10 | 33 / 33 | 16 | 197717 | 24 / 15 | 5 / 6 | 19 / 19 | 13 | 53437 | ${t}^{2} \left( t-1 \right) \left( 5\,t-1 \right) \left( 3\,t+1
\right) \left( t+1 \right) \left( 4\,{t}^{2}+4\,t-1 \right) \left(
12\,{t}^{2}+4\,t+1 \right) \left( 22656\,{t}^{10}+29504\,{t}^{9}+36608
\,{t}^{8}+36240\,{t}^{7}+23436\,{t}^{6}+12592\,{t}^{5}+3913\,{t}^{4}+
1378\,{t}^{3}+248\,{t}^{2}+22\,t+3 \right)
$ | 1 | 1 | Mathematica | $u$, then $v$ | 752 | n.a. | 5 | 20 | 11 | 1685 | 31 / 21 | 11 / 11 | 10 / 10 | 21 | 103031 | 31 / 21 | 9 / 8 | 9 / 8 | 20 | 46228 | ${t}^{2} \left( t-1 \right) \left( 5\,t-1 \right) \left( 3\,t+1
\right) \left( t+1 \right) \left( 4\,{t}^{2}+4\,t-1 \right) \left(
12\,{t}^{2}+4\,t+1 \right) \left( 22656\,{t}^{10}+29504\,{t}^{9}+36608
\,{t}^{8}+36240\,{t}^{7}+23436\,{t}^{6}+12592\,{t}^{5}+3913\,{t}^{4}+
1378\,{t}^{3}+248\,{t}^{2}+22\,t+3 \right)
$ | 1 | 1 | Mathematica | $v$, then $u$ | 74.9 | n.a. | 5 | 20 | 11 | 1685 | 31 / 21 | 11 / 11 | 10 / 10 | 21 | 103031 | 31 / 21 | 9 / 8 | 9 / 8 | 20 | 46228 | ${t}^{2} \left( t-1 \right) \left( 5\,t-1 \right) \left( 3\,t+1
\right) \left( t+1 \right) \left( 4\,{t}^{2}+4\,t-1 \right) \left(
12\,{t}^{2}+4\,t+1 \right) \left( 22656\,{t}^{10}+29504\,{t}^{9}+36608
\,{t}^{8}+36240\,{t}^{7}+23436\,{t}^{6}+12592\,{t}^{5}+3913\,{t}^{4}+
1378\,{t}^{3}+248\,{t}^{2}+22\,t+3 \right)
$ | x | 0 | Mathematica | $u$, then $v$ | 709 | n.a. | 5 | 17 | 9 | 11090 | 19 / 12 | 9 / 10 | 9 / 8 | 11 | 448765 | 21 / 14 | 8 / 10 | 10 / 10 | 11 | 442113 | ${t}^{3} \left( t+1 \right) \left( 4\,{t}^{2}+4\,t-1 \right) \left( 12
\,{t}^{2}+4\,t+1 \right) \left( {t}^{2}{x}^{4}-4\,{t}^{2}{x}^{3}+2\,{t
}^{2}{x}^{2}-2\,t{x}^{3}-4\,{t}^{2}x+{t}^{2}-2\,tx+{x}^{2} \right)
\left( 16\,{t}^{7}{x}^{4}+96\,{t}^{7}{x}^{3}-16\,{t}^{6}{x}^{4}+32\,{t
}^{7}{x}^{2}+352\,{t}^{6}{x}^{3}-8\,{t}^{5}{x}^{4}+96\,{t}^{7}x-32\,{t}
^{6}{x}^{2}+336\,{t}^{5}{x}^{3}+4\,{t}^{4}{x}^{4}+16\,{t}^{7}+352\,{t}^
{6}x+80\,{t}^{5}{x}^{2}+96\,{t}^{4}{x}^{3}+{t}^{3}{x}^{4}-16\,{t}^{6}+
336\,{t}^{5}x+200\,{t}^{4}{x}^{2}-18\,{t}^{3}{x}^{3}-8\,{t}^{5}+96\,{t}
^{4}x+146\,{t}^{3}{x}^{2}-14\,{t}^{2}{x}^{3}+4\,{t}^{4}-18\,{t}^{3}x+68
\,{t}^{2}{x}^{2}-4\,t{x}^{3}+{t}^{3}-14\,{t}^{2}x+26\,t{x}^{2}-4\,tx+3
\,{x}^{2} \right)
$ | 0 | y | Mathematica | $u$, then $v$ | 2090 | n.a. | 6 | 22 | 13 | 37971 | 35 / 25 | 13 / 14 | 12 / 12 | 27 | 4510873 | 35 / 25 | 10 / 10 | 11 / 10 | 26 | 1718071 | ${t}^{3} \left( t+1 \right) \left( 4\,{t}^{2}+4\,t-1 \right) \left( 12
\,{t}^{2}+4\,t+1 \right) \left( 2\,t{y}^{2}+2\,ty-t+y \right) \left(
-y+t \right) \left( 2\,t{y}^{2}+2\,ty+t-y \right) \left( 147456\,{t}^
{11}{y}^{10}+405504\,{t}^{11}{y}^{9}+221184\,{t}^{10}{y}^{10}+382976\,{
t}^{11}{y}^{8}+454656\,{t}^{10}{y}^{9}+92160\,{t}^{9}{y}^{10}+26624\,{t
}^{11}{y}^{7}+598016\,{t}^{10}{y}^{8}-49152\,{t}^{9}{y}^{9}-36864\,{t}^
{8}{y}^{10}-185344\,{t}^{11}{y}^{6}+512000\,{t}^{10}{y}^{7}+422400\,{t}
^{9}{y}^{8}-429056\,{t}^{8}{y}^{9}-56832\,{t}^{7}{y}^{10}-50688\,{t}^{
11}{y}^{5}-120832\,{t}^{10}{y}^{6}+1205760\,{t}^{9}{y}^{7}-105984\,{t}^
{8}{y}^{8}-359168\,{t}^{7}{y}^{9}-23040\,{t}^{6}{y}^{10}+43008\,{t}^{11
}{y}^{4}-307200\,{t}^{10}{y}^{5}+243840\,{t}^{9}{y}^{6}+919296\,{t}^{8}
{y}^{7}-289152\,{t}^{7}{y}^{8}-133632\,{t}^{6}{y}^{9}-7936\,{t}^{5}{y}^
{10}-8960\,{t}^{11}{y}^{3}+16128\,{t}^{10}{y}^{4}-596352\,{t}^{9}{y}^{5
}+370432\,{t}^{8}{y}^{6}+320064\,{t}^{7}{y}^{7}-113280\,{t}^{6}{y}^{8}-
42240\,{t}^{5}{y}^{9}-2176\,{t}^{4}{y}^{10}-13824\,{t}^{11}{y}^{2}+
39424\,{t}^{10}{y}^{3}-100032\,{t}^{9}{y}^{4}-470528\,{t}^{8}{y}^{5}+
262720\,{t}^{7}{y}^{6}+83328\,{t}^{6}{y}^{7}-40320\,{t}^{5}{y}^{8}-8448
\,{t}^{4}{y}^{9}-192\,{t}^{3}{y}^{10}+3072\,{t}^{11}y-18432\,{t}^{10}{y
}^{2}+98304\,{t}^{9}{y}^{3}-138944\,{t}^{8}{y}^{4}-114464\,{t}^{7}{y}^{
5}+117504\,{t}^{6}{y}^{6}-7072\,{t}^{5}{y}^{7}-8544\,{t}^{4}{y}^{8}-576
\,{t}^{3}{y}^{9}+1280\,{t}^{11}-1536\,{t}^{10}y-12576\,{t}^{9}{y}^{2}+
94368\,{t}^{8}{y}^{3}-50144\,{t}^{7}{y}^{4}+40800\,{t}^{6}{y}^{5}+20776
\,{t}^{5}{y}^{6}-10480\,{t}^{4}{y}^{7}-1368\,{t}^{3}{y}^{8}-64\,{t}^{10
}-5472\,{t}^{9}y+6976\,{t}^{8}{y}^{2}+44640\,{t}^{7}{y}^{3}+11136\,{t}^
{6}{y}^{4}+30248\,{t}^{5}{y}^{5}-368\,{t}^{4}{y}^{6}-3516\,{t}^{3}{y}^{
7}-112\,{t}^{2}{y}^{8}-528\,{t}^{9}-848\,{t}^{8}y+6688\,{t}^{7}{y}^{2}+
7968\,{t}^{6}{y}^{3}+11364\,{t}^{5}{y}^{4}+8984\,{t}^{4}{y}^{5}-1380\,{
t}^{3}{y}^{6}-304\,{t}^{2}{y}^{7}-4\,t{y}^{8}-256\,{t}^{8}+1456\,{t}^{7
}y-816\,{t}^{6}{y}^{2}-1656\,{t}^{5}{y}^{3}+4260\,{t}^{4}{y}^{4}+1032\,
{t}^{3}{y}^{5}-132\,{t}^{2}{y}^{6}-4\,t{y}^{7}+80\,{t}^{7}+192\,{t}^{6}
y-282\,{t}^{5}{y}^{2}-2574\,{t}^{4}{y}^{3}+1392\,{t}^{3}{y}^{4}+88\,{t}
^{2}{y}^{5}-12\,t{y}^{6}+36\,{t}^{6}-70\,{t}^{5}y-72\,{t}^{4}{y}^{2}-
741\,{t}^{3}{y}^{3}+343\,{t}^{2}{y}^{4}-11\,t{y}^{5}-3\,{y}^{6}-11\,{t}
^{5}+17\,{t}^{4}y-3\,{t}^{3}{y}^{2}-75\,{t}^{2}{y}^{3}+25\,t{y}^{4}-3\,
{y}^{5}-2\,{t}^{4}+20\,{t}^{2}{y}^{2}-12\,t{y}^{3}+5\,t{y}^{2}-3\,{y}^{
3} \right)
$ | | ss | vx | vy | CAS used | integrate | time (sec) | memory (GB) | $\operatorname{ord}P$ | $\deg_tP$ | height of $P$ | length of $P$ | $\deg_tU$ | $\deg_uU$ | $\deg_vU$ | height of $U$ | length of $U$ | $\deg_tV$ | $\deg_uV$ | $\deg_vV$ | height of $V$ | length of $V$ | leading coefficient of $P$ |
|---|
| 07 |
0 | 0 | Maple | $v$, then $u$ | 1.28 | 0.0447 | 3 | 6 | 3 | 128 | 5 / 7 | 9 / 8 | 4 / 4 | 3 | 680 | 40 / 123 | 40 / 114 | 15 / 6 | 6 | 47046 | ${t}^{2} \left( 4\,{t}^{2}+1 \right) \left( 12\,{t}^{2}-1 \right)
$ |
0 | 0 | Maple | $u$, then $v$ | 3.27 | 0.0466 | 3 | 6 | 3 | 128 | 17 / 22 | 14 / 10 | 31 / 31 | 6 | 17231 | 8 / 39 | 6 / 58 | 11 / 32 | 5 | 3638 | ${t}^{2} \left( 4\,{t}^{2}+1 \right) \left( 12\,{t}^{2}-1 \right)
$ | 0 | 1 | Maple | $v$, then $u$ | 64.3 | 0.616 | 6 | 17 | 9 | 1248 | 36 / 15 | 41 / 28 | 29 / 5 | 13 | 168313 | 38 / 221 | 101 / 196 | 21 / 13 | 22 | 1453730 | ${t}^{5} \left( t-1 \right) \left( 4\,t-1 \right) \left( 4\,{t}^{2}+1
\right) \left( 12\,{t}^{2}-1 \right) \left( 432\,{t}^{6}-288\,{t}^{4
}+176\,{t}^{3}-39\,{t}^{2}-t-5 \right)
$ | 0 | 1 | Maple | $u$, then $v$ | 65.8 | 0.473 | 6 | 17 | 9 | 1248 | 27 / 22 | 13 / 12 | 35 / 38 | 14 | 198905 | 22 / 109 | 6 / 181 | 23 / 116 | 11 | 48075 | ${t}^{5} \left( t-1 \right) \left( 4\,t-1 \right) \left( 4\,{t}^{2}+1
\right) \left( 12\,{t}^{2}-1 \right) \left( 432\,{t}^{6}-288\,{t}^{4
}+176\,{t}^{3}-39\,{t}^{2}-t-5 \right)
$ | 1 | 0 | Maple | $v$, then $u$ | 1.36 | 0.0446 | 3 | 6 | 3 | 127 | 5 / 7 | 8 / 8 | 4 / 4 | 2 | 573 | 26 / 104 | 53 / 105 | 30 / 72 | 5 | 42475 | ${t}^{2} \left( 4\,{t}^{2}+1 \right) \left( 12\,{t}^{2}-1 \right)
$ | 1 | 0 | Maple | $u$, then $v$ | 3.23 | 0.0448 | 3 | 6 | 3 | 127 | 9 / 10 | 6 / 6 | 14 / 16 | 4 | 3422 | 24 / 41 | 26 / 58 | 9 / 33 | 5 | 10323 | ${t}^{2} \left( 4\,{t}^{2}+1 \right) \left( 12\,{t}^{2}-1 \right)
$ | 1 | 1 | Maple | $v$, then $u$ | 25.4 | 0.509 | 5 | 15 | 9 | 1076 | 20 / 15 | 16 / 16 | 4 / 5 | 11 | 25715 | 29 / 24 | 29 / 29 | 10 / 10 | 16 | 157488 | ${t}^{2} \left( t-1 \right) \left( 4\,t-1 \right) \left( 12\,{t}^{2}-1
\right) \left( 5184\,{t}^{7}-4128\,{t}^{6}+4416\,{t}^{5}+400\,{t}^{4}
+252\,{t}^{3}-90\,{t}^{2}-42\,t+3 \right) \left( 4\,{t}^{2}+1 \right)
$ | 1 | 1 | Maple | $u$, then $v$ | 42.4 | 0.562 | 5 | 15 | 9 | 1076 | 25 / 20 | 9 / 10 | 30 / 31 | 12 | 113028 | 27 / 84 | 74 / 129 | 18 / 97 | 12 | 126550 | ${t}^{2} \left( t-1 \right) \left( 4\,t-1 \right) \left( 12\,{t}^{2}-1
\right) \left( 5184\,{t}^{7}-4128\,{t}^{6}+4416\,{t}^{5}+400\,{t}^{4}
+252\,{t}^{3}-90\,{t}^{2}-42\,t+3 \right) \left( 4\,{t}^{2}+1 \right)
$ | 1 | 1 | Mathematica | $u$, then $v$ | 530 | n.a. | 5 | 15 | 9 | 1076 | 29 / 22 | 11 / 11 | 9 / 10 | 20 | 88931 | 29 / 22 | 11 / 8 | 9 / 8 | 18 | 41357 | ${t}^{2} \left( t-1 \right) \left( 4\,t-1 \right) \left( 12\,{t}^{2}-1
\right) \left( 5184\,{t}^{7}-4128\,{t}^{6}+4416\,{t}^{5}+400\,{t}^{4}
+252\,{t}^{3}-90\,{t}^{2}-42\,t+3 \right) \left( 4\,{t}^{2}+1 \right)
$ | 1 | 1 | Mathematica | $v$, then $u$ | 41.8 | n.a. | 5 | 15 | 9 | 1076 | 29 / 22 | 11 / 11 | 9 / 10 | 20 | 88931 | 29 / 22 | 11 / 8 | 9 / 8 | 18 | 41357 | ${t}^{2} \left( t-1 \right) \left( 4\,t-1 \right) \left( 12\,{t}^{2}-1
\right) \left( 5184\,{t}^{7}-4128\,{t}^{6}+4416\,{t}^{5}+400\,{t}^{4}
+252\,{t}^{3}-90\,{t}^{2}-42\,t+3 \right) \left( 4\,{t}^{2}+1 \right)
$ | x | 0 | Mathematica | $u$, then $v$ | 235 | n.a. | 4 | 9 | 5 | 637 | 10 / 8 | 8 / 8 | 6 / 6 | 5 | 16556 | 12 / 10 | 8 / 8 | 9 / 8 | 5 | 25412 | ${t}^{3} \left( 4\,{t}^{2}+1 \right) \left( 12\,{t}^{2}-1 \right)
\left( 4\,{t}^{2}{x}^{2}+4\,{t}^{2}x+4\,{t}^{2}-x \right)
$ | 0 | y | Mathematica | $u$, then $v$ | 1170 | n.a. | 6 | 18 | 11 | 13035 | 34 / 27 | 13 / 14 | 11 / 12 | 28 | 2090476 | 34 / 27 | 13 / 10 | 11 / 10 | 27 | 808934 | ${t}^{3} \left( 4\,{t}^{2}+1 \right) \left( 12\,{t}^{2}-1 \right)
\left( t{y}^{2}-t+y \right) \left( -y+t \right) \left( 3\,t{y}^{2}+t
-y \right) \left( 13824\,{t}^{8}{y}^{9}+30816\,{t}^{8}{y}^{7}+4104\,{t
}^{7}{y}^{8}-13392\,{t}^{6}{y}^{9}-1080\,{t}^{5}{y}^{10}+5760\,{t}^{8}{
y}^{5}-1440\,{t}^{7}{y}^{6}-18216\,{t}^{6}{y}^{7}+4656\,{t}^{5}{y}^{8}+
216\,{t}^{4}{y}^{9}+1440\,{t}^{8}{y}^{3}-3312\,{t}^{7}{y}^{4}+792\,{t}^
{6}{y}^{5}+10172\,{t}^{5}{y}^{6}-2622\,{t}^{4}{y}^{7}-792\,{t}^{3}{y}^{
8}+576\,{t}^{7}{y}^{2}-3096\,{t}^{6}{y}^{3}+5236\,{t}^{5}{y}^{4}+276\,{
t}^{4}{y}^{5}-186\,{t}^{3}{y}^{6}-553\,{t}^{2}{y}^{7}+72\,{t}^{7}-648\,
{t}^{6}y+2140\,{t}^{5}{y}^{2}-2586\,{t}^{4}{y}^{3}+858\,{t}^{3}{y}^{4}+
124\,{t}^{2}{y}^{5}-111\,t{y}^{6}-4\,{t}^{5}+36\,{t}^{4}y-161\,{t}^{2}{
y}^{3}+87\,t{y}^{4}+12\,{y}^{5}-10\,{t}^{2}y+24\,t{y}^{2}-12\,{y}^{3}
\right)
$ | | ss | vx | vy | CAS used | integrate | time (sec) | memory (GB) | $\operatorname{ord}P$ | $\deg_tP$ | height of $P$ | length of $P$ | $\deg_tU$ | $\deg_uU$ | $\deg_vU$ | height of $U$ | length of $U$ | $\deg_tV$ | $\deg_uV$ | $\deg_vV$ | height of $V$ | length of $V$ | leading coefficient of $P$ |
|---|
| 08 |
0 | 0 | Maple | $v$, then $u$ | 3.78 | 0.0467 | 4 | 10 | 6 | 461 | 8 / 7 | 14 / 14 | 4 / 4 | 4 | 3733 | 40 / 109 | 46 / 137 | 17 / 44 | 11 | 189381 | ${t}^{3} \left( 1+2\,t \right) \left( 8\,{t}^{2}+4\,t+1 \right)
\left( 8\,{t}^{2}+8\,t+3 \right) \left( 8\,{t}^{2}+4\,t-1 \right)
$ |
0 | 0 | Maple | $u$, then $v$ | 21.6 | 0.514 | 4 | 10 | 6 | 461 | 17 / 16 | 9 / 8 | 23 / 25 | 10 | 56531 | 15 / 127 | 6 / 83 | 20 / 40 | 8 | 33027 | ${t}^{3} \left( 1+2\,t \right) \left( 8\,{t}^{2}+4\,t+1 \right)
