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Input data and context
% 3_1
r1.y0.y0.y0.u1
,1
% Simplifies with options '-dop.l1.y0.y2.u1.s' to l2.r3.y1.y0.y2.y1.y1.y2.x3.y0.y1.y1.u2.x2.y0.u1.l1.y2.y0.u1
% With options '-c2-dop.l1.y0.y2.u1.s', add these twists to optimize: y0
% Simplifies with options '-dop.l1.y0.y2.u1.s' to l2.y1.y0.r2.y1.y1.y0.x3.y2.x3.x4.y1.y1.u2.y0.u1.l1.y2.x1.u0
% With options '-c2-dop.l1.y0.y2.u1.', add these twists to optimize: y0
% Simplifies with options '-dp.l1.y2.y0.u1.s' to l1.x2.r3.y0.y2.y1.y1.y0.y2.x3.y1.y1.u2.x2.y0.u1.l0.x1.x1.u2
% Simplifies with options '-dp.l1.y2.y0.u1.s' to l0.x1.r1.x2.y1.y0.x4.x3.y2.x3.x4.y1.y1.u2.x1.u0.l2.x1.x1.u0
Bar-Natan multicurve \(\mathrm{\widetilde{BN}}(T)\)
options -c0-dp.l1.y2.y0.u1.s
(diagram)
(metadata)
% file 'examples/SInvariantAndTorsion/3_1/cxBNr-c0-dp.l1.y2.y0.u1.s', generated by kht++ v0.1-23-ga307146 on Tue May 18 16:30:08 2021 GMT
1) h^ 0 q^ 1 δ^1/2 ⬯——D—>⬯~>⬮
2) h^ 2 q^ 5 δ^1/2 ⬯~~(-S)~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬯<—
3) h^ 3 q^ 7 δ^1/2 ⬯~~(-S)~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬯<—
4) h^-2 q^-1 δ^3/2 ⬯~~(-S)~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬯<—
5) h^-6 q^-7 δ^5/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<—
options -c2-dp.l1.y2.y0.u1.s
(diagram)
(metadata)
% file 'examples/SInvariantAndTorsion/3_1/cxBNr-c2-dp.l1.y2.y0.u1.s', generated by kht++ v0.1-23-ga307146 on Tue May 18 16:30:08 2021 GMT
1) h^ 0 q^ 2 δ^ 1 ⬮——D—>⬮~>⬯—>⬯<~⬮
2) h^ 0 q^ 1 δ^1/2 ⬯~~S~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<—
3) h^ 1 q^ 3 δ^1/2 ⬯~~S~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<—
4) h^-2 q^-1 δ^3/2 ⬯~~S~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<—
5) h^-6 q^-7 δ^5/2 ⬯~~S~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<—
options -c3-dp.l1.y2.y0.u1.s
(diagram)
(metadata)
% file 'examples/SInvariantAndTorsion/3_1/cxBNr-c3-dp.l1.y2.y0.u1.s', generated by kht++ v0.1-23-ga307146 on Tue May 18 16:30:08 2021 GMT
1) h^ 0 q^ 1 δ^1/2 ⬯——D—>⬯~>⬮
2) h^ 2 q^ 5 δ^1/2 ⬯~~(-S)~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬯<—
3) h^ 3 q^ 7 δ^1/2 ⬯~~(-S)~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬯<—
4) h^-2 q^-1 δ^3/2 ⬯~~(-S)~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬯<—
5) h^-6 q^-7 δ^5/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<—
options -c5-dp.l1.y2.y0.u1.s
(diagram)
(metadata)
% file 'examples/SInvariantAndTorsion/3_1/cxBNr-c5-dp.l1.y2.y0.u1.s', generated by kht++ v0.1-23-ga307146 on Tue May 18 16:30:08 2021 GMT
1) h^ 0 q^ 1 δ^1/2 ⬯——D—>⬯~>⬮
2) h^ 2 q^ 5 δ^1/2 ⬯~~(-S)~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬯<—
3) h^ 3 q^ 7 δ^1/2 ⬯~~(-S)~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬯<—
4) h^-2 q^-1 δ^3/2 ⬯~~(-S)~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬯<—
