Merge pull request #53 from master-csmi/develop

Adding some minors corrections and final correction

Notebook_test.ipynb

@@ -743,7 +743,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "#### Let's implement a test with Pytest to verify that the errors are less than 0.01 for the property f($f^{-1}(B) + f^{-1}(C)$)"
+    "#### Let's implement a test with Pytest to verify that the errors are less than 0.01 for the property $f(f^{-1}(B) + f^{-1}(C))$"
    ]
   },
   {
@@ -1045,7 +1045,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "#### Let's implement a test with Pytest to verify that the errors are less than 0.01 for the property f($\\alpha \\cdot f^{-1}(B)$)"
+    "#### Let's implement a test with Pytest to verify that the errors are less than 0.01 for the property $f(\\alpha \\cdot f^{-1}(B))$"
    ]
   },
   {
@@ -1055,8 +1055,8 @@
    "outputs": [],
    "source": [
     "\n",
-    "assert all(float(erreur) < 0.01 for erreur in erreur_list_l2), \"Au moins une erreur L^2 est supérieure à 0.01\"\n",
-    "assert all(float(erreur) < 0.01 for erreur in erreur_list_inf), \"Au moins une erreur inf est supérieure à 0.01\""
+    "assert all(float(erreur) <= 0.01 for erreur in erreur_list_l2), \"Au moins une erreur L^2 est supérieure à 0.01\"\n",
+    "assert all(float(erreur) <= 0.01 for erreur in erreur_list_inf), \"Au moins une erreur inf est supérieure à 0.01\""
    ]
   },
   {

Pres_Slid.tex

@@ -191,11 +191,11 @@
         \begin{enumerate}
             \item Loss for vector addition:
             \[
-                L_1(\theta) = \sum_{(x, y) \in V \times V} \left\lVert x \oplus y - f(f^{-1}(x) + f^{-1}(y))\right\rVert_{V}^2
+                L_1(\theta) = \sum_{(x, y) \in V \times V} \left\lVert x \oplus_{\theta} y - f(f^{-1}(x) + f^{-1}(y))\right\rVert_{V}^2
             \]
             \item Loss for scalar multiplication:
             \[
-                L_2(\theta) = \sum_{(\alpha, x) \in \mathbb{R} \times V} \left\lVert \alpha \odot x - f(\alpha \cdot f^{-1}(x)) \right\rVert_{V}^2
+                L_2(\theta) = \sum_{(\alpha, x) \in \mathbb{R} \times V} \left\lVert \alpha \odot_{\theta} x - f(\alpha \cdot f^{-1}(x)) \right\rVert_{V}^2
             \]
         \end{enumerate}