update readme

math-tutor/README.md

-## Run the app
+# DER Tutor
+
+## Prequisits
+
+- Postgres-Database [Database (pgvector) setup]
+- sources folder with your markdown files structured with section, subsection and child
+- OpenAI endpoint
+- Ollama Instanz
+
+if you want to use the task mode you need :
+
+- task folder in sources with your tasks
+- `_subsection_map.json`.
+
+## Setup
+
+Configurate the `backend/.env`-file based on the `backend/.env-example`. You can che following modes:
+
+- QA : Direct answer based on the retrieval
+- Tutor: Helps with tips on a task given by the user
+- Task: A mode where you can select from the list in the taskfolder and get help with this Task.
 
 Backend (Python):
-```powershell
+
+``` powershell
 cd math-tutor/backend
 python -m venv .venv
 .\.venv\Scripts\Activate.ps1
 pip install -r requirements.txt
+```
+
+Frontend (Vite):
+
+```
+cd math-tutor/frontend
+npm install
+```
+
+## Run the app
+
+Backend (Python):
+
+```powershell
+cd math-tutor/backend
+.\.venv\Scripts\Activate.ps1
 python -m uvicorn app.main:app --reload
 ```
 
 Frontend (Vite):
+
 ```powershell
 cd math-tutor/frontend
-npm install
 npm run dev
 ```
+
 To make it accessible over the network.
-Add the frontend- and backend-adress in the .env file in the frontend- and backend-folder.
+Add the frontend- and backend-adress in the `backend/.env`-file in the frontend- and backend-folder. Use the following command to run the front- and backend.
 
+```powershell
 python -m uvicorn app.main:app --reload --host 0.0.0.0 --port 8000
 npm run dev -- --host 0.0.0.0
+```
+
 ## Database (pgvector) setup
 
 Ensure `POSTGRES_URL` and embedding env vars are in `backend/.env`:
-```
+
+``` env
 POSTGRES_URL=postgresql://user:pass@host:5432/db
 OPENAI_BASE_URL=...
 OPENAI_API_KEY=...
@@ -33,6 +75,7 @@ OPENAI_EMBED_MODEL=...
 Create the Postgres database before running init.
 
 Init DB schema:
+
 ```powershell
 cd math-tutor/backend
 .\.venv\Scripts\Activate.ps1
@@ -40,6 +83,7 @@ python -m scripts.retrieval_cli init-db
 ```
 
 Ingest markdown docs (expects `markdown/sections`, `markdown/subsections`, `markdown/childs`):
+
 ```powershell
 cd math-tutor/backend
 .\.venv\Scripts\Activate.ps1
@@ -47,6 +91,7 @@ python -m scripts.retrieval_cli ingest --base markdown --clear
 ```
 
 Query via CLI:
+
 ```powershell
 cd math-tutor/backend
 .\.venv\Scripts\Activate.ps1
@@ -56,9 +101,11 @@ python -m scripts.retrieval_cli query --q "Was ist eine Teilmenge?" --k 8 --expa
 ## Configuration
 
 Differend Orchestrators:
+
 - Edit `math-tutor/backend/app/api/chat.py` and update `SYSTEM_PROMPT`.
 
 Retrieval settings:
+
 - Frontend request parameters live in `math-tutor/frontend/src/pages/App.tsx`:
   - `k`
   - `expand_links`
@@ -67,8 +114,17 @@ Retrieval settings:
 - Core retrieval logic is in `math-tutor/backend/app/services/vector_store.py` (`retrieve`).
 
 ## Testing
+
+currently there a multiple test to test some components seperatly. Check the test files for specific calling. Here are some example calls. 
+
+```powershell
 python -m test.hint_test --chat-id draft_session_mlgmxxzc_avmjfb
+
 python -m test.retrieval_store_test --query "Was ist eine Teilmenge?" --k 8 --expand
+
 python -m test.retrieval_store_test --query "Was ist eine Teilmenge?" --k 3 --subsections 1:1
+
 python -m test.math_intent_test --input "Integrate x^2" --input "Was ist 2+2?"
+
 python -m test.decision_test --chat-id draft_session_mlgmxxzc_avmjfb
+```