vault backup: 2026-02-04 14:01:55
This commit is contained in:
3
.obsidian/community-plugins.json
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3
.obsidian/community-plugins.json
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[
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"obsidian-git",
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"obsidian-style-settings",
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"obsidian-tikzjax"
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"obsidian-tikzjax",
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"obsidian-completr"
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]
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164
.obsidian/plugins/obsidian-completr/callout_suggestions.json
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164
.obsidian/plugins/obsidian-completr/callout_suggestions.json
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[
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{
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"displayName": "Note",
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"replacement": "note",
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"icon": "lucide-pencil",
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"color": "#448aff"
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},
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{
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"displayName": "Summary",
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"replacement": "summary",
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"icon": "lucide-clipboard-list",
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"color": "#00b0ff"
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},
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{
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"displayName": "Abstract",
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"replacement": "abstract",
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"icon": "lucide-clipboard-list",
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"color": "#00b0ff"
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},
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{
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"displayName": "TL;DR",
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"replacement": "tldr",
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"icon": "lucide-clipboard-list",
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"color": "#00b0ff"
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},
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{
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"displayName": "Info",
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"replacement": "info",
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"icon": "lucide-info",
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"color": "#00b8d4"
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},
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{
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"displayName": "To-Do",
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"replacement": "todo",
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"icon": "lucide-check-circle-2",
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"color": "#00b8d4"
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},
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{
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"displayName": "Tip",
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"replacement": "tip",
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"icon": "lucide-flame",
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"color": "#00bfa6"
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},
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{
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"displayName": "Hint",
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"replacement": "hint",
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"icon": "lucide-flame",
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"color": "#00bfa6"
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},
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{
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"displayName": "Important",
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"replacement": "important",
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"icon": "lucide-flame",
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"color": "#00bfa6"
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},
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{
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"displayName": "Success",
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"replacement": "success",
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"icon": "lucide-check",
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"color": "#00c853"
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},
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{
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"displayName": "Check",
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"replacement": "check",
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"icon": "lucide-check",
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"color": "#00c853"
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},
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{
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"displayName": "Done",
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"replacement": "done",
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"icon": "lucide-check",
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"color": "#00c853"
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},
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{
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"displayName": "Question",
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"replacement": "question",
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"icon": "lucide-help-circle",
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"color": "#63dd17"
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},
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{
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"displayName": "Help",
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"replacement": "Help",
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"icon": "lucide-help-circle",
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"color": "#63dd17"
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},
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{
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"displayName": "FAQ",
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"replacement": "faq",
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"icon": "lucide-help-circle",
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"color": "#63dd17"
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},
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{
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"displayName": "Warning",
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"replacement": "warning",
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"icon": "lucide-alert-triangle",
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"color": "#ff9100"
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},
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{
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"displayName": "Caution",
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"replacement": "caution",
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"icon": "lucide-alert-triangle",
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"color": "#ff9100"
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},
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{
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"displayName": "Attention",
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"replacement": "attention",
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"icon": "lucide-alert-triangle",
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"color": "#ff9100"
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},
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{
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"displayName": "Failure",
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"replacement": "failure",
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"icon": "lucide-x",
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"color": "#ff5252"
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},
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{
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"displayName": "Fail",
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"replacement": "fail",
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"icon": "lucide-x",
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"color": "#ff5252"
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},
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{
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"displayName": "Missing",
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"replacement": "missing",
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"icon": "lucide-x",
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"color": "#ff5252"
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},
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{
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"displayName": "Danger",
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"replacement": "danger",
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"icon": "lucide-zap",
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"color": "#ff1744"
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},
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{
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"displayName": "Error",
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"replacement": "error",
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"icon": "lucide-zap",
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"color": "#ff1744"
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},
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{
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"displayName": "Bug",
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"replacement": "bug",
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"icon": "lucide-bug",
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"color": "#f50057"
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},
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{
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"displayName": "Example",
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"replacement": "example",
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"icon": "lucide-list",
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"color": "#7c4dff"
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},
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{
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"displayName": "Quote",
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"replacement": "quote",
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"icon": "quote-glyph",
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"color": "#9e9e9e"
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},
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{
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"displayName": "Cite",
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"replacement": "cite",
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"icon": "quote-glyph",
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"color": "#9e9e9e"
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}
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]
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4342
.obsidian/plugins/obsidian-completr/latex_commands.json
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4342
.obsidian/plugins/obsidian-completr/latex_commands.json
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Load Diff
80685
.obsidian/plugins/obsidian-completr/main.js
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80685
.obsidian/plugins/obsidian-completr/main.js
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Load Diff
10
.obsidian/plugins/obsidian-completr/manifest.json
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10
.obsidian/plugins/obsidian-completr/manifest.json
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{
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"id": "obsidian-completr",
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"name": "Completr",
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"version": "3.2.0",
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"minAppVersion": "1.0.0",
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"description": "This plugin provides advanced auto-completion functionality for LaTeX, Frontmatter and standard writing.",
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"author": "tth05",
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"authorUrl": "https://github.com/tth05",
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"isDesktopOnly": true
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}
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110
.obsidian/plugins/obsidian-completr/styles.css
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110
.obsidian/plugins/obsidian-completr/styles.css
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body {
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--completr-suggestion-icon-height: 14px;
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}
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.completr-suggestion-item {
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padding: 5px 10px 5px 10px;
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white-space: nowrap;
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overflow: hidden;
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text-overflow: ellipsis;
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display: flex;
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align-items: center;
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}
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.completr-suggestion-item > * {
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display: inline-block;
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}
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.completr-suggestion-icon {
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height: var(--completr-suggestion-icon-height);
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min-height: var(--completr-suggestion-icon-height);
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max-height: var(--completr-suggestion-icon-height);
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margin-right: 0.5ch;
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color: var(--completr-suggestion-color);
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}
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.completr-suggestion-text {
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}
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.completr-suggestion-placeholder {
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border-width: 1px 0 1px 0;
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border-style: solid;
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}
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.completr-settings-no-border {
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border: none;
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}
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.completr-settings-list-item {
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border-top: 1px solid grey;
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padding: 4px 0 0 0;
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}
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.completr-settings-error {
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border: 1px solid red !important;
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}
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/**
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Snippet color classes.
