let's fully embrace the rust and use `make.rs` even in the CI with `make ci`

## changelog
- move inner logic to functions, e.g. `clippy` and `test`
- add `ci` command
  - runs all the CI stages by default
  - runs only the "fmt" stage with `--fmt`
  - runs only the "test" stage with `--test`
  - runs all the CI stages with `--fmt` and `--test`
- remove useless `json` variable in `docker_images_to_table`
- update the CI files to use `./make.rs ci ...`

## mirror
| id                                                                             | head_sha                                 | status    | conclusion | run_started_at      |
| ------------------------------------------------------------------------------ | ---------------------------------------- | --------- | ---------- | ------------------- |
| [`14495015473`](https://github.com/dragoon-rs/komodo/actions/runs/14495015473) | b185b5b4 | completed | success    | 2025-04-16T14:18:13 |
| [`14592505804`](https://github.com/dragoon-rs/komodo/actions/runs/14592505804) | cbce02c7 | completed | success    | 2025-04-22T10:24:17 |

this is an attempt at finishing the documentation for real.

the convention is
- start sentences with capital letter, speaks as 3rd person and end with period
- specify non-trivial cases and returns in the doc, otherwise, leave that to the tests
- use mathematical formulae to make things more clear

> 💡 **Note**
>
> might supersede !184

For now, i completely skipped FRI because i thought we could do that in a later MR, as it was added later and is not even part of a public release yet.

I also went a bit faster on _aPlonK_ as it is so complex and we will likely never use it.

## changelog
> - 🗞️ is for documentation changes
> - ⚙️ is for code changes

- (🗞️) moves the `RUSTDOCFLAGS` for Katex activation to `.cargo/config.toml`
- (🗞️) adds `simple_mermaid` for Mermaid graphs
- (🗞️) upgrades Katex from `0.10.0` to `0.16.21` for matrix support
- documentation
  - [x] (🗞️) (⚙️) `algebra`: check the length for `algebra::powers_of`
  - [x] (🗞️) (⚙️) `algebra::linalg`: use exact matches in the error tests and use struct errors
  - [x] (🗞️) (⚙️) `error`: change some errors to struct errors
  - [x] (🗞️) (⚙️) `fs`: rename some arguments, e.g. `block_hashes` to `hashes` and `dump_dir` to `directory`
  - [x] (🗞️) (⚙️) `zk`: inline `check_degree_is_too_large`
  - [x] (🗞️)          `fec`
  - [x] (🗞️)          `semi_avid`
  - [x] (🗞️)          `kzg`
  - [x] (🗞️) (⚙️) `aplonk`: remove `Commitment` and `VerifierKey`
  - [ ] (🗞️)          `fri`
  - [x] (🗞️)          Komodo (`lib.rs`)

This MR explains the use of `make.rs` and `nob.rs` in the README for newcomers.

## examples
```bash
./make.rs container list --json
    | from ndjson
    | into datetime CreatedAt
    | into filesize Size VirtualSize
    | reject CreatedSince
```
or
```bash
./make.rs container list --json
    | from ndjson
    | into datetime CreatedAt
    | into filesize Size VirtualSize
    | reject CreatedSince
    | select ID Repository Tag CreatedAt VirtualSize
    | update Tag { str substring 0..<7 }
```

## changelog
- transform options of `container` to sub-subcommands
  - `container` --> `container build`
  - `container --login` --> `container login`
  - `container --push` --> `container push`
- add `container list` to print the local images for the GitLab and GitHub repositories
  - `container list` will print in a pretty table
  - `container list --json` will print as NDJSON, i.e. one image per line as JSON
- use wrappers around `nob::run_cmd_as_vec_and_fail!`
  - `extend_and_run` to run a partial command with an extra vector of args
  - `extend_and_run_and_capture_silent` to run a partial command with an extra vector of args and silently capture the stdout into a string
  - this allows to get rid of the `#[rustfmt::skip]` _directive_ on `main` and format the code not too aggressively

This adds a Dockerfile to build an image for the pipelines, once and for all, until we decide to bump the Rust toolchain.

