12a
1051
(K12a
1051
)
A knot diagram
1
Linearized knot diagam
4 7 9 10 11 12 3 1 2 5 6 8
Solving Sequence
5,10
11 6 12 7
2,4
1 9 3 8
c
10
c
5
c
11
c
6
c
4
c
1
c
9
c
3
c
8
c
2
, c
7
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h3.30422 × 10
51
u
68
+ 3.51426 × 10
52
u
67
+ ··· + 1.74141 × 10
53
b − 1.35897 × 10
53
,
− 7.04019 × 10
53
u
68
+ 7.16957 × 10
53
u
67
+ ··· + 1.74141 × 10
53
a − 5.55666 × 10
54
, u
69
− u
68
+ ··· + 16u + 1i
I
u
2
= h−u
12
+ 9u
10
− 30u
8
− u
7
+ 45u
6
+ 5u
5
− 29u
4
− 7u
3
+ 6u
2
+ b + 2u,
− u
12
+ 9u
10
− 30u
8
− 2u
7
+ 45u
6
+ 11u
5
− 29u
4
− 18u
3
+ 5u
2
+ a + 8u + 2,
u
13
− 10u
11
+ 38u
9
+ u
8
− 68u
7
− 6u
6
+ 57u
5
+ 11u
4
− 18u
3
− 6u
2
+ 1i
* 2 irreducible components of dim
C
= 0, with total 82 representations.
1
The image of knot diagram is generated by the software “Draw programme” developed by An-
drew Bartholomew(http://www.layer8.co.uk/maths/draw/index.htm#Running-draw), where we modi-
fied some parts for our purpose(https://github.com/CATsTAILs/LinksPainter).
2
All coefficients of polynomials are rational numbers. But the coefficients are sometimes approximated
in decimal forms when there is not enough margin.
1
I.
I
u
1
= h3.30×10
51
u
68
+3.51×10
52
u
67
+· · ·+1.74×10
53
b−1.36×10
53
, −7.04×
10
53
u
68
+7.17×10
53
u
67
+· · ·+1.74×10
53
a−5.56×10
54
, u
69
−u
68
+· · ·+16u+1i
(i) Arc colorings
a
5
=
0
u
a
10
=
1
0
a
11
=
1
u
2
a
6
=
−u
−u
3
+ u
a
12
=
−u
2
+ 1
−u
4
+ 2u
2
a
7
=
u
3
− 2u
u
5
− 3u
3
+ u
a
2
=
4.04281u
68
− 4.11711u
67
+ ··· + 265.966u + 31.9090
−0.0189744u
68
− 0.201805u
67
+ ··· + 5.33487u + 0.780384
a
4
=
u
u
a
1
=
3.79040u
68
− 5.00863u
67
+ ··· + 272.372u + 32.0554
−0.271387u
68
− 1.09333u
67
+ ··· + 11.7404u + 0.926866
a
9
=
2.63776u
68
− 3.52798u
67
+ ··· + 242.870u + 30.7339
−0.418007u
68
− 0.165084u
67
+ ··· + 29.6232u + 2.50226
a
3
=
3.93419u
68
− 4.98353u
67
+ ··· + 286.492u + 33.7569
−0.370235u
68
− 0.800602u
67
+ ··· + 8.34849u + 0.696586
a
8
=
3.11909u
68
− 4.03119u
67
+ ··· + 270.222u + 39.5046
−0.648080u
68
− 0.0452525u
67
+ ··· + 36.0775u + 4.08566
(ii) Obstruction class = −1
(iii) Cusp Shapes = 6.92150u
68
− 8.70612u
67
+ ··· + 422.323u + 41.9072
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
69
− 7u
68
+ ··· + 6887u − 689
c
2
, c
7
u
69
− 18u
67
+ ··· − u − 1
c
3
u
69
− u
68
+ ··· + 8u + 1
c
4
, c
5
, c
6
c
10
, c
11
u
69
+ u
68
+ ··· + 16u − 1
c
8
