New script and readme for computing the centers of the AnyonWiki multiplicity-free fusion categories

.gitignore

@@ -8,3 +8,4 @@ Codecov.jl
 docs/build/
 .vscode/
 coverage/
+computations/anyonwiki_centers/center_runs/

.vscode/settings.json

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 {
-    "git.enabled": false
+    "git.enabled": true
 }

computations/anyonwiki_centers/Readme.md

@@ -0,0 +1,82 @@
+# Computation of centers from the AnyonWiki
+
+With the scripts in this folder you can compute the centers of the [multiplicity-free fusion categories](https://anyonwiki.github.io/pages/Lists/losmffc.html) from the [AnyonWiki](https://anyonwiki.github.io/). The AnyonWiki introduced a labeling system for these categories in the form $\mathrm{FC}^{a,b,c}_{d,e,f,g}$, see the [conventions](https://anyonwiki.github.io/pages/Lists/Conventions.html). The first entry $a$ is the rank of the category; the two last entries $f$ and $g$ correspond to different braidings and pivotal structures, respectively. 
+
+The corresponding category can be loaded into TensorCategories.jl with the command
+
+```julia
+anyonwiki(a,b,c,d,e,f,g)
+```
+
+So, in TensorCategories.jl we use a single 7-tuple as key. With the command `anyonwiki_keys(n)` you can get a list of all the keys from the AnyonWiki of rank $\leq n$. Since different braidings and pivotal structures do not change the center, we can pick one entry among the 5-tuples given by the first 5 entries. In the script we do this deterministically as follows:
+
+```julia
+codes_all = sort!(
+    collect(unique(c -> c[1:5], anyonwiki_keys(5)));
+    by = c -> Tuple(c[1:5])
+)
+```
+
+The core computations that are done in the scripts are computing the center (over a defining number field), find a splitting field of this category and extend to it, compute the F-symbols and save them (numerically in the numeric script), and do a randomized check on the pentagon axiom of the center:
+
+```julia
+C = anyonwiki(cat...)
+Z = center(C)
+
+local Z2
+local Z3
+
+simples(Z)
+Z2 = split(Z)[1]
+Z3 = six_j_category(Z2) #This involves computation of F-symbols
+
+save_fusion_category(Z3, dir, filename)
+
+randomized_pentagon_axiom(Z2, 3)
+randomized_pentagon_axiom(Z3, 3)
+```
+
+You can start the scripts with
+
+```bash
+julia anyonwiki_center.jl --threads=N
+```
+
+and
+
+```bash
+julia anyonwiki_center_numerically.jl --threads=N
+```
+
+where N is the numner of threads. This uses internal threading of TensorCategories.
+
+> [!WARNING]
+> If you interrupt the script with `Ctrl+C` there will still be worker processes. You can kill all julia processes with `pkill julia`. 
+
+There is also a more advanced script `anyonwiki_center_dist.jl` for distributed computation. It has several options:
+
+* `--workers`: The number of seperate processes (each working on one category). Notice that each worker is a julia process that needs to load TensorCategories and OSCAR, so this will take some time. The default is 1.
+* `--threads`: The number of threads for each worker. This uses the internal threading of TensorCategories. The default is 1.
+* `--first`: The entry number in `codes_all` where to start the compution. The default is 1.
+* `--last`: The entry in `codes_all` where to stop the compution. The default is the last entry.
+
+The `--first` and `--last` option help to resume computations, potentially with different workers and threads.
+
+So, an example call would be:
+
+```bash
+julia anyonwiki_centers_dist.jl \
+  --workers 4 \
+  --threads 4 \
+  --first 1 \
+  --last 40
+```
+
+The script saves timings in the table `center_runs/timings_all.tsv`.
+
+We have stored the centers of the also in our database and you can load it with the command
+
+```julia
+anyonwiki_center(a,b,c,d,e,f,g)
+```
+

src/Scripts/Centers of multiplicity-free fusion categories up to rank 5.jl → computations/anyonwiki_centers/anyonwiki_centers.jl

@@ -9,7 +9,7 @@
     with julia --threads=N to speed up the computation.
 ----------------------------------------------------------=#
 
-using TensorCategories, Oscar, ProgressMeter 
+using TensorCategories, Oscar
 
 # Specify the directory to store the centers
 dir = mktempdir(cleanup = true)