mirror of
https://github.com/reonokiy/blog.nokiy.net.git
synced 2025-06-15 11:12:54 +02:00
✨ feat: add KaTeX support and update theme configuration
- Update @astrojs/mdx and astro dependencies - Enable KaTeX in theme config for mathematical formula rendering - Update scrollbar component to hide overflow content - Add KaTeX mathematical demonstration document - Update multilingual theme guides to include KaTeX configuration
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13 changed files with 264 additions and 83 deletions
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@ -13,16 +13,17 @@
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"lint:fix": "eslint . --fix"
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},
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157
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generated
157
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@ -65,7 +68,7 @@ importers:
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|
||||
comment-parser: 1.4.1
|
||||
esquery: 1.6.0
|
||||
jsdoc-type-pratt-parser: 4.1.0
|
||||
|
@ -4493,7 +4496,7 @@ snapshots:
|
|||
|
||||
'@stylistic/eslint-plugin@4.2.0(eslint@9.23.0(jiti@2.4.2))(typescript@5.8.2)':
|
||||
dependencies:
|
||||
'@typescript-eslint/utils': 8.28.0(eslint@9.23.0(jiti@2.4.2))(typescript@5.8.2)
|
||||
'@typescript-eslint/utils': 8.29.0(eslint@9.23.0(jiti@2.4.2))(typescript@5.8.2)
|
||||
eslint: 9.23.0(jiti@2.4.2)
|
||||
eslint-visitor-keys: 4.2.0
|
||||
espree: 10.3.0
|
||||
|
@ -4586,14 +4589,14 @@ snapshots:
|
|||
|
||||
'@types/web-bluetooth@0.0.21': {}
|
||||
|
||||
'@typescript-eslint/eslint-plugin@8.28.0(@typescript-eslint/parser@8.28.0(eslint@9.23.0(jiti@2.4.2))(typescript@5.8.2))(eslint@9.23.0(jiti@2.4.2))(typescript@5.8.2)':
|
||||
'@typescript-eslint/eslint-plugin@8.29.0(@typescript-eslint/parser@8.29.0(eslint@9.23.0(jiti@2.4.2))(typescript@5.8.2))(eslint@9.23.0(jiti@2.4.2))(typescript@5.8.2)':
|
||||
dependencies:
|
||||
'@eslint-community/regexpp': 4.12.1
|
||||
'@typescript-eslint/parser': 8.28.0(eslint@9.23.0(jiti@2.4.2))(typescript@5.8.2)
|
||||
'@typescript-eslint/scope-manager': 8.28.0
|
||||
'@typescript-eslint/type-utils': 8.28.0(eslint@9.23.0(jiti@2.4.2))(typescript@5.8.2)
|
||||
'@typescript-eslint/utils': 8.28.0(eslint@9.23.0(jiti@2.4.2))(typescript@5.8.2)
|
||||
'@typescript-eslint/visitor-keys': 8.28.0
|
||||
'@typescript-eslint/parser': 8.29.0(eslint@9.23.0(jiti@2.4.2))(typescript@5.8.2)
|
||||
'@typescript-eslint/scope-manager': 8.29.0
|
||||
'@typescript-eslint/type-utils': 8.29.0(eslint@9.23.0(jiti@2.4.2))(typescript@5.8.2)
|
||||
'@typescript-eslint/utils': 8.29.0(eslint@9.23.0(jiti@2.4.2))(typescript@5.8.2)
|
||||
'@typescript-eslint/visitor-keys': 8.29.0
|
||||
eslint: 9.23.0(jiti@2.4.2)
|
||||
graphemer: 1.4.0
|
||||
ignore: 5.3.2
|
||||
|
