update github workflow, the build part

.github/workflows/python-publish.yml

@@ -1,7 +1,4 @@
-# This workflow will install Python dependencies, run tests and lint with a single version of Python
-# For more information see: https://help.github.com/actions/language-and-framework-guides/using-python-with-github-actions
-
-name: Python application
+name: PyReduce application
 
 on:
   push:
@@ -12,14 +9,25 @@ on:
 jobs:
   build:
     runs-on: ubuntu-latest
+    strategy:
+      matrix:
+        python-version: [3.9, 3.10, 3.11, 3.12]
 
     steps:
-    - uses: actions/checkout@v2
+    - uses: actions/checkout@v4
 
-    - name: Set up Python 3.8
-      uses: actions/setup-python@v2
+    - name: Set up Python
+      uses: actions/setup-python@v5
       with:
-        python-version: 3.8
+        python-version: ${{ matrix.python-version }}
+
+    - name: Cache Python dependencies
+      uses: actions/cache@v3
+      with:
+        path: ~/.cache/pip
+        key: ${{ runner.os }}-pip-${{ hashFiles('**/requirements.txt') }}
+        restore-keys: |
+          ${{ runner.os }}-pip-
 
     - name: Install dependencies
       run: |
@@ -43,7 +51,7 @@ jobs:
     needs: [build]
     if: github.event_name == 'push'
     steps:
-    - uses: actions/checkout@v2
+    - uses: actions/checkout@v4
 
     - name: GitHub Tag
       id: tag_release