show all invariants|show all metadata
Input data and context
% (2,-3)-pretzel tangle
r1.x2.y0.x2.y0.x2.y0.x2.y0.x2.y0.x2.y0.x2.u1
,1,0
Bar-Natan multicurve \(\mathrm{\widetilde{BN}}(T)\)
options -c0
(diagram)
(metadata)
% file 'examples/pretzeltangles/PT6m7/cxBNr-c0', generated by kht, version v0.1, on Sun Mar 7 14:27:17 2021 GMT
1) h^-3 q^ -6 δ^ 0 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<—
2) h^-5 q^-10 δ^ 0 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬮<—⬮<~⬮<—⬮<~⬯<—
3) h^ 0 q^ -1 δ^-1/2 ⬮<—D——⬮<~⬮<—⬮<~⬮<—⬮<~⬯<—⬯~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬯
options -c2
(diagram)
(metadata)
% file 'examples/pretzeltangles/PT6m7/cxBNr-c2', generated by kht, version v0.1, on Sun Mar 7 14:27:17 2021 GMT
1) h^-3 q^ -6 δ^ 0 ⬯~~S~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<—
2) h^-5 q^-10 δ^ 0 ⬯~~S~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬮<—⬮<~⬮<—⬮<~⬯<—
3) h^ 0 q^ -1 δ^-1/2 ⬮<—D——⬮<~⬮<—⬮<~⬮<—⬮<~⬯<—⬯~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬯
options -c3
(diagram)
(metadata)
% file 'examples/pretzeltangles/PT6m7/cxBNr-c3', generated by kht, version v0.1, on Sun Mar 7 14:27:17 2021 GMT
1) h^-3 q^ -6 δ^ 0 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<—
2) h^-5 q^-10 δ^ 0 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬮<—⬮<~⬮<—⬮<~⬯<—
3) h^ 0 q^ -1 δ^-1/2 ⬮<—D——⬮<~⬮<—⬮<~⬮<—⬮<~⬯<—⬯~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬯
options -c5
(diagram)
(metadata)
% file 'examples/pretzeltangles/PT6m7/cxBNr-c5', generated by kht, version v0.1, on Sun Mar 7 14:27:17 2021 GMT
1) h^-3 q^ -6 δ^ 0 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<—
2) h^-5 q^-10 δ^ 0 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬮<—⬮<~⬮<—⬮<~⬯<—
3) h^ 0 q^ -1 δ^-1/2 ⬮<—D——⬮<~⬮<—⬮<~⬮<—⬮<~⬯<—⬯~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬯
options -c7
(diagram)
(metadata)
% file 'examples/pretzeltangles/PT6m7/cxBNr-c7', generated by kht, version v0.1, on Sun Mar 7 14:27:17 2021 GMT
1) h^-3 q^ -6 δ^ 0 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<—
2) h^-5 q^-10 δ^ 0 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬮<—⬮<~⬮<—⬮<~⬯<—
3) h^ 0 q^ -1 δ^-1/2 ⬮<—D——⬮<~⬮<—⬮<~⬮<—⬮<~⬯<—⬯~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬯
options -c11
(diagram)
(metadata)
% file 'examples/pretzeltangles/PT6m7/cxBNr-c11', generated by kht, version v0.1, on Sun Mar 7 14:27:17 2021 GMT
1) h^-3 q^ -6 δ^ 0 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<—
2) h^-5 q^-10 δ^ 0 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬮<—⬮<~⬮<—⬮<~⬯<—
3) h^ 0 q^ -1 δ^-1/2 ⬮<—D——⬮<~⬮<—⬮<~⬮<—⬮<~⬯<—⬯~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬯
Khovanov multicurve \(\mathrm{\widetilde{Kh}}(T)\)
options -c0
(diagram)
(metadata)
% file 'examples/pretzeltangles/PT6m7/cxKhr-c0', generated by kht, version v0.1, on Sun Mar 7 14:27:17 2021 GMT
1) h^-4 q^ -7 δ^1/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^-2 δ|^0
2) h^-3 q^ -5 δ^1/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^0 δ|^0
3) h^-7 q^-13 δ^1/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬮<—⬮<~⬮<—⬮<~⬮<—⬮<~⬯<— r(1/6) q^-48/7 δ|^0
4) h^-6 q^-11 δ^1/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬮<—⬮<~⬮<—⬮<~⬯<— s4(0) q^-2 δ|^0
5) h^-5 q^ -9 δ^1/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬮<—⬮<~⬮<—⬮<~⬯<— s4(0) q^0 δ|^0
6) h^-8 q^-15 δ^1/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬮<—⬮<~⬮<—⬮<~⬮<—⬮<~⬮<—⬮<~⬯<— s6(0) q^-2 δ|^0
options -c2
(diagram)
(metadata)
% file 'examples/pretzeltangles/PT6m7/cxKhr-c2', generated by kht, version v0.1, on Sun Mar 7 14:27:17 2021 GMT