5) h^-6 q^-7 δ^5/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<—
options -c7-dp.l1.y2.y0.u1.s
(diagram)
(metadata)
% file 'examples/SInvariantAndTorsion/3_1/cxBNr-c7-dp.l1.y2.y0.u1.s', generated by kht++ v0.1-23-ga307146 on Tue May 18 16:30:08 2021 GMT
1) h^ 0 q^ 1 δ^1/2 ⬯——D—>⬯~>⬮
2) h^ 2 q^ 5 δ^1/2 ⬯~~(-S)~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬯<—
3) h^ 3 q^ 7 δ^1/2 ⬯~~(-S)~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬯<—
4) h^-2 q^-1 δ^3/2 ⬯~~(-S)~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬯<—
5) h^-6 q^-7 δ^5/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<—
options -c11-dp.l1.y2.y0.u1.s
(diagram)
(metadata)
% file 'examples/SInvariantAndTorsion/3_1/cxBNr-c11-dp.l1.y2.y0.u1.s', generated by kht++ v0.1-23-ga307146 on Tue May 18 16:30:08 2021 GMT
1) h^ 0 q^ 1 δ^1/2 ⬯——D—>⬯~>⬮
2) h^ 2 q^ 5 δ^1/2 ⬯~~(-S)~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬯<—
3) h^ 3 q^ 7 δ^1/2 ⬯~~(-S)~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬯<—
4) h^-2 q^-1 δ^3/2 ⬯~~(-S)~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬯<—
5) h^-6 q^-7 δ^5/2 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<—
Khovanov multicurve \(\mathrm{\widetilde{Kh}}(T)\)
options -c0-dp.l1.y2.y0.u1.s
(diagram)
(metadata)
% file 'examples/SInvariantAndTorsion/3_1/cxKhr-c0-dp.l1.y2.y0.u1.s', generated by kht++ v0.1-23-ga307146 on Tue May 18 16:30:08 2021 GMT
1) h^-1 q^ 0 δ^1 ⬯~~(-S^2)~>⬯—>⬯~>⬮<—⬮<~⬯<— r(2) q^8/3 δ|^1
2) h^ 1 q^ 4 δ^1 ⬯~~(-S)~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬯<— s2(0) q^7 δ|^1/2
3) h^ 2 q^ 6 δ^1 ⬯~~(-S)~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬯<— s2(0) q^9 δ|^1/2
4) h^ 2 q^ 6 δ^1 ⬯~~(-S)~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬯<— s2(0) q^9 δ|^1/2
5) h^ 3 q^ 8 δ^1 ⬯~~(-S)~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬯<— s2(0) q^11 δ|^1/2
6) h^-3 q^-2 δ^2 ⬯~~(-S)~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬯<— s2(0) q^1 δ|^3/2
7) h^-2 q^ 0 δ^2 ⬯~~(-S)~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬯<— s2(0) q^3 δ|^3/2
8) h^-7 q^-8 δ^3 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s4(0) q^-3 δ|^5/2
9) h^-6 q^-6 δ^3 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s4(0) q^-1 δ|^5/2
options -c2-dp.l1.y2.y0.u1.s
(diagram)
(metadata)
% file 'examples/SInvariantAndTorsion/3_1/cxKhr-c2-dp.l1.y2.y0.u1.s', generated by kht++ v0.1-23-ga307146 on Tue May 18 16:30:08 2021 GMT
1) h^-1 q^ 1 δ^3/2 ⬮~~S^2~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮~>⬯<—⬯<~⬮<— r(-2/3) q^24/5 δ|^3/2
2) h^-1 q^ 0 δ^ 1 ⬯~~S~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s4(0) q^5 δ|^1/2
3) h^ 0 q^ 2 δ^ 1 ⬯~~S~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s4(0) q^7 δ|^1/2
4) h^ 0 q^ 2 δ^ 1 ⬯~~S~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s4(0) q^7 δ|^1/2
5) h^ 1 q^ 4 δ^ 1 ⬯~~S~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s4(0) q^9 δ|^1/2