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["lightskyblue", "orange", "lime", "pink", "cornsilk", "magenta", "navajowhite"]
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*/
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.completr-suggestion-placeholder0 {
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border-color: lightskyblue;
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}
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/* These extra selectors enforce their color on all children, because CodeMirror does weird nesting of spans when
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nesting multiple decorations. */
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span.completr-suggestion-placeholder0 span {
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border-color: lightskyblue;
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}
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.completr-suggestion-placeholder1 {
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border-color: orange;
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}
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span.completr-suggestion-placeholder1 span {
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border-color: orange;
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}
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.completr-suggestion-placeholder2 {
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border-color: lime;
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}
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span.completr-suggestion-placeholder2 span {
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border-color: lime;
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}
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.completr-suggestion-placeholder3 {
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border-color: pink;
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}
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span.completr-suggestion-placeholder3 span {
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border-color: pink;
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}
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.completr-suggestion-placeholder4 {
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border-color: cornsilk;
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}
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span.completr-suggestion-placeholder4 span {
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border-color: cornsilk;
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}
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.completr-suggestion-placeholder5 {
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border-color: magenta;
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}
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span.completr-suggestion-placeholder5 span {
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border-color: magenta;
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}
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.completr-suggestion-placeholder6 {
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border-color: navajowhite;
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}
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span.completr-suggestion-placeholder6 span {
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border-color: navajowhite;
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}
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@@ -30,6 +30,23 @@
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- *Eftersom $z$ är en fri variabler kan $z=t$, och $t\in\mathbb{R}$. sampt* $$\begin{aligned}y-z=-\frac52\Rightarrow{y}=z-\frac52=t-\frac52\\x-2y+z=3\Rightarrow{x}=2y-z+3=2\left(t-\frac52\right)-t+3=t-2\\\end{aligned}$$
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3. **Exakt-bestämnd system/Saknar lösningar** $$\begin{aligned}\begin{aligned}x-3y+2z&=&3\\x-2y&=&2\\2x-5y+2z&=&4\end{aligned}\Rightarrow\begin{pmatrix}1&-3&2&|&3\\1&-2&2&|&2\\2&-5&2&|&-4\end{pmatrix}\begin{aligned}R_2-R_1\rightarrow{R_2}\\R_3-2R_1\rightarrow{R_3}\\\xrightarrow{}\end{aligned}\begin{pmatrix}1&-3&2&|&3\\0&1&0&|&-1\\0&1&-2&|&-2\end{pmatrix}\\\begin{aligned}R_3-R_2\rightarrow{R_3}\\\xrightarrow{}\end{aligned}\pmatrix{1&-3&2&|&3\\0&1&2&|&-1\\0&0&0&|&-1}\end{aligned}$$