## changelog
- add `.gitlab-ci.dockerfile` which
  - uses `rust:latest` as a base (it appears using `alpine:latest` is both bigger and slower 🤷)
  - installs basic system dependencies
  - uses `rust-toolchain.toml` to install the toolchain of the project
  - installs `cargo-script`
- use [`gitlab-registry.isae-supaero.fr/dragoon/komodo:bcb0e6b5`](https://gitlab.isae-supaero.fr/dragoon/komodo/container_registry/42) in the GitLab pipelines and [`ghcr.io/dragoon-rs/dragoon/komodo:bcb0e6b5`](https://github.com/orgs/dragoon-rs/packages/container/dragoon%2Fkomodo/388672772?tag=bcb0e6b5f73420762f6208700a43291e0066c2c3) in the GitHub pipelines and remove the "manual" dependency installation
- add `./make.rs container`, `./make.rs container --login` and `./make.rs container --push`
  - uses `nob.rs@7ea6be8` to capture output of commands with `+` syntax
  - get the current Git SHA as the tag of the image
- instructions have been added to the `README.md` for later reference

## mirror
| id                                                                             | head_sha                                                                                                                           | status    | conclusion | run_started_at        |
| ------------------------------------------------------------------------------ | ---------------------------------------------------------------------------------------------------------------------------------- | --------- | ---------- | --------------------- |
| [`14262324842`](https://github.com/dragoon-rs/komodo/actions/runs/14262324842) | [`c93d9c87`](https://github.com/dragoon-rs/komodo/commit/c93d9c87928964aa20f347c1302757a06d2da628) | completed | success    | `2025-04-04T11:28:30` |
| [`14262372440`](https://github.com/dragoon-rs/komodo/actions/runs/14262372440) | [`f905e576`](https://github.com/dragoon-rs/komodo/commit/f905e57633f5e3dc7b1c38faa463daf54fb674bb) | completed | cancelled  | `2025-04-04T11:31:12` |
| [`14262477396`](https://github.com/dragoon-rs/komodo/actions/runs/14262477396) | [`21b26efd`](https://github.com/dragoon-rs/komodo/commit/21b26efd988b2d8d7159d24cae37341135cfb1b9) | completed | success    | `2025-04-04T11:36:59` |
| [`14263257396`](https://github.com/dragoon-rs/komodo/actions/runs/14263257396) | [`5bdca8cd`](https://github.com/dragoon-rs/komodo/commit/5bdca8cdb96e6ac2c25035513721485bcb08645d) | completed | success    | `2025-04-04T12:22:10` |
| [`14263314072`](https://github.com/dragoon-rs/komodo/actions/runs/14263314072) | [`bcb0e6b5`](https://github.com/dragoon-rs/komodo/commit/bcb0e6b5f73420762f6208700a43291e0066c2c3) | completed | success    | `2025-04-04T12:25:27` |
| [`14263368772`](https://github.com/dragoon-rs/komodo/actions/runs/14263368772) | [`ddd4a2a9`](https://github.com/dragoon-rs/komodo/commit/ddd4a2a9c1c28f4502814065de6aeca00b8b7a2f) | completed | success    | `2025-04-04T12:28:30` |
| [`14263575177`](https://github.com/dragoon-rs/komodo/actions/runs/14263575177) | [`f9400e61`](https://github.com/dragoon-rs/komodo/commit/f9400e619a066294714024174dacd4a0501a369c) | completed | success    | `2025-04-04T12:40:44` |