@ -4603,27 +4606,27 @@ snapshots:
|
|||
transitivePeerDependencies:
|
||||
- supports-color
|
||||
|
||||
'@typescript-eslint/parser@8.28.0(eslint@9.23.0(jiti@2.4.2))(typescript@5.8.2)':
|
||||
'@typescript-eslint/parser@8.29.0(eslint@9.23.0(jiti@2.4.2))(typescript@5.8.2)':
|
||||
dependencies:
|
||||
'@typescript-eslint/scope-manager': 8.28.0
|
||||
'@typescript-eslint/types': 8.28.0
|
||||
'@typescript-eslint/typescript-estree': 8.28.0(typescript@5.8.2)
|
||||
'@typescript-eslint/visitor-keys': 8.28.0
|
||||
'@typescript-eslint/scope-manager': 8.29.0
|
||||
'@typescript-eslint/types': 8.29.0
|
||||
'@typescript-eslint/typescript-estree': 8.29.0(typescript@5.8.2)
|
||||
'@typescript-eslint/visitor-keys': 8.29.0
|
||||
debug: 4.4.0
|
||||
eslint: 9.23.0(jiti@2.4.2)
|
||||
typescript: 5.8.2
|
||||
transitivePeerDependencies:
|
||||
- supports-color
|
||||
|
||||
'@typescript-eslint/scope-manager@8.28.0':
|
||||
'@typescript-eslint/scope-manager@8.29.0':
|
||||
dependencies:
|
||||
'@typescript-eslint/types': 8.28.0
|
||||
'@typescript-eslint/visitor-keys': 8.28.0
|
||||
'@typescript-eslint/types': 8.29.0
|
||||
'@typescript-eslint/visitor-keys': 8.29.0
|
||||
|
||||
'@typescript-eslint/type-utils@8.28.0(eslint@9.23.0(jiti@2.4.2))(typescript@5.8.2)':
|
||||
'@typescript-eslint/type-utils@8.29.0(eslint@9.23.0(jiti@2.4.2))(typescript@5.8.2)':
|
||||
dependencies:
|
||||
'@typescript-eslint/typescript-estree': 8.28.0(typescript@5.8.2)
|
||||
'@typescript-eslint/utils': 8.28.0(eslint@9.23.0(jiti@2.4.2))(typescript@5.8.2)
|
||||
'@typescript-eslint/typescript-estree': 8.29.0(typescript@5.8.2)
|
||||
'@typescript-eslint/utils': 8.29.0(eslint@9.23.0(jiti@2.4.2))(typescript@5.8.2)
|
||||
debug: 4.4.0
|
||||
eslint: 9.23.0(jiti@2.4.2)
|
||||
ts-api-utils: 2.1.0(typescript@5.8.2)
|
||||
|
@ -4631,12 +4634,12 @@ snapshots:
|
|||
transitivePeerDependencies:
|
||||
- supports-color
|
||||
|
||||
'@typescript-eslint/types@8.28.0': {}
|
||||
'@typescript-eslint/types@8.29.0': {}
|
||||
|
||||
'@typescript-eslint/typescript-estree@8.28.0(typescript@5.8.2)':
|
||||
'@typescript-eslint/typescript-estree@8.29.0(typescript@5.8.2)':
|
||||
dependencies:
|
||||
'@typescript-eslint/types': 8.28.0
|
||||
'@typescript-eslint/visitor-keys': 8.28.0
|
||||
'@typescript-eslint/types': 8.29.0
|
||||
'@typescript-eslint/visitor-keys': 8.29.0
|
||||
debug: 4.4.0
|
||||
fast-glob: 3.3.3
|
||||
is-glob: 4.0.3
|
||||
|
@ -4647,20 +4650,20 @@ snapshots:
|
|||
transitivePeerDependencies:
|
||||
- supports-color
|
||||
|
||||
'@typescript-eslint/utils@8.28.0(eslint@9.23.0(jiti@2.4.2))(typescript@5.8.2)':
|
||||
'@typescript-eslint/utils@8.29.0(eslint@9.23.0(jiti@2.4.2))(typescript@5.8.2)':
|
||||
dependencies:
|
||||
'@eslint-community/eslint-utils': 4.5.1(eslint@9.23.0(jiti@2.4.2))
|
||||
'@typescript-eslint/scope-manager': 8.28.0
