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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.

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Bar-Natan'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: 2020-01-21               │
│ 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               
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