, c
12
u
69
− 26u
67
+ ··· − 45u + 29
c
9
u
69
+ 3u
68
+ ··· + 280u − 139
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
69
− 31y
68
+ ··· + 26893057y −474721
c
2
, c
7
y
69
− 36y
68
+ ··· + 25y −1
c
3
y
69
+ y
68
+ ··· + 16y −1
c
4
, c
5
, c
6
c
10
, c
11
y
69
− 95y
68
+ ··· + 96y −1
c
8
, c
12
y
69
− 52y
68
+ ··· + 25341y −841
c
9
y
69
+ 17y
68
+ ··· − 608816y −19321
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.970523 + 0.108303I
a = −0.854816 + 1.050670I
b = −0.104041 + 0.201502I
−1.13069 − 0.85474I 0
u = 0.970523 − 0.108303I
a = −0.854816 − 1.050670I
b = −0.104041 − 0.201502I
−1.13069 + 0.85474I 0
u = 1.033950 + 0.073948I
a = −0.51792 − 1.53260I
b = −1.21908 − 1.48587I
−5.24202 − 3.64411I 0
u = 1.033950 − 0.073948I
a = −0.51792 + 1.53260I
b = −1.21908 + 1.48587I
−5.24202 + 3.64411I 0
u = −0.960213
a = 0.604404
b = −1.23574
−0.118191 0
u = −0.922631 + 0.233585I
a = −0.75796 + 1.45099I
b = 0.403514 + 0.999659I
−3.71809 + 2.97804I 0
u = −0.922631 − 0.233585I
a = −0.75796 − 1.45099I
b = 0.403514 − 0.999659I
−3.71809 − 2.97804I 0
u = −0.917023 + 0.212783I
a = 0.08094 + 1.94171I
b = 0.374010 + 0.305925I
−2.30574 + 5.04357I 0
u = −0.917023 − 0.212783I
a = 0.08094 − 1.94171I
b = 0.374010 − 0.305925I
−2.30574 − 5.04357I 0
u = −0.900768 + 0.078956I
a = −0.69952 + 1.99893I
b = 0.389187 + 1.261770I
−3.54279 + 2.91613I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.900768 − 0.078956I
a = −0.69952 − 1.99893I
b = 0.389187 − 1.261770I
−3.54279 − 2.91613I 0
u = 1.093250 + 0.272776I
a = 0.19450 − 1.67030I
b = 1.09950 − 1.25535I
−1.31596 − 6.29242I 0
u = 1.093250 − 0.272776I
a = 0.19450 + 1.67030I
b = 1.09950 + 1.25535I
−1.31596 + 6.29242I 0
u = 1.044710 + 0.433897I
a = 0.686500 + 0.770259I
b = −0.021208 + 1.131490I
−5.90299 − 3.46414I 0
u = 1.044710 − 0.433897I
a = 0.686500 − 0.770259I
b = −0.021208 − 1.131490I
−5.90299 + 3.46414I 0
u = 1.127140 + 0.222152I
a = 0.52291 + 1.41806I
b = −0.862853 + 0.977792I
−8.33525 − 5.88314I 0
u = 1.127140 − 0.222152I
a = 0.52291 − 1.41806I
b = −0.862853 − 0.977792I
−8.33525 + 5.88314I 0
u = 0.480235 + 0.689334I
a = −0.568720 + 0.491028I
b = −0.450178 − 0.761446I
−1.51842 + 4.43214I 0
u = 0.480235 − 0.689334I
a = −0.568720 − 0.491028I
b = −0.450178 + 0.761446I
−1.51842 − 4.43214I 0
u = −1.115900 + 0.395594I
a = 0.24502 − 1.47620I
b = −1.00488 − 1.21839I
−5.66016 + 12.60390I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.115900 − 0.395594I
