vault backup: 2026-02-04 14:01:55

.obsidian/community-plugins.json

@@ -1,5 +1,6 @@
 [
   "obsidian-git",
   "obsidian-style-settings",
-  "obsidian-tikzjax"
+  "obsidian-tikzjax",
+  "obsidian-completr"
 ]

.obsidian/plugins/obsidian-completr/callout_suggestions.json

@@ -0,0 +1,164 @@
+[
+  {
+    "displayName": "Note",
+    "replacement": "note",
+    "icon": "lucide-pencil",
+    "color": "#448aff"
+  },
+  {
+    "displayName": "Summary",
+    "replacement": "summary",
+    "icon": "lucide-clipboard-list",
+    "color": "#00b0ff"
+  },
+  {
+    "displayName": "Abstract",
+    "replacement": "abstract",
+    "icon": "lucide-clipboard-list",
+    "color": "#00b0ff"
+  },
+  {
+    "displayName": "TL;DR",
+    "replacement": "tldr",
+    "icon": "lucide-clipboard-list",
+    "color": "#00b0ff"
+  },
+  {
+    "displayName": "Info",
+    "replacement": "info",
+    "icon": "lucide-info",
+    "color": "#00b8d4"
+  },
+  {
+    "displayName": "To-Do",
+    "replacement": "todo",
+    "icon": "lucide-check-circle-2",
+    "color": "#00b8d4"
+  },
+  {
+    "displayName": "Tip",
+    "replacement": "tip",
+    "icon": "lucide-flame",
+    "color": "#00bfa6"
+  },
+  {
+    "displayName": "Hint",
+    "replacement": "hint",
+    "icon": "lucide-flame",
+    "color": "#00bfa6"
+  },
+  {
+    "displayName": "Important",
+    "replacement": "important",
+    "icon": "lucide-flame",
+    "color": "#00bfa6"
+  },
+  {
+    "displayName": "Success",
+    "replacement": "success",
+    "icon": "lucide-check",
+    "color": "#00c853"
+  },
+  {
+    "displayName": "Check",
+    "replacement": "check",
+    "icon": "lucide-check",
+    "color": "#00c853"
+  },
+  {
+    "displayName": "Done",
+    "replacement": "done",
+    "icon": "lucide-check",
+    "color": "#00c853"
+  },
+  {
+    "displayName": "Question",
+    "replacement": "question",
+    "icon": "lucide-help-circle",
+    "color": "#63dd17"
+  },
+  {
+    "displayName": "Help",
+    "replacement": "Help",
+    "icon": "lucide-help-circle",
+    "color": "#63dd17"
+  },
+  {
+    "displayName": "FAQ",
+    "replacement": "faq",
+    "icon": "lucide-help-circle",
+    "color": "#63dd17"
+  },
+  {
+    "displayName": "Warning",
+    "replacement": "warning",
+    "icon": "lucide-alert-triangle",
+    "color": "#ff9100"
+  },
+  {
+    "displayName": "Caution",
+    "replacement": "caution",
+    "icon": "lucide-alert-triangle",
+    "color": "#ff9100"
+  },
+  {
+    "displayName": "Attention",
+    "replacement": "attention",
+    "icon": "lucide-alert-triangle",
+    "color": "#ff9100"
+  },
+  {
+    "displayName": "Failure",
+    "replacement": "failure",
+    "icon": "lucide-x",
+    "color": "#ff5252"
+  },
+  {
+    "displayName": "Fail",
+    "replacement": "fail",
+    "icon": "lucide-x",
+    "color": "#ff5252"
+  },
+  {
+    "displayName": "Missing",
+    "replacement": "missing",
+    "icon": "lucide-x",
+    "color": "#ff5252"
+  },
+  {
+    "displayName": "Danger",
+    "replacement": "danger",
+    "icon": "lucide-zap",
+    "color": "#ff1744"
+  },
+  {
+    "displayName": "Error",
+    "replacement": "error",
+    "icon": "lucide-zap",
+    "color": "#ff1744"
+  },
+  {
+    "displayName": "Bug",
+    "replacement": "bug",
+    "icon": "lucide-bug",
+    "color": "#f50057"
+  },
+  {
+    "displayName": "Example",
+    "replacement": "example",
+    "icon": "lucide-list",
+    "color": "#7c4dff"
+  },
+  {
+    "displayName": "Quote",
+    "replacement": "quote",
+    "icon": "quote-glyph",
+    "color": "#9e9e9e"
+  },
+  {
+    "displayName": "Cite",
+    "replacement": "cite",
+    "icon": "quote-glyph",
+    "color": "#9e9e9e"
+  }
+]