|
||||
'@typescript-eslint/types': 8.28.0
|
||||
'@typescript-eslint/typescript-estree': 8.28.0(typescript@5.8.2)
|
||||
'@typescript-eslint/scope-manager': 8.29.0
|
||||
'@typescript-eslint/types': 8.29.0
|
||||
'@typescript-eslint/typescript-estree': 8.29.0(typescript@5.8.2)
|
||||
eslint: 9.23.0(jiti@2.4.2)
|
||||
typescript: 5.8.2
|
||||
transitivePeerDependencies:
|
||||
- supports-color
|
||||
|
||||
'@typescript-eslint/visitor-keys@8.28.0':
|
||||
'@typescript-eslint/visitor-keys@8.29.0':
|
||||
dependencies:
|
||||
'@typescript-eslint/types': 8.28.0
|
||||
'@typescript-eslint/types': 8.29.0
|
||||
eslint-visitor-keys: 4.2.0
|
||||
|
||||
'@ungap/structured-clone@1.3.0': {}
|
||||
|
@ -4702,7 +4705,7 @@ snapshots:
|
|||
|
||||
'@unocss/eslint-plugin@66.1.0-beta.8(eslint@9.23.0(jiti@2.4.2))(typescript@5.8.2)':
|
||||
dependencies:
|
||||
'@typescript-eslint/utils': 8.28.0(eslint@9.23.0(jiti@2.4.2))(typescript@5.8.2)
|
||||
'@typescript-eslint/utils': 8.29.0(eslint@9.23.0(jiti@2.4.2))(typescript@5.8.2)
|
||||
'@unocss/config': 66.1.0-beta.8
|
||||
'@unocss/core': 66.1.0-beta.8
|
||||
'@unocss/rule-utils': 66.1.0-beta.8
|
||||
|
@ -4883,9 +4886,9 @@ snapshots:
|
|||
'@unrs/resolver-binding-win32-x64-msvc@1.3.3':
|
||||
optional: true
|
||||
|
||||
'@vitest/eslint-plugin@1.1.38(@typescript-eslint/utils@8.28.0(eslint@9.23.0(jiti@2.4.2))(typescript@5.8.2))(eslint@9.23.0(jiti@2.4.2))(typescript@5.8.2)':
|
||||
'@vitest/eslint-plugin@1.1.38(@typescript-eslint/utils@8.29.0(eslint@9.23.0(jiti@2.4.2))(typescript@5.8.2))(eslint@9.23.0(jiti@2.4.2))(typescript@5.8.2)':
|
||||
dependencies:
|
||||
'@typescript-eslint/utils': 8.28.0(eslint@9.23.0(jiti@2.4.2))(typescript@5.8.2)
|
||||
'@typescript-eslint/utils': 8.29.0(eslint@9.23.0(jiti@2.4.2))(typescript@5.8.2)
|
||||
eslint: 9.23.0(jiti@2.4.2)
|
||||
optionalDependencies:
|
||||
typescript: 5.8.2
|
||||
|
@ -5085,7 +5088,7 @@ snapshots:
|
|||
'@playform/pipe': 0.1.3
|
||||
'@types/csso': 5.0.4
|
||||
'@types/html-minifier-terser': 7.0.2
|
||||
astro: 5.5.5(@types/node@22.13.14)(jiti@2.4.2)(lightningcss@1.29.3)(rollup@4.38.0)(terser@5.39.0)(typescript@5.8.2)(yaml@2.7.1)
|
||||
astro: 5.5.6(@types/node@22.13.14)(jiti@2.4.2)(lightningcss@1.29.3)(rollup@4.38.0)(terser@5.39.0)(typescript@5.8.2)(yaml@2.7.1)
|
||||
commander: 13.1.0
|
||||
csso: 5.0.5
|
||||
deepmerge-ts: 7.1.5
|
||||
|
@ -5131,8 +5134,8 @@ snapshots:
|
|||
astro-eslint-parser@1.2.2:
|
||||
dependencies:
|
||||
'@astrojs/compiler': 2.11.0
|
||||
'@typescript-eslint/scope-manager': 8.28.0
|
||||
'@typescript-eslint/types': 8.28.0
|
||||
'@typescript-eslint/scope-manager': 8.29.0
|
||||
'@typescript-eslint/types': 8.29.0
|
||||
astrojs-compiler-sync: 1.0.1(@astrojs/compiler@2.11.0)
|
||||
debug: 4.4.0
|
||||
entities: 6.0.0
|
||||
|
@ -5145,9 +5148,9 @@ snapshots:
|
|||