\left( 8\,{t}^{2}+8\,t+3 \right) \left( 8\,{t}^{2}+4\,t-1 \right)
$ | 0 | 1 | Maple | $v$, then $u$ | 100 | 0.444 | 6 | 19 | 12 | 1643 | 40 / 42 | 37 / 41 | 35 / 8 | 16 | 265334 | 73 / 216 | 129 / 331 | 55 / 130 | 33 | 11429765 | ${t}^{3} \left( 6\,t-1 \right) \left( 8\,{t}^{2}+4\,t+1 \right)
\left( 8\,{t}^{2}+4\,t-1 \right) \left( 24576\,{t}^{9}+55296\,{t}^{8}
+64320\,{t}^{7}+65632\,{t}^{6}+55128\,{t}^{5}+28428\,{t}^{4}+7760\,{t}^
{3}+1020\,{t}^{2}+63\,t+4 \right) \left( 1+2\,t \right) ^{2}
$ | 0 | 1 | Maple | $u$, then $v$ | 289000 | 32.5 | 6 | 19 | 12 | 1643 | 31 / 24 | 13 / 12 | 38 / 40 | 18 | 334299 | 25 / 18 | 6 / 6 | 22 / 24 | 15 | 66819 | ${t}^{3} \left( 6\,t-1 \right) \left( 8\,{t}^{2}+4\,t+1 \right)
\left( 8\,{t}^{2}+4\,t-1 \right) \left( 24576\,{t}^{9}+55296\,{t}^{8}
+64320\,{t}^{7}+65632\,{t}^{6}+55128\,{t}^{5}+28428\,{t}^{4}+7760\,{t}^
{3}+1020\,{t}^{2}+63\,t+4 \right) \left( 1+2\,t \right) ^{2}
$ | 1 | 0 | Maple | $v$, then $u$ | 5.86 | 0.412 | 4 | 11 | 6 | 534 | 10 / 8 | 14 / 14 | 4 / 4 | 5 | 4834 | 19 / 110 | 30 / 151 | 15 / 33 | 11 | 99197 | ${t}^{3} \left( 1+2\,t \right) \left( 8\,{t}^{2}+4\,t-1 \right)
\left( 24\,{t}^{3}+24\,{t}^{2}+11\,t+2 \right) \left( 8\,{t}^{2}+4\,t
+1 \right)
$ | 1 | 0 | Maple | $u$, then $v$ | 23.5 | 0.472 | 4 | 11 | 6 | 534 | 19 / 17 | 7 / 8 | 25 / 25 | 10 | 56475 | 13 / 11 | 5 / 6 | 14 / 14 | 7 | 15875 | ${t}^{3} \left( 1+2\,t \right) \left( 8\,{t}^{2}+4\,t-1 \right)
\left( 24\,{t}^{3}+24\,{t}^{2}+11\,t+2 \right) \left( 8\,{t}^{2}+4\,t
+1 \right)
$ | 1 | 1 | Maple | $v$, then $u$ | 834 | 5.29 | 5 | 18 | 11 | 1318 | 23 / 15 | 22 / 22 | 4 / 5 | 14 | 47466 | 29 / 21 | 37 / 37 | 9 / 10 | 18 | 213798 | ${t}^{2} \left( 6\,t-1 \right) \left( 8\,{t}^{2}+4\,t+1 \right)
\left( 8\,{t}^{2}+4\,t-1 \right) \left( 8192\,{t}^{9}+29696\,{t}^{8}+
37440\,{t}^{7}+29824\,{t}^{6}+21944\,{t}^{5}+13912\,{t}^{4}+5774\,{t}^{
3}+1338\,{t}^{2}+160\,t+9 \right) \left( 1+2\,t \right) ^{2}
$ | 1 | 1 | Maple | $u$, then $v$ | 1380 | 6.51 | 5 | 18 | 11 | 1318 | 29 / 21 | 9 / 10 | 33 / 33 | 16 | 195332 | 44 / 198 | 39 / 175 | 13 / 26 | 16 | 218186 | ${t}^{2} \left( 6\,t-1 \right) \left( 8\,{t}^{2}+4\,t+1 \right)
\left( 8\,{t}^{2}+4\,t-1 \right) \left( 8192\,{t}^{9}+29696\,{t}^{8}+
37440\,{t}^{7}+29824\,{t}^{6}+21944\,{t}^{5}+13912\,{t}^{4}+5774\,{t}^{
3}+1338\,{t}^{2}+160\,t+9 \right) \left( 1+2\,t \right) ^{2}
$ | 1 | 1 | Mathematica | $u$, then $v$ | 725 | n.a. | 5 | 18 | 11 | 1318 | 28 / 19 | 11 / 11 | 10 / 10 | 21 | 93506 | 28 / 19 | 9 / 8 | 9 / 8 | 19 | 41848 | ${t}^{2} \left( 6\,t-1 \right) \left( 8\,{t}^{2}+4\,t+1 \right)
\left( 8\,{t}^{2}+4\,t-1 \right) \left( 8192\,{t}^{9}+29696\,{t}^{8}+
37440\,{t}^{7}+29824\,{t}^{6}+21944\,{t}^{5}+13912\,{t}^{4}+5774\,{t}^{
3}+1338\,{t}^{2}+160\,t+9 \right) \left( 1+2\,t \right) ^{2}
$ | 1 | 1 | Mathematica | $v$, then $u$ | 92.9 | n.a. | 5 | 18 | 11 | 1318 | 28 / 19 | 11 / 11 | 10 / 10 | 21 | 93506 | 28 / 19 | 9 / 8 | 9 / 8 | 19 | 41848 | ${t}^{2} \left( 6\,t-1 \right) \left( 8\,{t}^{2}+4\,t+1 \right)
\left( 8\,{t}^{2}+4\,t-1 \right) \left( 8192\,{t}^{9}+29696\,{t}^{8}+
37440\,{t}^{7}+29824\,{t}^{6}+21944\,{t}^{5}+13912\,{t}^{4}+5774\,{t}^{
3}+1338\,{t}^{2}+160\,t+9 \right) \left( 1+2\,t \right) ^{2}
$ | x | 0 | Mathematica | $u$, then $v$ | 890 | n.a. | 5 | 17 | 10 | 11484 | 19 / 12 | 9 / 10 | 9 / 8 | 13 | 505536 | 21 / 14 | 8 / 10 | 10 / 10 | 13 | 486583 | ${t}^{3} \left( 1+2\,t \right) \left( 8\,{t}^{2}+4\,t+1 \right)
\left( 8\,{t}^{2}+4\,t-1 \right) \left( 16\,{t}^{7}{x}^{4}+320\,{t}^{
7}{x}^{3}+16\,{t}^{6}{x}^{4}+480\,{t}^{7}{x}^{2}+544\,{t}^{6}{x}^{3}+22
\,{t}^{5}{x}^{4}+320\,{t}^{7}x+1120\,{t}^{6}{x}^{2}+312\,{t}^{5}{x}^{3}
+12\,{t}^{4}{x}^{4}+16\,{t}^{7}+544\,{t}^{6}x+1252\,{t}^{5}{x}^{2}+12\,
{t}^{4}{x}^{3}+2\,{t}^{3}{x}^{4}+16\,{t}^{6}+312\,{t}^{5}x+872\,{t}^{4}
{x}^{2}-58\,{t}^{3}{x}^{3}+22\,{t}^{5}+12\,{t}^{4}x+438\,{t}^{3}{x}^{2}
-25\,{t}^{2}{x}^{3}+12\,{t}^{4}-58\,{t}^{3}x+158\,{t}^{2}{x}^{2}-4\,t{x
}^{3}+2\,{t}^{3}-25\,{t}^{2}x+34\,t{x}^{2}-4\,tx+3\,{x}^{2} \right)
\left( {t}^{2}{x}^{4}-4\,{t}^{2}{x}^{3}-2\,{t}^{2}{x}^{2}-2\,t{x}^{3}-
4\,{t}^{2}x+{t}^{2}-2\,tx+{x}^{2} \right)
$ | 0 | y | Mathematica | $u$, then $v$ | 2350 | n.a. | 6 | 22 | 14 | 37064 | 36 / 26 | 13 / 14 | 12 / 12 | 30 | 4814420 | 36 / 26 | 10 / 10 | 11 / 10 | 29 | 1813285 | ${t}^{3} \left( 1+2\,t \right) \left( 8\,{t}^{2}+4\,t+1 \right)
\left( 8\,{t}^{2}+4\,t-1 \right) \left( yt-t+y \right) \left( t{y}^{
2}+2\,yt-t+y \right) \left( 3\,t{y}^{2}+2\,yt+t-y \right) \left(
60048\,{t}^{11}{y}^{9}-34992\,{t}^{11}{y}^{8}+92880\,{t}^{10}{y}^{9}+
159456\,{t}^{11}{y}^{7}-329184\,{t}^{10}{y}^{8}+30294\,{t}^{9}{y}^{9}-
34784\,{t}^{11}{y}^{6}+504240\,{t}^{10}{y}^{7}-731106\,{t}^{9}{y}^{8}-
27648\,{t}^{8}{y}^{9}-286912\,{t}^{11}{y}^{5}+67952\,{t}^{10}{y}^{6}+
587124\,{t}^{9}{y}^{7}-776538\,{t}^{8}{y}^{8}-29214\,{t}^{7}{y}^{9}+
8960\,{t}^{11}{y}^{4}-796016\,{t}^{10}{y}^{5}+148140\,{t}^{9}{y}^{6}+
333822\,{t}^{8}{y}^{7}-466758\,{t}^{7}{y}^{8}-14256\,{t}^{6}{y}^{9}+
35616\,{t}^{11}{y}^{3}+54832\,{t}^{10}{y}^{4}-868824\,{t}^{9}{y}^{5}-
23202\,{t}^{8}{y}^{6}+112038\,{t}^{7}{y}^{7}-167940\,{t}^{6}{y}^{8}-
5076\,{t}^{5}{y}^{9}-9248\,{t}^{11}{y}^{2}+143184\,{t}^{10}{y}^{3}+
242064\,{t}^{9}{y}^{4}-504834\,{t}^{8}{y}^{5}-215586\,{t}^{7}{y}^{6}+
39168\,{t}^{6}{y}^{7}-35307\,{t}^{5}{y}^{8}-1080\,{t}^{4}{y}^{9}+3120\,
{t}^{11}y-11632\,{t}^{10}{y}^{2}+209292\,{t}^{9}{y}^{3}+447634\,{t}^{8}
{y}^{4}-227760\,{t}^{7}{y}^{5}-200034\,{t}^{6}{y}^{6}+21582\,{t}^{5}{y}
^{7}-3384\,{t}^{4}{y}^{8}-81\,{t}^{3}{y}^{9}+432\,{t}^{11}+3744\,{t}^{
10}y+7764\,{t}^{9}{y}^{2}+136690\,{t}^{8}{y}^{3}+447488\,{t}^{7}{y}^{4}
-133770\,{t}^{6}{y}^{5}-87597\,{t}^{5}{y}^{6}+9747\,{t}^{4}{y}^{7}+81\,
{t}^{3}{y}^{8}-336\,{t}^{10}+7938\,{t}^{9}y+13522\,{t}^{8}{y}^{2}+22706
\,{t}^{7}{y}^{3}+280458\,{t}^{6}{y}^{4}-80194\,{t}^{5}{y}^{5}-19596\,{t
}^{4}{y}^{6}+2574\,{t}^{3}{y}^{7}+27\,{t}^{2}{y}^{8}-558\,{t}^{9}+9586
\,{t}^{8}y+146\,{t}^{7}{y}^{2}-23706\,{t}^{6}{y}^{3}+119729\,{t}^{5}{y}
^{4}-34220\,{t}^{4}{y}^{5}-1506\,{t}^{3}{y}^{6}+351\,{t}^{2}{y}^{7}-200
\,{t}^{8}+5222\,{t}^{7}y-5196\,{t}^{6}{y}^{2}-18864\,{t}^{5}{y}^{3}+
36370\,{t}^{4}{y}^{4}-9744\,{t}^{3}{y}^{5}+289\,{t}^{2}{y}^{6}+18\,t{y}
^{7}-58\,{t}^{7}+1380\,{t}^{6}y-2381\,{t}^{5}{y}^{2}-7161\,{t}^{4}{y}^{
3}+8019\,{t}^{3}{y}^{4}-1823\,{t}^{2}{y}^{5}+80\,t{y}^{6}-72\,{t}^{6}+
244\,{t}^{5}y-316\,{t}^{4}{y}^{2}-1728\,{t}^{3}{y}^{3}+1275\,{t}^{2}{y}
^{4}-211\,t{y}^{5}+6\,{y}^{6}-32\,{t}^{5}+44\,{t}^{4}y+90\,{t}^{3}{y}^{
2}-304\,{t}^{2}{y}^{3}+141\,t{y}^{4}-12\,{y}^{5}-4\,{t}^{4}+3\,{t}^{3}y
+43\,{t}^{2}{y}^{2}-41\,t{y}^{3}+9\,{y}^{4}+5\,t{y}^{2}-3\,{y}^{3}
\right)
$ | | ss | vx | vy | CAS used | integrate | time (sec) | memory (GB) | $\operatorname{ord}P$ | $\deg_tP$ | height of $P$ | length of $P$ | $\deg_tU$ | $\deg_uU$ | $\deg_vU$ | height of $U$ | length of $U$ | $\deg_tV$ | $\deg_uV$ | $\deg_vV$ | height of $V$ | length of $V$ | leading coefficient of $P$ |
|---|
| 09 |
0 | 0 | Maple | $v$, then $u$ | 3.71 | 0.0867 | 4 | 11 | 6 | 292 | 9 / 9 | 14 / 14 | 4 / 4 | 5 | 2620 | 22 / 93 | 36 / 114 | 11 / 10 | 12 | 63684 | ${t}^{3} \left( 14\,{t}^{2}-1 \right) \left( 24\,{t}^{2}-1 \right)
\left( 8\,{t}^{2}-1 \right) \left( {t}^{2}+1 \right)
$ |
0 | 0 | Maple | $u$, then $v$ | 17.3 | 0.444 | 4 | 11 | 6 | 292 | 18 / 15 | 9 / 8 | 25 / 27 | 10 | 38783 | 81 / 313 | 61 / 93 | 12 / 54 | 8 | 43207 | ${t}^{3} \left( 14\,{t}^{2}-1 \right) \left( 24\,{t}^{2}-1 \right)
\left( 8\,{t}^{2}-1 \right) \left( {t}^{2}+1 \right)
$ | 0 | 1 | Maple | $v$, then $u$ | 129 | 0.744 | 6 | 27 | 16 | 3085 | 41 / 57 | 37 / 56 | 26 / 69 | 23 | 355145 | 63 / 165 | 72 / 190 | 23 / 32 | 34 | 2714311 | ${t}^{3} \left( 3\,t+1 \right) \left( 5\,t-1 \right) \left( t+1
\right) \left( {t}^{2}+1 \right) \left( 8\,{t}^{2}-1 \right)
\left( 24\,{t}^{2}-1 \right) \left( 7575552\,{t}^{15}+52695360\,{t}^{
14}-79023168\,{t}^{13}-42726912\,{t}^{12}+49317984\,{t}^{11}-4024620\,{
t}^{10}-3772728\,{t}^{9}+815652\,{t}^{8}-302496\,{t}^{7}+13422\,{t}^{6}
+43725\,{t}^{5}-5535\,{t}^{4}-1586\,{t}^{3}+240\,{t}^{2}+25\,t-3
\right)
$ | 0 | 1 | Maple | $u$, then $v$ | not available | 1 | 0 | Maple | $v$, then $u$ | 3.37 | 0.0453 | 4 | 11 | 6 | 304 | 8 / 8 | 14 / 14 | 4 / 4 | 4 | 781 | 17 / 84 | 26 / 88 | 11 / 17 | 10 | 36937 | ${t}^{3} \left( 13\,{t}^{2}-2 \right) \left( 24\,{t}^{2}-1 \right)
\left( 8\,{t}^{2}-1 \right) \left( {t}^{2}+1 \right)
$ | 1 | 0 | Maple | $u$, then $v$ | 14.9 | 0.444 | 4 | 11 | 6 | 304 | 18 / 15 | 7 / 8 | 24 / 27 | 9 | 30900 | 54 / 312 | 26 / 93 | 20 / 54 | 8 | 47053 | ${t}^{3} \left( 13\,{t}^{2}-2 \right) \left( 24\,{t}^{2}-1 \right)
\left( 8\,{t}^{2}-1 \right) \left( {t}^{2}+1 \right)
$ | 1 | 1 | Maple | $v$, then $u$ | 569 | 3.5 | 5 | 24 | 14 | 2288 | 32 / 18 | 22 / 22 | 4 / 5 | 18 | 83192 | 85 / 229 | 85 / 219 | 18 / 18 | 31 | 3524149 | ${t}^{2} \left( 3\,t+1 \right) \left( 5\,t-1 \right) \left( t+1
\right) \left( {t}^{2}+1 \right) \left( 8\,{t}^{2}-1 \right)
\left( 24\,{t}^{2}-1 \right) \left( 2944512\,{t}^{13}-6994944\,{t}^{
12}-12219648\,{t}^{11}+80088\,{t}^{10}+1723824\,{t}^{9}+648742\,{t}^{8}
-42124\,{t}^{7}-133223\,{t}^{6}+9836\,{t}^{5}+15063\,{t}^{4}-528\,{t}^{
3}-801\,{t}^{2}-72\,t+3 \right)
$ | 1 | 1 | Maple | $u$, then $v$ | 8720 | 9.59 | 5 | 24 | 14 | 2288 | 35 / 22 | 9 / 10 | 33 / 35 | 20 | 284854 | 70 / 432 | 26 / 124 | 30 / 76 | 20 | 294072 | ${t}^{2} \left( 3\,t+1 \right) \left( 5\,t-1 \right) \left( t+1
\right) \left( {t}^{2}+1 \right) \left( 8\,{t}^{2}-1 \right)
\left( 24\,{t}^{2}-1 \right) \left( 2944512\,{t}^{13}-6994944\,{t}^{
12}-12219648\,{t}^{11}+80088\,{t}^{10}+1723824\,{t}^{9}+648742\,{t}^{8}
-42124\,{t}^{7}-133223\,{t}^{6}+9836\,{t}^{5}+15063\,{t}^{4}-528\,{t}^{
3}-801\,{t}^{2}-72\,t+3 \right)
$ | 1 | 1 | Mathematica | $u$, then $v$ | 1020 | n.a. | 5 | 24 | 14 | 2288 | 37 / 23 | 11 / 9 | 11 / 8 | 22 | 158810 | 38 / 24 | 11 / 10 | 11 / 10 | 22 | 102471 | ${t}^{2} \left( 3\,t+1 \right) \left( 5\,t-1 \right) \left( t+1
\right) \left( {t}^{2}+1 \right) \left( 8\,{t}^{2}-1 \right)
\left( 24\,{t}^{2}-1 \right) \left( 2944512\,{t}^{13}-6994944\,{t}^{
12}-12219648\,{t}^{11}+80088\,{t}^{10}+1723824\,{t}^{9}+648742\,{t}^{8}
-42124\,{t}^{7}-133223\,{t}^{6}+9836\,{t}^{5}+15063\,{t}^{4}-528\,{t}^{
3}-801\,{t}^{2}-72\,t+3 \right)
$ | 1 | 1 | Mathematica | $v$, then $u$ | 88.7 | n.a. | 5 | 24 | 14 | 2288 | 37 / 23 | 11 / 9 | 11 / 8 | 22 | 158810 | 38 / 24 | 11 / 10 | 11 / 10 | 22 | 102471 | ${t}^{2} \left( 3\,t+1 \right) \left( 5\,t-1 \right) \left( t+1
