eduroam-prg-og-1-29-184.net.univ-paris-diderot.fr 2026-3-23:11:26:56

.obsidian/graph.json

@@ -130,6 +130,6 @@
   "repelStrength": 5.263671875,
   "linkStrength": 1,
   "linkDistance": 30,
-  "scale": 0.0989427787267463,
+  "scale": 0.13320413080202398,
   "close": true
 }

.obsidian/plugins/breadcrumbs/data.json

@@ -631,7 +631,7 @@
           "prevs"
         ],
         "lock_view": false,
-        "lock_path": "anneau.md"
+        "lock_path": "sources/Alan Perlis.md"
       },
       "tree": {
         "collapse": false,
@@ -651,7 +651,7 @@
           "alias": false
         },
         "lock_view": false,
-        "lock_path": "anneau.md"
+        "lock_path": "sources/Alan Perlis.md"
       }
     },
     "codeblocks": {

anneau.md

@@ -60,7 +60,7 @@ depth: [0, 2]
 > $a^{n} - b^{n} = (a-b) \sum\limits_{k=0}^{n-1}a^{k}b^{n-1-k}$
 > > [!démonstration]- Démonstration
 > > Réécrivons le terme de droite de manière développée :
-> > $\begin{align} (a-b)\sum\limits_{k=0}^{n-1}a^{k}b^{n-1-k} &= (a-b)(a^{0}b^{n-1} + a^{1}b^{n-2} + \cdots + a^{n-2}b^{1}+a^{n-1}b^{0}) \\&= \bcancel{\color{darkred}a^{1}b^{n-1}} + \bcancel{\color{chartreuse}a^{2}b^{n-2}}+\bcancel{\color{deepskyblue} a^{3}b^{n-3}} + \cdots + \bcancel{\color{orange} a^{n-1}b^{1}} +a^{n}b^{0} \\ &\quad \,- a^{0}b^{n}-a^{1}b^{n-1}- a^{2}b^{n-2}-\cdots -a^{n-2}b^{2}-a^{n-1}b^{1} \end{align}$
+> > $\begin{align} (a-b)\sum\limits_{k=0}^{n-1}a^{k}b^{n-1-k} &= (a-b)(a^{0}b^{n-1} + a^{1}b^{n-2} + \cdots + a^{n-2}b^{1}+a^{n-1}b^{0}) \\&= \bcancel{\color{deepskyblue}a^{1}b^{n-1}} + \bcancel{\color{chartreuse}a^{2}b^{n-2}}+\bcancel{\color{#ffaaff} a^{3}b^{n-3}} + \cdots + \bcancel{\color{orange} a^{n-1}b^{1}} +a^{n}b^{0} \\ &\quad \,- a^{0}b^{n} - \bcancel{\color{deepskyblue}a^{1}b^{n-1}} \bcancel{\color{chartreuse} - a^{2}b^{n-2}}- \cdots \bcancel{\color{#aaaaff}-a^{n-2}b^{2}} \bcancel{\color{orange}-a^{n-1}b^{1}} \\&= a^{n}b^{0} - a^{0}b^{n} \\&= \boxed{a^{n} - b^{n}} \end{align}$
 > >    
 
 # Exemples

morphisme d'anneaux.md

@@ -2,6 +2,7 @@
 aliases:
 up:
   - "[[morphisme]]"
+  - "[[anneau]]"
 tags:
   - s/maths/algèbre
 ---

morphisme.md

@@ -8,7 +8,7 @@
 ```breadcrumbs
 title: "Sous-notes"
 type: tree
-collapse: false
+collapse: true
 show-attributes: [field]
 field-groups: [downs]
 depth: [0, 1]