.obsidian/plugins/obsidian-completr/manifest.json

@@ -0,0 +1,10 @@
+{
+    "id": "obsidian-completr",
+    "name": "Completr",
+    "version": "3.2.0",
+    "minAppVersion": "1.0.0",
+    "description": "This plugin provides advanced auto-completion functionality for LaTeX, Frontmatter and standard writing.",
+    "author": "tth05",
+    "authorUrl": "https://github.com/tth05",
+    "isDesktopOnly": true
+}

.obsidian/plugins/obsidian-completr/styles.css

@@ -0,0 +1,110 @@
+body {
+    --completr-suggestion-icon-height: 14px;
+}
+
+.completr-suggestion-item {
+    padding: 5px 10px 5px 10px;
+    white-space: nowrap;
+    overflow: hidden;
+    text-overflow: ellipsis;
+
+    display: flex;
+    align-items: center;
+}
+
+.completr-suggestion-item > * {
+    display: inline-block;
+}
+
+.completr-suggestion-icon {
+    height: var(--completr-suggestion-icon-height);
+    min-height: var(--completr-suggestion-icon-height);
+    max-height: var(--completr-suggestion-icon-height);
+
+    margin-right: 0.5ch;
+    color: var(--completr-suggestion-color);
+}
+
+.completr-suggestion-text {
+}
+
+.completr-suggestion-placeholder {
+    border-width: 1px 0 1px 0;
+    border-style: solid;
+}
+
+.completr-settings-no-border {
+    border: none;
+}
+
+.completr-settings-list-item {
+    border-top: 1px solid grey;
+    padding: 4px 0 0 0;
+}
+
+.completr-settings-error {
+    border: 1px solid red !important;
+}
+
+/**
+Snippet color classes.
+["lightskyblue", "orange", "lime", "pink", "cornsilk", "magenta", "navajowhite"]
+ */
+
+.completr-suggestion-placeholder0 {
+    border-color: lightskyblue;
+}
+
+/* These extra selectors enforce their color on all children, because CodeMirror does weird nesting of spans when
+ nesting multiple decorations. */
+span.completr-suggestion-placeholder0 span {
+    border-color: lightskyblue;
+}
+
+.completr-suggestion-placeholder1 {
+    border-color: orange;
+}
+
+span.completr-suggestion-placeholder1 span {
+    border-color: orange;
+}
+
+.completr-suggestion-placeholder2 {
+    border-color: lime;
+}
+
+span.completr-suggestion-placeholder2 span {
+    border-color: lime;
+}
+
+.completr-suggestion-placeholder3 {
+    border-color: pink;
+}
+
+span.completr-suggestion-placeholder3 span {
+    border-color: pink;
+}
+
+.completr-suggestion-placeholder4 {
+    border-color: cornsilk;
+}
+
+span.completr-suggestion-placeholder4 span {
+    border-color: cornsilk;
+}
+
+.completr-suggestion-placeholder5 {
+    border-color: magenta;
+}
+
+span.completr-suggestion-placeholder5 span {
+    border-color: magenta;
+}
+
+.completr-suggestion-placeholder6 {
+    border-color: navajowhite;
+}
+
+span.completr-suggestion-placeholder6 span {
+    border-color: navajowhite;
+}

