https://github.com/dylex/conwayrats
exploration for conway's RATS
https://github.com/dylex/conwayrats
Last synced: 8 months ago
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exploration for conway's RATS
- Host: GitHub
- URL: https://github.com/dylex/conwayrats
- Owner: dylex
- Created: 2023-06-25T23:56:25.000Z (almost 3 years ago)
- Default Branch: main
- Last Pushed: 2023-10-24T02:50:15.000Z (over 2 years ago)
- Last Synced: 2025-01-23T19:14:34.839Z (over 1 year ago)
- Language: Haskell
- Size: 27.3 KB
- Stars: 0
- Watchers: 2
- Forks: 0
- Open Issues: 0
-
Metadata Files:
- Readme: README.md
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README
# Conway's RATS exploration tool
## Installation
- Clone this repo
- Install glpk (e.g., `apt-get install libglpk-dev`)
- Install [Haskell Stack](https://www.fpcomplete.com/haskell/get-started/) (e.g., `wget -qO- https://get.haskellstack.org/ | sh`)
- Run `stack build`
## Running
Either:
- `stack run -- --help`, or
- `stack install`, `rats --help`
```
rats [OPTIONS] CASEPATH|NUMBER
Run Conway's RATS, base 4.
If given a simple number, follow it forever.
If given a list of cases by letter (as specified in the case4 file),
evaluate the conditions on the initial digit counts (a=1s,b=2s,...)
that would lead to this path of cases, and compute the minimum initial
digit counts necessary.
-i --ilp Find minimum integral solution to constraints (rather than just simplex)
-t[DEPTH] --tree[=DEPTH] Explore a tree of possibilites after specified case path
-d --decrease Allow exploring cases that decrease count
```
## Example
```
> rats -t3 -i HECJ
a, b, c if [] 0 a+b+c >= 0 (0,0,0)
2+b-c, -1+2c, 0 if b-c>=0,c>=1,-a>=0 [H] 1 1+b+c >= 2 (0,1,1)
0, 3+b-3c, -2+4c if 2c>=2,b-3c>=-3,-a>=0,b-c>=0 [HE] 1 1+b+c >= 2 (0,1,1)
1, 1, -3+4c if 4c>=3,-b+3c>=3,b-c>=0,-a>=0,b-3c>=-3 [HEC] 2 -1+4c >= 5 (0,3,2)
2, 2, -5+4c if b-3c>=-3,-a>=0,b-c>=0,-b+3c>=3 [HECJ] 2 -1+4c >= 5 (0,3,2)
4, 4, -9+4c if 4c>=9,-b+3c>=3,-a>=0,b-3c>=-3 [HECJJ] 2 -1+4c >= 9 (0,6,3)
0, 0, 8 if -4c>=-9,b-3c>=-3,-a>=0,-b+3c>=3,4c>=9 [HECJJE] 2 8
8, 8, -17+4c if 4c>=17,b-3c>=-3,-a>=0,-b+3c>=3 [HECJJJ] 2 -1+4c >= 17 (0,12,5)
0, 0, 16 if -4c>=-17,-b+3c>=3,-a>=0,b-3c>=-3,4c>=17 [HECJJJE] 2 16
16, 16, -33+4c if 4c>=33,-b+3c>=3,-a>=0,b-3c>=-3 [HECJJJJ] 2 -1+4c >= 33 (0,24,9)
49-4c, -50+8c, 0 if 4c>=25,-4c>=-32,-b+3c>=3,-a>=0,b-3c>=-3 [HECJJJK] 2 -1+4c >= 25 (0,18,7)
-51+12c, 0, 0 if -4c>=-24,4c>=18,-b+3c>=3,-a>=0,b-3c>=-3 [HECJJJL] -48+8c -51+12c >= 17 (0,12,5)
25-4c, -26+8c, 0 if 4c>=13,-4c>=-16,b-3c>=-3,-a>=0,-b+3c>=3 [HECJJK] 2 -1+4c bounded
-27+12c, 0, 0 if -4c>=-12,4c>=10,b-3c>=-3,-a>=0,-b+3c>=3 [HECJJL] -24+8c -27+12c bounded
13-4c, -14+8c, 0 if 4c>=7,-4c>=-8,-b+3c>=3,-a>=0,b-3c>=-3 [HECJK] 2 -1+4c >= 5 (0,3,2)
0, 13-4c, 0 if -8c>=-14,8c>=14,b-3c>=-3,-a>=0,-b+3c>=3,4c>=7 [HECJKA] 2 13-4c bounded
0, 27-12c, -28+16c if 8c>=15,b-3c>=-3,-a>=0,-b+3c>=3,-4c>=-8 [HECJKE] 2 -1+4c bounded
-15+12c, 0, 0 if -4c>=-6,4c>=5,4c>=6,-b+3c>=3,b-c>=0,-a>=0 [HECJL] -12+8c -15+12c bounded
```
- We ask what initial conditions can follow the sequence of cases H,E,C,J:
- Starting with a 1s, b 2s, and c 3s
- this can expand (using case H) to 2+b-c 1s, 2c-1 2s, 0 cs if b>=c,c>=1,a=0
- for a total of 1+b+c initial digits
- and requires at least 2 total initial digits (0 1s, 1 2, 1 3)
- which can expand (using case E) to 0 1s, 3+b-3c 2s, 4c-2 3s if ...
- ... which can expand (using case C and the J) to 2 1s, 2 2s, 4c-5 3s if ...
- and we now have a total of 4c-1 digits
- which must be at least 5
- And then ask for a tree of all possible cases (that don't decrease, `-d`):
- cases J, K, and L are possible (HECJJ, HECJK, HECJL)...
- case HECJL requires a set of initial conditions that are bounded above (an upper bound on the number of possible digits), so the search terminates
## Base 4
Currently everything is hard-coded for base 4, but this can (partially) be changed by editing `Param.hs` and creating the appropriate `caseN` file.