K12a197
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^4-2 q^3+4 q^2-6 q+8-9 q^{-1} +10 q^{-2} -9 q^{-3} +7 q^{-4} -6 q^{-5} +4 q^{-6} -2 q^{-7} + q^{-8} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 3 t^2-17 t+29-17 t^{-1} +3 t^{-2} }[/math] |
| Conway polynomial | [math]\displaystyle{ 3 z^4-5 z^2+1 }[/math] |
| Determinant | 69 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ a^8-2 z^2 a^6-a^6+z^4 a^4+z^4 a^2-z^2 a^2+z^4+1-2 z^2 a^{-2} - a^{-2} + a^{-4} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ a^5 z^{11}+a^3 z^{11}+2 a^6 z^{10}+4 a^4 z^{10}+2 a^2 z^{10}+2 a^7 z^9-2 a^5 z^9-2 a^3 z^9+2 a z^9+a^8 z^8-9 a^6 z^8-19 a^4 z^8-7 a^2 z^8+2 z^8-11 a^7 z^7-7 a^5 z^7-2 a^3 z^7-4 a z^7+2 z^7 a^{-1} -6 a^8 z^6+8 a^6 z^6+28 a^4 z^6+10 a^2 z^6+2 z^6 a^{-2} -2 z^6+18 a^7 z^5+15 a^5 z^5+2 a^3 z^5+3 a z^5+2 z^5 a^{-3} +11 a^8 z^4+4 a^6 z^4-18 a^4 z^4-8 a^2 z^4+z^4 a^{-4} +2 z^4-11 a^7 z^3-8 a^5 z^3+a^3 z^3-a z^3-2 z^3 a^{-1} -3 z^3 a^{-3} -7 a^8 z^2-5 a^6 z^2+4 a^4 z^2+a^2 z^2-3 z^2 a^{-2} -2 z^2 a^{-4} -2 z^2+3 a^7 z+2 a^5 z-a^3 z+z a^{-1} +z a^{-3} +a^8+a^6+ a^{-2} + a^{-4} +1 }[/math] |
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