10
113
(K10a
36
)
1
Arc Sequences
4 7 6 8 1 10 9 5 2 3
Solving Sequence
3,10 1,7
2 6 4 5 9 8
c
10
c
2
c
6
c
3
c
5
c
9
c
7
c
1
, c
4
, c
8
Representation Ideals
I =
5
\
i=1
I
u
i
I
u
1
= hu
2
u + 1, b, a ui
I
u
2
= hu
3
+ u
2
1, a + u + 1, u
2
+ b 1i
I
u
3
= hu
4
u
3
+ 1, u
2
+ a + u, u
2
+ b 1i
I
u
4
= hu
26
+ 3u
24
+ ··· + 2u + 1, 2.08948 × 10
18
u
25
2.58092 × 10
17
u
24
+ ··· + 3.26704 × 10
19
b + 4.47222 × 10
19
,
8.38515 × 10
18
u
25
+ 2.22348 × 10
19
u
24
+ ··· + 3.26704 × 10
19
a + 5.90553 × 10
19
i
I
u
5
= hu
38
2u
37
+ ··· 109u + 11,
4.62930 × 10
70
u
37
+ 1.37098 × 10
71
u
36
+ ··· + 3.02448 × 10
71
b + 7.78840 × 10
71
,
6.64552 × 10
71
u
37
9.81622 × 10
71
u
36
+ ··· + 3.32693 × 10
72
a 4.68072 × 10
73
i
There are 5 irreducible components with 73 representations.
1
The knot diagram image is adapter from “C. Livingston and A. H. Moore, KnotInfo: Table of Knot
Invariants, http://www.indiana.edu/ knotinfo”
1
I. I
u
1
= hu
2
u + 1, b, a ui
(i) Arc colorings
a
3
=
1
0
a
10
=
u
0
a
1
=
u
0
a
7
=
0
u
a
2
=
1
u + 1
a
6
=
1
u
a
4
=
u + 1
u + 1
a
5
=
0
u
a
9
=
u 1
u 1
a
8
=
u 1
2u 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 9
2
(iv) Complex Volumes and Cusp Shapes
Solution to I
u
1
1(vol +
1CS) Cusp shape
u = 0.500000 0.866025I
a = 0.500000 0.866025I
b = 0
3.28987 9.00000
u = 0.500000 + 0.866025I
a = 0.500000 + 0.866025I
b = 0
3.28987 9.00000
3
II. I
u
2
= hu
3
+ u
2
1, a + u + 1, u
2
+ b 1i
(i) Arc colorings
a
3
=
1
0
a
10
=
u 1
u
2
+ 1
a
1
=
u
2
u
u
2
+ 1
a
7
=
0
u
a
2
=
1
u
2
a
6
=
u
2
u 1
u
2
+ u
a
4
=
u
2
+ 2u + 2
u 1
a
5
=
u
2
u
1
a
9
=
u
2
u 1
u
a
8
=
u
2
2u 2
u
2
+ 2u
(ii) Obstruction class = 1
(iii) Cusp Shapes = 3u
2
11u 10
4
(iv) Complex Volumes and Cusp Shapes
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 0.877439 0.744862I
a = 0.122561 + 0.744862I
b = 0.78492 1.30714I
1.37919 2.82812I 0.99341 + 4.27206I
u = 0.877439 + 0.744862I
a = 0.122561 0.744862I
b = 0.78492 + 1.30714I
1.37919 + 2.82812I 0.99341 4.27206I
u = 0.754878
a = 1.75488
b = 0.430160
2.75839 20.0132
5
III. I
u
3
= hu
4
u
3
+ 1, u
2
+ a + u, u
2
+ b 1i
(i) Arc colorings
a
3
=
1
0
a
10
=
u
2
u
u
2
+ 1
a
1
=
u + 1
u
2
+ 1
a
7
=
0
u
a
2
=
1
u
2
a
6
=
u 1
u
3
+ u
2
a
4
=
u
3
+ u
2
u
2
u
a
5
=
u
2
1
u
2
u
a
9
=
u
u
3
u
2
a
8
=
u
3
0
(ii) Obstruction class = 1
(iii) Cusp Shapes = 2u
3
+ 6u
2
3u 4
6
(iv) Complex Volumes and Cusp Shapes
Solution to I
u
3
1(vol +
1CS) Cusp shape
u = 0.518913 0.666610I
a = 0.343815 + 1.358435I
b = 1.175098 0.691825I