## speed
the performance appears to be around
- ~ 1min 35sec on GitLab (see
    [8331](https://gitlab.isae-supaero.fr/dragoon/komodo/-/pipelines/8331),
    [8332](https://gitlab.isae-supaero.fr/dragoon/komodo/-/pipelines/8332),
    [8333](https://gitlab.isae-supaero.fr/dragoon/komodo/-/pipelines/8333),
    [8334](https://gitlab.isae-supaero.fr/dragoon/komodo/-/pipelines/8334),
    [8335](https://gitlab.isae-supaero.fr/dragoon/komodo/-/pipelines/8335),
    [8336](https://gitlab.isae-supaero.fr/dragoon/komodo/-/pipelines/8336),
    [8337](https://gitlab.isae-supaero.fr/dragoon/komodo/-/pipelines/8337),
    [8338](https://gitlab.isae-supaero.fr/dragoon/komodo/-/pipelines/8338),
    [8339](https://gitlab.isae-supaero.fr/dragoon/komodo/-/pipelines/8339),
    [8340](https://gitlab.isae-supaero.fr/dragoon/komodo/-/pipelines/8340),
    [8341](https://gitlab.isae-supaero.fr/dragoon/komodo/-/pipelines/8341),
    all after b82e8950)
- ~ 4min on GitHub (see
    [14263257396](https://github.com/dragoon-rs/komodo/actions/runs/14263257396),
    [14263314072](https://github.com/dragoon-rs/komodo/actions/runs/14263314072),
    [14263368772](https://github.com/dragoon-rs/komodo/actions/runs/14263368772),
    [14263575177](https://github.com/dragoon-rs/komodo/actions/runs/14263575177),
    all after [5bdca8cd](https://github.com/dragoon-rs/komodo/commit/5bdca8cdb96e6ac2c25035513721485bcb08645d))

This should close #19.

## changelog
- triggers pipeline in the GitHub mirror on each push
- add `./scripts/get-mirror-pipelines.nu`

## the pipelines
> ❗ **Important**
>
> i just had to add `run-mirror-pipeline-everytime` to the list of protected branches and trigger the push with an empty commit and it runs
>
> and then a single call to `nu scripts/get-mirror-pipelines.nu "run-mirror-pipeline-everytime"` gives the table below

| id                                                                             | head_sha                                 | status    | conclusion | run_started_at      |
| ------------------------------------------------------------------------------ | ---------------------------------------- | --------- | ---------- | ------------------- |
| [`14238533729`](https://github.com/dragoon-rs/komodo/actions/runs/14238533729) | 2f32ee59 | completed | success    | 2025-04-03T08:32:31 |
| [`14238724666`](https://github.com/dragoon-rs/komodo/actions/runs/14238724666) | e7587675 | completed | success    | 2025-04-03T08:42:19 |
| [`14240494187`](https://github.com/dragoon-rs/komodo/actions/runs/14240494187) | 3c223dd6 | completed | success    | 2025-04-03T10:13:02 |
| [`14240642763`](https://github.com/dragoon-rs/komodo/actions/runs/14240642763) | cbc1f7f9 | completed | success    | 2025-04-03T10:21:04 |
| [`14240848529`](https://github.com/dragoon-rs/komodo/actions/runs/14240848529) | 7b34fc8a | completed | success    | 2025-04-03T10:32:06 |

this removes the `check-nushell-files.nu` script i left in !200.

that's an attempt at using Rust to build itself.

this is using [`gitlab.isae-supaero.fr:a.stevan/nob.rs@e4b03cdd`](a.stevan/nob.rs@e4b03cdd).

> 💡 **Note**
>
> to be honest, this is not a 100% replacement of the `Makefile`...
>
> `make.rs` does a lot more and provides a full CLI with easy-to-use options, e.g. instead of `make fmt` and `make fmt-check`, we now have `./make.rs fmt` and `./make.rs fmt --check`
>
> (see the API below)

## the API
```
Usage: make [OPTIONS] [COMMAND]

Commands:
  fmt      Formats the code
  check    Checks the code
  clippy   Runs Clippy
  test     Runs the tests
  version  Shows the version of all the tools used,
  doc      Builds the documentation
  help     Print this message or the help of the given subcommand(s)

Options:
  -h, --help      Print help
  -V, --version   Print version
```
```
Usage: make fmt [OPTIONS]

Options:
  -c, --check  Only checks instead of really formatting
```
```
Usage: make check
```
```
Usage: make clippy
```
```
Usage: make test [OPTIONS]

Options:
  -v, --verbose   Be extra verbose with the output of the tests
  -e, --examples  Run the examples instead of regular tests
```
```
Usage: make version
```
```
Usage: make doc [OPTIONS]

Options:
  -o, --open      Open the documentation in the browser
  -p, --private   Document private items
  -f, --features  Document all features
```