a = 0.24502 + 1.47620I
b = −1.00488 + 1.21839I
−5.66016 − 12.60390I 0
u = 0.337583 + 0.691942I
a = −0.659876 − 0.083894I
b = 0.778722 − 0.958452I
−1.13098 − 8.91114I −4.00000 + 8.49340I
u = 0.337583 − 0.691942I
a = −0.659876 + 0.083894I
b = 0.778722 + 0.958452I
−1.13098 + 8.91114I −4.00000 − 8.49340I
u = −1.278510 + 0.014060I
a = −0.530795 − 0.268501I
b = −1.083720 − 0.300872I
−7.37922 − 0.04313I 0
u = −1.278510 − 0.014060I
a = −0.530795 + 0.268501I
b = −1.083720 + 0.300872I
−7.37922 + 0.04313I 0
u = 0.655716 + 0.240239I
a = −0.291654 − 0.184454I
b = 0.966260 + 0.067900I
−1.031510 + 0.312804I −8.34035 + 1.35782I
u = 0.655716 − 0.240239I
a = −0.291654 + 0.184454I
b = 0.966260 − 0.067900I
−1.031510 − 0.312804I −8.34035 − 1.35782I
u = −0.165954 + 0.649062I
a = 0.003498 − 0.456639I
b = −0.255335 + 0.985701I
−2.17679 − 0.26649I −8.08515 − 0.77789I
u = −0.165954 − 0.649062I
a = 0.003498 + 0.456639I
b = −0.255335 − 0.985701I
−2.17679 + 0.26649I −8.08515 + 0.77789I
u = −0.468363 + 0.413877I
a = −1.59539 + 0.60353I
b = 0.496715 + 0.910892I
−3.36016 + 3.70048I −9.81035 − 6.09222I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.468363 − 0.413877I
a = −1.59539 − 0.60353I
b = 0.496715 − 0.910892I
−3.36016 − 3.70048I −9.81035 + 6.09222I
u = −1.337030 + 0.327168I
a = 0.464853 − 0.302329I
b = −0.078909 − 0.591498I
−7.29700 − 0.75484I 0
u = −1.337030 − 0.327168I
a = 0.464853 + 0.302329I
b = −0.078909 + 0.591498I
−7.29700 + 0.75484I 0
u = 0.607599
a = −0.226329
b = 0.516562
−1.12956 −8.41060
u = −0.314959 + 0.499815I
a = 0.599510 − 0.307709I
b = −0.951155 − 0.796839I
3.10870 + 3.65525I −0.44555 − 7.33044I
u = −0.314959 − 0.499815I
a = 0.599510 + 0.307709I
b = −0.951155 + 0.796839I
3.10870 − 3.65525I −0.44555 + 7.33044I
u = −0.371311 + 0.394330I
a = 0.97740 + 1.13892I
b = 0.739429 − 0.343891I
2.88878 − 0.59529I 0.335042 − 1.258913I
u = −0.371311 − 0.394330I
a = 0.97740 − 1.13892I
b = 0.739429 + 0.343891I
2.88878 + 0.59529I 0.335042 + 1.258913I
u = 1.51600
a = −0.972604
b = −0.823418
−3.18079 0
u = 0.083281 + 0.453009I
a = 1.35995 + 1.51466I
b = −0.724939 + 0.127054I
0.70817 − 2.77944I −0.09198 + 6.13173I
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.083281 − 0.453009I
a = 1.35995 − 1.51466I
b = −0.724939 − 0.127054I
0.70817 + 2.77944I −0.09198 − 6.13173I
u = 0.195749 + 0.351698I
a = 1.169440 − 0.099926I