6) h^-3 q^-2 δ^ 2 ⬯~~S~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s4(0) q^3 δ|^3/2
7) h^-2 q^ 0 δ^ 2 ⬯~~S~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s4(0) q^5 δ|^3/2
8) h^-7 q^-8 δ^ 3 ⬯~~S~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s4(0) q^-3 δ|^5/2
9) h^-6 q^-6 δ^ 3 ⬯~~S~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s4(0) q^-1 δ|^5/2
options -c3-dp.l1.y2.y0.u1.s
(diagram)
(metadata)
% file 'examples/SInvariantAndTorsion/3_1/cxKhr-c3-dp.l1.y2.y0.u1.s', generated by kht++ v0.1-23-ga307146 on Tue May 18 16:30:08 2021 GMT
1) h^-1 q^ 0 δ^1 ⬯~~(-S^2)~>⬯—>⬯~>⬮<—⬮<~⬯<— r(2) q^8/3 δ|^1
2) h^ 1 q^ 4 δ^1 ⬯~~(-S)~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬯<— s2(0) q^7 δ|^1/2
3) h^ 2 q^ 6 δ^1 ⬯~~(-S)~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬯<— s2(0) q^9 δ|^1/2
4) h^ 2 q^ 6 δ^1 ⬯~~(-S)~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬯<— s2(0) q^9 δ|^1/2
5) h^ 3 q^ 8 δ^1 ⬯~~(-S)~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬯<— s2(0) q^11 δ|^1/2
6) h^-3 q^-2 δ^2 ⬯~~(-S)~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬯<— s2(0) q^1 δ|^3/2
7) h^-2 q^ 0 δ^2 ⬯~~(-S)~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬯<— s2(0) q^3 δ|^3/2
8) h^-7 q^-8 δ^3 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s4(0) q^-3 δ|^5/2
9) h^-6 q^-6 δ^3 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s4(0) q^-1 δ|^5/2
options -c5-dp.l1.y2.y0.u1.s
(diagram)
(metadata)
% file 'examples/SInvariantAndTorsion/3_1/cxKhr-c5-dp.l1.y2.y0.u1.s', generated by kht++ v0.1-23-ga307146 on Tue May 18 16:30:08 2021 GMT
1) h^-1 q^ 0 δ^1 ⬯~~(-S^2)~>⬯—>⬯~>⬮<—⬮<~⬯<— r(2) q^8/3 δ|^1
2) h^ 1 q^ 4 δ^1 ⬯~~(-S)~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬯<— s2(0) q^7 δ|^1/2
3) h^ 2 q^ 6 δ^1 ⬯~~(-S)~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬯<— s2(0) q^9 δ|^1/2
4) h^ 2 q^ 6 δ^1 ⬯~~(-S)~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬯<— s2(0) q^9 δ|^1/2
5) h^ 3 q^ 8 δ^1 ⬯~~(-S)~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬯<— s2(0) q^11 δ|^1/2
6) h^-3 q^-2 δ^2 ⬯~~(-S)~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬯<— s2(0) q^1 δ|^3/2
7) h^-2 q^ 0 δ^2 ⬯~~(-S)~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬯<— s2(0) q^3 δ|^3/2
8) h^-7 q^-8 δ^3 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s4(0) q^-3 δ|^5/2
9) h^-6 q^-6 δ^3 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s4(0) q^-1 δ|^5/2
options -c7-dp.l1.y2.y0.u1.s
(diagram)
(metadata)
% file 'examples/SInvariantAndTorsion/3_1/cxKhr-c7-dp.l1.y2.y0.u1.s', generated by kht++ v0.1-23-ga307146 on Tue May 18 16:30:08 2021 GMT
1) h^-1 q^ 0 δ^1 ⬯~~(-S^2)~>⬯—>⬯~>⬮<—⬮<~⬯<— r(2) q^8/3 δ|^1
2) h^ 1 q^ 4 δ^1 ⬯~~(-S)~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬯<— s2(0) q^7 δ|^1/2
3) h^ 2 q^ 6 δ^1 ⬯~~(-S)~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬯<— s2(0) q^9 δ|^1/2