## running the pipeline in the GitHub mirror
```bash
const GH_API_OPTIONS = [
    -H "Accept: application/vnd.github+json"
    -H "X-GitHub-Api-Version: 2022-11-28"
]
let res = gh api ...$GH_API_OPTIONS /repos/dragoon-rs/komodo/actions/runs | from json
```
```bash
let runs = $res.workflow_runs
    | where head_branch == "use-nob-to-build"
    | select id head_sha status conclusion run_started_at
    | into datetime run_started_at
    | sort-by run_started_at
```
```bash
$runs
    | update id { $"[`($in)`]\(https://github.com/($GITHUB_MIRROR)/actions/runs/($in)\)" }
    | update run_started_at { format date "%Y-%m-%dT%H:%M:%S" }
    | to md --pretty
```
| id                                                                             | head_sha                                 | status    | conclusion | run_started_at      |
| ------------------------------------------------------------------------------ | ---------------------------------------- | --------- | ---------- | ------------------- |
| [`14237650542`](https://github.com/dragoon-rs/komodo/actions/runs/14237650542) | d67f1cfd | completed | success    | 2025-04-03T07:44:14 |
| [`14237741570`](https://github.com/dragoon-rs/komodo/actions/runs/14237741570) | 9ef598a1 | completed | success    | 2025-04-03T07:49:40 |
| [`14238086977`](https://github.com/dragoon-rs/komodo/actions/runs/14238086977) | 0a79edf3 | completed | success    | 2025-04-03T08:09:13 |
| [`14238175174`](https://github.com/dragoon-rs/komodo/actions/runs/14238175174) | a84b2b12 | completed | success    | 2025-04-03T08:13:52 |
| [`14239395984`](https://github.com/dragoon-rs/komodo/actions/runs/14239395984) | 8594c9bf | completed | success    | 2025-04-03T09:16:00 |

This is to complete the `check-mirror.nu` script with information about the CI runs.

The current output of
```bash
nu scripts/check-mirror.nu ...[
    https://gitlab.isae-supaero.fr/dragoon/komodo
    https://github.com/dragoon-rs/komodo
    main
]
```
is
```
[INF] adding remotes
[INF] fetching
[INF] cleaning
[ OK] mirror is up to date
[INF] pulling mirror runs
#─┬────id─────┬────────────────head_sha────────────────┬─status──┬conclusion┬run_started_at
0 │11950217125│de4266c0│completed│success   │4 months ago
1 │11950604920│202d8bcc│completed│success   │4 months ago
2 │11950873603│702cd5eb│completed│success   │4 months ago
3 │12028360471│57a96c02│completed│success   │4 months ago
4 │12028432364│07602875│completed│success   │4 months ago
5 │12028781541│f2a76fbb│completed│success   │4 months ago
6 │12631165433│11a5b59d│completed│success   │2 months ago
7 │13008608156│cc412625│completed│success   │2 months ago
8 │13033206333│5511404f│completed│success   │2 months ago
9 │13113244065│ab0d9a8b│completed│success   │2 months ago
10│13679188387│3c8afac4│completed│success   │3 weeks ago
11│14191103891│b5381fda│completed│success   │a day ago
12│14214853530│b7e2d99d│completed│success   │an hour ago
13│14215431531│0d7a5cd6│completed│success   │32 minutes ago
──┴───────────┴────────────────────────────────────────┴─────────┴──────────┴──────────────
```

this should close #17.

SACLIN has been moved to [`gitlab.isae-supaero.fr:dragoon/komodo.nu`](https://gitlab.isae-supaero.fr/dragoon/komodo.nu).

## usage
```bash
nu scripts/check-mirror.nu ...[
    https://gitlab.isae-supaero.fr/dragoon/komodo
    https://github.com/dragoon-rs/komodo
    main
]
```
will
- check the Nushell version and throw a warning if mismatch
- add temporary remotes with random names
- fetch the temporary remotes
- get the revision of the `$branch` for both temporary remotes
- clean the temporary remotes
- show a message if the two revisions are not the same and how many commits they are different

> **Note**
>
> this does not conflict with #17

HEME Clement authored 1 month ago and STEVAN Antoine committed 1 month ago

Added a html header files, an added metadata line in Cargo.toml and some formatting changes in the doc to have Latex formulas in docs.rs. It works locally, should work online

this is to avoid having to change the toolchain in the CI everytime.