transitivePeerDependencies:
|
||||
- supports-color
|
||||
|
||||
astro-og-canvas@0.7.0(astro@5.5.5(@types/node@22.13.14)(jiti@2.4.2)(lightningcss@1.29.3)(rollup@4.38.0)(terser@5.39.0)(typescript@5.8.2)(yaml@2.7.1)):
|
||||
astro-og-canvas@0.7.0(astro@5.5.6(@types/node@22.13.14)(jiti@2.4.2)(lightningcss@1.29.3)(rollup@4.38.0)(terser@5.39.0)(typescript@5.8.2)(yaml@2.7.1)):
|
||||
dependencies:
|
||||
astro: 5.5.5(@types/node@22.13.14)(jiti@2.4.2)(lightningcss@1.29.3)(rollup@4.38.0)(terser@5.39.0)(typescript@5.8.2)(yaml@2.7.1)
|
||||
astro: 5.5.6(@types/node@22.13.14)(jiti@2.4.2)(lightningcss@1.29.3)(rollup@4.38.0)(terser@5.39.0)(typescript@5.8.2)(yaml@2.7.1)
|
||||
canvaskit-wasm: 0.39.1
|
||||
deterministic-object-hash: 2.0.2
|
||||
entities: 4.5.0
|
||||
|
@ -5157,7 +5160,7 @@ snapshots:
|
|||
valid-filename: 4.0.0
|
||||
zod: 3.24.2
|
||||
|
||||
astro@5.5.5(@types/node@22.13.14)(jiti@2.4.2)(lightningcss@1.29.3)(rollup@4.38.0)(terser@5.39.0)(typescript@5.8.2)(yaml@2.7.1):
|
||||
astro@5.5.6(@types/node@22.13.14)(jiti@2.4.2)(lightningcss@1.29.3)(rollup@4.38.0)(terser@5.39.0)(typescript@5.8.2)(yaml@2.7.1):
|
||||
dependencies:
|
||||
'@astrojs/compiler': 2.11.0
|
||||
'@astrojs/internal-helpers': 0.6.1
|
||||
|
@ -5678,7 +5681,7 @@ snapshots:
|
|||
dependencies:
|
||||
'@eslint-community/eslint-utils': 4.5.1(eslint@9.23.0(jiti@2.4.2))
|
||||
'@jridgewell/sourcemap-codec': 1.5.0
|
||||
'@typescript-eslint/types': 8.28.0
|
||||
'@typescript-eslint/types': 8.29.0
|
||||
astro-eslint-parser: 1.2.2
|
||||
eslint: 9.23.0(jiti@2.4.2)
|
||||
eslint-compat-utils: 0.6.4(eslint@9.23.0(jiti@2.4.2))
|
||||
|
@ -5703,7 +5706,7 @@ snapshots:
|
|||
eslint-plugin-import-x@4.9.4(eslint@9.23.0(jiti@2.4.2))(typescript@5.8.2):
|
||||
dependencies:
|
||||
'@types/doctrine': 0.0.9
|
||||
'@typescript-eslint/utils': 8.28.0(eslint@9.23.0(jiti@2.4.2))(typescript@5.8.2)
|
||||
'@typescript-eslint/utils': 8.29.0(eslint@9.23.0(jiti@2.4.2))(typescript@5.8.2)
|
||||
debug: 4.4.0
|
||||
doctrine: 3.0.0
|
||||
eslint: 9.23.0(jiti@2.4.2)
|
||||
|
@ -5766,8 +5769,8 @@ snapshots:
|
|||
|
||||
eslint-plugin-perfectionist@4.10.1(eslint@9.23.0(jiti@2.4.2))(typescript@5.8.2):
|
||||
dependencies:
|
||||
'@typescript-eslint/types': 8.28.0
|
||||
'@typescript-eslint/utils': 8.28.0(eslint@9.23.0(jiti@2.4.2))(typescript@5.8.2)
|
||||
'@typescript-eslint/types': 8.29.0
|
||||
'@typescript-eslint/utils': 8.29.0(eslint@9.23.0(jiti@2.4.2))(typescript@5.8.2)
|
||||
eslint: 9.23.0(jiti@2.4.2)
|
||||
natural-orderby: 5.0.0
|
||||
transitivePeerDependencies:
|
||||
|
@ -5825,11 +5828,11 @@ snapshots:
|
|||
semver: 7.7.1
|
||||
strip-indent: 4.0.0
|
||||
|
||||
eslint-plugin-unused-imports@4.1.4(@typescript-eslint/eslint-plugin@8.28.0(@typescript-eslint/parser@8.28.0(eslint@9.23.0(jiti@2.4.2))(typescript@5.8.2))(eslint@9.23.0(jiti@2.4.2))(typescript@5.8.2))(eslint@9.23.0(jiti@2.4.2)):