4) h^ 2 q^ 6 δ^1 ⬯~~(-S)~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬯<— s2(0) q^9 δ|^1/2
5) h^ 3 q^ 8 δ^1 ⬯~~(-S)~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬯<— s2(0) q^11 δ|^1/2
6) h^-3 q^-2 δ^2 ⬯~~(-S)~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬯<— s2(0) q^1 δ|^3/2
7) h^-2 q^ 0 δ^2 ⬯~~(-S)~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬯<— s2(0) q^3 δ|^3/2
8) h^-7 q^-8 δ^3 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s4(0) q^-3 δ|^5/2
9) h^-6 q^-6 δ^3 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s4(0) q^-1 δ|^5/2
options -c11-dp.l1.y2.y0.u1.s
(diagram)
(metadata)
% file 'examples/SInvariantAndTorsion/3_1/cxKhr-c11-dp.l1.y2.y0.u1.s', generated by kht++ v0.1-23-ga307146 on Tue May 18 16:30:08 2021 GMT
1) h^-1 q^ 0 δ^1 ⬯~~(-S^2)~>⬯—>⬯~>⬮<—⬮<~⬯<— r(2) q^8/3 δ|^1
2) h^ 1 q^ 4 δ^1 ⬯~~(-S)~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬯<— s2(0) q^7 δ|^1/2
3) h^ 2 q^ 6 δ^1 ⬯~~(-S)~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬯<— s2(0) q^9 δ|^1/2
4) h^ 2 q^ 6 δ^1 ⬯~~(-S)~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬯<— s2(0) q^9 δ|^1/2
5) h^ 3 q^ 8 δ^1 ⬯~~(-S)~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬯<— s2(0) q^11 δ|^1/2
6) h^-3 q^-2 δ^2 ⬯~~(-S)~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬯<— s2(0) q^1 δ|^3/2
7) h^-2 q^ 0 δ^2 ⬯~~(-S)~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬯<— s2(0) q^3 δ|^3/2
8) h^-7 q^-8 δ^3 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s4(0) q^-3 δ|^5/2
9) h^-6 q^-6 δ^3 ⬯~~(-S)~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s4(0) q^-1 δ|^5/2
Khovanov type D structure \(\mathrm{\widetilde{CKh}}(L)\)
options -c0
(diagram)
(metadata)
% file 'examples/SInvariantAndTorsion/3_1/cxCKh-c0', generated by kht++ v0.1-23-ga307146 on Tue May 18 16:29:27 2021 GMT
1) h^0 q^2 δ^1 ⬮
2) h^2 q^6 δ^1 ⬮——H—>⬮
options -c2
(diagram)
(metadata)
% file 'examples/SInvariantAndTorsion/3_1/cxCKh-c2', generated by kht++ v0.1-23-ga307146 on Tue May 18 16:29:27 2021 GMT
1) h^0 q^2 δ^1 ⬮
2) h^2 q^6 δ^1 ⬮——H—>⬮
options -c3
(diagram)
(metadata)
% file 'examples/SInvariantAndTorsion/3_1/cxCKh-c3', generated by kht++ v0.1-23-ga307146 on Tue May 18 16:29:27 2021 GMT
1) h^0 q^2 δ^1 ⬮
2) h^2 q^6 δ^1 ⬮——H—>⬮
options -c5
(diagram)
(metadata)
% file 'examples/SInvariantAndTorsion/3_1/cxCKh-c5', generated by kht++ v0.1-23-ga307146 on Tue May 18 16:29:27 2021 GMT
1) h^0 q^2 δ^1 ⬮
2) h^2 q^6 δ^1 ⬮——H—>⬮
options -c7
(diagram)
(metadata)
% file 'examples/SInvariantAndTorsion/3_1/cxCKh-c7', generated by kht++ v0.1-23-ga307146 on Tue May 18 16:29:27 2021 GMT
1) h^0 q^2 δ^1 ⬮
2) h^2 q^6 δ^1 ⬮——H—>⬮
options -c11
(diagram)
(metadata)
% file 'examples/SInvariantAndTorsion/3_1/cxCKh-c11', generated by kht++ v0.1-23-ga307146 on Tue May 18 16:29:27 2021 GMT
1) h^0 q^2 δ^1 ⬮
2) h^2 q^6 δ^1 ⬮——H—>⬮