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- **OBS** *Rad $2$ och $3$ säger att det skall vara $-2$ medans de int har samma $VL$, detta går inte! samt säger det $0x+0y+0z=-1\Leftrightarrow{0=-1}$*
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4. **Över-bestämd system/Entydlig Lösning** $$\begin{aligned}\begin{aligned}x-3y+2z&=&3\\x-2y&=&2\\x-y-z&=&2\\2x-5y+2z&=&5\end{aligned}\Rightarrow\begin{pmatrix}1&-3&2&|&3\\1&-2&0&|&2\\1&-1&-1&|&2\\2&-5&2&|&5\end{pmatrix}\begin{aligned}R_2-R_1\rightarrow{R_2}\\R_3-R_1\rightarrow{R_3}\\R_4-2R_1\rightarrow{R_4}\\\xrightarrow{}\end{aligned}\\\begin{pmatrix}1&-3&2&|&3\\0&1&-2&|&-1\\0&2&-3&|&-1\\0&1&-2&|&-1\end{pmatrix}\begin{aligned}R_3-2R_2\rightarrow{R_3}\\R_4-R_2\rightarrow{R_4}\\\xrightarrow{}\end{aligned}\begin{pmatrix}1&-3&2&|&3\\0&1&-2&|&-1\\0&0&1&|&1\\0&0&0&|&0\end{pmatrix}\end{aligned}$$
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- *Vi har fott en entydlig lösning med*$$\begin{aligned}z=1\\y-2z=-1\Rightarrow{}y=2z-1=1\\x-3y+2z=3\Rightarrow{}x=3y-2z+3=4\end{aligned}$$
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5. **Över-bestämd system/oändliga lösningar** $$\begin{aligned}\begin{aligned}x-3y+2z=3\\x-2z=3\\-3y+4z=0\\3x-3y+2z=9\end{aligned}\Rightarrow\begin{pmatrix}1&-3&2&|&3\\1&0&-2&|&3\\0&-3&4&|&0\\3&-3&2&|&9\end{pmatrix}\begin{aligned}R_2-R_1\rightarrow{R_2}\\R_4-3R_1\rightarrow{R_4}\\\xrightarrow{}\end{aligned}\begin{pmatrix}1&-3&2&|&3\\0&3&-4&|&0\\0&-3&4&|&0\\0&6&-8&|&0\end{pmatrix}\\\begin{aligned}R_3+R_2\rightarrow{R_3}\\R_4-2R_2\rightarrow{R_4}\\\xrightarrow{}\end{aligned}\begin{pmatrix}1&-3&2&|&3\\0&3&-4&|&0\\0&0&0&|&0\\0&0&0&|&0\end{pmatrix}\begin{aligned}\frac13R_2\rightarrow{R_2}\\\xrightarrow{}\end{aligned}\begin{pmatrix}1&-3&2&3\\0&1&-\frac34&|&0\\0&0&0&|&0\\0&0&0&|&0\end{pmatrix}\end{aligned}$$
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- *Ty att vi har en fri variable i ekvations systemet* $$\begin{aligned}z=t,\;t\in\mathbb{R}\\y=-\frac43z=0\Rightarrow{}y=\frac43t\\x-3y+2z=3\Rightarrow x=3y-2x+3=2t+3\end{aligned}$$
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6. **Över-bestämd system/Saknar lösning**$$\begin{aligned}\begin{aligned}x-4y+2z&=&2\\x-z&=&3\\4y-3z&=&1\\3x-4y&=&1\end{aligned}\Rightarrow\begin{pmatrix}1&-4&2&|&2\\1&0&-1&|&3\\0&4&-3&|&1\\3&-4&0&|&1\end{pmatrix}\begin{aligned}R_2-R_1\rightarrow{R_2}\\R_4-3R_1\rightarrow{R_4}\\\xrightarrow{}\end{aligned}\begin{pmatrix}1&-4&2&|&2\\0&4&-3&|&1\\0&3&-3&|&1\\0&8&-6&|&-5\end{pmatrix}\\\begin{aligned}R_3-R_2\rightarrow{R_3}\\R_4-2R_2\rightarrow{R_4}\\\xrightarrow{}\end{aligned}\begin{pmatrix}1&-4&2&|&2\\0&4&-3&|&1\\0&0&0&|&0\\0&0&0&|&-7\end{pmatrix}\end{aligned}$$
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- *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*
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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*
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8. **Under-bestämd system/Oändliga lösningar**$$\begin{aligned}
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\begin{aligned}
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x-y-z&=&1\\
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x+z&=&2
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\end{aligned}
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\Rightarrow
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\begin{pmatrix}
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\end{pmatrix}
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\end{aligned}$$
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- **Ex**: $$\begin{aligned}\begin{aligned}x_1-2x_2-3x_x&=&0\\x_1-x_4&=&-2\end{aligned}\\\\\Rightarrow\begin{pmatrix}1&-2&-3&0&|&0\\1&0&0&-1&|&-2\end{pmatrix}\end{aligned}$$
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- **Ex**: $$\left.\begin{aligned}x+2y-u+3v&=&2\\2x+3y+2z-2u+10v&=&0\\x+3y-2z-4u+2v&=&3\\\underbrace{-x-3y+2z+3u-v}_{\substack{\text{VL $4\times5$}\\\text{=20 platser i schemat}}}&=&\underbrace{-4}_{\substack{\text{HL $4$}\\\text{ platser}}}\\\end{aligned}\right.\Rightarrow\left(a\mid\overrightarrow{b}\right)=\begin{pmatrix}1&2&0&-1&3&|&2\\2&3&2&-2&10&|&0\\1&3&-2&-3&2&|&3\\-1&-3&2&3&1&|&-4\end{pmatrix}$$
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*Hur räknar man med ett gauss schema? Man räknar med hjälp av elemäntera radoperationer:*
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Block a user