See issue #15

Needs review: stupid copy of fec::recode_random code.

more user-oriented examples
links to komodo error doc

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`

- 1c9077f6 add documentation to the errors
- c388cbbb better FEC doc
- 8d58278d doc of `zk.nb_elements_in_setup`

this MR is two-fold
- it restructures the two main Nushell modules so that they are easier to read and use
- it improves the "run" and "plot" modules for the benchmarks

## changelog
- `.nushell/` is now renamed to `nu-utils/`
- `benchmarks/` is now a valid Nushell module which exports a bunch of modules
  - `benchmarks linalg`: measure and plot linear algebra operations
  - `benchmarks setup`: measure and plot trusted setup building
  - `benchmarks commit`: measure and plot crafting commitments
  - `benchmarks recoding`: measure and plot the recoding of shards
  - `benchmarks fec`: measure and plot FEC operations, such as encoding and recoding, and allow combining these results with the pure recoding ones
- the submodules of `benchmarks` typically have a `run` and a `plot` command, whith the exception of `benchmarks fec` which has a `run` module and multiple "plot" commands in `benchmarks fec plot`
- the "run" commands will create a random temp file by default and ask for confirmation otherwise if the output file already exists, unless `--force` is used
- snippetds in `benchmarks/README.md` have been updated

## results
![setup](/uploads/1f3a383689d3c8fd5a3f1331deabdec0/setup.png)
![commit](/uploads/bcf3bfdd991725abb97cbe4f8890840b/commit.png)
![inverse](/uploads/35316c887c6b2347baa86c4db119f762/inverse.png)
![mul](/uploads/262c27e99d7f2b5c8fb45761607a8717/mul.png)
![transpose](/uploads/2378460cb687d0a9320a24a840ed2eef/transpose.png)

see the changelogs of
- [Nushell `0.94.0`](https://www.nushell.sh/blog/2024-05-28-nushell_0_94_0.html)
- [Nushell `0.94.1`](https://www.nushell.sh/blog/2024-05-30-nushell_0_94_1.html)
- [Nushell `0.94.2`](https://www.nushell.sh/blog/2024-06-03-nushell_0_94_2.html)

i also removed the `bytes encode` and `bytes decode` commands from `.nushell/binary.nu` because... well they did not work anymore and they were not used anywhere 👀