K12a789
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^7+3 q^6-6 q^5+9 q^4-13 q^3+16 q^2-16 q+16-12 q^{-1} +9 q^{-2} -5 q^{-3} +2 q^{-4} - q^{-5} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 2 t^4-7 t^3+14 t^2-20 t+23-20 t^{-1} +14 t^{-2} -7 t^{-3} +2 t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ 2 z^8+9 z^6+12 z^4+5 z^2+1 }[/math] |
| Determinant | 109 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^8 a^{-2} +z^8-a^2 z^6+5 z^6 a^{-2} -z^6 a^{-4} +6 z^6-5 a^2 z^4+7 z^4 a^{-2} -4 z^4 a^{-4} +14 z^4-8 a^2 z^2+z^2 a^{-2} -4 z^2 a^{-4} +16 z^2-4 a^2-2 a^{-2} - a^{-4} +8 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{11} a^{-1} +z^{11} a^{-3} +5 z^{10} a^{-2} +3 z^{10} a^{-4} +2 z^{10}+3 a z^9+z^9 a^{-1} +2 z^9 a^{-3} +4 z^9 a^{-5} +4 a^2 z^8-16 z^8 a^{-2} -9 z^8 a^{-4} +3 z^8 a^{-6} +3 a^3 z^7-3 a z^7-3 z^7 a^{-1} -13 z^7 a^{-3} -15 z^7 a^{-5} +z^7 a^{-7} +2 a^4 z^6-10 a^2 z^6+22 z^6 a^{-2} +8 z^6 a^{-4} -12 z^6 a^{-6} -10 z^6+a^5 z^5-5 a^3 z^5-4 a z^5-3 z^5 a^{-1} +14 z^5 a^{-3} +15 z^5 a^{-5} -4 z^5 a^{-7} -4 a^4 z^4+16 a^2 z^4-15 z^4 a^{-2} -8 z^4 a^{-4} +12 z^4 a^{-6} +25 z^4-3 a^5 z^3+2 a^3 z^3+15 a z^3+12 z^3 a^{-1} -7 z^3 a^{-3} -5 z^3 a^{-5} +4 z^3 a^{-7} +a^4 z^2-13 a^2 z^2+5 z^2 a^{-4} -2 z^2 a^{-6} -21 z^2+2 a^5 z-a^3 z-8 a z-7 z a^{-1} +z a^{-5} -z a^{-7} +4 a^2+2 a^{-2} - a^{-4} +8 }[/math] |
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