\right) \left( {t}^{2}+1 \right) \left( 8\,{t}^{2}-1 \right)
\left( 24\,{t}^{2}-1 \right) \left( 2944512\,{t}^{13}-6994944\,{t}^{
12}-12219648\,{t}^{11}+80088\,{t}^{10}+1723824\,{t}^{9}+648742\,{t}^{8}
-42124\,{t}^{7}-133223\,{t}^{6}+9836\,{t}^{5}+15063\,{t}^{4}-528\,{t}^{
3}-801\,{t}^{2}-72\,t+3 \right)
$ | x | 0 | Mathematica | $u$, then $v$ | 1240 | n.a. | 5 | 16 | 9 | 5722 | 24 / 16 | 11 / 10 | 7 / 8 | 15 | 533073 | 21 / 13 | 11 / 10 | 10 / 10 | 14 | 383322 | ${t}^{4} \left( {t}^{2}+1 \right) \left( 8\,{t}^{2}-1 \right) \left(
24\,{t}^{2}-1 \right) \left( 4\,{t}^{2}{x}^{4}+4\,{t}^{2}{x}^{3}+8\,{t
}^{2}{x}^{2}+4\,{t}^{2}x+4\,{t}^{2}-{x}^{2} \right) \left( 270\,{t}^{4
}{x}^{4}-148\,{t}^{4}{x}^{3}+402\,{t}^{4}{x}^{2}-29\,{t}^{2}{x}^{4}-148
\,{t}^{4}x+3\,{t}^{2}{x}^{3}+270\,{t}^{4}-46\,{t}^{2}{x}^{2}+{x}^{4}+3
\,{t}^{2}x+{x}^{3}-29\,{t}^{2}+2\,{x}^{2}+x+1 \right)
$ | 0 | y | Mathematica | $u$, then $v$ | 2450 | n.a. | 6 | 27 | 16 | 26810 | 53 / 37 | 14 / 14 | 11 / 12 | 33 | 5164299 | 45 / 29 | 8 / 10 | 11 / 10 | 29 | 908968 | ${t}^{3} \left( {t}^{2}+1 \right) \left( 8\,{t}^{2}-1 \right) \left(
24\,{t}^{2}-1 \right) \left( t+y \right) \left( 3\,t{y}^{2}+2\,t-y
\right) \left( 3538944\,{t}^{15}{y}^{9}+8534016\,{t}^{15}{y}^{7}+
17608320\,{t}^{14}{y}^{8}-5329152\,{t}^{13}{y}^{9}-13357440\,{t}^{12}{y
}^{10}+5289984\,{t}^{15}{y}^{5}+46596096\,{t}^{14}{y}^{6}-42028416\,{t}
^{13}{y}^{7}-44301504\,{t}^{12}{y}^{8}-9649152\,{t}^{11}{y}^{9}+5175360
\,{t}^{10}{y}^{10}-958464\,{t}^{15}{y}^{3}+37555200\,{t}^{14}{y}^{4}-
70778880\,{t}^{13}{y}^{5}-39816640\,{t}^{12}{y}^{6}+6112416\,{t}^{11}{y
}^{7}+19388904\,{t}^{10}{y}^{8}-525528\,{t}^{9}{y}^{9}-541080\,{t}^{8}{
y}^{10}-1253376\,{t}^{15}y+6119424\,{t}^{14}{y}^{2}-36813312\,{t}^{13}{
y}^{3}-540928\,{t}^{12}{y}^{4}+47722272\,{t}^{11}{y}^{5}+5744864\,{t}^{
10}{y}^{6}+1337272\,{t}^{9}{y}^{7}-3034548\,{t}^{8}{y}^{8}+196560\,{t}^
{7}{y}^{9}+25380\,{t}^{6}{y}^{10}-2488320\,{t}^{14}-3096576\,{t}^{13}y+
9767168\,{t}^{12}{y}^{2}+41923968\,{t}^{11}{y}^{3}-25051744\,{t}^{10}{y
}^{4}-651552\,{t}^{9}{y}^{5}-1819116\,{t}^{8}{y}^{6}-320390\,{t}^{7}{y}
^{7}+207420\,{t}^{6}{y}^{8}-10260\,{t}^{5}{y}^{9}-540\,{t}^{4}{y}^{10}+
2795520\,{t}^{12}+12526464\,{t}^{11}y-13667584\,{t}^{10}{y}^{2}-4441840
\,{t}^{9}{y}^{3}+4130448\,{t}^{8}{y}^{4}-753666\,{t}^{7}{y}^{5}+254098
\,{t}^{6}{y}^{6}+22695\,{t}^{5}{y}^{7}-6960\,{t}^{4}{y}^{8}+108\,{t}^{3
}{y}^{9}+360960\,{t}^{10}-3263808\,{t}^{9}y+2975088\,{t}^{8}{y}^{2}-
51016\,{t}^{7}{y}^{3}-222022\,{t}^{6}{y}^{4}+65091\,{t}^{5}{y}^{5}-
14987\,{t}^{4}{y}^{6}-860\,{t}^{3}{y}^{7}+144\,{t}^{2}{y}^{8}-79488\,{t
}^{8}+323520\,{t}^{7}y-242896\,{t}^{6}{y}^{2}+23940\,{t}^{5}{y}^{3}+
3353\,{t}^{4}{y}^{4}-1716\,{t}^{3}{y}^{5}+396\,{t}^{2}{y}^{6}+31\,t{y}^
{7}+4864\,{t}^{6}-14016\,{t}^{5}y+8192\,{t}^{4}{y}^{2}-896\,{t}^{3}{y}^
{3}+36\,{t}^{2}{y}^{4}+15\,t{y}^{5}-3\,{y}^{6}-128\,{t}^{4}+192\,{t}^{3
}y-96\,{t}^{2}{y}^{2}+4\,t{y}^{3}-3\,{y}^{4} \right) \left( t{y}^{2}+2
\,t+y \right)
$ | | ss | vx | vy | CAS used | integrate | time (sec) | memory (GB) | $\operatorname{ord}P$ | $\deg_tP$ | height of $P$ | length of $P$ | $\deg_tU$ | $\deg_uU$ | $\deg_vU$ | height of $U$ | length of $U$ | $\deg_tV$ | $\deg_uV$ | $\deg_vV$ | height of $V$ | length of $V$ | leading coefficient of $P$ |
|---|
| 10 |
0 | 0 | Maple | $v$, then $u$ | 5.45 | 0.0903 | 4 | 12 | 6 | 572 | 12 / 9 | 14 / 14 | 4 / 4 | 6 | 7305 | 21 / 91 | 32 / 81 | 15 / 14 | 12 | 174215 | ${t}^{3} \left( {t}^{2}+t+1 \right) \left( 20\,{t}^{2}+4\,t-1 \right)
\left( 4\,{t}^{2}-4\,t-1 \right) \left( 12\,{t}^{3}+20\,{t}^{2}-3\,t-
2 \right)
$ |
0 | 0 | Maple | $u$, then $v$ | 60.1 | 1.47 | 4 | 12 | 6 | 572 | 21 / 18 | 9 / 8 | 25 / 27 | 12 | 100020 | 18 / 13 | 6 / 6 | 18 / 16 | 11 | 38557 | ${t}^{3} \left( {t}^{2}+t+1 \right) \left( 20\,{t}^{2}+4\,t-1 \right)
\left( 4\,{t}^{2}-4\,t-1 \right) \left( 12\,{t}^{3}+20\,{t}^{2}-3\,t-
2 \right)
$ | 0 | 1 | Maple | $v$, then $u$ | 141 | 0.801 | 6 | 27 | 16 | 3192 | 40 / 23 | 38 / 37 | 35 / 5 | 22 | 357209 | 101 / 109 | 152 / 124 | 51 / 69 | 60 | 22696302 | ${t}^{3} \left( 5\,t+1 \right) \left( 1+2\,t \right) \left( 7\,t-1
\right) \left( {t}^{2}+t+1 \right) \left( 20\,{t}^{2}+4\,t-1
\right) \left( 4\,{t}^{2}-4\,t-1 \right) \left( 1720320\,{t}^{15}-
7335936\,{t}^{14}-15458304\,{t}^{13}+17353216\,{t}^{12}+39173248\,{t}^{
11}+15160576\,{t}^{10}-5888512\,{t}^{9}-5109856\,{t}^{8}-987976\,{t}^{7
}-11248\,{t}^{6}+9440\,{t}^{5}+1700\,{t}^{4}-434\,{t}^{3}-344\,{t}^{2}-
17\,t+3 \right)
$ | 0 | 1 | Maple | $u$, then $v$ | 145 | 0.702 | 6 | 27 | 16 | 3192 | 45 / 27 | 27 / 18 | 42 / 44 | 37 | 1086765 | 37 / 20 | 6 / 6 | 32 / 29 | 23 | 193746 | ${t}^{3} \left( 5\,t+1 \right) \left( 1+2\,t \right) \left( 7\,t-1
\right) \left( {t}^{2}+t+1 \right) \left( 20\,{t}^{2}+4\,t-1
\right) \left( 4\,{t}^{2}-4\,t-1 \right) \left( 1720320\,{t}^{15}-
7335936\,{t}^{14}-15458304\,{t}^{13}+17353216\,{t}^{12}+39173248\,{t}^{
11}+15160576\,{t}^{10}-5888512\,{t}^{9}-5109856\,{t}^{8}-987976\,{t}^{7
}-11248\,{t}^{6}+9440\,{t}^{5}+1700\,{t}^{4}-434\,{t}^{3}-344\,{t}^{2}-
17\,t+3 \right)
$ | 1 | 0 | Maple | $v$, then $u$ | 7.08 | 0.439 | 4 | 12 | 6 | 573 | 13 / 9 | 14 / 14 | 4 / 4 | 6 | 7790 | 16 / 30 | 23 / 40 | 11 / 10 | 9 | 57775 | ${t}^{3} \left( 4\,{t}^{2}-4\,t-1 \right) \left( 20\,{t}^{2}+4\,t-1
\right) \left( 8\,{t}^{3}+40\,{t}^{2}+4\,t-1 \right) \left( {t}^{2}+
t+1 \right)
$ | 1 | 0 | Maple | $u$, then $v$ | 24.2 | 0.0978 | 4 | 12 | 6 | 573 | 31 / 14 | 14 / 21 | 32 / 25 | 12 | 276267 | 20 / 9 | 28 / 6 | 13 / 18 | 2 | 1894 | ${t}^{3} \left( 4\,{t}^{2}-4\,t-1 \right) \left( 20\,{t}^{2}+4\,t-1
\right) \left( 8\,{t}^{3}+40\,{t}^{2}+4\,t-1 \right) \left( {t}^{2}+
t+1 \right)
$ | 1 | 1 | Maple | $v$, then $u$ | 1540 | 6.37 | 5 | 24 | 14 | 2391 | 31 / 18 | 22 / 22 | 4 / 5 | 18 | 81014 | 45 / 89 | 48 / 93 | 18 / 18 | 24 | 939302 | ${t}^{2} \left( 7\,t-1 \right) \left( 1+2\,t \right) \left( 5\,t+1
\right) \left( 4\,{t}^{2}-4\,t-1 \right) \left( 20\,{t}^{2}+4\,t-1
\right) \left( {t}^{2}+t+1 \right) \left( 337920\,{t}^{13}+1373184\,
{t}^{12}-4304640\,{t}^{11}-6344576\,{t}^{10}-444096\,{t}^{9}+2010720\,{
t}^{8}+901808\,{t}^{7}+180552\,{t}^{6}+55164\,{t}^{5}+31010\,{t}^{4}+
11106\,{t}^{3}+1914\,{t}^{2}+106\,t-3 \right)
$ | 1 | 1 | Maple | $u$, then $v$ | 18300 | 11.5 | 5 | 24 | 14 | 2391 | 35 / 22 | 9 / 10 | 33 / 35 | 22 | 307345 | 31 / 16 | 5 / 6 | 19 / 19 | 19 | 94522 | ${t}^{2} \left( 7\,t-1 \right) \left( 1+2\,t \right) \left( 5\,t+1
\right) \left( 4\,{t}^{2}-4\,t-1 \right) \left( 20\,{t}^{2}+4\,t-1
\right) \left( {t}^{2}+t+1 \right) \left( 337920\,{t}^{13}+1373184\,
{t}^{12}-4304640\,{t}^{11}-6344576\,{t}^{10}-444096\,{t}^{9}+2010720\,{
t}^{8}+901808\,{t}^{7}+180552\,{t}^{6}+55164\,{t}^{5}+31010\,{t}^{4}+
11106\,{t}^{3}+1914\,{t}^{2}+106\,t-3 \right)
$ | 1 | 1 | Mathematica | $u$, then $v$ | 1150 | n.a. | 5 | 24 | 14 | 2391 | 37 / 23 | 11 / 9 | 11 / 8 | 26 | 172720 | 38 / 24 | 11 / 10 | 11 / 10 | 26 | 110029 | ${t}^{2} \left( 7\,t-1 \right) \left( 1+2\,t \right) \left( 5\,t+1
\right) \left( 4\,{t}^{2}-4\,t-1 \right) \left( 20\,{t}^{2}+4\,t-1
\right) \left( {t}^{2}+t+1 \right) \left( 337920\,{t}^{13}+1373184\,
{t}^{12}-4304640\,{t}^{11}-6344576\,{t}^{10}-444096\,{t}^{9}+2010720\,{
t}^{8}+901808\,{t}^{7}+180552\,{t}^{6}+55164\,{t}^{5}+31010\,{t}^{4}+
11106\,{t}^{3}+1914\,{t}^{2}+106\,t-3 \right)
$ | 1 | 1 | Mathematica | $v$, then $u$ | 106 | n.a. | 5 | 24 | 14 | 2391 | 37 / 23 | 11 / 9 | 11 / 8 | 26 | 172720 | 38 / 24 | 11 / 10 | 11 / 10 | 26 | 110029 | ${t}^{2} \left( 7\,t-1 \right) \left( 1+2\,t \right) \left( 5\,t+1
\right) \left( 4\,{t}^{2}-4\,t-1 \right) \left( 20\,{t}^{2}+4\,t-1
\right) \left( {t}^{2}+t+1 \right) \left( 337920\,{t}^{13}+1373184\,
{t}^{12}-4304640\,{t}^{11}-6344576\,{t}^{10}-444096\,{t}^{9}+2010720\,{
t}^{8}+901808\,{t}^{7}+180552\,{t}^{6}+55164\,{t}^{5}+31010\,{t}^{4}+
11106\,{t}^{3}+1914\,{t}^{2}+106\,t-3 \right)
$ | x | 0 | Mathematica | $u$, then $v$ | 2030 | n.a. | 5 | 20 | 10 | 15341 | 30 / 17 | 11 / 10 | 7 / 8 | 17 | 1412738 | 27 / 14 | 11 / 10 | 10 / 10 | 17 | 1078634 | ${t}^{3} \left( {t}^{2}+t+1 \right) \left( 4\,{t}^{2}-4\,t-1 \right)
\left( 20\,{t}^{2}+4\,t-1 \right) \left( 720\,{t}^{9}{x}^{4}-480\,{t}
^{9}{x}^{3}+4896\,{t}^{8}{x}^{4}+1440\,{t}^{9}{x}^{2}+288\,{t}^{8}{x}^{
3}+7272\,{t}^{7}{x}^{4}-480\,{t}^{9}x+9792\,{t}^{8}{x}^{2}+864\,{t}^{7}
{x}^{3}+3420\,{t}^{6}{x}^{4}+720\,{t}^{9}+288\,{t}^{8}x+14064\,{t}^{7}{
x}^{2}+336\,{t}^{6}{x}^{3}-207\,{t}^{5}{x}^{4}+4896\,{t}^{8}+864\,{t}^{
7}x+6088\,{t}^{6}{x}^{2}+834\,{t}^{5}{x}^{3}-225\,{t}^{4}{x}^{4}+7272\,
{t}^{7}+336\,{t}^{6}x-174\,{t}^{5}{x}^{2}+1182\,{t}^{4}{x}^{3}+18\,{t}^
{3}{x}^{4}+3420\,{t}^{6}+834\,{t}^{5}x+234\,{t}^{4}{x}^{2}+315\,{t}^{3}
{x}^{3}+9\,{t}^{2}{x}^{4}-207\,{t}^{5}+1182\,{t}^{4}x+222\,{t}^{3}{x}^{
2}+3\,{t}^{2}{x}^{3}-225\,{t}^{4}+315\,{t}^{3}x+6\,{t}^{2}{x}^{2}-3\,t{
x}^{3}+18\,{t}^{3}+3\,{t}^{2}x-9\,t{x}^{2}+9\,{t}^{2}-3\,tx-{x}^{2}
\right) \left( 3\,{t}^{2}{x}^{4}+4\,{t}^{2}{x}^{3}+6\,{t}^{2}{x}^{2}+
2\,t{x}^{3}+4\,{t}^{2}x+3\,{t}^{2}+2\,tx-{x}^{2} \right)
$ | 0 | y | Mathematica | $u$, then $v$ | 3590 | n.a. | 6 | 27 | 16 | 55920 | 53 / 38 | 14 / 14 | 11 / 12 | 35 | 10898310 | 45 / 30 | 8 / 10 | 11 / 10 | 31 | 1934114 | ${t}^{3} \left( {t}^{2}+t+1 \right) \left( 4\,{t}^{2}-4\,t-1 \right)
\left( 20\,{t}^{2}+4\,t-1 \right) \left( yt+t+y \right) \left( t{y}^
{2}+2\,yt+2\,t+y \right) \left( 1036800\,{t}^{15}{y}^{10}+1181952\,{t}
^{15}{y}^{9}+10471680\,{t}^{14}{y}^{10}-910080\,{t}^{15}{y}^{8}+
39591936\,{t}^{14}{y}^{9}+17521920\,{t}^{13}{y}^{10}-3158784\,{t}^{15}{
y}^{7}+71875584\,{t}^{14}{y}^{8}+90657792\,{t}^{13}{y}^{9}+3792960\,{t}
^{12}{y}^{10}-4628736\,{t}^{15}{y}^{6}+72695040\,{t}^{14}{y}^{7}+
196669440\,{t}^{13}{y}^{8}+57312000\,{t}^{12}{y}^{9}-9400320\,{t}^{11}{
y}^{10}-94208\,{t}^{15}{y}^{5}+19311360\,{t}^{14}{y}^{6}+228911616\,{t}
^{13}{y}^{7}+156566976\,{t}^{12}{y}^{8}-4752576\,{t}^{11}{y}^{9}-
5739120\,{t}^{10}{y}^{10}+2586624\,{t}^{15}{y}^{4}-45313280\,{t}^{14}{y
}^{5}+119357952\,{t}^{13}{y}^{6}+220910720\,{t}^{12}{y}^{7}+31113600\,{
t}^{11}{y}^{8}-16396704\,{t}^{10}{y}^{9}-223560\,{t}^{9}{y}^{10}+
5801984\,{t}^{15}{y}^{3}-82440192\,{t}^{14}{y}^{4}-84521984\,{t}^{13}{y
}^{5}+175711872\,{t}^{12}{y}^{6}+82289792\,{t}^{11}{y}^{7}-13272240\,{t