1.43949 4.22398I 2.38978 + 5.66623I
u = 0.518913 + 0.666610I
a = 0.343815 1.358435I
b = 1.175098 + 0.691825I
1.43949 + 4.22398I 2.38978 5.66623I
u = 1.018913 0.602565I
a = 0.343815 0.625358I
b = 0.324902 + 1.227923I
0.20545 + 7.54387I 3.11022 8.87572I
u = 1.018913 + 0.602565I
a = 0.343815 + 0.625358I
b = 0.324902 1.227923I
0.20545 7.54387I 3.11022 + 8.87572I
7
IV. I
u
4
=
hu
26
+ 3u
24
+ · · · +2u + 1, 2.09 × 10
18
u
25
2.58 × 10
17
u
24
+ · · · + 3.27 × 10
19
b +
4.47× 10
19
, 8.39×10
18
u
25
+2.22 × 10
19
u
24
+· · · +3.27 × 10
19
a + 5.91 ×10
19
i
(i) Arc colorings
a
3
=
1
0
a
10
=
0.256659u
25
0.680581u
24
+ ··· + 3.94614u 1.80761
0.0639564u
25
+ 0.00789987u
24
+ ··· 0.313001u 1.36889
a
1
=
0.192703u
25
0.672681u
24
+ ··· + 3.63314u 3.17650
0.0639564u
25
+ 0.00789987u
24
+ ··· 0.313001u 1.36889
a
7
=
0
u
a
2
=
1
u
2
a
6
=
1.42499u
25
+ 0.372889u
24
+ ··· 10.4135u 2.87982
0.680581u
25
+ 0.107028u
24
+ ··· 2.32093u 0.256659
a
4
=
0.711701u
25
+ 0.736679u
24
+ ··· 0.763417u + 5.04112
0.372889u
25
+ 0.433512u
24
+ ··· 0.0298444u + 1.42499
a
5
=
2.09767u
25
+ 0.499273u
24
+ ··· 13.9754u 3.07253
0.672681u
25
+ 0.126384u
24
+ ··· 3.56191u 0.192703
a
9
=
0.299731u
25
0.757454u
24
+ ··· + 4.73765u 2.49592
0.0184802u
25
0.0430479u
24
+ ··· 0.423674u 1.44576
a
8
=
1.96176u
25
+ 0.415679u
24
+ ··· 16.5180u 4.20135
0.983898u
25
+ 0.0563061u
24
+ ··· 3.59319u 0.276297
(ii) Obstruction class = 1
(iii) Cusp Shapes =
63656280343415714705
32670363981352566673
u
25
+
17212180266005913506
32670363981352566673
u
24
+ ···
224534007236589542280
32670363981352566673
u
327044583770662035253
32670363981352566673
8
(iv) Complex Volumes and Cusp Shapes
Solution to I
u
4
1(vol +
1CS) Cusp shape
u = 0.958405 0.564440I
a = 0.110913 + 0.546879I
b = 0.64380 1.75632I
0.95700 7.52275I 10.71557 + 8.78919I
u = 0.958405 + 0.564440I
a = 0.110913 0.546879I
b = 0.64380 + 1.75632I
0.95700 + 7.52275I 10.71557 8.78919I
u = 0.86309 1.22809I
a = 0.284013 0.994901I
b = 1.26531 + 0.92939I
2.62082 10.45440I 1.93774 + 5.95159I
u = 0.86309 + 1.22809I
a = 0.284013 + 0.994901I
b = 1.26531 0.92939I
2.62082 + 10.45440I 1.93774 5.95159I
u = 0.739194 0.239104I
a = 0.031277 + 0.982631I
b = 0.967641 1.016646I
4.93342 1.67636I 14.6461 + 4.2929I
u = 0.739194 + 0.239104I
a = 0.031277 0.982631I
b = 0.967641 + 1.016646I
4.93342 + 1.67636I 14.6461 4.2929I
u = 0.686275 0.867659I
a = 0.847167 + 0.342621I
b = 0.014473 0.410285I
1.92544 + 2.11547I 8.52748 4.72090I
u = 0.686275 + 0.867659I