`rust-toolchain.toml` and `.gitlab-ci.yml` will have to be updated in pairs when bumping / changing the Rust toolchain.

this is an attempt at making benchmarks easier to work with
- `benchmarks run` will read benchmarks from NUON data and run them
- `benchmarks plot` will plot benchmark results
- the output format will be something 
  - a directory whose name is the hash of the CPU spec and the Komodo commit hash
  - contains `cpu.json` with the CPU info
  - contains `komodo.txt` with the Komodo commit hash
  - contains NDJSON result files

> 💡 **Note**
>
> results will typically be uploaded to https://gitlab.isae-supaero.fr/dragoon/komodo-benchmark-results

> 💡 **Note**
>
> this MR goes alongside the [`komodo-benchmark-results@restart`](https://gitlab.isae-supaero.fr/dragoon/komodo-benchmark-results/-/compare/main...restart) branch

## changelog
- bump Nushell to 0.101.0
  - parallel `$in` => remove useless `let input = $in` when possible, e.g. still required when using the function's `$in` in a `for` loop
  - `group-by` changed => `group-by x --to-table` will now produce a table with columns `x` and `items` instead of `group` and `items` as in 0.95.0
- add link to results repo
- the Nushell benchmarks lib
  - rename `--force` to `--no-confirm (-y)`
  - add `--append` 
  - reject columns that GPLT will complain about, e.g. `$.points.k` for the FRI plots
  - add `--save` to the FRI plot
- move the "field" and "curve group" benchmarks from `benchmarks/src/bin/operations/` to `benchmarks/src/bin/`
- remove `benchmarks/params/fri.nu` because it's been uniformized with the other methods
- rewrite the README
- add main function to `benchmarks/` that runs the benchmarks from a NUON record specification
- simplify the output of FRI run

## TODO
- [x] fix "_atomic operations_" (done in 4f69a1d6)
- [x] check that _plotting_ still works

## images

### Field
![complex_curve_group_operations](/uploads/57b36926cce041cf405a9b44f190b8b8/complex_curve_group_operations.png)
![complex_field_operations](/uploads/0747c85dbaff8980561aa9d922fcd5e7/complex_field_operations.png)
![simple_curve_group_operations](/uploads/974cf70fed68f8d8ac898d54be3f27be/simple_curve_group_operations.png)
![simple_field_operations](/uploads/a3d4d0dcdeb35d4c434eaa38fb51e7b5/simple_field_operations.png)

### Linear algebra
![linalg-inverse](/uploads/bc290ffa39459ce0f9bbd393b50b7b98/linalg-inverse.png)
![linalg-mul](/uploads/96d8c2a63ed48d6a0d3508b4a948153b/linalg-mul.png)
![linalg-transpose](/uploads/128e35eca91497d8aadb0130c05aeee3/linalg-transpose.png)

### FEC
![encoding](/uploads/405c4d3ef9ec5135ebdd7ce2e6c96bfe/encoding.png)
![decoding](/uploads/d793234d44e9fc6f34f0c2a9372863cd/decoding.png)
![recoding](/uploads/413021de997c86d45b1287fcfe7804c7/recoding.png)
![combined](/uploads/6d1c3ae6d3bf5547434ca29ae80b5536/combined.png)
![ratio](/uploads/6cebd7a0bcef57d1b1256bc3941c1b0a/ratio.png)

### ZK
![setup](/uploads/1feb169452aa3274dc924edf772c9a5b/setup.png)
![commit](/uploads/0a2775c2116ca7d3fa7b956b934d1565/commit.png)

### FRI
![commits_single](/uploads/4602725e551a025d42815183a61d11b2/commits_single.png)
![commits_single_normalized](/uploads/2ffebea940af1cbbe9bd64499343e0e9/commits_single_normalized.png)
![end_to_end](/uploads/46917abd2f5976dfa6d3039cc0ab2c0e/end_to_end.png)
![evaluating](/uploads/cf4dc496cd5144615bf5f9b06d27dccd/evaluating.png)
![proofs](/uploads/b0828bfa62c2226c8d63c9ecd387049f/proofs.png)
![proofs_normalized](/uploads/8fbf0d713884e2e147c62313a001f379/proofs_normalized.png)
![proving](/uploads/161539dc412330be1878cdda82c3d966/proving.png)
![verifying_single](/uploads/2df7e777481d7789478386f8e83e0783/verifying_single.png)

the idea is to make the installation of Nushell easier to maintain, especially regarding versions, currently pinned to `0.95.0`