}^{10}{y}^{8}-4289328\,{t}^{9}{y}^{9}+341820\,{t}^{8}{y}^{10}+3828736\,
{t}^{15}{y}^{2}-69646336\,{t}^{14}{y}^{3}-215676672\,{t}^{13}{y}^{4}+
5598976\,{t}^{12}{y}^{5}+108297600\,{t}^{11}{y}^{6}+1508288\,{t}^{10}{y
}^{7}-8533512\,{t}^{9}{y}^{8}+157032\,{t}^{8}{y}^{9}-16200\,{t}^{7}{y}^
{10}+2400256\,{t}^{15}y-39163904\,{t}^{14}{y}^{2}-227806720\,{t}^{13}{y
}^{3}-135161856\,{t}^{12}{y}^{4}+68862400\,{t}^{11}{y}^{5}+21146496\,{t
}^{10}{y}^{6}-12617104\,{t}^{9}{y}^{7}-3346524\,{t}^{8}{y}^{8}+160299\,
{t}^{7}{y}^{9}-16740\,{t}^{6}{y}^{10}+557056\,{t}^{15}-12541952\,{t}^{
14}y-137959424\,{t}^{13}{y}^{2}-194395904\,{t}^{12}{y}^{3}+9551232\,{t}
^{11}{y}^{4}+28839232\,{t}^{10}{y}^{5}-14106368\,{t}^{9}{y}^{6}-8509648
\,{t}^{8}{y}^{7}-947079\,{t}^{7}{y}^{8}+73260\,{t}^{6}{y}^{9}+3915\,{t}
^{5}{y}^{10}-1519616\,{t}^{14}-55175168\,{t}^{13}y-131443200\,{t}^{12}{
y}^{2}-32233088\,{t}^{11}{y}^{3}+22857024\,{t}^{10}{y}^{4}-5092736\,{t}
^{9}{y}^{5}-12237656\,{t}^{8}{y}^{6}-2931529\,{t}^{7}{y}^{7}-4767\,{t}^
{6}{y}^{8}+31869\,{t}^{5}{y}^{9}+1080\,{t}^{4}{y}^{10}-9270272\,{t}^{13
}-60045312\,{t}^{12}y-32731392\,{t}^{11}{y}^{2}+22264192\,{t}^{10}{y}^{
3}+153328\,{t}^{9}{y}^{4}-5708336\,{t}^{8}{y}^{5}-3876587\,{t}^{7}{y}^{
6}-372707\,{t}^{6}{y}^{7}+39909\,{t}^{5}{y}^{8}+3573\,{t}^{4}{y}^{9}-
12081152\,{t}^{12}-18213888\,{t}^{11}y+9899904\,{t}^{10}{y}^{2}+7931168
\,{t}^{9}{y}^{3}+241312\,{t}^{8}{y}^{4}-1562636\,{t}^{7}{y}^{5}-378303
\,{t}^{6}{y}^{6}+11920\,{t}^{5}{y}^{7}-6441\,{t}^{4}{y}^{8}-216\,{t}^{3
}{y}^{9}-6917120\,{t}^{11}+6239232\,{t}^{10}y+3583040\,{t}^{9}{y}^{2}+
2921264\,{t}^{8}{y}^{3}+1481608\,{t}^{7}{y}^{4}-316267\,{t}^{6}{y}^{5}+
92241\,{t}^{5}{y}^{6}-12617\,{t}^{4}{y}^{7}-3762\,{t}^{3}{y}^{8}-
1543424\,{t}^{10}+3436544\,{t}^{9}y+656096\,{t}^{8}{y}^{2}+1899968\,{t}
^{7}{y}^{3}+277572\,{t}^{6}{y}^{4}-18088\,{t}^{5}{y}^{5}+23700\,{t}^{4}
{y}^{6}-8153\,{t}^{3}{y}^{7}-288\,{t}^{2}{y}^{8}+315968\,{t}^{9}-233344
\,{t}^{8}y+1009844\,{t}^{7}{y}^{2}+290144\,{t}^{6}{y}^{3}-39402\,{t}^{5
}{y}^{4}+23765\,{t}^{4}{y}^{5}-1789\,{t}^{3}{y}^{6}-1274\,{t}^{2}{y}^{7
}+168704\,{t}^{8}-159808\,{t}^{7}y+348048\,{t}^{6}{y}^{2}-94372\,{t}^{5
}{y}^{3}+6480\,{t}^{4}{y}^{4}+5002\,{t}^{3}{y}^{5}-931\,{t}^{2}{y}^{6}-
62\,t{y}^{7}+2240\,{t}^{7}+47616\,{t}^{6}y+3336\,{t}^{5}{y}^{2}-20560\,
{t}^{4}{y}^{3}+5672\,{t}^{3}{y}^{4}-77\,{t}^{2}{y}^{5}-22\,t{y}^{6}-
4096\,{t}^{6}+15552\,{t}^{5}y-10608\,{t}^{4}{y}^{2}+1736\,{t}^{3}{y}^{3
}+386\,{t}^{2}{y}^{4}+t{y}^{5}+6\,{y}^{6}+320\,{t}^{5}-468\,{t}^{3}{y}^
{2}+368\,{t}^{2}{y}^{3}+2\,t{y}^{4}+6\,{y}^{5}+128\,{t}^{4}-192\,{t}^{3
}y+96\,{t}^{2}{y}^{2}-4\,t{y}^{3}+3\,{y}^{4} \right) \left( 3\,t{y}^{2
}+2\,yt+2\,t-y \right)
$ | | ss | vx | vy | CAS used | integrate | time (sec) | memory (GB) | $\operatorname{ord}P$ | $\deg_tP$ | height of $P$ | length of $P$ | $\deg_tU$ | $\deg_uU$ | $\deg_vU$ | height of $U$ | length of $U$ | $\deg_tV$ | $\deg_uV$ | $\deg_vV$ | height of $V$ | length of $V$ | leading coefficient of $P$ |
|---|
| 11 |
0 | 0 | Maple | $v$, then $u$ | 1.21 | 0.0441 | 3 | 6 | 3 | 128 | 5 / 7 | 8 / 6 | 4 / 4 | 3 | 708 | 9 / 42 | 14 / 32 | 7 / 6 | 5 | 4623 | ${t}^{2} \left( 4\,{t}^{2}+1 \right) \left( 12\,{t}^{2}-1 \right)
$ |
0 | 0 | Maple | $u$, then $v$ | 2.39 | 0.0452 | 3 | 6 | 3 | 128 | 8 / 9 | 7 / 6 | 13 / 15 | 4 | 3659 | 20 / 48 | 31 / 174 | 9 / 25 | 4 | 7499 | ${t}^{2} \left( 4\,{t}^{2}+1 \right) \left( 12\,{t}^{2}-1 \right)
$ | 0 | 1 | Maple | $v$, then $u$ | 20.3 | 0.437 | 5 | 15 | 9 | 1008 | 24 / 18 | 23 / 21 | 32 / 5 | 13 | 65249 | 33 / 26 | 34 / 33 | 18 / 16 | 19 | 366435 | ${t}^{3} \left( 4\,t-1 \right) \left( 12\,{t}^{2}-1 \right) \left(
1728\,{t}^{7}+576\,{t}^{6}+864\,{t}^{5}+768\,{t}^{4}-108\,{t}^{3}+28\,{
t}^{2}-22\,t-5 \right) \left( 4\,{t}^{2}+1 \right)
$ | 0 | 1 | Maple | $u$, then $v$ | 68 | 1.61 | 5 | 15 | 9 | 1008 | 27 / 20 | 17 / 16 | 32 / 34 | 13 | 249359 | 17 / 138 | 6 / 512 | 16 / 61 | 9 | 26168 | ${t}^{3} \left( 4\,t-1 \right) \left( 12\,{t}^{2}-1 \right) \left(
1728\,{t}^{7}+576\,{t}^{6}+864\,{t}^{5}+768\,{t}^{4}-108\,{t}^{3}+28\,{
t}^{2}-22\,t-5 \right) \left( 4\,{t}^{2}+1 \right)
$ | 1 | 0 | Maple | $v$, then $u$ | 1.08 | 0.0439 | 3 | 6 | 3 | 127 | 5 / 7 | 7 / 6 | 4 / 4 | 2 | 585 | 9 / 10 | 11 / 11 | 7 / 6 | 4 | 2579 | ${t}^{2} \left( 4\,{t}^{2}+1 \right) \left( 12\,{t}^{2}-1 \right)
$ | 1 | 0 | Maple | $u$, then $v$ | 2.31 | 0.0435 | 3 | 6 | 3 | 127 | 10 / 11 | 6 / 6 | 16 / 18 | 5 | 6697 | 8 / 7 | 5 / 5 | 9 / 8 | 4 | 2665 | ${t}^{2} \left( 4\,{t}^{2}+1 \right) \left( 12\,{t}^{2}-1 \right)
$ | 1 | 1 | Maple | $v$, then $u$ | 18 | 0.128 | 5 | 15 | 8 | 987 | 21 / 16 | 16 / 16 | 4 / 5 | 10 | 26628 | 29 / 21 | 25 / 26 | 10 / 10 | 13 | 103867 | ${t}^{3} \left( 4\,t-1 \right) \left( 12\,{t}^{2}-1 \right) \left( 4\,
{t}^{2}+1 \right) \left( 576\,{t}^{7}-288\,{t}^{6}-80\,{t}^{4}-100\,{t
}^{3}-42\,{t}^{2}-14\,t-3 \right)
$ | 1 | 1 | Maple | $u$, then $v$ | 38.1 | 1.1 | 5 | 15 | 8 | 987 | 21 / 16 | 9 / 10 | 26 / 28 | 10 | 77540 | 15 / 10 | 3 / 4 | 16 / 16 | 7 | 12855 | ${t}^{3} \left( 4\,t-1 \right) \left( 12\,{t}^{2}-1 \right) \left( 4\,
{t}^{2}+1 \right) \left( 576\,{t}^{7}-288\,{t}^{6}-80\,{t}^{4}-100\,{t
}^{3}-42\,{t}^{2}-14\,t-3 \right)
$ | 1 | 1 | Mathematica | $u$, then $v$ | 262 | n.a. | 5 | 15 | 8 | 987 | 23 / 16 | 10 / 11 | 9 / 10 | 16 | 53309 | 21 / 14 | 10 / 8 | 9 / 8 | 14 | 21994 | ${t}^{3} \left( 4\,t-1 \right) \left( 12\,{t}^{2}-1 \right) \left( 4\,
{t}^{2}+1 \right) \left( 576\,{t}^{7}-288\,{t}^{6}-80\,{t}^{4}-100\,{t
}^{3}-42\,{t}^{2}-14\,t-3 \right)
$ | 1 | 1 | Mathematica | $v$, then $u$ | 33 | n.a. | 5 | 15 | 8 | 987 | 23 / 16 | 10 / 11 | 9 / 10 | 16 | 53309 | 21 / 14 | 10 / 8 | 9 / 8 | 14 | 21994 | ${t}^{3} \left( 4\,t-1 \right) \left( 12\,{t}^{2}-1 \right) \left( 4\,
{t}^{2}+1 \right) \left( 576\,{t}^{7}-288\,{t}^{6}-80\,{t}^{4}-100\,{t
}^{3}-42\,{t}^{2}-14\,t-3 \right)
$ | x | 0 | Mathematica | $u$, then $v$ | 152 | n.a. | 4 | 9 | 5 | 637 | 7 / 5 | 8 / 8 | 6 / 6 | 5 | 19972 | 8 / 6 | 8 / 8 | 9 / 8 | 5 | 18604 | ${t}^{3} \left( 4\,{t}^{2}+1 \right) \left( 12\,{t}^{2}-1 \right)
\left( 4\,{t}^{2}{x}^{2}+4\,{t}^{2}x+4\,{t}^{2}-x \right)
$ | 0 | y | Mathematica | $u$, then $v$ | 352 | n.a. | 5 | 16 | 9 | 7642 | 25 / 18 | 12 / 12 | 9 / 10 | 14 | 334795 | 19 / 12 | 10 / 8 | 7 / 6 | 12 | 77334 | ${t}^{3} \left( 4\,{t}^{2}+1 \right) \left( 12\,{t}^{2}-1 \right)
\left( t{y}^{2}-t-y \right) \left( t{y}^{2}+3\,t-y \right) \left(
144\,{t}^{7}{y}^{7}+432\,{t}^{7}{y}^{5}-288\,{t}^{6}{y}^{6}+48\,{t}^{5}
{y}^{7}+60\,{t}^{4}{y}^{8}+2448\,{t}^{7}{y}^{3}+144\,{t}^{6}{y}^{4}+648
\,{t}^{5}{y}^{5}+114\,{t}^{4}{y}^{6}-152\,{t}^{3}{y}^{7}+6\,{t}^{2}{y}^
{8}+432\,{t}^{7}y+1296\,{t}^{6}{y}^{2}+672\,{t}^{5}{y}^{3}+438\,{t}^{4}
{y}^{4}-48\,{t}^{3}{y}^{5}+103\,{t}^{2}{y}^{6}-16\,t{y}^{7}+360\,{t}^{5
}y+870\,{t}^{4}{y}^{2}-142\,{t}^{3}{y}^{3}-65\,{t}^{2}{y}^{4}+2\,t{y}^{
5}+10\,{y}^{6}+54\,{t}^{4}+126\,{t}^{3}y+12\,{t}^{2}{y}^{2}-30\,t{y}^{3
}-20\,{y}^{4} \right)
$ | | ss | vx | vy | CAS used | integrate | time (sec) | memory (GB) | $\operatorname{ord}P$ | $\deg_tP$ | height of $P$ | length of $P$ | $\deg_tU$ | $\deg_uU$ | $\deg_vU$ | height of $U$ | length of $U$ | $\deg_tV$ | $\deg_uV$ | $\deg_vV$ | height of $V$ | length of $V$ | leading coefficient of $P$ |
|---|
| 12 |
0 | 0 | Maple | $v$, then $u$ | 4.78 | 0.128 | 4 | 10 | 6 | 461 | 8 / 7 | 13 / 12 | 4 / 4 | 4 | 3801 | 17 / 10 | 25 / 10 | 9 / 19 | 9 | 53630 | ${t}^{3} \left( 1+2\,t \right) \left( 8\,{t}^{2}+4\,t+1 \right)
\left( 8\,{t}^{2}+8\,t+3 \right) \left( 8\,{t}^{2}+4\,t-1 \right)
$ |
0 | 0 | Maple | $u$, then $v$ | 17.7 | 0.451 | 4 | 10 | 6 | 461 | 22 / 23 | 24 / 24 | 29 / 39 | 9 | 89752 | 9 / 58 | 4 / 318 | 14 / 10 | 5 | 6744 | ${t}^{3} \left( 1+2\,t \right) \left( 8\,{t}^{2}+4\,t+1 \right)
\left( 8\,{t}^{2}+8\,t+3 \right) \left( 8\,{t}^{2}+4\,t-1 \right)
$ | 0 | 1 | Maple | $v$, then $u$ | 120 | 1.14 | 6 | 21 | 12 | 1994 | 28 / 43 | 33 / 37 | 28 / 8 | 15 | 175394 | 81 / 54 | 55 / 33 | 21 / 24 | 23 | 2011675 | ${t}^{4} \left( 6\,t-1 \right) \left( 8\,{t}^{2}+4\,t+1 \right)
\left( 8\,{t}^{2}+4\,t-1 \right) \left( 4224\,{t}^{10}+11456\,{t}^{9}
+13808\,{t}^{8}+9560\,{t}^{7}+2656\,{t}^{6}-1608\,{t}^{5}-1862\,{t}^{4}
-740\,{t}^{3}-146\,{t}^{2}-16\,t-1 \right) \left( 1+2\,t \right) ^{2}
$ | 0 | 1 | Maple | $u$, then $v$ | 56200 | 18.2 | 6 | 21 | 12 | 1994 | 39 / 22 | 21 / 18 | 40 / 40 | 20 | 669690 | 21 / 95 | 4 / 578 | 22 / 14 | 11 | 31632 | ${t}^{4} \left( 6\,t-1 \right) \left( 8\,{t}^{2}+4\,t+1 \right)
\left( 8\,{t}^{2}+4\,t-1 \right) \left( 4224\,{t}^{10}+11456\,{t}^{9}
+13808\,{t}^{8}+9560\,{t}^{7}+2656\,{t}^{6}-1608\,{t}^{5}-1862\,{t}^{4}
-740\,{t}^{3}-146\,{t}^{2}-16\,t-1 \right) \left( 1+2\,t \right) ^{2}
$ | 1 | 0 | Maple | $v$, then $u$ | 5.2 | 0.376 | 4 | 11 | 6 | 534 | 10 / 8 | 13 / 12 | 4 / 4 | 5 | 4914 | 14 / 12 | 20 / 20 | 9 / 8 | 8 | 34379 | ${t}^{3} \left( 1+2\,t \right) \left( 8\,{t}^{2}+4\,t-1 \right)
\left( 24\,{t}^{3}+24\,{t}^{2}+11\,t+2 \right) \left( 8\,{t}^{2}+4\,t
+1 \right)
$ | 1 | 0 | Maple | $u$, then $v$ | 25.1 | 0.996 | 4 | 11 | 6 | 534 | 15 / 13 | 7 / 8 | 22 / 24 | 9 | 37793 | 10 / 8 | 3 / 4 | 12 / 12 | 6 | 6577 | ${t}^{3} \left( 1+2\,t \right) \left( 8\,{t}^{2}+4\,t-1 \right)
\left( 24\,{t}^{3}+24\,{t}^{2}+11\,t+2 \right) \left( 8\,{t}^{2}+4\,t
+1 \right)
$ | 1 | 1 | Maple | $v$, then $u$ | 119 | 1.74 | 5 | 18 | 11 | 1447 | 21 / 14 | 22 / 22 | 4 / 5 | 13 | 43137 | 31 / 20 | 32 / 34 | 12 / 10 | 17 | 209546 | ${t}^{3} \left( 6\,t-1 \right) \left( 8\,{t}^{2}+4\,t+1 \right)
\left( 8\,{t}^{2}+4\,t-1 \right) \left( 1824\,{t}^{8}-4996\,{t}^{6}-
7188\,{t}^{5}-5321\,{t}^{4}-2353\,{t}^{3}-618\,{t}^{2}-89\,t-6 \right)
\left( 1+2\,t \right) ^{2}
$ | 1 | 1 | Maple | $u$, then $v$ | 3930 | 7.27 | 5 | 18 | 11 | 1447 | 24 / 17 | 9 / 10 | 29 / 31 | 14 | 123081 | 27 / 77 | 81 / 449 | 17 / 16 | 12 | 161913 | ${t}^{3} \left( 6\,t-1 \right) \left( 8\,{t}^{2}+4\,t+1 \right)
\left( 8\,{t}^{2}+4\,t-1 \right) \left( 1824\,{t}^{8}-4996\,{t}^{6}-
7188\,{t}^{5}-5321\,{t}^{4}-2353\,{t}^{3}-618\,{t}^{2}-89\,t-6 \right)
\left( 1+2\,t \right) ^{2}
$ | 1 | 1 | Mathematica | $u$, then $v$ | 354 | n.a. | 5 | 18 | 11 | 1447 | 24 / 16 | 11 / 11 | 9 / 10 | 18 | 65757 | 21 / 13 | 8 / 8 | 9 / 8 | 15 | 17562 | ${t}^{3} \left( 6\,t-1 \right) \left( 8\,{t}^{2}+4\,t+1 \right)
\left( 8\,{t}^{2}+4\,t-1 \right) \left( 1824\,{t}^{8}-4996\,{t}^{6}-
7188\,{t}^{5}-5321\,{t}^{4}-2353\,{t}^{3}-618\,{t}^{2}-89\,t-6 \right)