b = −0.278714 + 0.641393I
−0.314860 − 1.014580I −5.61645 + 6.17705I
u = 0.195749 − 0.351698I
a = 1.169440 + 0.099926I
b = −0.278714 − 0.641393I
−0.314860 + 1.014580I −5.61645 − 6.17705I
u = −1.66089
a = −0.179607
b = −1.14488
−9.16005 0
u = 1.70441 + 0.07129I
a = 0.22559 + 1.66331I
b = −0.494925 + 1.140110I
−13.04310 − 4.25845I 0
u = 1.70441 − 0.07129I
a = 0.22559 − 1.66331I
b = −0.494925 − 1.140110I
−13.04310 + 4.25845I 0
u = 1.70688 + 0.04723I
a = −0.15217 + 1.71603I
b = −0.216141 + 0.574577I
−11.67470 − 6.01387I 0
u = 1.70688 − 0.04723I
a = −0.15217 − 1.71603I
b = −0.216141 − 0.574577I
−11.67470 + 6.01387I 0
u = 1.71727 + 0.01724I
a = −0.14976 + 2.06323I
b = −0.76930 + 1.55036I
−13.04020 − 3.28190I 0
u = 1.71727 − 0.01724I
a = −0.14976 − 2.06323I
b = −0.76930 − 1.55036I
−13.04020 + 3.28190I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.72043 + 0.01720I
a = 0.319134 + 1.230620I
b = −0.152732 + 0.585019I
−10.78490 + 1.28215I 0
u = −1.72043 − 0.01720I
a = 0.319134 − 1.230620I
b = −0.152732 − 0.585019I
−10.78490 − 1.28215I 0
u = 1.72209
a = 0.327354
b = 1.49160
−9.78852 0
u = −1.73799 + 0.01931I
a = 1.08020 − 1.84615I
b = 1.55088 − 1.72505I
−15.2509 + 4.0310I 0
u = −1.73799 − 0.01931I
a = 1.08020 + 1.84615I
b = 1.55088 + 1.72505I
−15.2509 − 4.0310I 0
u = −1.74421 + 0.11729I
a = −0.28874 + 1.41097I
b = 0.263478 + 1.336250I
−15.7999 + 5.7580I 0
u = −1.74421 − 0.11729I
a = −0.28874 − 1.41097I
b = 0.263478 − 1.336250I
−15.7999 − 5.7580I 0
u = −1.75104 + 0.07156I
a = −0.67507 − 1.98321I
b = −1.25654 − 1.57527I
−11.53150 + 7.74332I 0
u = −1.75104 − 0.07156I
a = −0.67507 + 1.98321I
b = −1.25654 + 1.57527I
−11.53150 − 7.74332I 0
u = −1.75568 + 0.05812I
a = 0.13855 + 1.50571I
b = 1.11222 + 1.06448I
−18.7148 + 7.0816I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.75568 − 0.05812I
a = 0.13855 − 1.50571I
b = 1.11222 − 1.06448I
−18.7148 − 7.0816I 0
u = 1.75461 + 0.10664I
a = 0.32391 − 1.84018I
b = 1.17322 − 1.41872I
−15.8746 − 14.7349I 0
u = 1.75461 − 0.10664I
a = 0.32391 + 1.84018I
b = 1.17322 + 1.41872I
−15.8746 + 14.7349I 0
u = 1.79142 + 0.04126I
a = 0.376682 − 0.961683I
b = 0.885083 − 0.907630I
−18.8425 − 0.5002I 0
u = 1.79142 − 0.04126I
a = 0.376682 + 0.961683I
b = 0.885083 + 0.907630I
−18.8425 + 0.5002I 0
u = −0.153507 + 0.114938I
a = −3.62976 − 1.49255I
b = 0.550095 − 1.156120I
−1.43627 + 2.95426I −9.8137 − 11.3357I
u = −0.153507 − 0.114938I