> successful run on GitHub: [13032726635](https://github.com/dragoon-rs/komodo/actions/runs/13032726635)

this is also to allow easier testing locally with the same Nushell version as in the CI, e.g.
```bash
# install in `~/.local/bin/` and have multiple versions
make install-nu

hash=$(/tmp/nu --no-config-file --commands 'version | get commit_hash')
nu_bin=$"$HOME/.local/bin/nu-$hash"
cp /tmp/nu $nu_bin

make NU=$nu_bin show test
```
or
```bash
# install in the repo and overwrite each time
make NU_DEST=. install-nu
make NU=./nu show test
```

# changelog
- Makefile
  - split the global `.PHONY` rule into _atomic_ rules next to each _phony_ rule
  - define `NU` and `NU_FLAGS` to allow changing which and how Nushell runs
  - define `NU_ARCH`, `NU_VERSION`, `NU_BUILD` and `NU_DEST` for Nushell installation
  - tweak the output of `make show` a bit
  - add `print-%` rules to print `Makefile` variables, e.g. `make print-NU_FLAGS` would print `--no-config-file`
  - add `make install-nu` to replace the ones from the CIs
- GitLab CI
  - use `make install-nu`
  - export `PATH` with `make print-NU_DEST`
- GitHub CI 
  - use `make install-nu` instead of [github.com:hustcer/setup-nu](https://github.com/hustcer/setup-nu)
  - export `PATH` with `make print-NU_DEST` and `GITHUB_ENV`

mainly fixes a few typos and improves `algebra` and `semi_avid` tests

## changelog
- fix some typos and notes in the documentation
- test more cases for `algebra::split_data_into_field_elements` and `algebra::merge_elements_into_bytes`, more data lengths and more modulus respectively
- remove a useless `::<Vec<_>>` on a `collect` in `fec`
- `semi_avid::tests`
  - refactor `bls12-381` into a constant
  - write an "_attack_" function to alter a particular block, `attack<F, G>(block: Block<F, G>, c: usize, base: u128, pow: u64) -> Block<F, G>`
  - pass a list of attacks, i.e. `attacks: Vec<(usize, usize, u128, u64)>`, to `verify_with_errors_template`, use the same as the previous hardcoded one
  - pass a list of "_recodings_", i.e. `recodings: Vec<Vec<usize>>`, to `verify_recoding_template` and assert the number of blocks, e.g. `vec![vec![2, 3], vec![3, 5]]` means that recoding 2 and 3 together should verify, and same with 3 and 5, and also that there must be at least 6 blocks
  - pass a list of "_recodings_", i.e. `recodings: Vec<(Vec<Vec<usize>>, bool)>`, to `end_to_end_with_recoding_template` and assert the number of blocks and the number of source shards, e.g. `vec![(vec![vec![0, 1], vec![2], vec![3]], true)]` means that trying to decode with blocks 2, 3 and a recoded block from 0 and 1 should work, and also that there must be at least 4 blocks and at most 3 source shards
  - pass `k` and `n` to `run_template`

this should avoid the following error when trying to rust the LSP in a toolchain which does not have the `rust-analyzer` component and without running `rustup component add rust-analyzer` manually:
```
error: Unknown binary 'rust-analyzer' in official toolchain 'stable-x86_64-unknown-linux-gnu'.
```

in order to help catch issues with the various Nushell scripts and modules in the source base, i propose to add a CI script that will check them all.

below is an example error, e.g. when introducing a syntax error in `.env.nu`:
```
Error:   × Failed to parse content:
  │     file: .env.nu
  │     err:  Expected keyword.
```

## changelog
- add more snippets and instructions
- add missing imports
- update the "atomic operations" section
- add a table of contents

this replaces the "_nothing to do_" messages from Nushell commands with more explicite errors.