\left( 1+2\,t \right) ^{2}
$ | 1 | 1 | Mathematica | $v$, then $u$ | 61.4 | n.a. | 5 | 18 | 11 | 1447 | 24 / 16 | 11 / 11 | 9 / 10 | 18 | 65757 | 21 / 13 | 8 / 8 | 9 / 8 | 15 | 17562 | ${t}^{3} \left( 6\,t-1 \right) \left( 8\,{t}^{2}+4\,t+1 \right)
\left( 8\,{t}^{2}+4\,t-1 \right) \left( 1824\,{t}^{8}-4996\,{t}^{6}-
7188\,{t}^{5}-5321\,{t}^{4}-2353\,{t}^{3}-618\,{t}^{2}-89\,t-6 \right)
\left( 1+2\,t \right) ^{2}
$ | x | 0 | Mathematica | $u$, then $v$ | 862 | n.a. | 5 | 17 | 10 | 11484 | 26 / 19 | 10 / 10 | 7 / 8 | 18 | 1015082 | 24 / 17 | 10 / 10 | 10 / 10 | 16 | 678434 | ${t}^{3} \left( 1+2\,t \right) \left( 8\,{t}^{2}+4\,t+1 \right)
\left( 8\,{t}^{2}+4\,t-1 \right) \left( {t}^{2}{x}^{4}-4\,{t}^{2}{x}^
{3}-2\,{t}^{2}{x}^{2}-2\,t{x}^{3}-4\,{t}^{2}x+{t}^{2}-2\,tx+{x}^{2}
\right) \left( 16\,{t}^{7}{x}^{4}+320\,{t}^{7}{x}^{3}+16\,{t}^{6}{x}^
{4}+480\,{t}^{7}{x}^{2}+544\,{t}^{6}{x}^{3}+22\,{t}^{5}{x}^{4}+320\,{t}
^{7}x+1120\,{t}^{6}{x}^{2}+312\,{t}^{5}{x}^{3}+12\,{t}^{4}{x}^{4}+16\,{
t}^{7}+544\,{t}^{6}x+1252\,{t}^{5}{x}^{2}+12\,{t}^{4}{x}^{3}+2\,{t}^{3}
{x}^{4}+16\,{t}^{6}+312\,{t}^{5}x+872\,{t}^{4}{x}^{2}-58\,{t}^{3}{x}^{3
}+22\,{t}^{5}+12\,{t}^{4}x+438\,{t}^{3}{x}^{2}-25\,{t}^{2}{x}^{3}+12\,{
t}^{4}-58\,{t}^{3}x+158\,{t}^{2}{x}^{2}-4\,t{x}^{3}+2\,{t}^{3}-25\,{t}^
{2}x+34\,t{x}^{2}-4\,tx+3\,{x}^{2} \right)
$ | 0 | y | Mathematica | $u$, then $v$ | 1710 | n.a. | 6 | 22 | 13 | 27504 | 34 / 24 | 13 / 14 | 10 / 12 | 22 | 3067977 | 31 / 21 | 9 / 10 | 9 / 8 | 20 | 731683 | ${t}^{4} \left( 1+2\,t \right) \left( 8\,{t}^{2}+4\,t+1 \right)
\left( 8\,{t}^{2}+4\,t-1 \right) \left( t{y}^{2}+2\,ty+3\,t-y
\right) \left( t{y}^{2}-2\,ty-t-y \right) \left( 2384\,{t}^{11}{y}^{
7}+6512\,{t}^{11}{y}^{6}+7600\,{t}^{10}{y}^{7}+13232\,{t}^{11}{y}^{5}+
7360\,{t}^{10}{y}^{6}+8238\,{t}^{9}{y}^{7}-28464\,{t}^{11}{y}^{4}+53824
\,{t}^{10}{y}^{5}-12774\,{t}^{9}{y}^{6}+4924\,{t}^{8}{y}^{7}-99600\,{t}
^{11}{y}^{3}-62928\,{t}^{10}{y}^{4}+89826\,{t}^{9}{y}^{5}-29002\,{t}^{8
}{y}^{6}+1376\,{t}^{7}{y}^{7}+13776\,{t}^{11}{y}^{2}-330960\,{t}^{10}{y
}^{3}-69234\,{t}^{9}{y}^{4}+66158\,{t}^{8}{y}^{5}-24428\,{t}^{7}{y}^{6}
-36\,{t}^{6}{y}^{7}+78480\,{t}^{11}y+63840\,{t}^{10}{y}^{2}-490950\,{t}
^{9}{y}^{3}-59812\,{t}^{8}{y}^{4}+18028\,{t}^{7}{y}^{5}-9570\,{t}^{6}{y
}^{6}-133\,{t}^{5}{y}^{7}-11664\,{t}^{11}+170784\,{t}^{10}y+168462\,{t}
^{9}{y}^{2}-389872\,{t}^{8}{y}^{3}-50000\,{t}^{7}{y}^{4}-7014\,{t}^{6}{
y}^{5}-608\,{t}^{5}{y}^{6}-32\,{t}^{4}{y}^{7}+9072\,{t}^{10}+174150\,{t
}^{9}y+189534\,{t}^{8}{y}^{2}-175358\,{t}^{7}{y}^{3}-34236\,{t}^{6}{y}^
{4}-9230\,{t}^{5}{y}^{5}+941\,{t}^{4}{y}^{6}-3\,{t}^{3}{y}^{7}+15066\,{
t}^{9}+113886\,{t}^{8}y+126258\,{t}^{7}{y}^{2}-33972\,{t}^{6}{y}^{3}-
14654\,{t}^{5}{y}^{4}-5104\,{t}^{4}{y}^{5}+387\,{t}^{3}{y}^{6}+5400\,{t
}^{8}+57942\,{t}^{7}y+60048\,{t}^{6}{y}^{2}+9637\,{t}^{5}{y}^{3}-2809\,
{t}^{4}{y}^{4}-1812\,{t}^{3}{y}^{5}+67\,{t}^{2}{y}^{6}+1566\,{t}^{7}+
24516\,{t}^{6}y+22470\,{t}^{5}{y}^{2}+9080\,{t}^{4}{y}^{3}+327\,{t}^{3}
{y}^{4}-407\,{t}^{2}{y}^{5}+5\,t{y}^{6}+1944\,{t}^{6}+7650\,{t}^{5}y+
6366\,{t}^{4}{y}^{2}+2910\,{t}^{3}{y}^{3}+305\,{t}^{2}{y}^{4}-52\,t{y}^
{5}+864\,{t}^{5}+1476\,{t}^{4}y+1152\,{t}^{3}{y}^{2}+470\,{t}^{2}{y}^{3
}+67\,t{y}^{4}-3\,{y}^{5}+108\,{t}^{4}+135\,{t}^{3}y+99\,{t}^{2}{y}^{2}
+34\,t{y}^{3}+6\,{y}^{4} \right)
$ | | ss | vx | vy | CAS used | integrate | time (sec) | memory (GB) | $\operatorname{ord}P$ | $\deg_tP$ | height of $P$ | length of $P$ | $\deg_tU$ | $\deg_uU$ | $\deg_vU$ | height of $U$ | length of $U$ | $\deg_tV$ | $\deg_uV$ | $\deg_vV$ | height of $V$ | length of $V$ | leading coefficient of $P$ |
|---|
| 13 |
0 | 0 | Maple | $v$, then $u$ | 3.51 | 0.0862 | 4 | 11 | 6 | 292 | 9 / 9 | 14 / 14 | 4 / 4 | 5 | 2628 | 43 / 55 | 47 / 89 | 32 / 52 | 14 | 325461 | ${t}^{3} \left( 14\,{t}^{2}-1 \right) \left( 24\,{t}^{2}-1 \right)
\left( 8\,{t}^{2}-1 \right) \left( {t}^{2}+1 \right)
$ |
0 | 0 | Maple | $u$, then $v$ | 14 | 0.0978 | 4 | 11 | 6 | 292 | 17 / 14 | 9 / 8 | 23 / 25 | 9 | 29244 | 14 / 9 | 6 / 6 | 14 / 14 | 7 | 9911 | ${t}^{3} \left( 14\,{t}^{2}-1 \right) \left( 24\,{t}^{2}-1 \right)
\left( 8\,{t}^{2}-1 \right) \left( {t}^{2}+1 \right)
$ | 0 | 1 | Maple | $v$, then $u$ | 87.7 | 0.533 | 6 | 26 | 16 | 2991 | 39 / 25 | 28 / 28 | 4 / 5 | 22 | 145443 | 46 / 32 | 42 / 44 | 12 / 12 | 26 | 576677 | ${t}^{3} \left( t-1 \right) \left( 3\,t+1 \right) \left( 5\,t-1
\right) \left( {t}^{2}+1 \right) \left( 8\,{t}^{2}-1 \right)
\left( 24\,{t}^{2}-1 \right) \left( 13782528\,{t}^{14}-38406960\,{t}^
{13}-77842512\,{t}^{12}+85746312\,{t}^{11}+11011536\,{t}^{10}-19136520
\,{t}^{9}+188933\,{t}^{8}+1163673\,{t}^{7}-98884\,{t}^{6}+36476\,{t}^{5
}+12477\,{t}^{4}-4747\,{t}^{3}-870\,{t}^{2}+42\,t+12 \right)
$ | 0 | 1 | Maple | $u$, then $v$ | 245 | 1.73 | 6 | 26 | 16 | 2991 | 36 / 23 | 13 / 12 | 37 / 40 | 22 | 435019 | 34 / 18 | 6 / 6 | 24 / 24 | 19 | 118039 | ${t}^{3} \left( t-1 \right) \left( 3\,t+1 \right) \left( 5\,t-1
\right) \left( {t}^{2}+1 \right) \left( 8\,{t}^{2}-1 \right)
\left( 24\,{t}^{2}-1 \right) \left( 13782528\,{t}^{14}-38406960\,{t}^
{13}-77842512\,{t}^{12}+85746312\,{t}^{11}+11011536\,{t}^{10}-19136520
\,{t}^{9}+188933\,{t}^{8}+1163673\,{t}^{7}-98884\,{t}^{6}+36476\,{t}^{5
}+12477\,{t}^{4}-4747\,{t}^{3}-870\,{t}^{2}+42\,t+12 \right)
$ | 1 | 0 | Maple | $v$, then $u$ | 3.41 | 0.0863 | 4 | 11 | 6 | 304 | 8 / 8 | 14 / 14 | 4 / 4 | 4 | 793 | 43 / 19 | 45 / 14 | 30 / 27 | 14 | 532569 | ${t}^{3} \left( 13\,{t}^{2}-2 \right) \left( 24\,{t}^{2}-1 \right)
\left( 8\,{t}^{2}-1 \right) \left( {t}^{2}+1 \right)
$ | 1 | 0 | Maple | $u$, then $v$ | 15.1 | 0.448 | 4 | 11 | 6 | 304 | 32 / 87 | 15 / 16 | 33 / 101 | 12 | 121497 | 55 / 50 | 26 / 27 | 20 / 16 | 9 | 37221 | ${t}^{3} \left( 13\,{t}^{2}-2 \right) \left( 24\,{t}^{2}-1 \right)
\left( 8\,{t}^{2}-1 \right) \left( {t}^{2}+1 \right)
$ | 1 | 1 | Maple | $v$, then $u$ | 39.7 | 0.379 | 5 | 24 | 13 | 2257 | 32 / 18 | 22 / 22 | 4 / 5 | 18 | 82120 | 38 / 24 | 34 / 36 | 10 / 10 | 21 | 291052 | ${t}^{2} \left( t-1 \right) \left( 5\,t-1 \right) \left( 3\,t+1
\right) \left( 8\,{t}^{2}-1 \right) \left( 1021248\,{t}^{13}+4416768
\,{t}^{12}-3034800\,{t}^{11}-4202781\,{t}^{10}-298284\,{t}^{9}+594729\,
{t}^{8}+357600\,{t}^{7}+37999\,{t}^{6}-49192\,{t}^{5}-11299\,{t}^{4}+
1788\,{t}^{3}+574\,{t}^{2}+16\,t-6 \right) \left( 24\,{t}^{2}-1
\right) \left( {t}^{2}+1 \right)
$ | 1 | 1 | Maple | $u$, then $v$ | 3900 | 9.59 | 5 | 24 | 13 | 2257 | 35 / 22 | 9 / 10 | 33 / 35 | 19 | 278733 | 74 / 55 | 26 / 27 | 32 / 23 | 20 | 356693 | ${t}^{2} \left( t-1 \right) \left( 5\,t-1 \right) \left( 3\,t+1
\right) \left( 8\,{t}^{2}-1 \right) \left( 1021248\,{t}^{13}+4416768
\,{t}^{12}-3034800\,{t}^{11}-4202781\,{t}^{10}-298284\,{t}^{9}+594729\,
{t}^{8}+357600\,{t}^{7}+37999\,{t}^{6}-49192\,{t}^{5}-11299\,{t}^{4}+
1788\,{t}^{3}+574\,{t}^{2}+16\,t-6 \right) \left( 24\,{t}^{2}-1
\right) \left( {t}^{2}+1 \right)
$ | 1 | 1 | Mathematica | $u$, then $v$ | 1030 | n.a. | 5 | 24 | 13 | 2257 | 37 / 23 | 11 / 9 | 11 / 8 | 22 | 158688 | 38 / 24 | 11 / 10 | 11 / 10 | 23 | 103726 | ${t}^{2} \left( t-1 \right) \left( 5\,t-1 \right) \left( 3\,t+1
\right) \left( 8\,{t}^{2}-1 \right) \left( 1021248\,{t}^{13}+4416768
\,{t}^{12}-3034800\,{t}^{11}-4202781\,{t}^{10}-298284\,{t}^{9}+594729\,
{t}^{8}+357600\,{t}^{7}+37999\,{t}^{6}-49192\,{t}^{5}-11299\,{t}^{4}+
1788\,{t}^{3}+574\,{t}^{2}+16\,t-6 \right) \left( 24\,{t}^{2}-1
\right) \left( {t}^{2}+1 \right)
$ | 1 | 1 | Mathematica | $v$, then $u$ | 89.1 | n.a. | 5 | 24 | 13 | 2257 | 37 / 23 | 11 / 9 | 11 / 8 | 22 | 158688 | 38 / 24 | 11 / 10 | 11 / 10 | 23 | 103726 | ${t}^{2} \left( t-1 \right) \left( 5\,t-1 \right) \left( 3\,t+1
\right) \left( 8\,{t}^{2}-1 \right) \left( 1021248\,{t}^{13}+4416768
\,{t}^{12}-3034800\,{t}^{11}-4202781\,{t}^{10}-298284\,{t}^{9}+594729\,
{t}^{8}+357600\,{t}^{7}+37999\,{t}^{6}-49192\,{t}^{5}-11299\,{t}^{4}+
1788\,{t}^{3}+574\,{t}^{2}+16\,t-6 \right) \left( 24\,{t}^{2}-1
\right) \left( {t}^{2}+1 \right)
$ | x | 0 | Mathematica | $u$, then $v$ | 1430 | n.a. | 5 | 16 | 9 | 5722 | 24 / 16 | 11 / 10 | 7 / 8 | 15 | 547807 | 21 / 13 | 11 / 10 | 10 / 10 | 14 | 395386 | ${t}^{4} \left( 24\,{t}^{2}-1 \right) \left( 8\,{t}^{2}-1 \right)
\left( {t}^{2}+1 \right) \left( 4\,{t}^{2}{x}^{4}+4\,{t}^{2}{x}^{3}+8
\,{t}^{2}{x}^{2}+4\,{t}^{2}x+4\,{t}^{2}-{x}^{2} \right) \left( 270\,{t
}^{4}{x}^{4}-148\,{t}^{4}{x}^{3}+402\,{t}^{4}{x}^{2}-29\,{t}^{2}{x}^{4}
-148\,{t}^{4}x+3\,{t}^{2}{x}^{3}+270\,{t}^{4}-46\,{t}^{2}{x}^{2}+{x}^{4
}+3\,{t}^{2}x+{x}^{3}-29\,{t}^{2}+2\,{x}^{2}+x+1 \right)
$ | 0 | y | Mathematica | $u$, then $v$ | 3150 | n.a. | 6 | 26 | 15 | 25838 | 53 / 38 | 14 / 14 | 11 / 12 | 33 | 5130832 | 45 / 30 | 8 / 10 | 11 / 10 | 30 | 916181 | ${t}^{3} \left( 24\,{t}^{2}-1 \right) \left( 8\,{t}^{2}-1 \right)
\left( {t}^{2}+1 \right) \left( -y+t \right) \left( 2\,t{y}^{2}+3\,t
-y \right) \left( 2\,t{y}^{2}+t+y \right) \left( 1769472\,{t}^{14}{y}
^{9}+5667840\,{t}^{14}{y}^{7}-6144768\,{t}^{13}{y}^{8}-8114688\,{t}^{12
}{y}^{9}+7107840\,{t}^{11}{y}^{10}+5557248\,{t}^{14}{y}^{5}-16201728\,{
t}^{13}{y}^{6}-26901504\,{t}^{12}{y}^{7}+30774144\,{t}^{11}{y}^{8}-
5061888\,{t}^{10}{y}^{9}-3669120\,{t}^{9}{y}^{10}+1223424\,{t}^{14}{y}^
{3}-13578624\,{t}^{13}{y}^{4}-30155328\,{t}^{12}{y}^{5}+39205920\,{t}^{
11}{y}^{6}-7269264\,{t}^{10}{y}^{7}-8899392\,{t}^{9}{y}^{8}+2301376\,{t
}^{8}{y}^{9}+583680\,{t}^{7}{y}^{10}-435456\,{t}^{14}y-3006720\,{t}^{13
}{y}^{2}-11975040\,{t}^{12}{y}^{3}+12520992\,{t}^{11}{y}^{4}+7052688\,{
t}^{10}{y}^{5}-7156704\,{t}^{9}{y}^{6}+3250096\,{t}^{8}{y}^{7}+1028544
\,{t}^{7}{y}^{8}-265760\,{t}^{6}{y}^{9}-42880\,{t}^{5}{y}^{10}+524880\,
{t}^{13}-695952\,{t}^{12}y-3272904\,{t}^{11}{y}^{2}+12458052\,{t}^{10}{
y}^{3}-274368\,{t}^{9}{y}^{4}-1537122\,{t}^{8}{y}^{5}+137016\,{t}^{7}{y
}^{6}-358964\,{t}^{6}{y}^{7}-66240\,{t}^{5}{y}^{8}+8832\,{t}^{4}{y}^{9}
+1280\,{t}^{3}{y}^{10}-589680\,{t}^{11}+3831948\,{t}^{10}y+939204\,{t}^
{9}{y}^{2}-2986194\,{t}^{8}{y}^{3}-514656\,{t}^{7}{y}^{4}+159930\,{t}^{
6}{y}^{5}+47864\,{t}^{5}{y}^{6}+15210\,{t}^{4}{y}^{7}+2112\,{t}^{3}{y}^
{8}+96\,{t}^{2}{y}^{9}-76140\,{t}^{9}-839223\,{t}^{8}y-87678\,{t}^{7}{y
}^{2}+294774\,{t}^{6}{y}^{3}+88594\,{t}^{5}{y}^{4}+762\,{t}^{4}{y}^{5}-
2704\,{t}^{3}{y}^{6}-208\,{t}^{2}{y}^{7}+16767\,{t}^{7}+71136\,{t}^{6}y
+10164\,{t}^{5}{y}^{2}-9384\,{t}^{4}{y}^{3}-4610\,{t}^{3}{y}^{4}-648\,{