|
||||
eslint-plugin-unused-imports@4.1.4(@typescript-eslint/eslint-plugin@8.29.0(@typescript-eslint/parser@8.29.0(eslint@9.23.0(jiti@2.4.2))(typescript@5.8.2))(eslint@9.23.0(jiti@2.4.2))(typescript@5.8.2))(eslint@9.23.0(jiti@2.4.2)):
|
||||
dependencies:
|
||||
eslint: 9.23.0(jiti@2.4.2)
|
||||
optionalDependencies:
|
||||
'@typescript-eslint/eslint-plugin': 8.28.0(@typescript-eslint/parser@8.28.0(eslint@9.23.0(jiti@2.4.2))(typescript@5.8.2))(eslint@9.23.0(jiti@2.4.2))(typescript@5.8.2)
|
||||
'@typescript-eslint/eslint-plugin': 8.29.0(@typescript-eslint/parser@8.29.0(eslint@9.23.0(jiti@2.4.2))(typescript@5.8.2))(eslint@9.23.0(jiti@2.4.2))(typescript@5.8.2)
|
||||
|
||||
eslint-plugin-vue@10.0.0(eslint@9.23.0(jiti@2.4.2))(vue-eslint-parser@10.1.1(eslint@9.23.0(jiti@2.4.2))):
|
||||
dependencies:
|
||||
|
|
|
@ -16,6 +16,9 @@ function setupScrollbar() {
|
|||
autoHide: 'scroll',
|
||||
autoHideDelay: 800,
|
||||
},
|
||||
overflow: {
|
||||
x: 'hidden',
|
||||
},
|
||||
})
|
||||
|
||||
bodyElement.setAttribute('data-scrollbar-initialized', 'true')
|
||||
|
@ -33,6 +36,9 @@ function setupScrollbar() {
|
|||
autoHide: 'leave',
|
||||
autoHideDelay: 500,
|
||||
},
|
||||
overflow: {
|
||||
y: 'hidden',
|
||||
},
|
||||
})
|
||||
|
||||
pre.setAttribute('data-scrollbar-initialized', 'true')
|
||||
|
@ -50,6 +56,9 @@ function setupScrollbar() {
|
|||
autoHide: 'leave',
|
||||
autoHideDelay: 500,
|
||||
},
|
||||
overflow: {
|
||||
x: 'hidden',
|
||||
},
|
||||
})
|
||||
|
||||
tocElement.setAttribute('data-scrollbar-initialized', 'true')
|
||||
|
|
|
@ -63,6 +63,8 @@ export const themeConfig: ThemeConfig = {
|
|||
dateFormat: 'YYYY-MM-DD', // YYYY-MM-DD, MM-DD-YYYY, DD-MM-YYYY, MONTH DAY YYYY, DAY MONTH YYYY
|
||||
// gap between title and subtitle
|
||||
titleGap: 2, // 1, 2, 3
|
||||
// enable KaTeX for mathematical formulas rendering
|
||||
katex: true, // true, false
|
||||
},
|
||||
// GLOBAL SETTINGS >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> END
|
||||
|
||||
|
|
150
src/content/posts/KaTeX Mathematical Demo.md
Normal file
150
src/content/posts/KaTeX Mathematical Demo.md
Normal file
|
@ -0,0 +1,150 @@
|
|||
---
|
||||
title: KaTeX Mathematical Demo
|
||||
published: 2025-04-01
|
||||
description: KaTeX is a cross-browser JavaScript library that displays mathematical notation in web browsers. It puts special emphasis on being fast and easy to use. It was initially developed by Khan Academy, and became one of the top five trending projects on GitHub.
|
||||
---
|
||||
|
||||
$\KaTeX$ is a cross-browser JavaScript library that displays mathematical notation in web browsers. It puts special emphasis on being fast and easy to use. It was initially developed by Khan Academy, and became one of the top five trending projects on GitHub.