DETCHART Jonathan authored 5 months ago and STEVAN Antoine committed 5 months ago

This MR adds an option to perform erasure coding using FFT rather than using a matrix. It also adds the field FP128 in the list of curves

Note that there is a redundant function `random_loss` into benchmarks/bin/fec.rs and examples/fec.rs

FRI protocol from [`dragoon/fri`](https://gitlab.isae-supaero.fr/dragoon/fri)

## changelog
- add binary assets to be used as inputs
- add `fri` and `fri_test_utils` as local dependencies until [`dragoon/fri`](https://gitlab.isae-supaero.fr/dragoon/fri) becomes public
- add `fri` feature and module (see section below for the public definitions)
- fix bug in 32bd6566
- bump Rust in e7a2c244
- add a versatile example
- add Nushell pipeline to run benchmarks and plot results
- add some tests

## `fri` module API
```rust
struct Block<F: PrimeField, H: Hasher>
```

```rust
fn evaluate<F: PrimeField>(bytes: &[u8], k: usize, n: usize) -> Vec<Vec<F>>
```

```rust
fn encode<F: PrimeField>(
    bytes: &[u8],
    evaluations: Vec<Vec<F>>,
    k: usize,
) -> Vec<fec::Shard<F>>
```

```rust
fn prove<const N: usize, F: PrimeField, H: Hasher, P>(
    evaluations: Vec<Vec<F>>,
    shards: Vec<fec::Shard<F>>,
    blowup_factor: usize,
    remainder_plus_one: usize,
    nb_queries: usize,
) -> Result<Vec<Block<F, H>>, KomodoError>
where
    P: DenseUVPolynomial<F>,
    for<'a, 'b> &'a P: Div<&'b P, Output = P>,
    <H as rs_merkle::Hasher>::Hash: AsRef<[u8]>,
```

```rust
fn verify<const N: usize, F: PrimeField, H: Hasher, P>(
    block: Block<F, H>,
    domain_size: usize,
    nb_queries: usize,
) -> Result<(), KomodoError>
where
    P: DenseUVPolynomial<F>,
    for<'a, 'b> &'a P: Div<&'b P, Output = P>,
    <H as rs_merkle::Hasher>::Hash: AsRef<[u8]>,
```

```rust
fn decode<F: PrimeField, H: Hasher>(blocks: Vec<Block<F, H>>, n: usize) -> Vec<u8>
```

## results

### times

![evaluating](/uploads/69607a2f987e26c23dd172d469c682c5/evaluating.png)
![encoding](/uploads/540ac15c21ba7500ad34b068c5d9d7dc/encoding.png)
![proving](/uploads/a694525c7d1277fe0b53dd87b6443900/proving.png)
![verifying_single](/uploads/8f03a3a0abca329eea396f3ba8b76512/verifying_single.png)
![decoding](/uploads/ba2cb0aa54f2ecff16340333121f16ca/decoding.png)

### sizes

![commits_single](/uploads/59a96661482fb1d918efc098e060cd45/commits_single.png)
![commits_single_normalized](/uploads/11398ed3f37ab4917b717cb717c9070d/commits_single_normalized.png)
![proofs](/uploads/17da07f4ef4ee637236deba7835cc022/proofs.png)
![proofs_normalized](/uploads/b2aae9491c56767ad1bf5674cf980361/proofs_normalized.png)

see the successful CI on GitHub: https://github.com/dragoon-rs/komodo/actions/runs/11950087413/job/33310881686

this MR adds two new badges to the README
- the crate (links to the [Komodo crate](https://crates.io/crates/komodo))
- the documentation (links to the [doc](https://docs.rs/komodo/latest/komodo/))

this adds three badges to the README:
- the latest release (links to the [release page](https://gitlab.isae-supaero.fr/dragoon/komodo/-/releases))
- the GitLab CI status (links to the [GitLab pipeline dashboard](https://gitlab.isae-supaero.fr/dragoon/komodo/-/pipelines))
- the GitHub CI status (links to the [GitHub workflow runs dashboard](https://github.com/dragoon-rs/komodo/actions))

This MR enables by default `kzg` and `aplonk`. By doing that, both modules should be visible in the doc.