t}^{2}{y}^{5}+2\,{y}^{7}-1026\,{t}^{5}-2943\,{t}^{4}y-852\,{t}^{3}{y}^{
2}-164\,{t}^{2}{y}^{3}+24\,t{y}^{4}+6\,{y}^{5}+27\,{t}^{3}+54\,{t}^{2}y
+18\,t{y}^{2}+4\,{y}^{3} \right)
$ | | ss | vx | vy | CAS used | integrate | time (sec) | memory (GB) | $\operatorname{ord}P$ | $\deg_tP$ | height of $P$ | length of $P$ | $\deg_tU$ | $\deg_uU$ | $\deg_vU$ | height of $U$ | length of $U$ | $\deg_tV$ | $\deg_uV$ | $\deg_vV$ | height of $V$ | length of $V$ | leading coefficient of $P$ |
|---|
| 14 |
0 | 0 | Maple | $v$, then $u$ | 5.25 | 0.0808 | 4 | 12 | 6 | 572 | 12 / 9 | 14 / 14 | 4 / 4 | 6 | 7321 | 43 / 178 | 48 / 138 | 18 / 33 | 14 | 462421 | ${t}^{3} \left( {t}^{2}+t+1 \right) \left( 20\,{t}^{2}+4\,t-1 \right)
\left( 4\,{t}^{2}-4\,t-1 \right) \left( 12\,{t}^{3}+20\,{t}^{2}-3\,t-
2 \right)
$ |
0 | 0 | Maple | $u$, then $v$ | 28.9 | 0.351 | 4 | 12 | 6 | 572 | 17 / 14 | 9 / 8 | 23 / 25 | 10 | 61106 | 15 / 9 | 6 / 6 | 14 / 14 | 8 | 22211 | ${t}^{3} \left( {t}^{2}+t+1 \right) \left( 20\,{t}^{2}+4\,t-1 \right)
\left( 4\,{t}^{2}-4\,t-1 \right) \left( 12\,{t}^{3}+20\,{t}^{2}-3\,t-
2 \right)
$ | 0 | 1 | Maple | $v$, then $u$ | 5930 | 10.9 | 6 | 26 | 15 | 3045 | 42 / 22 | 38 / 37 | 41 / 5 | 21 | 379716 | 53 / 244 | 100 / 204 | 25 / 51 | 29 | 2237103 | ${t}^{3} \left( t-1 \right) \left( 7\,t-1 \right) \left( 5\,t+1
\right) \left( {t}^{2}+t+1 \right) \left( 20\,{t}^{2}+4\,t-1
\right) \left( 4\,{t}^{2}-4\,t-1 \right) \left( 819200\,{t}^{14}+
820800\,{t}^{13}-4159888\,{t}^{12}-2894800\,{t}^{11}+8830560\,{t}^{10}+
7001852\,{t}^{9}-6123915\,{t}^{8}-8131545\,{t}^{7}-3582534\,{t}^{6}-
811538\,{t}^{5}-118344\,{t}^{4}-16058\,{t}^{3}-1268\,{t}^{2}+108\,t+16
\right)
$ | 0 | 1 | Maple | $u$, then $v$ | 489 | 3.46 | 6 | 26 | 15 | 3045 | 44 / 38 | 26 / 24 | 47 / 62 | 28 | 1588714 | 34 / 16 | 6 / 6 | 24 / 24 | 20 | 128037 | ${t}^{3} \left( t-1 \right) \left( 7\,t-1 \right) \left( 5\,t+1
\right) \left( {t}^{2}+t+1 \right) \left( 20\,{t}^{2}+4\,t-1
\right) \left( 4\,{t}^{2}-4\,t-1 \right) \left( 819200\,{t}^{14}+
820800\,{t}^{13}-4159888\,{t}^{12}-2894800\,{t}^{11}+8830560\,{t}^{10}+
7001852\,{t}^{9}-6123915\,{t}^{8}-8131545\,{t}^{7}-3582534\,{t}^{6}-
811538\,{t}^{5}-118344\,{t}^{4}-16058\,{t}^{3}-1268\,{t}^{2}+108\,t+16
\right)
$ | 1 | 0 | Maple | $v$, then $u$ | 6.65 | 0.439 | 4 | 12 | 6 | 573 | 13 / 9 | 14 / 14 | 4 / 4 | 6 | 7798 | 17 / 13 | 22 / 24 | 9 / 8 | 9 | 59655 | ${t}^{3} \left( 4\,{t}^{2}-4\,t-1 \right) \left( 20\,{t}^{2}+4\,t-1
\right) \left( 8\,{t}^{3}+40\,{t}^{2}+4\,t-1 \right) \left( {t}^{2}+
t+1 \right)
$ | 1 | 0 | Maple | $u$, then $v$ | 26.8 | 0.0978 | 4 | 12 | 6 | 573 | 21 / 17 | 7 / 8 | 25 / 27 | 12 | 80574 | 18 / 12 | 5 / 6 | 19 / 16 | 10 | 40713 | ${t}^{3} \left( 4\,{t}^{2}-4\,t-1 \right) \left( 20\,{t}^{2}+4\,t-1
\right) \left( 8\,{t}^{3}+40\,{t}^{2}+4\,t-1 \right) \left( {t}^{2}+
t+1 \right)
$ | 1 | 1 | Maple | $v$, then $u$ | 83 | 0.912 | 5 | 24 | 14 | 2396 | 14 / 18 | 16 / 30 | 24 / 5 | 7 | 69254 | 40 / 27 | 40 / 42 | 17 / 17 | 23 | 686048 | ${t}^{2} \left( t-1 \right) \left( 5\,t+1 \right) \left( 7\,t-1
\right) \left( {t}^{2}+t+1 \right) \left( 4\,{t}^{2}-4\,t-1 \right)
\left( 20\,{t}^{2}+4\,t-1 \right) \left( 643520\,{t}^{13}-4876736\,{t
}^{12}-1882848\,{t}^{11}+12036464\,{t}^{10}+4658084\,{t}^{9}-6348144\,{
t}^{8}-5177466\,{t}^{7}-1301230\,{t}^{6}+32550\,{t}^{5}+113956\,{t}^{4}
+33223\,{t}^{3}+3780\,{t}^{2}+37\,t-15 \right)
$ | 1 | 1 | Maple | $u$, then $v$ | 14500 | 11.5 | 5 | 24 | 14 | 2396 | 34 / 21 | 9 / 10 | 32 / 35 | 20 | 277394 | 31 / 14 | 5 / 6 | 19 / 19 | 18 | 90009 | ${t}^{2} \left( t-1 \right) \left( 5\,t+1 \right) \left( 7\,t-1
\right) \left( {t}^{2}+t+1 \right) \left( 4\,{t}^{2}-4\,t-1 \right)
\left( 20\,{t}^{2}+4\,t-1 \right) \left( 643520\,{t}^{13}-4876736\,{t
}^{12}-1882848\,{t}^{11}+12036464\,{t}^{10}+4658084\,{t}^{9}-6348144\,{
t}^{8}-5177466\,{t}^{7}-1301230\,{t}^{6}+32550\,{t}^{5}+113956\,{t}^{4}
+33223\,{t}^{3}+3780\,{t}^{2}+37\,t-15 \right)
$ | 1 | 1 | Mathematica | $u$, then $v$ | 1160 | n.a. | 5 | 24 | 14 | 2396 | 37 / 23 | 11 / 9 | 11 / 8 | 26 | 175762 | 38 / 24 | 11 / 10 | 11 / 10 | 26 | 111199 | ${t}^{2} \left( t-1 \right) \left( 5\,t+1 \right) \left( 7\,t-1
\right) \left( {t}^{2}+t+1 \right) \left( 4\,{t}^{2}-4\,t-1 \right)
\left( 20\,{t}^{2}+4\,t-1 \right) \left( 643520\,{t}^{13}-4876736\,{t
}^{12}-1882848\,{t}^{11}+12036464\,{t}^{10}+4658084\,{t}^{9}-6348144\,{
t}^{8}-5177466\,{t}^{7}-1301230\,{t}^{6}+32550\,{t}^{5}+113956\,{t}^{4}
+33223\,{t}^{3}+3780\,{t}^{2}+37\,t-15 \right)
$ | 1 | 1 | Mathematica | $v$, then $u$ | 106 | n.a. | 5 | 24 | 14 | 2396 | 37 / 23 | 11 / 9 | 11 / 8 | 26 | 175762 | 38 / 24 | 11 / 10 | 11 / 10 | 26 | 111199 | $-{t}^{2} \left( t-1 \right) \left( 5\,t+1 \right) \left( 7\,t-1
\right) \left( {t}^{2}+t+1 \right) \left( 4\,{t}^{2}-4\,t-1 \right)
\left( 20\,{t}^{2}+4\,t-1 \right) \left( 643520\,{t}^{13}-4876736\,{t
}^{12}-1882848\,{t}^{11}+12036464\,{t}^{10}+4658084\,{t}^{9}-6348144\,{
t}^{8}-5177466\,{t}^{7}-1301230\,{t}^{6}+32550\,{t}^{5}+113956\,{t}^{4}
+33223\,{t}^{3}+3780\,{t}^{2}+37\,t-15 \right)
$ | x | 0 | Mathematica | $u$, then $v$ | 2370 | n.a. | 5 | 20 | 10 | 15341 | 30 / 20 | 11 / 10 | 7 / 8 | 18 | 1448326 | 27 / 17 | 11 / 10 | 10 / 10 | 16 | 1106811 | ${t}^{3} \left( {t}^{2}+t+1 \right) \left( 4\,{t}^{2}-4\,t-1 \right)
\left( 20\,{t}^{2}+4\,t-1 \right) \left( 3\,{t}^{2}{x}^{4}+4\,{t}^{2}
{x}^{3}+6\,{t}^{2}{x}^{2}+2\,t{x}^{3}+4\,{t}^{2}x+3\,{t}^{2}+2\,tx-{x}^
{2} \right) \left( 720\,{t}^{9}{x}^{4}-480\,{t}^{9}{x}^{3}+4896\,{t}^{
8}{x}^{4}+1440\,{t}^{9}{x}^{2}+288\,{t}^{8}{x}^{3}+7272\,{t}^{7}{x}^{4}
-480\,{t}^{9}x+9792\,{t}^{8}{x}^{2}+864\,{t}^{7}{x}^{3}+3420\,{t}^{6}{x
}^{4}+720\,{t}^{9}+288\,{t}^{8}x+14064\,{t}^{7}{x}^{2}+336\,{t}^{6}{x}^
{3}-207\,{t}^{5}{x}^{4}+4896\,{t}^{8}+864\,{t}^{7}x+6088\,{t}^{6}{x}^{2
}+834\,{t}^{5}{x}^{3}-225\,{t}^{4}{x}^{4}+7272\,{t}^{7}+336\,{t}^{6}x-
174\,{t}^{5}{x}^{2}+1182\,{t}^{4}{x}^{3}+18\,{t}^{3}{x}^{4}+3420\,{t}^{
6}+834\,{t}^{5}x+234\,{t}^{4}{x}^{2}+315\,{t}^{3}{x}^{3}+9\,{t}^{2}{x}^
{4}-207\,{t}^{5}+1182\,{t}^{4}x+222\,{t}^{3}{x}^{2}+3\,{t}^{2}{x}^{3}-
225\,{t}^{4}+315\,{t}^{3}x+6\,{t}^{2}{x}^{2}-3\,t{x}^{3}+18\,{t}^{3}+3
\,{t}^{2}x-9\,t{x}^{2}+9\,{t}^{2}-3\,tx-{x}^{2} \right)
$ | 0 | y | Mathematica | $u$, then $v$ | 5290 | n.a. | 6 | 26 | 15 | 53733 | 53 / 39 | 14 / 14 | 11 / 12 | 35 | 10841419 | 45 / 31 | 8 / 10 | 11 / 10 | 31 | 1903731 | ${t}^{3} \left( {t}^{2}+t+1 \right) \left( 4\,{t}^{2}-4\,t-1 \right)
\left( 20\,{t}^{2}+4\,t-1 \right) \left( -y+t \right) \left( 2\,t{y}
^{2}+2\,yt+t+y \right) \left( 2\,t{y}^{2}+2\,yt+3\,t-y \right)
\left( 1228800\,{t}^{14}{y}^{10}+2248704\,{t}^{14}{y}^{9}+3219456\,{t}
^{13}{y}^{10}+4761600\,{t}^{14}{y}^{8}+2617344\,{t}^{13}{y}^{9}-2955264
\,{t}^{12}{y}^{10}+3624960\,{t}^{14}{y}^{7}+8343552\,{t}^{13}{y}^{8}-
14321664\,{t}^{12}{y}^{9}-13025280\,{t}^{11}{y}^{10}+1707008\,{t}^{14}{
y}^{6}-1155072\,{t}^{13}{y}^{7}-23910912\,{t}^{12}{y}^{8}-28941312\,{t}
^{11}{y}^{9}-5724672\,{t}^{10}{y}^{10}-3413504\,{t}^{14}{y}^{5}-790528
\,{t}^{13}{y}^{6}-33748992\,{t}^{12}{y}^{7}-47809024\,{t}^{11}{y}^{8}-
4146432\,{t}^{10}{y}^{9}+6741504\,{t}^{9}{y}^{10}-4950016\,{t}^{14}{y}^
{4}-10191872\,{t}^{13}{y}^{5}-13732480\,{t}^{12}{y}^{6}-26180864\,{t}^{
11}{y}^{7}-2355328\,{t}^{10}{y}^{8}+18496512\,{t}^{9}{y}^{9}+4237824\,{
t}^{8}{y}^{10}-3383552\,{t}^{14}{y}^{3}-3514624\,{t}^{13}{y}^{4}+
12618112\,{t}^{12}{y}^{5}+11229696\,{t}^{11}{y}^{6}+28202944\,{t}^{10}{
y}^{7}+33091712\,{t}^{9}{y}^{8}+8653440\,{t}^{8}{y}^{9}-66432\,{t}^{7}{
y}^{10}-470016\,{t}^{14}{y}^{2}-700928\,{t}^{13}{y}^{3}+36684224\,{t}^{
12}{y}^{4}+53643264\,{t}^{11}{y}^{5}+46059264\,{t}^{10}{y}^{6}+39746176
\,{t}^{9}{y}^{7}+18144896\,{t}^{8}{y}^{8}+675456\,{t}^{7}{y}^{9}-328512
\,{t}^{6}{y}^{10}+868608\,{t}^{14}y+3025152\,{t}^{13}{y}^{2}+26896384\,
{t}^{12}{y}^{3}+51610816\,{t}^{11}{y}^{4}+43753824\,{t}^{10}{y}^{5}+
31586688\,{t}^{9}{y}^{6}+15886144\,{t}^{8}{y}^{7}+4514720\,{t}^{7}{y}^{
8}+362112\,{t}^{6}{y}^{9}+12288\,{t}^{5}{y}^{10}+235008\,{t}^{14}+
2251008\,{t}^{13}y+7293600\,{t}^{12}{y}^{2}+19818848\,{t}^{11}{y}^{3}+
4197088\,{t}^{10}{y}^{4}+4607136\,{t}^{9}{y}^{5}+6283352\,{t}^{8}{y}^{6
}+3547984\,{t}^{7}{y}^{7}+1686872\,{t}^{6}{y}^{8}+443520\,{t}^{5}{y}^{9
}+28608\,{t}^{4}{y}^{10}-641088\,{t}^{13}-3391776\,{t}^{12}y-9665280\,{
t}^{11}{y}^{2}-29279584\,{t}^{10}{y}^{3}-29837984\,{t}^{9}{y}^{4}-
13281896\,{t}^{8}{y}^{5}-2291968\,{t}^{7}{y}^{6}+1296052\,{t}^{6}{y}^{7
}+785776\,{t}^{5}{y}^{8}+145344\,{t}^{4}{y}^{9}+4608\,{t}^{3}{y}^{10}-
3910896\,{t}^{12}-14268528\,{t}^{11}y-33072912\,{t}^{10}{y}^{2}-
42415024\,{t}^{9}{y}^{3}-24716196\,{t}^{8}{y}^{4}-11934152\,{t}^{7}{y}^
{5}-2047840\,{t}^{6}{y}^{6}+551840\,{t}^{5}{y}^{7}+192508\,{t}^{4}{y}^{
8}+18816\,{t}^{3}{y}^{9}+192\,{t}^{2}{y}^{10}-5096736\,{t}^{11}-
18224352\,{t}^{10}y-30027456\,{t}^{9}{y}^{2}-21676008\,{t}^{8}{y}^{3}-
12033636\,{t}^{7}{y}^{4}-5595776\,{t}^{6}{y}^{5}-713988\,{t}^{5}{y}^{6}
+115544\,{t}^{4}{y}^{7}+19456\,{t}^{3}{y}^{8}+768\,{t}^{2}{y}^{9}-
2918160\,{t}^{10}-10332576\,{t}^{9}y-10671462\,{t}^{8}{y}^{2}-6656010\,
{t}^{7}{y}^{3}-4666536\,{t}^{6}{y}^{4}-1594380\,{t}^{5}{y}^{5}-156024\,
{t}^{4}{y}^{6}+6416\,{t}^{3}{y}^{7}+400\,{t}^{2}{y}^{8}-651132\,{t}^{9}
-1365138\,{t}^{8}y-908604\,{t}^{7}{y}^{2}-1797279\,{t}^{6}{y}^{3}-
1365595\,{t}^{5}{y}^{4}-290553\,{t}^{4}{y}^{5}-24957\,{t}^{3}{y}^{6}-
520\,{t}^{2}{y}^{7}+16\,t{y}^{8}+133299\,{t}^{8}+686835\,{t}^{7}y+
169038\,{t}^{6}{y}^{2}-487070\,{t}^{5}{y}^{3}-261862\,{t}^{4}{y}^{4}-
33594\,{t}^{3}{y}^{5}-2248\,{t}^{2}{y}^{6}+32\,t{y}^{7}+4\,{y}^{8}+
71172\,{t}^{7}+173322\,{t}^{6}y-48402\,{t}^{5}{y}^{2}-98726\,{t}^{4}{y}
^{3}-28846\,{t}^{3}{y}^{4}-1604\,{t}^{2}{y}^{5}-4\,t{y}^{6}+8\,{y}^{7}+
945\,{t}^{6}-16875\,{t}^{5}y-25038\,{t}^{4}{y}^{2}-10262\,{t}^{3}{y}^{3
}-1394\,{t}^{2}{y}^{4}+130\,t{y}^{5}+8\,{y}^{6}-1728\,{t}^{5}-4968\,{t}
^{4}y-432\,{t}^{3}{y}^{2}-28\,{t}^{2}{y}^{3}+16\,t{y}^{4}+16\,{y}^{5}+
135\,{t}^{4}+567\,{t}^{3}y+522\,{t}^{2}{y}^{2}+98\,t{y}^{3}+4\,{y}^{4}+
54\,{t}^{3}+108\,{t}^{2}y+36\,t{y}^{2}+8\,{y}^{3} \right)
$ | | ss | vx | vy | CAS used | integrate | time (sec) | memory (GB) | $\operatorname{ord}P$ | $\deg_tP$ | height of $P$ | length of $P$ | $\deg_tU$ | $\deg_uU$ | $\deg_vU$ | height of $U$ | length of $U$ | $\deg_tV$ | $\deg_uV$ | $\deg_vV$ | height of $V$ | length of $V$ | leading coefficient of $P$ |
|---|
| 15 |
