I am doing a project on the invariants of knots and links specifically working on Kauffman bracket polynomial but drawing the states for knots with high crossings is tedious. I am searching for a working code that can generate the states and the type of smoothings used.

3$\begingroup$ tex.stackexchange.com $\endgroup$ – Fernando Muro Jan 28 at 21:10

1$\begingroup$ Hi Martha, welcome to MO. I think your question might not misinterpreted as question about putting diagrams in a paper. Are you looking for something along these lines: katlas.org/wiki/The_Kauffman_Polynomial? $\endgroup$ – Neil Hoffman Jan 29 at 6:26
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BarNatan's KnotTheory` Mathematica package can compute the Kauffman polynomial. If you need the actual state diagrams, I recommend looking here
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Sage has also some code about knots, but maybe not what you need.
┌────────────────────────────────────────────────────────────────────┐
│ SageMath version 9.1.beta1, Release Date: 20200121 │
│ Using Python 3.7.3. Type "help()" for help. │
└────────────────────────────────────────────────────────────────────┘
┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┓
┃ Warning: this is a prerelease version, and it may be unstable. ┃
┗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┛
sage: K = Knots()
sage: J = K.from_table(8,10)
sage: J.
J.alexander_polynomial J.gauss_code J.orientation
J.arcs J.genus J.oriented_gauss_code
J.arf_invariant J.homfly_polynomial J.parent
J.base_extend J.is_alternating J.pd_code
J.base_ring J.is_colorable J.plot
J.braid J.is_idempotent J.powers
J.cartesian_product J.is_knot J.regions
J.category J.is_one J.rename
J.colorings J.is_zero J.reset_name
J.connected_sum J.jones_polynomial J.save
J.determinant J.khovanov_homology J.seifert_circles
J.dowker_notation J.mirror_image J.seifert_matrix
J.dt_code J.n J.signature
J.dump J.number_of_components J.subs
J.dumps J.numerical_approx J.substitute
J.fundamental_group J.omega_signature J.writhe

$\begingroup$ The documentation for knots/links may be useful here. $\endgroup$ – Mark Jan 27 at 20:14