1) h^-4 q^ -7 δ^1/2 ⬯~~S~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^-2 δ|^0
2) h^-3 q^ -5 δ^1/2 ⬯~~S~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^0 δ|^0
3) h^-7 q^-13 δ^1/2 ⬯~~S~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬮<—⬮<~⬮<—⬮<~⬮<—⬮<~⬯<— r(1/6) q^-48/7 δ|^0
4) h^-6 q^-11 δ^1/2 ⬯~~S~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬮<—⬮<~⬮<—⬮<~⬯<— s4(0) q^-2 δ|^0
5) h^-5 q^ -9 δ^1/2 ⬯~~S~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬮<—⬮<~⬮<—⬮<~⬯<— s4(0) q^0 δ|^0
6) h^-8 q^-15 δ^1/2 ⬯~~S~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬮<—⬮<~⬮<—⬮<~⬮<—⬮<~⬮<—⬮<~⬯<— s6(0) q^-2 δ|^0
options -c3
(diagram)
(metadata)
% file 'examples/pretzeltangles/PT6m7/cxKhr-c3', generated by kht, version v0.1, on Sun Mar 7 14:27:17 2021 GMT
1) h^-4 q^ -7 δ^1/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^-2 δ|^0
2) h^-3 q^ -5 δ^1/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^0 δ|^0
3) h^-7 q^-13 δ^1/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬮<—⬮<~⬮<—⬮<~⬮<—⬮<~⬯<— r(1/6) q^-48/7 δ|^0
4) h^-6 q^-11 δ^1/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬮<—⬮<~⬮<—⬮<~⬯<— s4(0) q^-2 δ|^0
5) h^-5 q^ -9 δ^1/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬮<—⬮<~⬮<—⬮<~⬯<— s4(0) q^0 δ|^0
6) h^-8 q^-15 δ^1/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬮<—⬮<~⬮<—⬮<~⬮<—⬮<~⬮<—⬮<~⬯<— s6(0) q^-2 δ|^0
options -c5
(diagram)
(metadata)
% file 'examples/pretzeltangles/PT6m7/cxKhr-c5', generated by kht, version v0.1, on Sun Mar 7 14:27:17 2021 GMT
1) h^-4 q^ -7 δ^1/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^-2 δ|^0
2) h^-3 q^ -5 δ^1/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^0 δ|^0
3) h^-7 q^-13 δ^1/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬮<—⬮<~⬮<—⬮<~⬮<—⬮<~⬯<— r(1/6) q^-48/7 δ|^0
4) h^-6 q^-11 δ^1/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬮<—⬮<~⬮<—⬮<~⬯<— s4(0) q^-2 δ|^0
5) h^-5 q^ -9 δ^1/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬮<—⬮<~⬮<—⬮<~⬯<— s4(0) q^0 δ|^0
6) h^-8 q^-15 δ^1/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬮<—⬮<~⬮<—⬮<~⬮<—⬮<~⬮<—⬮<~⬯<— s6(0) q^-2 δ|^0
options -c7
(diagram)
(metadata)
% file 'examples/pretzeltangles/PT6m7/cxKhr-c7', generated by kht, version v0.1, on Sun Mar 7 14:27:17 2021 GMT
1) h^-4 q^ -7 δ^1/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^-2 δ|^0
2) h^-3 q^ -5 δ^1/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^0 δ|^0
3) h^-7 q^-13 δ^1/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬮<—⬮<~⬮<—⬮<~⬮<—⬮<~⬯<— r(1/6) q^-48/7 δ|^0
4) h^-6 q^-11 δ^1/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬮<—⬮<~⬮<—⬮<~⬯<— s4(0) q^-2 δ|^0
5) h^-5 q^ -9 δ^1/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬮<—⬮<~⬮<—⬮<~⬯<— s4(0) q^0 δ|^0
6) h^-8 q^-15 δ^1/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬮<—⬮<~⬮<—⬮<~⬮<—⬮<~⬮<—⬮<~⬯<— s6(0) q^-2 δ|^0
options -c11
(diagram)
(metadata)
% file 'examples/pretzeltangles/PT6m7/cxKhr-c11', generated by kht, version v0.1, on Sun Mar 7 14:27:17 2021 GMT
1) h^-4 q^ -7 δ^1/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^-2 δ|^0
2) h^-3 q^ -5 δ^1/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s2(0) q^0 δ|^0
3) h^-7 q^-13 δ^1/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬮<—⬮<~⬮<—⬮<~⬮<—⬮<~⬯<— r(1/6) q^-48/7 δ|^0
4) h^-6 q^-11 δ^1/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬮<—⬮<~⬮<—⬮<~⬯<— s4(0) q^-2 δ|^0
5) h^-5 q^ -9 δ^1/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬮<—⬮<~⬮<—⬮<~⬯<— s4(0) q^0 δ|^0
6) h^-8 q^-15 δ^1/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬮<—⬮<~⬮<—⬮<~⬮<—⬮<~⬮<—⬮<~⬯<— s6(0) q^-2 δ|^0