0 | 0 | Maple | $v$, then $u$ | 1.03 | 0.0434 | 3 | 6 | 4 | 97 | 4 / 5 | 8 / 6 | 4 / 4 | 2 | 352 | 7 / 8 | 12 / 11 | 7 / 6 | 4 | 1456 | ${t}^{2} \left( 8\,{t}^{2}-1 \right) \left( 8\,{t}^{2}+1 \right)
$ |
0 | 0 | Maple | $u$, then $v$ | 1.83 | 0.0433 | 3 | 6 | 4 | 97 | 8 / 9 | 7 / 6 | 13 / 15 | 5 | 2227 | 41 / 20 | 38 / 38 | 9 / 21 | 5 | 4531 | ${t}^{2} \left( 8\,{t}^{2}-1 \right) \left( 8\,{t}^{2}+1 \right)
$ | 0 | 1 | Maple | $v$, then $u$ | 24.8 | 0.521 | 5 | 16 | 9 | 1106 | 7 / 75 | 11 / 32 | 12 / 8 | 2 | 555 | 34 / 26 | 35 / 33 | 17 / 17 | 15 | 308008 | ${t}^{3} \left( 3\,t-1 \right) \left( t+1 \right) \left( 8\,{t}^{2}+1
\right) \left( 8\,{t}^{2}-1 \right) \left( 2688\,{t}^{7}+768\,{t}^{6
}+960\,{t}^{5}+344\,{t}^{4}-424\,{t}^{3}+4\,{t}^{2}+8\,t-5 \right)
$ | 0 | 1 | Maple | $u$, then $v$ | 45 | 1.07 | 5 | 16 | 9 | 1106 | 20 / 88 | 19 / 61 | 29 / 66 | 10 | 143022 | 16 / 53 | 6 / 104 | 16 / 49 | 9 | 21897 | ${t}^{3} \left( 3\,t-1 \right) \left( t+1 \right) \left( 8\,{t}^{2}+1
\right) \left( 8\,{t}^{2}-1 \right) \left( 2688\,{t}^{7}+768\,{t}^{6
}+960\,{t}^{5}+344\,{t}^{4}-424\,{t}^{3}+4\,{t}^{2}+8\,t-5 \right)
$ | 1 | 0 | Maple | $v$, then $u$ | 1.01 | 0.0437 | 3 | 6 | 4 | 119 | 4 / 5 | 7 / 6 | 4 / 4 | 2 | 422 | 15 / 12 | 3 / 14 | 19 / 25 | 8 | 12541 | ${t}^{2} \left( 8\,{t}^{2}-1 \right) \left( 8\,{t}^{2}+1 \right)
$ | 1 | 0 | Maple | $u$, then $v$ | 2.35 | 0.0436 | 3 | 6 | 4 | 119 | 12 / 13 | 6 / 6 | 15 / 16 | 5 | 7157 | 8 / 9 | 5 / 5 | 9 / 8 | 4 | 2655 | ${t}^{2} \left( 8\,{t}^{2}-1 \right) \left( 8\,{t}^{2}+1 \right)
$ | 1 | 1 | Maple | $v$, then $u$ | 18.2 | 0.128 | 5 | 16 | 9 | 1111 | 21 / 16 | 16 / 16 | 4 / 5 | 10 | 27115 | 41 / 32 | 40 / 26 | 25 / 25 | 19 | 640214 | ${t}^{3} \left( 3\,t-1 \right) \left( t+1 \right) \left( 8\,{t}^{2}-1
\right) \left( 1536\,{t}^{7}-1536\,{t}^{6}-584\,{t}^{4}-472\,{t}^{3}-
90\,{t}^{2}-22\,t-3 \right) \left( 8\,{t}^{2}+1 \right)
$ | 1 | 1 | Maple | $u$, then $v$ | 38.2 | 1.34 | 5 | 16 | 9 | 1111 | 22 / 87 | 18 / 61 | 30 / 65 | 12 | 181683 | 52 / 53 | 45 / 104 | 19 / 49 | 9 | 82806 | ${t}^{3} \left( 3\,t-1 \right) \left( t+1 \right) \left( 8\,{t}^{2}-1
\right) \left( 1536\,{t}^{7}-1536\,{t}^{6}-584\,{t}^{4}-472\,{t}^{3}-
90\,{t}^{2}-22\,t-3 \right) \left( 8\,{t}^{2}+1 \right)
$ | 1 | 1 | Mathematica | $u$, then $v$ | 258 | n.a. | 5 | 16 | 9 | 1111 | 23 / 16 | 10 / 11 | 9 / 10 | 18 | 55489 | 21 / 14 | 10 / 8 | 9 / 8 | 16 | 23164 | ${t}^{3} \left( 3\,t-1 \right) \left( t+1 \right) \left( 8\,{t}^{2}-1
\right) \left( 1536\,{t}^{7}-1536\,{t}^{6}-584\,{t}^{4}-472\,{t}^{3}-
90\,{t}^{2}-22\,t-3 \right) \left( 8\,{t}^{2}+1 \right)
$ | 1 | 1 | Mathematica | $v$, then $u$ | 31.9 | n.a. | 5 | 16 | 9 | 1111 | 23 / 16 | 10 / 11 | 9 / 10 | 18 | 55489 | 21 / 14 | 10 / 8 | 9 / 8 | 16 | 23164 | ${t}^{3} \left( 3\,t-1 \right) \left( t+1 \right) \left( 8\,{t}^{2}-1
\right) \left( 1536\,{t}^{7}-1536\,{t}^{6}-584\,{t}^{4}-472\,{t}^{3}-
90\,{t}^{2}-22\,t-3 \right) \left( 8\,{t}^{2}+1 \right)
$ | x | 0 | Mathematica | $u$, then $v$ | 171 | n.a. | 4 | 9 | 5 | 372 | 7 / 5 | 8 / 8 | 6 / 6 | 5 | 10497 | 8 / 6 | 8 / 8 | 9 / 8 | 5 | 9446 | ${t}^{3} \left( 8\,{t}^{2}-1 \right) \left( 8\,{t}^{2}+1 \right)
\left( 4\,{t}^{2}{x}^{2}+4\,{t}^{2}-x \right)
$ | 0 | y | Mathematica | $u$, then $v$ | 351 | n.a. | 5 | 16 | 9 | 3867 | 25 / 17 | 12 / 12 | 9 / 10 | 15 | 157707 | 19 / 11 | 10 / 8 | 7 / 6 | 13 | 35627 | ${t}^{3} \left( 8\,{t}^{2}-1 \right) \left( 8\,{t}^{2}+1 \right)
\left( t{y}^{2}+2\,t-y \right) \left( t{y}^{2}-2\,t-y \right)
\left( 128\,{t}^{7}{y}^{7}-256\,{t}^{6}{y}^{6}+40\,{t}^{4}{y}^{8}+2560
\,{t}^{7}{y}^{3}+448\,{t}^{5}{y}^{5}-104\,{t}^{3}{y}^{7}+1024\,{t}^{6}{
y}^{2}+240\,{t}^{4}{y}^{4}+60\,{t}^{2}{y}^{6}+512\,{t}^{5}y-320\,{t}^{3
}{y}^{3}+8\,t{y}^{5}+64\,{t}^{4}-56\,{t}^{2}{y}^{2}-5\,{y}^{4} \right)
$ | | ss | vx | vy | CAS used | integrate | time (sec) | memory (GB) | $\operatorname{ord}P$ | $\deg_tP$ | height of $P$ | length of $P$ | $\deg_tU$ | $\deg_uU$ | $\deg_vU$ | height of $U$ | length of $U$ | $\deg_tV$ | $\deg_uV$ | $\deg_vV$ | height of $V$ | length of $V$ | leading coefficient of $P$ |
|---|
| 16 |
0 | 0 | Maple | $v$, then $u$ | 4.17 | 0.0885 | 4 | 10 | 5 | 447 | 11 / 16 | 14 / 9 | 19 / 22 | 4 | 9358 | 44 / 13 | 38 / 28 | 27 / 12 | 11 | 326650 | ${t}^{3} \left( t+1 \right) \left( 4\,{t}^{2}+4\,t+3 \right) \left( 12
\,{t}^{2}+4\,t+1 \right) \left( 4\,{t}^{2}+4\,t-1 \right)
$ |
0 | 0 | Maple | $u$, then $v$ | 21.4 | 0.508 | 4 | 10 | 5 | 447 | 13 / 12 | 9 / 8 | 19 / 21 | 8 | 27721 | 8 / 7 | 4 / 4 | 12 / 12 | 5 | 4585 | ${t}^{3} \left( t+1 \right) \left( 4\,{t}^{2}+4\,t+3 \right) \left( 12
\,{t}^{2}+4\,t+1 \right) \left( 4\,{t}^{2}+4\,t-1 \right)
$ | 0 | 1 | Maple | $v$, then $u$ | 141 | 1.28 | 6 | 22 | 13 | 2147 | 29 / 20 | 28 / 28 | 4 / 5 | 15 | 81098 | 35 / 26 | 41 / 42 | 12 / 12 | 19 | 326700 | ${t}^{4} \left( 3\,t+1 \right) \left( 5\,t-1 \right) \left( t+1
\right) \left( 4\,{t}^{2}+4\,t-1 \right) \left( 12\,{t}^{2}+4\,t+1
\right) \left( 17664\,{t}^{11}-130176\,{t}^{10}-134208\,{t}^{9}-40160
\,{t}^{8}+47536\,{t}^{7}+16824\,{t}^{6}+1808\,{t}^{5}-1342\,{t}^{4}-
1323\,{t}^{3}-173\,{t}^{2}+t-3 \right)
$ | 0 | 1 | Maple | $u$, then $v$ | 22200 | 12 | 6 | 22 | 13 | 2147 | 28 / 19 | 13 / 12 | 32 / 34 | 16 | 207662 | 21 / 12 | 4 / 4 | 20 / 20 | 12 | 27861 | ${t}^{4} \left( 3\,t+1 \right) \left( 5\,t-1 \right) \left( t+1
\right) \left( 4\,{t}^{2}+4\,t-1 \right) \left( 12\,{t}^{2}+4\,t+1
\right) \left( 17664\,{t}^{11}-130176\,{t}^{10}-134208\,{t}^{9}-40160
\,{t}^{8}+47536\,{t}^{7}+16824\,{t}^{6}+1808\,{t}^{5}-1342\,{t}^{4}-
1323\,{t}^{3}-173\,{t}^{2}+t-3 \right)
$ | 1 | 0 | Maple | $v$, then $u$ | 4.99 | 0.374 | 4 | 11 | 6 | 506 | 10 / 8 | 13 / 12 | 4 / 4 | 5 | 4691 | 44 / 113 | 37 / 70 | 27 / 100 | 10 | 326487 | ${t}^{3} \left( 1+2\,t \right) \left( t+1 \right) \left( 4\,{t}^{2}+4
\,t-1 \right) \left( 12\,{t}^{2}+4\,t+1 \right) \left( 4\,{t}^{2}+2\,
t+1 \right)
$ | 1 | 0 | Maple | $u$, then $v$ | 13.4 | 0.445 | 4 | 11 | 6 | 506 | 15 / 13 | 7 / 8 | 22 / 24 | 9 | 36524 | 10 / 8 | 3 / 4 | 12 / 12 | 6 | 5787 | ${t}^{3} \left( 1+2\,t \right) \left( t+1 \right) \left( 4\,{t}^{2}+4
\,t-1 \right) \left( 12\,{t}^{2}+4\,t+1 \right) \left( 4\,{t}^{2}+2\,
t+1 \right)
$ | 1 | 1 | Maple | $v$, then $u$ | 217 | 3.12 | 5 | 19 | 11 | 1524 | 23 / 15 | 22 / 22 | 4 / 5 | 12 | 47033 | 29 / 21 | 36 / 38 | 9 / 10 | 16 | 214354 | ${t}^{3} \left( 3\,t+1 \right) \left( 5\,t-1 \right) \left( t+1
\right) \left( 4\,{t}^{2}+4\,t-1 \right) \left( 12\,{t}^{2}+4\,t+1
\right) \left( 7872\,{t}^{9}+8512\,{t}^{8}+4656\,{t}^{7}-3376\,{t}^{6
}-4604\,{t}^{5}-3324\,{t}^{4}-1219\,{t}^{3}-315\,{t}^{2}-27\,t-3
\right)
$ | 1 | 1 | Maple | $u$, then $v$ | 377 | 4.23 | 5 | 19 | 11 | 1524 | 25 / 17 | 9 / 10 | 29 / 31 | 14 | 126461 | 42 / 180 | 39 / 95 | 15 / 20 | 12 | 155447 | ${t}^{3} \left( 3\,t+1 \right) \left( 5\,t-1 \right) \left( t+1
\right) \left( 4\,{t}^{2}+4\,t-1 \right) \left( 12\,{t}^{2}+4\,t+1
\right) \left( 7872\,{t}^{9}+8512\,{t}^{8}+4656\,{t}^{7}-3376\,{t}^{6
}-4604\,{t}^{5}-3324\,{t}^{4}-1219\,{t}^{3}-315\,{t}^{2}-27\,t-3
\right)
$ | 1 | 1 | Mathematica | $u$, then $v$ | 352 | n.a. | 5 | 19 | 11 | 1524 | 26 / 17 | 11 / 11 | 9 / 10 | 17 | 69230 | 23 / 14 | 8 / 8 | 9 / 8 | 15 | 19185 | ${t}^{3} \left( 3\,t+1 \right) \left( 5\,t-1 \right) \left( t+1
\right) \left( 4\,{t}^{2}+4\,t-1 \right) \left( 12\,{t}^{2}+4\,t+1
\right) \left( 7872\,{t}^{9}+8512\,{t}^{8}+4656\,{t}^{7}-3376\,{t}^{6
}-4604\,{t}^{5}-3324\,{t}^{4}-1219\,{t}^{3}-315\,{t}^{2}-27\,t-3
\right)
$ | 1 | 1 | Mathematica | $v$, then $u$ | 59.3 | n.a. | 5 | 19 | 11 | 1524 | 26 / 17 | 11 / 11 | 9 / 10 | 17 | 69230 | 23 / 14 | 8 / 8 | 9 / 8 | 15 | 19185 | ${t}^{3} \left( 3\,t+1 \right) \left( 5\,t-1 \right) \left( t+1
\right) \left( 4\,{t}^{2}+4\,t-1 \right) \left( 12\,{t}^{2}+4\,t+1
\right) \left( 7872\,{t}^{9}+8512\,{t}^{8}+4656\,{t}^{7}-3376\,{t}^{6
}-4604\,{t}^{5}-3324\,{t}^{4}-1219\,{t}^{3}-315\,{t}^{2}-27\,t-3
\right)
$ | x | 0 | Mathematica | $u$, then $v$ | 914 | n.a. | 5 | 17 | 9 | 11090 | 26 / 16 | 10 / 10 | 7 / 8 | 15 | 926935 | 24 / 14 | 10 / 10 | 10 / 10 | 13 | 621949 | ${t}^{3} \left( t+1 \right) \left( 4\,{t}^{2}+4\,t-1 \right) \left( 12
\,{t}^{2}+4\,t+1 \right) \left( {t}^{2}{x}^{4}-4\,{t}^{2}{x}^{3}+2\,{t
}^{2}{x}^{2}-2\,t{x}^{3}-4\,{t}^{2}x+{t}^{2}-2\,tx+{x}^{2} \right)
\left( 16\,{t}^{7}{x}^{4}+96\,{t}^{7}{x}^{3}-16\,{t}^{6}{x}^{4}+32\,{t
}^{7}{x}^{2}+352\,{t}^{6}{x}^{3}-8\,{t}^{5}{x}^{4}+96\,{t}^{7}x-32\,{t}
^{6}{x}^{2}+336\,{t}^{5}{x}^{3}+4\,{t}^{4}{x}^{4}+16\,{t}^{7}+352\,{t}^
{6}x+80\,{t}^{5}{x}^{2}+96\,{t}^{4}{x}^{3}+{t}^{3}{x}^{4}-16\,{t}^{6}+
336\,{t}^{5}x+200\,{t}^{4}{x}^{2}-18\,{t}^{3}{x}^{3}-8\,{t}^{5}+96\,{t}
^{4}x+146\,{t}^{3}{x}^{2}-14\,{t}^{2}{x}^{3}+4\,{t}^{4}-18\,{t}^{3}x+68
\,{t}^{2}{x}^{2}-4\,t{x}^{3}+{t}^{3}-14\,{t}^{2}x+26\,t{x}^{2}-4\,tx+3
\,{x}^{2} \right)
$ | 0 | y | Mathematica | $u$, then $v$ | 1550 | n.a. | 6 | 22 | 13 | 29005 | 33 / 23 | 13 / 14 | 10 / 12 | 20 | 2959046 | 30 / 20 | 9 / 10 | 9 / 8 | 18 | 720682 | ${t}^{4} \left( t+1 \right) \left( 4\,{t}^{2}+4\,t-1 \right) \left( 12
\,{t}^{2}+4\,t+1 \right) \left( t{y}^{2}-2\,ty-2\,t-y \right) \left(
t{y}^{2}+2\,ty+2\,t-y \right) \left( 768\,{t}^{11}{y}^{7}+3840\,{t}^{
10}{y}^{8}+4864\,{t}^{11}{y}^{6}+1536\,{t}^{10}{y}^{7}+1920\,{t}^{9}{y}
^{8}-2048\,{t}^{11}{y}^{5}-8960\,{t}^{10}{y}^{6}+768\,{t}^{9}{y}^{7}+
1600\,{t}^{8}{y}^{8}-46080\,{t}^{11}{y}^{4}+14080\,{t}^{10}{y}^{5}+
26112\,{t}^{9}{y}^{6}-2560\,{t}^{8}{y}^{7}+1120\,{t}^{7}{y}^{8}+8192\,{
t}^{11}{y}^{3}-98304\,{t}^{10}{y}^{4}-3840\,{t}^{9}{y}^{5}+39552\,{t}^{
8}{y}^{6}-4672\,{t}^{7}{y}^{7}+240\,{t}^{6}{y}^{8}+105472\,{t}^{11}{y}^
{2}-133120\,{t}^{10}{y}^{3}-203520\,{t}^{9}{y}^{4}-17664\,{t}^{8}{y}^{5
}+20544\,{t}^{7}{y}^{6}-5472\,{t}^{6}{y}^{7}-80\,{t}^{5}{y}^{8}-24576\,
{t}^{11}y+231424\,{t}^{10}{y}^{2}-96768\,{t}^{9}{y}^{3}-207104\,{t}^{8}
{y}^{4}-5184\,{t}^{7}{y}^{5}+1728\,{t}^{6}{y}^{6}-1664\,{t}^{5}{y}^{7}-
20\,{t}^{4}{y}^{8}-81920\,{t}^{11}+245760\,{t}^{10}y+282624\,{t}^{9}{y}
^{2}-20736\,{t}^{8}{y}^{3}-104960\,{t}^{7}{y}^{4}+1536\,{t}^{6}{y}^{5}-
896\,{t}^{5}{y}^{6}+232\,{t}^{4}{y}^{7}+4096\,{t}^{10}+227328\,{t}^{9}y
+199168\,{t}^{8}{y}^{2}-28032\,{t}^{7}{y}^{3}-33984\,{t}^{6}{y}^{4}-
4704\,{t}^{5}{y}^{5}-248\,{t}^{4}{y}^{6}+213\,{t}^{3}{y}^{7}+33792\,{t}
^{9}+71680\,{t}^{8}y+48640\,{t}^{7}{y}^{2}-16512\,{t}^{6}{y}^{3}-11344
\,{t}^{5}{y}^{4}-3600\,{t}^{4}{y}^{5}-243\,{t}^{3}{y}^{6}+30\,{t}^{2}{y