a = 0.847167 0.342621I
b = 0.014473 + 0.410285I
1.92544 2.11547I 8.52748 + 4.72090I
u = 0.585521 0.630291I
a = 0.21462 1.93408I
b = 1.056678 + 0.510753I
1.49747 5.09068I 3.0367 + 14.8892I
u = 0.585521 + 0.630291I
a = 0.21462 + 1.93408I
b = 1.056678 0.510753I
1.49747 + 5.09068I 3.0367 14.8892I
9
Solution to I
u
4
1(vol +
1CS) Cusp shape
u = 0.17865 1.47670I
a = 0.776288 + 0.057340I
b = 0.281192 0.094635I
1.56544 2.09555I 7.86102 + 3.20965I
u = 0.17865 + 1.47670I
a = 0.776288 0.057340I
b = 0.281192 + 0.094635I
1.56544 + 2.09555I 7.86102 3.20965I
u = 0.162548 0.356828I
a = 3.05619 0.78755I
b = 1.306830 + 0.079067I
0.13330 3.14853I 10.05225 + 4.78603I
u = 0.162548 + 0.356828I
a = 3.05619 + 0.78755I
b = 1.306830 0.079067I
0.13330 + 3.14853I 10.05225 4.78603I
u = 0.090156 1.024104I
a = 0.450473 0.045262I
b = 1.197703 + 0.220817I
2.92221 + 2.66541I 1.40924 2.72285I
u = 0.090156 + 1.024104I
a = 0.450473 + 0.045262I
b = 1.197703 0.220817I
2.92221 2.66541I 1.40924 + 2.72285I
u = 0.460493 0.566215I
a = 0.742937 0.548920I
b = 0.129304 + 0.643314I
0.924615 + 1.060120I 5.32469 4.59251I
u = 0.460493 + 0.566215I
a = 0.742937 + 0.548920I
b = 0.129304 0.643314I
0.924615 1.060120I 5.32469 + 4.59251I
u = 0.813146 0.019831I
a = 1.13436 + 0.97641I
b = 0.493624 0.435869I
2.18699 0.53885I 10.45014 + 2.98932I
u = 0.813146 + 0.019831I
a = 1.13436 0.97641I
b = 0.493624 + 0.435869I
2.18699 + 0.53885I 10.45014 2.98932I
10
Solution to I
u
4
1(vol +
1CS) Cusp shape
u = 0.821068 0.625736I
a = 0.228963 0.544758I
b = 0.34430 + 1.56008I
0.16560 + 2.24390I 7.60792 3.01225I
u = 0.821068 + 0.625736I
a = 0.228963 + 0.544758I
b = 0.34430 1.56008I
0.16560 2.24390I 7.60792 + 3.01225I
u = 0.97188 1.31522I
a = 0.237350 + 0.919945I
b = 1.26295 1.01918I
0.9109 + 16.4735I 4.11166 9.70500I
u = 0.97188 + 1.31522I
a = 0.237350 0.919945I
b = 1.26295 + 1.01918I
0.9109 16.4735I 4.11166 + 9.70500I
u = 1.016936 0.884943I
a = 0.030199 + 1.147218I
b = 1.022930 0.871070I
4.53791 + 8.53907I 8.63796 7.50515I
u = 1.016936 + 0.884943I
a = 0.030199 1.147218I
b = 1.022930 + 0.871070I
4.53791 8.53907I 8.63796 + 7.50515I
11
V. I
u
5
=
hu
38
2u
37
+· · ·109u+11, 4.63×10
70
u
37
+1.37×10
71
u
36
+· · ·+3.02×10
71
b+
7.79 × 10
71
, 6.65 × 10
71
u
37
9.82 × 10
71
u
36
+ · · · + 3.33 × 10
72
a 4.68 × 10
73
i
(i) Arc colorings
a
3
=
1
0
a
10
=
0.199749u
37
+ 0.295053u
36
+ ··· + 32.0946u + 14.0692
0.153061u
37
0.453293u
36
+ ··· + 25.0291u 2.57512
a
1
=
0.0466886u
37
0.158240u
36
