https://github.com/fuglede/burau4_mod_p

A simple program for finding kernel elements of the 4-strand Burau representation modulo $p$.
https://github.com/fuglede/burau4_mod_p

Last synced: about 2 months ago
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A simple program for finding kernel elements of the 4-strand Burau representation modulo $p$.

• Host: GitHub
• URL: https://github.com/fuglede/burau4_mod_p
• Owner: fuglede
• Created: 2024-03-06T20:23:35.000Z (10 months ago)
• Default Branch: master
• Last Pushed: 2024-05-17T18:30:05.000Z (8 months ago)
• Last Synced: 2024-05-17T19:37:05.257Z (8 months ago)
• Language: Rust
• Size: 38.1 KB
• Stars: 0
• Watchers: 2
• Forks: 1
• Open Issues: 2
• Metadata Files:
  • Readme: README.md

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README

        
# burau4_mod_p

A simple program for finding kernel elements of the 4-strand Burau representation modulo $p$.

## Example usage

To build this, run

```

$ cargo build --release

```

Then, to find an element of Burau mod 2:

```

$ time target/release/burau4_mod_p 2

Starting search for kernel elements of Burau mod 2. Random seed: 0

Found kernel element. Garside generators:

[13, 10, 13, 10, 13, 10, 13, 10]

real	0m0.010s

user	0m0.010s

sys	0m0.000s

```

Or Burau mod 3:

```

$ time target/release/burau4_mod_p 3

Starting search for kernel elements of Burau mod 3. Random seed: 0

Found kernel element. Garside generators:

[7, 8, 16, 13, 20, 13, 10, 13, 4, 13, 20, 17, 22, 17, 13, 10, 13, 8, 13, 11, 13, 10, 16, 3]

real	0m4.404s

user	0m4.192s

sys	0m0.212s

```

Or Burau mod 5:

```

$ time target/release/burau4_mod_p 5

Starting search for kernel elements of Burau mod 5. Random seed: 0

Found kernel element. Garside generators:

[19, 21, 7, 7, 10, 13, 8, 13, 8, 13, 21, 11, 13, 11, 13, 10, 2, 13, 8, 13, 8, 13, 21, 11, 13, 11, 13, 10, 2, 13, 8, 13, 8, 13, 21, 11, 13, 11, 13, 10, 2, 13, 8, 13, 8, 13, 21, 11, 13, 11, 13, 10, 2, 13, 8, 13, 8, 13, 21, 11, 13, 11, 13, 10, 16, 16, 16, 2, 3]

real	0m45.393s

user	0m45.271s

sys	0m0.100s

```