Ekvations System.md

@@ -30,6 +30,23 @@
 		- *Eftersom $z$ är en fri variabler kan $z=t$, och $t\in\mathbb{R}$. sampt* $$\begin{aligned}y-z=-\frac52\Rightarrow{y}=z-\frac52=t-\frac52\\x-2y+z=3\Rightarrow{x}=2y-z+3=2\left(t-\frac52\right)-t+3=t-2\\\end{aligned}$$
 	3. **Exakt-bestämnd system/Saknar lösningar** $$\begin{aligned}\begin{aligned}x-3y+2z&=&3\\x-2y&=&2\\2x-5y+2z&=&4\end{aligned}\Rightarrow\begin{pmatrix}1&-3&2&|&3\\1&-2&2&|&2\\2&-5&2&|&-4\end{pmatrix}\begin{aligned}R_2-R_1\rightarrow{R_2}\\R_3-2R_1\rightarrow{R_3}\\\xrightarrow{}\end{aligned}\begin{pmatrix}1&-3&2&|&3\\0&1&0&|&-1\\0&1&-2&|&-2\end{pmatrix}\\\begin{aligned}R_3-R_2\rightarrow{R_3}\\\xrightarrow{}\end{aligned}\pmatrix{1&-3&2&|&3\\0&1&2&|&-1\\0&0&0&|&-1}\end{aligned}$$
 		- **OBS** *Rad $2$ och $3$ säger att det skall vara $-2$ medans de int har samma $VL$, detta går inte! samt säger det $0x+0y+0z=-1\Leftrightarrow{0=-1}$*
+	4. **Över-bestämd system/Entydlig Lösning** $$\begin{aligned}\begin{aligned}x-3y+2z&=&3\\x-2y&=&2\\x-y-z&=&2\\2x-5y+2z&=&5\end{aligned}\Rightarrow\begin{pmatrix}1&-3&2&|&3\\1&-2&0&|&2\\1&-1&-1&|&2\\2&-5&2&|&5\end{pmatrix}\begin{aligned}R_2-R_1\rightarrow{R_2}\\R_3-R_1\rightarrow{R_3}\\R_4-2R_1\rightarrow{R_4}\\\xrightarrow{}\end{aligned}\\\begin{pmatrix}1&-3&2&|&3\\0&1&-2&|&-1\\0&2&-3&|&-1\\0&1&-2&|&-1\end{pmatrix}\begin{aligned}R_3-2R_2\rightarrow{R_3}\\R_4-R_2\rightarrow{R_4}\\\xrightarrow{}\end{aligned}\begin{pmatrix}1&-3&2&|&3\\0&1&-2&|&-1\\0&0&1&|&1\\0&0&0&|&0\end{pmatrix}\end{aligned}$$
+		- *Vi har fott en entydlig lösning med*$$\begin{aligned}z=1\\y-2z=-1\Rightarrow{}y=2z-1=1\\x-3y+2z=3\Rightarrow{}x=3y-2z+3=4\end{aligned}$$
+	5. **Över-bestämd system/oändliga lösningar** $$\begin{aligned}\begin{aligned}x-3y+2z=3\\x-2z=3\\-3y+4z=0\\3x-3y+2z=9\end{aligned}\Rightarrow\begin{pmatrix}1&-3&2&|&3\\1&0&-2&|&3\\0&-3&4&|&0\\3&-3&2&|&9\end{pmatrix}\begin{aligned}R_2-R_1\rightarrow{R_2}\\R_4-3R_1\rightarrow{R_4}\\\xrightarrow{}\end{aligned}\begin{pmatrix}1&-3&2&|&3\\0&3&-4&|&0\\0&-3&4&|&0\\0&6&-8&|&0\end{pmatrix}\\\begin{aligned}R_3+R_2\rightarrow{R_3}\\R_4-2R_2\rightarrow{R_4}\\\xrightarrow{}\end{aligned}\begin{pmatrix}1&-3&2&|&3\\0&3&-4&|&0\\0&0&0&|&0\\0&0&0&|&0\end{pmatrix}\begin{aligned}\frac13R_2\rightarrow{R_2}\\\xrightarrow{}\end{aligned}\begin{pmatrix}1&-3&2&3\\0&1&-\frac34&|&0\\0&0&0&|&0\\0&0&0&|&0\end{pmatrix}\end{aligned}$$
