update cookbook

docs/lang/python.md

@@ -57,10 +57,12 @@ The venv will need to be created manually with `python -m venv /path/to/venv` un
 
 ## mise & uv
 
-If you have installed `uv` (for example, with `mise use -g uv@latest`, `mise` will use it to create virtual environments. Otherwise, it will use the built-in `python -m venv` command.
+If you have installed `uv` (for example, with `mise use -g uv@latest`), `mise` will use it to create virtual environments. Otherwise, it will use the built-in `python -m venv` command.
 
 Note that `uv` does not include `pip` by default (as `uv` provides `uv pip` instead). If you need the `pip` package, add the `uv_create_args = ['--seed']` option.
 
+See the [mise + uv Cookbook](/mise-cookbook/python.html#mise-+-uv) for more examples.
+
 ## Default Python packages
 
 mise can automatically install a default set of Python packages with pip right after installing a

docs/mise-cookbook/python.md

@@ -1,6 +1,6 @@
 # Mise + Python Cookbook
 
-Here are some tips on managing Python projects with mise.
+Here are some tips on managing [Python](/lang/python.html) projects with mise.
 
 ## A Python Project with virtualenv
 
@@ -44,3 +44,56 @@ echo "Project: $PROJECT_NAME"
 echo "Virtual Environment: $VIRTUAL_ENV"
 '''
 ```
+
+## mise + uv
+
+If you are using a `uv` project initialized with `uv init .`, here is how you can use it with mise.
+
+Here is how the `uv` project will look like:
+
+```shell [uv-project]
+.
+├── .gitignore
+├── .python-version
+├── hello.py
+├── pyproject.toml
+└── README.md
+
+cat .python-version
+# 3.12
+```
+
+If you run `uv run hello.py` in the `uv` project, `uv` will automatically create a virtual environment for you using the python version specified in the `.python-version` file. This will also create a `uv.lock` file.
+
+`mise` will detect the python version in `.python-version`, however, it won't use the virtual env created by `uv` by default. So, using `which python` will show a global python installation from `mise`.
+
+```shell
+mise i
+which python
+# ~/.local/share/mise/installs/python/3.12.4/bin/python
+```
+
+If you want `mise` to use the virtual environment created by `uv`, you can set the [`python.uv_venv_auto`](/lang/python.html#python.uv_venv_auto) setting to `true` in your `mise.toml` file.
+
+```toml [mise.toml]
+[settings]
+python.uv_venv_auto = true
+```
+
+Using `which python` will now show the python version from the virtual environment created by `uv`.
+
+```shell
+which python
+# ./uv-project/.venv/bin/python
+```
+
+Another option is to use `_.python.venv` in your `mise.toml` file to specify the path to the virtual environment created by `uv`.
+
+```toml [mise.toml]
+[env]
+_.python.venv = { path = ".venv" }
+```
+
+### Syncing python versions installed by mise and uv
+
+You can use [uv sync python --uv](/cli/sync/python.html#uv) to sync the python version installed by `mise` with the python version specified in the `.python-version` file in the `uv` project.