yui-kr (結)

A program that computes the reduced HOMFLY homology of knots.
See: K. Nakagane, T. Sano "Computations of HOMFLY homology", arXiv:2111.00388.

Setup

• Install Rust.
• Download yui-kr.
• Build

$ cargo build -r

• Run

$ ./target/release/ykr <TARGET> [OPTIONS]

Usage

Usage: ykr <TARGET> [OPTIONS]

Arguments:
  <TARGET>  

Options:
  -b, --braid <BRAID>                
  -i, --int-type <INT_TYPE>          [default: i64] [possible values: i64, i128, bigint]
  -m, --mirror                       
  -f, --format <FORMAT>              [default: poincare] [possible values: poincare, poincare-tex, delta, table]
  -F, --force-compute                
  -c, --compute-mode <COMPUTE_MODE>  [default: default] [possible values: default, per-col, per-item]
  -l, --limit <LIMIT>                
  -p, --save-progress                
      --debug                        

Examples

$ ykr 3_1
q⁻²a² + t⁻²q²a² + t⁻³a⁴

$ ykr 5_1 -b '[1,1,1,1,1]'
q⁻⁴a⁴ + t⁻²a⁴ + t⁻³q⁻²a⁶ + t⁻⁴q⁴a⁴ + t⁻⁵q²a⁶

$ ykr 4_1 -f delta
Δ: 0
 j\i  -2  0  2 
 2    .   1  . 
 0    1   1  1 
 -2   .   1  .

$ ykr 11a_263 -f delta
Δ: 6
 j\i  -2  0  2 
 14   .   1  . 
 12   1   .  1 
 10   .   1  . 

Δ: 8
 j\i  -8  -6  -4  -2  0  2  4  6  8 
 12   .   1   3   3   5  3  3  1  . 
 10   1   4   4   9   6  9  4  4  1 
 8    1   1   4   3   6  3  4  1  1 

Note: If precomputed result for the specified target exist in the results directory, ykr will load the data and print the result without computation. Specify -F option if you want to force computation.

Computation Results

Computations are peformed for all prime knots with up to 11 crossings. The braid representatives of prime knots provided in KnotInfo were used as the input data.

• PDF (Human friendly)
• JSON (Machine friendly)

License

yui-kr is released under the MIT license.