A program that computes the reduced HOMFLY homology of knots.
See: K. Nakagane, T. Sano "Computations of HOMFLY homology", arXiv:2111.00388.
$ cargo build -r
- Run
$ ./target/release/ykr <TARGET> [OPTIONS]
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
$ 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.
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.
yui-kr
is released under the MIT license.