a = −3.62976 + 1.49255I
b = 0.550095 + 1.156120I
−1.43627 − 2.95426I −9.8137 + 11.3357I
u = 1.80975
a = 1.20100
b = 1.65732
−18.8871 0
u = −0.117170
a = 11.4529
b = 0.823225
2.72284 13.1210
11
II. I
u
2
=
h−u
12
+9u
10
+· · ·+b+2u, −u
12
+9u
10
+· · ·+a+2, u
13
−10u
11
+· · ·−6u
2
+1i
(i) Arc colorings
a
5
=
0
u
a
10
=
1
0
a
11
=
1
u
2
a
6
=
−u
−u
3
+ u
a
12
=
−u
2
+ 1
−u
4
+ 2u
2
a
7
=
u
3
− 2u
u
5
− 3u
3
+ u
a
2
=
u
12
− 9u
10
+ 30u
8
+ 2u
7
− 45u
6
− 11u
5
+ 29u
4
+ 18u
3
− 5u
2
− 8u − 2
u
12
− 9u
10
+ 30u
8
+ u
7
− 45u
6
− 5u
5
+ 29u
4
+ 7u
3
− 6u
2
− 2u
a
4
=
u
u
a
1
=
u
12
− 9u
10
+ ··· − 8u − 2
u
12
− 9u
10
− u
9
+ 30u
8
+ 7u
7
− 45u
6
− 16u
5
+ 28u
4
+ 13u
3
− 4u
2
− 2u
a
9
=
−u
12
+ 10u
10
− 37u
8
− u
7
+ 61u
6
+ 6u
5
− 41u
4
− 11u
3
+ 5u
2
+ 5u + 3
−u
3
+ 2u
a
3
=
u
12
− 9u
10
+ ··· − 10u − 3
u
12
− 9u
10
+ 30u
8
+ u
7
− 45u
6
− 5u
5
+ 29u
4
+ 7u
3
− 6u
2
− u
a
8
=
−u
12
+ 10u
10
+ ··· + 11u + 4
u
11
− 8u
9
− u
8
+ 23u
7
+ 7u
6
− 28u
5
− 15u
4
+ 11u
3
+ 10u
2
+ 2u − 1
(ii) Obstruction class = 1
(iii) Cusp Shapes
= u
12
+ 5u
11
− 10u
10
− 44u
9
+ 41u
8
+ 143u
7
− 80u
6
− 210u
5
+ 62u
4
+ 133u
3
− 23u − 17
12
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
13
− 4u
11
+ ··· + 5u − 1
c
2
u
13
+ u
12
+ ··· + u + 1
c
3
u
13
− 2u
11
− u
10
− 2u
9
− 3u
8
+ u
6
+ u
5
+ 4u
4
+ u
3
− 1
c
4
, c
5
, c
6
u
13
− 10u
11
+ 38u
9
− u
8
− 68u
7
+ 6u
6
+ 57u
5
− 11u
4
− 18u
3
+ 6u
2
− 1
c
7
u
13
− u
12
+ ··· + u − 1
c
8
u
13
− u
12
+ ··· + u − 1
c
9
u
13
− u
10
− 4u
9
− u
8
− u
7
+ 3u
5
+ 2u
4
+ u
3
+ 2u
2
− 1
c
10
, c
11
u
13
− 10u
11
+ 38u
9
+ u
8
− 68u
7
− 6u
6
+ 57u
5
+ 11u
4
− 18u
3
− 6u
2
+ 1
c
12
u
13
+ u
12
+ ··· + u + 1
13
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
13
− 8y
12
+ ··· + 9y −1
c
2
, c
7
y
13
− 13y
12
+ ··· + 13y −1
c
3
y
13
− 4y
12
+ 7y
10
− 9y
8
+ 6y
7
+ 19y
6
− 9y
5
− 20y
4
+ 3y
3
+ 8y
2
− 1
c
4
, c
5
, c
6
c
10
, c
11
y
13
− 20y
12
+ ··· + 12y −1
c
8
, c
12
y
13
− 13y
12
+ ··· + 13y −1
c
9
y
13
− 8y
11
− 3y
10
+ 20y
9
+ 9y
8
− 19y
7
− 6y
6
+ 9y
5
− 7y
3
+ 4y −1
14
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.900642 + 0.211290I
a = −0.89953 + 1.86106I
b = −0.037612 + 1.092140I
−3.44781 + 4.22361I −9.99869 − 7.63221I
u = −0.900642 − 0.211290I
a = −0.89953 − 1.86106I
b = −0.037612 − 1.092140I
−3.44781 − 4.22361I −9.99869 + 7.63221I
u = 0.835287
a = −1.01640
b = 1.04297
0.774317 −0.352240