|
||||
|
||||
## Group Theory
|
||||
|
||||
Burnside's lemma, sometimes also called Burnside's counting theorem, the Cauchy-Frobenius lemma or the orbit-counting theorem
|
||||
|
||||
Let $\wedge$ be a group action of a finite group $G$ on a finite set $X$. Then the number $t$ of orbits of the action is given by the formula
|
||||
|
||||
$$
|
||||
t=\frac{1}{|G|}\sum_{g\in G}|\text{Fix}(g)|
|
||||
$$
|
||||
|
||||
For each integer $n\ge2$, the quotient group $\mathbb{Z}/n\mathbb{Z}$ is a cyclic group generated by $1+n\mathbb{Z}$ and so $\color{red}{\mathbb{Z}/n\mathbb{Z}\cong\mathbb{Z}_n}$
|
||||
|
||||
The quotient group $\mathbb{R}/\mathbb{Z}$ is isomorphic to $([0,1),+_1)$, the group of real numbers in the interval $[0,1)$, under addition modulo 1.
|
||||
|
||||
Isomorphism Theorem. Let $\phi\colon(G,\circ)\to(H,*)$ be a homomorphism. Then the function
|
||||
|
||||
$$
|
||||
\begin{aligned}
|
||||
f\colon G/\text{Ker}(\phi)&\to\text{Im}(\phi)\\
|
||||
x\text{Ker}(\phi)&\mapsto\phi(x)
|
||||
\end{aligned}
|
||||
$$
|
||||
|
||||
is an isomorphism, so
|
||||
|
||||
$$
|
||||
G/\text{Ker}(\phi)\cong \text{Im}(\phi)
|
||||
$$
|
||||
|
||||
## Taylor's Theorem
|
||||
|
||||
Let the function $f$ be an $(n+1)$-times differentiable on an open interval containing the points $a$ and $x$. Then
|
||||
|
||||
$$
|
||||
f(x)=f(a)+f'(a)(x-a)+\cdots+\frac{f^{(n)}(a)}{n!}(x-a)^n+R_n(x)
|
||||
$$
|
||||
|
||||
where
|
||||
|
||||
$$
|
||||
R_n(x)=\frac{f^{(n+1)}(c)}{(n+1)!}(x-a)^{n+1},
|
||||
$$
|
||||
|
||||
for some $c$ between $a$ and $x$.
|
||||
|
||||
$\KaTeX$ doesn't have a right-align option so an extra aligned column is used for equation numbers. They are pushed to the right by mkern spacing, default \mkern100mu. Both align & align* environments can be used, as can \tag and \notag.
|
||||
|
||||
## Align environment
|
||||
|
||||
$$
|
||||
\begin{align}
|
||||
\frac{\pi}{4n^2} &= \frac{4^n(n!)^2}{2n^2(2n)!}n(2n-1)J_{n-1}-\frac{4^n(n!)^2}{2n^2(2n)!}2n^2J_n \tag{1} \\
|
||||
&= \frac{4^n}{4(2n)!}\left(\frac{n!}{n}\right)^22n(2n-1)J_{n-1}-\frac{4^n(n!)^2}{(2n)!}J_n \tag{$\ddagger$} \\
|
||||
&= \frac{4^{n-1}((n-1)!)^2}{(2n-2)!}J_{n-1}-\frac{4^n(n!)^2}{(2n)!}J_n \tag{2}
|
||||
\end{align}
|
||||
$$
|
||||
|
||||
## Align* environment
|
||||
|
||||
$$
|
||||
\begin{align}
|
||||
\frac{4^N(N!)^2}{(2N)!}J_N &\leq \frac{4^N(N!)^2}{(2N)!}\frac{\pi^2}{4}\frac{1}{2n+2}I_{2N} \tag{*} \\
|
||||
&= \frac{\pi^2}{8(N+1)}\frac{4^N(N!)^2}{(2N)!}I_{2N} \\
|
||||
&= \frac{\pi^2}{8(N+1)}\frac{\pi}{2} \tag{**} \\
|
||||
&= \frac{\pi^3}{16(N+1)} \\
|
||||
\frac{x}{\sin x} &\leq \frac{\pi}{2} \tag{3} \\
|
||||
\text{so} \qquad\qquad x &\leq \frac{\pi}{2}\sin x \tag{4}
|
||||
\end{align}
|
||||
$$
|
||||
|
||||
## Sum of a Series
|
||||
|
||||
$$
|
||||
\begin{align*}
|
||||
\sum_{i=1}^{k+1}i &= \left(\sum_{i=1}^{k}i\right) +(k+1) \tag{1} \\
|
||||
&= \frac{k(k+1)}{2}+k+1 \tag{2} \\
|
||||
&= \frac{k(k+1)+2(k+1)}{2} \tag{3} \\
|
||||
&= \frac{(k+1)(k+2)}{2} \tag{4} \\
|
||||
&= \frac{(k+1)((k+1)+1)}{2} \tag{5}
|
||||
\end{align*}
|
||||
$$
|
||||
|
||||
## Product notation
|
||||
|
||||
$$
|
||||
1 + \frac{q^2}{(1-q)}+\frac{q^6}{(1-q)(1-q^2)}+\cdots
|
||||
= \prod_{j=0}^{\infty}\frac{1}{(1-q^{5j+2})(1-q^{5j+3})},
|
||||
\text{ for }\lvert q\rvert < 1.