+ ··· + 57.1237u + 11.4941
0.153061u
37
0.453293u
36
+ ··· + 25.0291u 2.57512
a
7
=
0
u
a
2
=
1
u
2
a
6
=
0.182527u
37
0.603747u
36
+ ··· + 17.7615u 30.9850
0.0435977u
37
0.225541u
36
+ ··· + 27.6951u 1.98391
a
4
=
0.0193942u
37
0.0220594u
36
+ ··· + 52.8728u + 22.1056
0.0783042u
37
+ 0.0834136u
36
+ ··· + 6.74309u 1.73076
a
5
=
0.323975u
37
0.581768u
36
+ ··· 21.5058u 6.06441
0.166633u
37
0.188781u
36
+ ··· 37.9966u + 4.34275
a
9
=
0.0382548u
37
0.122537u
36
+ ··· + 47.9364u + 12.6430
0.220520u
37
0.662593u
36
+ ··· + 37.1171u 3.61573
a
8
=
0.200909u
37
0.381918u
36
+ ··· 41.5801u 24.0311
0.00763090u
37
+ 0.256562u
36
+ ··· 56.9704u + 6.53098
(ii) Obstruction class = 1
(iii) Cusp Shapes = 0.720948u
37
+ 1.68485u
36
+ ··· 48.4619u + 10.2609
12
(iv) Complex Volumes and Cusp Shapes
Solution to I
u
5
1(vol +
1CS) Cusp shape
u = 1.253839 0.297107I
a = 0.232413 + 0.620292I
b = 0.865146 1.042814I
0.09217 3.26203I 7.82857 + 4.58696I
u = 1.253839 + 0.297107I
a = 0.232413 0.620292I
b = 0.865146 + 1.042814I
0.09217 + 3.26203I 7.82857 4.58696I
u = 1.24065 1.30301I
a = 0.120903 + 0.589236I
b = 1.18917 1.13858I
2.32292 6.77576I 0.09240 + 8.89089I
u = 1.24065 + 1.30301I
a = 0.120903 0.589236I
b = 1.18917 + 1.13858I
2.32292 + 6.77576I 0.09240 8.89089I
u = 1.128930 0.237982I
a = 0.409666 0.425256I
b = 0.752606 + 0.874521I
0.10793 + 3.14909I 5.58222 3.79428I
u = 1.128930 + 0.237982I
a = 0.409666 + 0.425256I
b = 0.752606 0.874521I
0.10793 3.14909I 5.58222 + 3.79428I
u = 0.787302 1.164657I
a = 0.057443 0.791027I
b = 0.689008 + 0.139635I
4.26470 2.32942I 3.40004 + 3.00608I
u = 0.787302 + 1.164657I
a = 0.057443 + 0.791027I
b = 0.689008 0.139635I
4.26470 + 2.32942I 3.40004 3.00608I
u = 0.715200 0.943971I
a = 0.110589 + 1.282512I
b = 0.488744 1.038283I
1.59095 7.59815I 9.53397 + 8.95368I
u = 0.715200 + 0.943971I
a = 0.110589 1.282512I
b = 0.488744 + 1.038283I
1.59095 + 7.59815I 9.53397 8.95368I
13
Solution to I
u
5
1(vol +
1CS) Cusp shape
u = 0.488322 0.653949I
a = 0.66434 + 2.06238I
b = 0.378245 0.567353I
3.84277 0.76131I 13.4982 + 7.0538I
u = 0.488322 + 0.653949I
a = 0.66434 2.06238I
b = 0.378245 + 0.567353I
3.84277 + 0.76131I 13.4982 7.0538I
u = 0.317119 0.770978I
a = 1.48741 + 1.26875I
b = 0.687103 + 0.235969I
2.42247 8.22022I 0.13214 + 8.57000I
u = 0.317119 + 0.770978I
a = 1.48741 1.26875I
b = 0.687103 0.235969I
2.42247 + 8.22022I 0.13214 8.57000I
u = 0.007708 0.752058I
a = 0.62080 1.27491I
b = 1.18917 + 1.13858I
2.32292 + 6.77576I 0.09240 8.89089I