+		- *Ty att vi har en fri variable i ekvations systemet* $$\begin{aligned}z=t,\;t\in\mathbb{R}\\y=-\frac43z=0\Rightarrow{}y=\frac43t\\x-3y+2z=3\Rightarrow x=3y-2x+3=2t+3\end{aligned}$$
+	6. **Över-bestämd system/Saknar lösning**$$\begin{aligned}\begin{aligned}x-4y+2z&=&2\\x-z&=&3\\4y-3z&=&1\\3x-4y&=&1\end{aligned}\Rightarrow\begin{pmatrix}1&-4&2&|&2\\1&0&-1&|&3\\0&4&-3&|&1\\3&-4&0&|&1\end{pmatrix}\begin{aligned}R_2-R_1\rightarrow{R_2}\\R_4-3R_1\rightarrow{R_4}\\\xrightarrow{}\end{aligned}\begin{pmatrix}1&-4&2&|&2\\0&4&-3&|&1\\0&3&-3&|&1\\0&8&-6&|&-5\end{pmatrix}\\\begin{aligned}R_3-R_2\rightarrow{R_3}\\R_4-2R_2\rightarrow{R_4}\\\xrightarrow{}\end{aligned}\begin{pmatrix}1&-4&2&|&2\\0&4&-3&|&1\\0&0&0&|&0\\0&0&0&|&-7\end{pmatrix}\end{aligned}$$
+		- *I sista raden ser vi att $0x+0y+0z=-7$, samt i näst sista som säger $0x+0y+0z=0$ dessa är motsägelse fulla, altså saknas det en lösning*
+	7. **Under-bestämd system/Entydlig lösning** *Falsk möjlighet! Ett under bestämt system har mindre antal ekvationer än antalet variabler. Men i så fall är det omöjligt att alal variabler vore pivåvariabler*
+	8. **Under-bestämd system/Oändliga lösningar**$$\begin{aligned}
+\begin{aligned}
+x-y-z&=&1\\
+x+z&=&2
+\end{aligned}
+\Rightarrow
+\begin{pmatrix}
+
+\end{pmatrix}
+\end{aligned}$$
 - **Ex**: $$\begin{aligned}\begin{aligned}x_1-2x_2-3x_x&=&0\\x_1-x_4&=&-2\end{aligned}\\\\\Rightarrow\begin{pmatrix}1&-2&-3&0&|&0\\1&0&0&-1&|&-2\end{pmatrix}\end{aligned}$$
 - **Ex**: $$\left.\begin{aligned}x+2y-u+3v&=&2\\2x+3y+2z-2u+10v&=&0\\x+3y-2z-4u+2v&=&3\\\underbrace{-x-3y+2z+3u-v}_{\substack{\text{VL $4\times5$}\\\text{=20 platser i schemat}}}&=&\underbrace{-4}_{\substack{\text{HL $4$}\\\text{ platser}}}\\\end{aligned}\right.\Rightarrow\left(a\mid\overrightarrow{b}\right)=\begin{pmatrix}1&2&0&-1&3&|&2\\2&3&2&-2&10&|&0\\1&3&-2&-3&2&|&3\\-1&-3&2&3&1&|&-4\end{pmatrix}$$
 *Hur räknar man med ett gauss schema? Man räknar med hjälp av elemäntera radoperationer:*