}^{7}+16384\,{t}^{8}-17408\,{t}^{7}y+22656\,{t}^{6}{y}^{2}-3872\,{t}^{5
}{y}^{3}-1600\,{t}^{4}{y}^{4}-900\,{t}^{3}{y}^{5}-157\,{t}^{2}{y}^{6}-
5120\,{t}^{7}-1536\,{t}^{6}y+12608\,{t}^{5}{y}^{2}+2512\,{t}^{4}{y}^{3}
+684\,{t}^{3}{y}^{4}-91\,{t}^{2}{y}^{5}-25\,t{y}^{6}-2304\,{t}^{6}+5632
\,{t}^{5}y+3872\,{t}^{4}{y}^{2}+1848\,{t}^{3}{y}^{3}+164\,{t}^{2}{y}^{4
}+5\,t{y}^{5}+704\,{t}^{5}+1408\,{t}^{4}y+852\,{t}^{3}{y}^{2}+304\,{t}^
{2}{y}^{3}+14\,t{y}^{4}+3\,{y}^{5}+128\,{t}^{4}+192\,{t}^{3}y+96\,{t}^{
2}{y}^{2}+4\,t{y}^{3}+3\,{y}^{4} \right)
$ | | ss | vx | vy | CAS used | integrate | time (sec) | memory (GB) | $\operatorname{ord}P$ | $\deg_tP$ | height of $P$ | length of $P$ | $\deg_tU$ | $\deg_uU$ | $\deg_vU$ | height of $U$ | length of $U$ | $\deg_tV$ | $\deg_uV$ | $\deg_vV$ | height of $V$ | length of $V$ | leading coefficient of $P$ |
|---|
| 17 |
0 | 0 | Maple | $v$, then $u$ | 3.27 | 0.0461 | 3 | 5 | 3 | 97 | 5 / 6 | 15 / 13 | 6 / 5 | 5 | 2623 | 26 / 82 | 46 / 77 | 20 / 40 | 7 | 57236 | ${t}^{2} \left( 3\,t-1 \right) \left( 9\,{t}^{2}+3\,t+1 \right)
$ |
0 | 0 | Maple | $u$, then $v$ | 4.79 | 0.0458 | 3 | 5 | 3 | 97 | 27 / 32 | 10 / 8 | 45 / 39 | 11 | 196675 | 8 / 9 | 6 / 5 | 16 / 14 | 5 | 3956 | ${t}^{2} \left( 3\,t-1 \right) \left( 9\,{t}^{2}+3\,t+1 \right)
$ | 0 | 1 | Maple | $v$, then $u$ | not available | 0 | 1 | Maple | $u$, then $v$ | 6490 | 9.68 | 6 | 11 | 8 | 686 | 262 / 255 | 62 / 42 | 133 / 121 | 23 | 20220772 | 13 / 13 | 6 / 5 | 23 / 23 | 7 | 27570 | ${t}^{4} \left( t+1 \right) \left( 9\,{t}^{2}+3\,t+1 \right) \left( 9
\,{t}^{2}+48\,t-10 \right) \left( 3\,t-1 \right) ^{2}
$ | 1 | 0 | Maple | $v$, then $u$ | 13000 | 10.7 | 6 | 11 | 8 | 686 | 15 / 15 | 24 / 24 | 6 / 5 | 10 | 32696 | 46 / 148 | 52 / 214 | 26 / 62 | 23 | 1063392 | ${t}^{4} \left( t+1 \right) \left( 9\,{t}^{2}+3\,t+1 \right) \left( 9
\,{t}^{2}+48\,t-10 \right) \left( 3\,t-1 \right) ^{2}
$ | 1 | 0 | Maple | $u$, then $v$ | 117000 | 22.5 | 6 | 11 | 8 | 686 | 43 / 42 | 26 / 25 | 134 / 136 | 30 | 4101077 | 17 / 19 | 8 / 8 | 32 / 32 | 10 | 70738 | ${t}^{4} \left( t+1 \right) \left( 9\,{t}^{2}+3\,t+1 \right) \left( 9
\,{t}^{2}+48\,t-10 \right) \left( 3\,t-1 \right) ^{2}
$ | 1 | 1 | Maple | $v$, then $u$ | 476 | 1.88 | 3 | 4 | 2 | 113 | 38 / 41 | 21 / 17 | 33 / 33 | 4 | 50540 | 32 / 117 | 52 / 113 | 17 / 56 | 16 | 421351 | ${t}^{2} \left( t+1 \right) \left( 3\,t-1 \right)
$ | 1 | 1 | Maple | $u$, then $v$ | 438 | 2.17 | 3 | 4 | 2 | 113 | 8 / 11 | 7 / 6 | 26 / 28 | 5 | 17919 | 5 / 8 | 8 / 8 | 17 / 17 | 3 | 7780 | ${t}^{2} \left( t+1 \right) \left( 3\,t-1 \right)
$ | 1 | 1 | Mathematica | $u$, then $v$ | 94.9 | n.a. | 3 | 4 | 2 | 113 | 7 / 6 | 7 / 7 | 6 / 6 | 4 | 4644 | 7 / 6 | 6 / 5 | 7 / 6 | 5 | 3480 | ${t}^{2} \left( t+1 \right) \left( 3\,t-1 \right)
$ | 1 | 1 | Mathematica | $v$, then $u$ | 487 | n.a. | 3 | 4 | 2 | 113 | 7 / 6 | 7 / 7 | 6 / 6 | 4 | 4644 | 7 / 6 | 6 / 5 | 7 / 6 | 5 | 3480 | ${t}^{2} \left( t+1 \right) \left( 3\,t-1 \right)
$ | x | 0 | Mathematica | $u$, then $v$ | 708 | n.a. | 6 | 12 | 8 | 2307 | 18 / 16 | 9 / 9 | 7 / 10 | 11 | 55451 | 20 / 18 | 9 / 14 | 12 / 14 | 13 | 139427 | ${t}^{4} \left( 3\,t-1 \right) \left( 9\,{t}^{2}+3\,t+1 \right)
\left( 4\,{t}^{2}{x}^{3}-{t}^{2}+2\,tx-{x}^{2} \right) \left( 27\,{t}
^{3}{x}^{2}+129\,{t}^{2}{x}^{3}-60\,t{x}^{4}+6\,{t}^{2}-18\,tx+10\,{x}^
{2} \right)
$ | 0 | y | Mathematica | $u$, then $v$ | 800 | n.a. | 6 | 12 | 8 | 2303 | 27 / 25 | 12 / 13 | 10 / 12 | 23 | 775667 | 27 / 25 | 12 / 11 | 10 / 12 | 23 | 419427 | ${t}^{4} \left( 3\,t-1 \right) \left( 9\,{t}^{2}+3\,t+1 \right)
\left( {t}^{2}{y}^{3}-2\,t{y}^{2}-4\,{t}^{2}+y \right) \left( 6\,{t}^
{2}{y}^{4}+27\,{t}^{3}{y}^{2}-18\,t{y}^{3}+129\,{t}^{2}y+10\,{y}^{2}-60
\,t \right)
$ | | ss | vx | vy | CAS used | integrate | time (sec) | memory (GB) | $\operatorname{ord}P$ | $\deg_tP$ | height of $P$ | length of $P$ | $\deg_tU$ | $\deg_uU$ | $\deg_vU$ | height of $U$ | length of $U$ | $\deg_tV$ | $\deg_uV$ | $\deg_vV$ | height of $V$ | length of $V$ | leading coefficient of $P$ |
|---|
| 18 |
0 | 0 | Maple | $v$, then $u$ | 30.4 | 0.483 | 4 | 6 | 4 | 209 | 6 / 9 | 20 / 19 | 5 / 4 | 4 | 9309 | 44 / 129 | 47 / 93 | 34 / 76 | 13 | 415456 | ${t}^{3} \left( 6\,t-1 \right) \left( 1+2\,t \right) \left( 3\,t+1
\right)
$ |
0 | 0 | Maple | $u$, then $v$ | 31.8 | 0.504 | 4 | 6 | 4 | 209 | 29 / 18 | 32 / 12 | 26 / 40 | 17 | 234564 | 10 / 9 | 6 / 5 | 20 / 19 | 5 | 14300 | ${t}^{3} \left( 6\,t-1 \right) \left( 1+2\,t \right) \left( 3\,t+1
\right)
$ | 0 | 1 | Maple | $v$, then $u$ | 1080 | 3.19 | 4 | 5 | 4 | 164 | 9 / 13 | 25 / 24 | 7 / 7 | 6 | 21468 | 23 / 27 | 84 / 84 | 9 / 8 | 20 | 419564 | ${t}^{3} \left( 1+2\,t \right) \left( 6\,t-1 \right)
$ | 0 | 1 | Maple | $u$, then $v$ | 39.6 | 0.819 | 4 | 5 | 4 | 164 | 14 / 18 | 10 / 8 | 36 / 36 | 9 | 77487 | 7 / 11 | 5 / 4 | 19 / 19 | 4 | 10265 | ${t}^{3} \left( 1+2\,t \right) \left( 6\,t-1 \right)
$ | 1 | 0 | Maple | $v$, then $u$ | 38.7 | 0.819 | 4 | 5 | 4 | 164 | 7 / 11 | 19 / 19 | 5 / 4 | 4 | 10265 | 55 / 163 | 156 / 200 | 24 / 78 | 21 | 2376326 | ${t}^{3} \left( 1+2\,t \right) \left( 6\,t-1 \right)
$ | 1 | 0 | Maple | $u$, then $v$ | 1240 | 2.97 | 4 | 5 | 4 | 164 | 37 / 29 | 37 / 21 | 96 / 97 | 22 | 1623157 | 18 / 13 | 24 / 8 | 30 / 27 | 9 | 98244 | ${t}^{3} \left( 1+2\,t \right) \left( 6\,t-1 \right)
$ | 1 | 1 | Maple | $v$, then $u$ | 1080 | 2.97 | 3 | 4 | 3 | 117 | 6 / 9 | 21 / 20 | 8 / 8 | 5 | 12467 | 34 / 145 | 64 / 57 | 17 / 74 | 13 | 339295 | ${t}^{2} \left( 1+2\,t \right) \left( 6\,t-1 \right)
$ | 1 | 1 | Maple | $u$, then $v$ | 1080 | 3.22 | 3 | 4 | 3 | 117 | 35 / 22 | 17 / 20 | 62 / 41 | 13 | 515693 | 31 / 47 | 43 / 12 | 23 / 24 | 5 | 27463 | ${t}^{2} \left( 1+2\,t \right) \left( 6\,t-1 \right)
$ | 1 | 1 | Mathematica | $u$, then $v$ | 133 | n.a. | 3 | 4 | 3 | 117 | 8 / 10 | 7 / 7 | 7 / 6 | 6 | 6783 | 8 / 10 | 5 / 7 | 7 / 7 | 6 | 4737 | ${t}^{2} \left( 1+2\,t \right) \left( 6\,t-1 \right)
$ | 1 | 1 | Mathematica | $v$, then $u$ | 1110 | n.a. | 3 | 4 | 3 | 117 | 8 / 10 | 7 / 7 | 7 / 6 | 6 | 6783 | 8 / 10 | 5 / 7 | 7 / 7 | 6 | 4737 | ${t}^{2} \left( 1+2\,t \right) \left( 6\,t-1 \right)
$ | x | 0 | Mathematica | $u$, then $v$ | 2140 | n.a. | 6 | 12 | 9 | 6491 | 21 / 21 | 9 / 9 | 7 / 10 | 15 | 346297 | 24 / 24 | 10 / 14 | 13 / 14 | 17 | 856805 | ${t}^{4} \left( 6\,t-1 \right) \left( 1+2\,t \right) \left( 3\,t+1
\right) \left( {t}^{2}{x}^{4}-4\,{t}^{2}{x}^{3}-6\,{t}^{2}{x}^{2}-2\,
t{x}^{3}-4\,{t}^{2}x+{t}^{2}-2\,tx+{x}^{2} \right) \left( 6\,{t}^{3}{x
}^{4}+18\,{t}^{3}{x}^{3}+168\,{t}^{3}{x}^{2}-16\,{t}^{2}{x}^{3}+18\,{t}
^{3}x+104\,{t}^{2}{x}^{2}-5\,t{x}^{3}+6\,{t}^{3}-16\,{t}^{2}x+28\,t{x}^
{2}-5\,tx+3\,{x}^{2} \right)
$ | 0 | y | Mathematica | $u$, then $v$ | 4500 | n.a. | 6 | 12 | 9 | 6491 | 33 / 33 | 12 / 13 | 12 / 12 | 32 | 5990402 | 33 / 33 | 8 / 11 | 12 / 12 | 32 | 2448491 | ${t}^{4} \left( 6\,t-1 \right) \left( 1+2\,t \right) \left( 3\,t+1
\right) \left( {t}^{2}{y}^{4}-4\,{t}^{2}{y}^{3}-6\,{t}^{2}{y}^{2}-2\,
t{y}^{3}-4\,{t}^{2}y+{t}^{2}-2\,ty+{y}^{2} \right) \left( 6\,{t}^{3}{y
}^{4}+18\,{t}^{3}{y}^{3}+168\,{t}^{3}{y}^{2}-16\,{t}^{2}{y}^{3}+18\,{t}
^{3}y+104\,{t}^{2}{y}^{2}-5\,t{y}^{3}+6\,{t}^{3}-16\,{t}^{2}y+28\,t{y}^
{2}-5\,ty+3\,{y}^{2} \right)
$ | | ss | vx | vy | CAS used | integrate | time (sec) | memory (GB) | $\operatorname{ord}P$ | $\deg_tP$ | height of $P$ | length of $P$ | $\deg_tU$ | $\deg_uU$ | $\deg_vU$ | height of $U$ | length of $U$ | $\deg_tV$ | $\deg_uV$ | $\deg_vV$ | height of $V$ | length of $V$ | leading coefficient of $P$ |
|---|
| 19 |
0 | 0 | Maple | $v$, then $u$ | 8.2 | 0.121 | 4 | 5 | 4 | 128 | 11 / 12 | 21 / 18 | 6 / 5 | 6 | 9562 | 18 / 96 | 37 / 112 | 11 / 57 | 9 | 42216 | ${t}^{3} \left( 4\,t-1 \right) \left( 1+4\,t \right)
$ |
0 | 0 | Maple | $u$, then $v$ | 26.1 | 0.437 | 4 | 5 | 4 | 128 | 18 / 19 | 12 / 9 | 29 / 28 | 10 | 45667 | 10 / 50 | 8 / 101 | 17 / 15 | 6 | 14941 | ${t}^{3} \left( 4\,t-1 \right) \left( 1+4\,t \right)
$ | 0 | 1 | Maple | $v$, then $u$ | 2.4 | 0.0439 | 3 | 4 | 3 | 91 | 6 / 5 | 13 / 10 | 5 / 5 | 3 | 2553 | 15 / 67 | 23 / 73 | 18 / 43 | 8 | 20528 | ${t}^{2} \left( 4\,t-1 \right) \left( 1+4\,t \right)
$ | 0 | 1 | Maple | $u$, then $v$ | 7.39 | 0.092 | 3 | 4 | 3 | 91 | 12 / 14 | 10 / 7 | 25 / 25 | 8 | 21511 | 20 / 27 | 39 / 69 | 11 / 12 | 3 | 9783 | ${t}^{2} \left( 4\,t-1 \right) \left( 1+4\,t \right)
$ | 1 | 0 | Maple | $v$, then $u$ | 13.7 | 0.414 | 4 | 6 | 4 | 214 | 28 / 27 | 22 / 19 | 23 / 27 | 5 | 22029 | 17 / 16 | 36 / 33 | 12 / 10 | 10 | 98922 | ${t}^{3} \left( 1+4\,t \right) \left( 2\,t-1 \right) \left( 4\,t-1
\right)
$ | 1 | 0 | Maple | $u$, then $v$ | 13.6 | 0.161 | 4 | 6 | 4 | 214 | 23 / 88 | 22 / 86 | 29 / 32 | 11 | 113354 | 7 / 44 | 7 / 70 | 14 / 12 | 6 | 8880 | ${t}^{3} \left( 1+4\,t \right) \left( 2\,t-1 \right) \left( 4\,t-1
\right)
$ | 1 | 1 | Maple | $v$, then $u$ | 5.05 | 0.084 | 4 | 6 | 4 | 216 | 6 / 7 | 12 / 12 | 4 / 4 | 3 | 3466 | 45 / 91 | 83 / 93 | 27 / 75 | 18 | 296204 | ${t}^{3} \left( 1+4\,t \right) \left( 4\,t+3 \right) \left( 4\,t-1
\right)
$ | 1 | 1 | Maple | $u$, then $v$ | 16.6 | 0.479 | 4 | 6 | 4 | 216 | 24 / 88 | 26 / 81 | 26 / 23 | 11 | 106907 | 10 / 44 | 7 / 70 | 15 / 12 | 5 | 12635 | ${t}^{3} \left( 1+4\,t \right) \left( 4\,t+3 \right) \left( 4\,t-1
\right)
$ | 1 | 1 | Mathematica | $u$, then $v$ | 122 | n.a. | 4 | 6 | 4 | 216 | 7 / 7 | 6 / 7 | 5 / 6 | 6 | 2752 | 9 / 9 | 8 / 10 | 8 / 9 | 7 | 5181 | ${t}^{3} \left( 1+4\,t \right) \left( 4\,t+3 \right) \left( 4\,t-1
\right)
$ | 1 | 1 | Mathematica | $v$, then $u$ | 7.93 | n.a. | 4 | 6 | 4 | 216 | 7 / 7 | 6 / 7 | 5 / 6 | 6 | 2752 | 9 / 9 | 8 / 10 | 8 / 9 | 7 | 5181 | ${t}^{3} \left( 1+4\,t \right) \left( 4\,t+3 \right) \left( 4\,t-1
\right)
$ | x | 0 | Mathematica | $u$, then $v$ | 2220 | n.a. | 6 | 10 | 7 | 2480 | 36 / 34 | 11 / 12 | 11 / 10 | 27 | 942101 | 38 / 36 | 11 / 14 | 12 / 14 | 28 | 1011969 | ${t}^{4} \left( 4\,t-1 \right) \left( 1+4\,t \right) \left( t{x}^{2}+2
\,tx+t-x \right) \left( t{x}^{2}-2\,tx+t-x \right) \left( 3\,{t}^{2}{
x}^{4}+34\,{t}^{2}{x}^{2}-9\,t{x}^{3}+3\,{t}^{2}-9\,tx+5\,{x}^{2}
\right)
$ | 0 | y | Mathematica | $u$, then $v$ | 1710 | n.a. | 5 | 8 | 5 | 560 | 30 / 30 | 14 / 13 | 10 / 10 | 27 | 1998626 | 30 / 30 | 11 / 9 | 10 / 10 | 26 | 1205581 | ${t}^{4} \left( 4\,t-1 \right) \left( 1+4\,t \right) \left( 4\,{t}^{2}
{y}^{2}+8\,{t}^{2}y+4\,{t}^{2}-y \right)
$ |