u = 0.007708 + 0.752058I
a = 0.62080 + 1.27491I
b = 1.18917 1.13858I
2.32292 6.77576I 0.09240 + 8.89089I
u = 0.014078 1.111601I
a = 0.654684 0.266519I
b = 1.211134 + 0.137559I
2.95026 + 2.66622I 1.58619 3.20879I
u = 0.014078 + 1.111601I
a = 0.654684 + 0.266519I
b = 1.211134 0.137559I
2.95026 2.66622I 1.58619 + 3.20879I
u = 0.049158 0.481460I
a = 0.96165 + 1.72351I
b = 1.23842 1.01885I
2.68628 1.90197I 1.62421 + 1.37993I
u = 0.049158 + 0.481460I
a = 0.96165 1.72351I
b = 1.23842 + 1.01885I
2.68628 + 1.90197I 1.62421 1.37993I
14
Solution to I
u
5
1(vol +
1CS) Cusp shape
u = 0.054797 0.921061I
a = 0.218220 + 0.270501I
b = 1.211134 + 0.137559I
2.95026 + 2.66622I 1.58619 3.20879I
u = 0.054797 + 0.921061I
a = 0.218220 0.270501I
b = 1.211134 0.137559I
2.95026 2.66622I 1.58619 + 3.20879I
u = 0.071606 0.809372I
a = 0.94200 1.61626I
b = 0.689008 0.139635I
4.26470 + 2.32942I 3.40004 3.00608I
u = 0.071606 + 0.809372I
a = 0.94200 + 1.61626I
b = 0.689008 + 0.139635I
4.26470 2.32942I 3.40004 + 3.00608I
u = 0.0873604
a = 18.9121
b = 0.494703
2.37666 7.11408
u = 0.521126 0.959893I
a = 0.248766 1.100115I
b = 0.865146 + 1.042814I
0.09217 + 3.26203I 7.82857 4.58696I
u = 0.521126 + 0.959893I
a = 0.248766 + 1.100115I
b = 0.865146 1.042814I
0.09217 3.26203I 7.82857 + 4.58696I
u = 0.551719 0.949796I
a = 0.368664 1.157224I
b = 0.752606 + 0.874521I
0.10793 + 3.14909I 5.58222 3.79428I
u = 0.551719 + 0.949796I
a = 0.368664 + 1.157224I
b = 0.752606 0.874521I
0.10793 3.14909I 5.58222 + 3.79428I
u = 0.96730 1.37620I
a = 0.205532 0.617961I
b = 1.23842 + 1.01885I
2.68628 + 1.90197I 1.62421 1.37993I
15
Solution to I
u
5
1(vol +
1CS) Cusp shape
u = 0.96730 + 1.37620I
a = 0.205532 + 0.617961I
b = 1.23842 1.01885I
2.68628 1.90197I 1.62421 + 1.37993I
u = 1.00452 1.35948I
a = 0.014256 + 0.618195I
b = 0.687103 0.235969I
2.42247 + 8.22022I 0.13214 8.57000I
u = 1.00452 + 1.35948I
a = 0.014256 0.618195I
b = 0.687103 + 0.235969I
2.42247 8.22022I 0.13214 + 8.57000I
u = 1.20461
a = 0.751024
b = 0.494703
2.37666 7.11408
u = 1.27043 1.23001I
a = 0.209357 + 0.169177I
b = 0.378245 0.567353I
3.84277 0.76131I 13.4982 + 7.0538I
u = 1.27043 + 1.23001I
a = 0.209357 0.169177I
b = 0.378245 + 0.567353I
3.84277 + 0.76131I 13.4982 7.0538I
u = 1.78834 0.44932I
a = 0.205634 + 0.356665I
b = 0.488744 1.038283I
1.59095 7.59815I 9.53397 + 8.95368I
u = 1.78834 + 0.44932I
a = 0.205634 0.356665I
b = 0.488744 + 1.038283I
1.59095 + 7.59815I 9.53397 8.95368I
16
VI. u-Polynomials
Crossings u-Polynomials at each crossings