## changelog
- _semi\_avid_, _kzg_ and _aplonk_ examples have been added
- the `fs` module has been hidden behind an `fs` feature
- the `conversions` module has been properly hidden behind the `test` config feature
- the documentation has been completed
- some error messages have been improved

> **Note**
>
> the documentation of aPlonK has been left as-is for now

`algebra`, `field` and `linalg` were doing extremely similar things before...

this MR merges them into a single module `algebra`
- old `algebra` and `field` are at the root of the new `algebra`
- old `linalg` is now `algebra::linalg`

all references to these have been fixed in the rest of the codebase and the features have been tuned to work fine.

in !162 and !163, i did only run `cargo ... --all-features` without checking the individual features...

this MR adds some `cargo check --features ...` to the `Makefile` and makes sure the imports make sense when compiling a single feature.

> ❗ **Important**
>
> the other notable change here is that `kzg::commit` has been moved to `zk::ark_commit` and is re-exported from `kzg` as `kzg::commit`.

this adds the aPlonK cryptographic method alongside Semi-AVID and KZG+.

## changelog
- new feature `aplonk`:
  - the `algebra` module is compiled when either `kzg` or `aplonk` features are enabled
  - `algebra::scalar_product_polynomial` compiles only with `kzg`
  - the other `algebra::*` functions compile with `aplonk`
- `u32_to_u8_vec` has been moved to new `conversions` module which compiles when either `kzg` or `aplonk` features are enabled
- new `aplonk` module which compiles only when the `aplonk` feature is enabled
  - public structures
    - `Block`
    - `Commitment`
    - `SetupParams`
    - `VerifierKey`
  - public functions
    - `setup`
    - `commit`
    - `prove`
    - `verify`
  - internals
    - `ipa::Params`
    - `ipa::Proof`
    - `ipa::prove`
    - `ipa::verify`
    - `polynomial::compute_g`
    - `transcript::initialize`
    - `transcript::reset`
    - `transcript::hash`

this adds the KZG+ cryptographic method alongside Semi-AVID.

## changelog
- the Makefile now uses `--all-features` to compile everything
- a new module `algebra` has been added, with tests for all functions
  - `algebra::scalar_product_polynomial` computes a linear combination of polynomials $(P_i)$
  - `algebra::powers_of` computes $n$ successive powers of a number $r$
- a new function `zk::trim` has been added from [`gitlab.isae-supaero.fr:a.stevan/poly-commit@19fc0d4a/src/kzg10/mod.rs#L513-L538`](https://gitlab.isae-supaero.fr/a.stevan/poly-commit/-/blob/19fc0d4ad2bcff7df030c952d09649918dba7ddb/src/kzg10/mod.rs#L513-L538)
- a new feature `kzg` has been added, with an optional dependency on [`gitlab.isae-supaero.fr:a.stevan/poly-commit@19fc0d4a`](https://gitlab.isae-supaero.fr/a.stevan/poly-commit/-/tree/19fc0d4ad2bcff7df030c952d09649918dba7ddb)
- a new module `kzg` has been added and exposes the following publicly
  - structures
      - `Block`
  - functions
    - `commit`
    - `prove`
    - `verify`
    - `batch_verify`
  - tests when block are left as-is and when one of them is corrupted

## changelog
- `src/main.rs` has been moved to a new crate: `bins/saclin` which stands for **S**emi-**A**VID **CLI** in **N**ushell
- dependencies of `komodo` have been fixed
- Nushell and Rust tests have been split in the Makefile: by default, only Rust tests will run locally and Nushell tests and examples can be run manually if desired. The CI will still run everything.
- the README has been updated
- test images have been moved to `assets/`
- the majority of the old `./nu-utils/` module have been moved to internals of `./benchmarks/` and imports have been fixed
- `cargo.nu` has been moved to `./bins/` and a new `./bins/README.md` mentions it
- `./bins/saclin/` has been created and should be a self-contained Rust crate + Nushell module

this is a refactor to prepare the addition of other cryptographic methods.

## changelog
- moves Semi-AVID code from `lib.rs` to `semi_avid.rs`