u = 1.349780 + 0.188354I
a = −0.360972 + 0.236906I
b = −0.753544 + 0.428711I
−6.62178 + 0.41146I −4.17258 − 0.90590I
u = 1.349780 − 0.188354I
a = −0.360972 − 0.236906I
b = −0.753544 − 0.428711I
−6.62178 − 0.41146I −4.17258 + 0.90590I
u = −1.48165
a = 1.01148
b = 0.537900
−3.72558 −14.4700
u = −0.246497 + 0.330591I
a = 0.528174 − 0.970691I
b = 0.379862 + 0.838529I
−1.26239 − 2.39614I −4.80417 − 1.14749I
u = −0.246497 − 0.330591I
a = 0.528174 + 0.970691I
b = 0.379862 − 0.838529I
−1.26239 + 2.39614I −4.80417 + 1.14749I
u = 0.333287
a = −4.29907
b = −0.793443
2.47324 −19.8810
u = −1.68760
a = 0.0537118
b = −1.19628
−8.25610 −1.28480
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.70777 + 0.05845I
a = 0.29300 + 1.93652I
b = −0.157231 + 1.253940I
−12.79170 − 5.30924I −11.13586 + 5.88346I
u = 1.70777 − 0.05845I
a = 0.29300 − 1.93652I
b = −0.157231 − 1.253940I
−12.79170 + 5.30924I −11.13586 − 5.88346I
u = −1.82016
a = 1.12892
b = 1.54590
−18.6855 11.2100
16
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
13
− 4u
11
+ ··· + 5u − 1)(u
69
− 7u
68
+ ··· + 6887u − 689)
c
2
(u
13
+ u
12
+ ··· + u + 1)(u
69
− 18u
67
+ ··· − u − 1)
c
3
(u
13
− 2u
11
− u
10
− 2u
9
− 3u
8
+ u
6
+ u
5
+ 4u
4
+ u
3
− 1)
· (u
69
− u
68
+ ··· + 8u + 1)
c
4
, c
5
, c
6
(u
13
− 10u
11
+ 38u
9
− u
8
− 68u
7
+ 6u
6
+ 57u
5
− 11u
4
− 18u
3
+ 6u
2
− 1)
· (u
69
+ u
68
+ ··· + 16u − 1)
c
7
(u
13
− u
12
+ ··· + u − 1)(u
69
− 18u
67
+ ··· − u − 1)
c
8
(u
13
− u
12
+ ··· + u − 1)(u
69
− 26u
67
+ ··· − 45u + 29)
c
9
(u
13
− u
10
− 4u
9
− u
8
− u
7
+ 3u
5
+ 2u
4
+ u
3
+ 2u
2
− 1)
· (u
69
+ 3u
68
+ ··· + 280u − 139)
c
10
, c
11
(u
13
− 10u
11
+ 38u
9
+ u
8
− 68u
7
− 6u
6
+ 57u
5
+ 11u
4
− 18u
3
− 6u
2
+ 1)
· (u
69
+ u
68
+ ··· + 16u − 1)
c
12
(u
13
+ u
12
+ ··· + u + 1)(u
69
− 26u
67
+ ··· − 45u + 29)
17
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
13
− 8y
12
+ ··· + 9y −1)(y
69
− 31y
68
+ ··· + 2.68931 × 10
7
y −474721)
c
2
, c
7
(y
13
− 13y
12
+ ··· + 13y −1)(y
69
− 36y
68
+ ··· + 25y −1)
c
3
(y
13
− 4y
12
+ 7y
10
− 9y
8
+ 6y
7
+ 19y
6
− 9y
5
− 20y
4
+ 3y
3
+ 8y
2
− 1)
· (y
69
+ y
68
+ ··· + 16y −1)
c
4
, c
5
, c
6
c
10
, c
11
(y
13
− 20y
12
+ ··· + 12y −1)(y
69
− 95y
68
+ ··· + 96y −1)
c
8
, c
12
(y
13
− 13y
12
+ ··· + 13y −1)(y
69
− 52y
68
+ ··· + 25341y −841)
c
9
(y
13
− 8y
11
− 3y
10
+ 20y
9
+ 9y
8
− 19y
7
− 6y
6
+ 9y
5
− 7y
3
+ 4y −1)
· (y
69
+ 17y
68
+ ··· − 608816y −19321)
18