c
1
, c
9
(u 1)
2
(u
3
u
2
+ 2u 1)(u
4
u
3
+ 2u
2
+ 1)(u
26
+ 4u
25
+ ··· 2u + 1)
(u
38
3u
37
+ ··· + 10u 1)
c
2
, c
5
(u
2
u + 1)(u
3
+ u
2
1)(u
4
u
3
+ 1)(u
26
+ 3u
24
+ ··· 2u + 1)
(u
38
+ 2u
37
+ ··· + 109u + 11)
c
3
, c
6
(u
2
u + 1)(u
3
u 1)(u
4
u + 1)(u
26
+ 2u
25
+ ··· + 2u + 1)
(u
38
+ 4u
37
+ ··· + 7u + 1)
c
4
(u 1)
2
(u
3
u 1)(u
4
+ u
3
+ 1)
(1 4u + 6u
2
+ u
3
14u
4
+ 10u
5
+ 18u
6
26u
7
9u
8
+ 36u
9
8u
10
29u
11
+ 19u
12
+ 14u
13
17u
14
2u
15
+ 9u
16
2u
17
2u
18
+ u
19
)
2
(u
26
+ 6u
25
+ ··· + 25u + 4)
c
7
(u 1)
2
(u
3
2u
2
+ u 1)(u
4
u
3
+ 2u
2
+ 1)
(1 + 4u + 16u
2
+ 53u
3
+ 166u
4
+ 388u
5
+ 734u
6
+ 1132u
7
+ 1483u
8
+ 1688u
9
+ 1702u
10
+ 1533u
11
+ 1231u
12
+ 870u
13
+ 531u
14
+ 272u
15
+ 113u
16
+ 36u
17
+ 8u
18
+ u
19
)
2
(u
26
+ 10u
25
+ ··· + 81u + 16)
c
8
(u + 1)
2
(u
3
u + 1)(u
4
u
3
+ 1)
(1 4u + 6u
2
+ u
3
14u
4
+ 10u
5
+ 18u
6
26u
7
9u
8
+ 36u
9
8u
10
29u
11
+ 19u
12
+ 14u
13
17u
14
2u
15
+ 9u
16
2u
17
2u
18
+ u
19
)
2
(u
26
+ 6u
25
+ ··· + 25u + 4)
c
10
u
2
(u
3
+ 2u
2
+ 3u + 1)(u
4
+ 3u
3
+ 5u
2
+ 5u + 3)
(2 u + 9u
2
+ 21u
3
4u
4
66u
5
74u
6
+ 44u
7
+ 182u
8
+ 145u
9
73u
10
247u
11
198u
12
+ u
13
+ 153u
14
+ 168u
15
+ 102u
16
+ 39u
17
+ 9u
18
+ u
19
)
2
(u
26
14u
25
+ ··· 5u + 2)
17
VII. Riley Polynomials
Crossings Riley Polynomials at each crossings
c
1
, c
9
(y 1)
2
(y
3
+ 3y
2
+ 2y 1)(y
4
+ 3y
3
+ 6y
2
+ 4y + 1)
(y
26
10y
25
+ ··· 18y + 1)(y
38
+ 13y
37
+ ··· + 2y + 1)
c
2
, c
5
(y
2
+ y + 1)(y
3
y
2
+ 2y 1)(y
4
y
3
+ 2y
2
+ 1)(y
26
+ 6y
25
+ ··· + 6y + 1)
(y
38
+ 4y
37
+ ··· 13311y + 121)
c
3
, c
6
(y
2
+ y + 1)(y
3
2y
2
+ y 1)(y
4
+ 2y
2
y + 1)
(y
26
+ 14y
25
+ ··· + 30y + 1)(y
38
8y
37
+ ··· + 5y + 1)
c
4
, c
8
(y 1)
2
(y
3
2y
2
+ y 1)(y
4
y
3
+ 2y
2
+ 1)
(1 + 4y 16y
2
+ 53y
3
166y
4
+ 388y
5
734y
6
+ 1132y
7
1483y
8
+ 1688y
9
1702y
10
+ 1533y
11
1231y
12
+ 870y
13
531y
14
+ 272y
15
113y
16
+ 36y
17
8y
18
+ y
19
)
2
(y
26
10y
25
+ ··· 81y + 16)
c
7
(y 1)
2
(y
3
2y
2
3y 1)(y
4
+ 3y
3
+ 6y
2
+ 4y + 1)
(1 16y 164y
2
867y
3
3826y
4
1.05 × 10
4
y
5
1.84 × 10
4
y
6
2.18 × 10
4
y
7
1.81 × 10
4
y
8
1.09 × 10
4
y
9
5246y
10
2751y
11
1815y
12
1050y
13
367y
14
12y
15
+ 59y
16
+ 32y
17
+ 8y
18
+ y
19
)
2
(y
26
+ 10y
25
+ ··· + 9439y + 256)
c
10
y
2
(y
3
+ 2y
2
+ 5y 1)(y
4
+ y
3
+ y
2
+ 5y + 9)
(4 + 37y 139y
2
+ 349y
3
816y
4
+ 1754y
5
2722y
6
+ 2948y
7
2788y
8
+ 2827y
9
2041y
10
+ 1545y
11
1136y
12
+ 611y
13
343y
14
+ 160y
15
52y
16
+ 21y
17
3y
18
+ y
19
)
2
(y
26
+ 8y
24
+ ··· 21y + 4)
18