|
||||
$$
|
||||
|
||||
## Cross Product
|
||||
|
||||
$$
|
||||
\mathbf{V}_1 \times \mathbf{V}_2 = \begin{vmatrix}
|
||||
\mathbf{i} & \mathbf{j} & \mathbf{k} \\[1ex]
|
||||
\frac{\partial X}{\partial u} & \frac{\partial Y}{\partial u} & 0 \\[2.5ex]
|
||||
\frac{\partial X}{\partial v} & \frac{\partial Y}{\partial v} & 0
|
||||
\end{vmatrix}
|
||||
$$
|
||||
|
||||
## Maxwell's Equations
|
||||
|
||||
$$
|
||||
\begin{align*}
|
||||
\nabla \times \vec{\mathbf{B}} -\, \frac1c\, \frac{\partial\vec{\mathbf{E}}}{\partial t} &= \frac{4\pi}{c}\vec{\mathbf{j}} \\
|
||||
\nabla \cdot \vec{\mathbf{E}} &= 4 \pi \rho \\
|
||||
\nabla \times \vec{\mathbf{E}}\, +\, \frac1c\, \frac{\partial\vec{\mathbf{B}}}{\partial t} &= \vec{\mathbf{0}} \\
|
||||
\nabla \cdot \vec{\mathbf{B}} &= 0
|
||||
\end{align*}
|
||||
$$
|
||||
|
||||
## Greek Letters
|
||||
|
||||
$$
|
||||
\begin{align*}
|
||||
&\Gamma\ \Delta\ \Theta\ \Lambda\ \Xi\ \Pi\ \Sigma\ \Upsilon\ \Phi\ \Psi\ \Omega\\
|
||||
&\alpha\ \beta\ \gamma\ \delta\ \epsilon\ \zeta\ \eta\ \theta\ \iota\ \kappa\ \lambda\ \mu\ \nu\ \xi\ \omicron\ \pi\ \rho\ \sigma\ \tau\ \upsilon\ \phi\ \chi\ \psi\ \omega\ \varepsilon\ \vartheta\ \varpi\ \varrho\ \varsigma\ \varphi
|
||||
\end{align*}
|
||||
$$
|
||||
|
||||
## Arrows
|
||||
|
||||
$$
|
||||
\begin{align*}
|
||||
&\gets\ \to\ \leftarrow\ \rightarrow\ \uparrow\ \Uparrow\ \downarrow\ \Downarrow\ \updownarrow\ \Updownarrow\\
|
||||
&\Leftarrow\ \Rightarrow\ \leftrightarrow\ \Leftrightarrow\ \mapsto\ \hookleftarrow\\
|
||||
&\leftharpoonup\ \leftharpoondown\ \rightleftharpoons\ \longleftarrow\ \Longleftarrow\ \longrightarrow\\
|
||||
&\Longrightarrow\ \longleftrightarrow\ \Longleftrightarrow\ \longmapsto\ \hookrightarrow\ \rightharpoonup\\
|
||||
&\rightharpoondown\ \leadsto\ \nearrow\ \searrow\ \swarrow\ \nwarrow
|
||||
\end{align*}
|
||||
$$
|
||||
|
||||
## Symbols
|
||||
|
||||
$$
|
||||
\begin{align*}
|
||||
&\surd\ \barwedge\ \veebar\ \odot\ \oplus\ \otimes\ \oslash\ \circledcirc\ \boxdot\ \bigtriangleup\\
|
||||
&\bigtriangledown\ \dagger\ \diamond\ \star\ \triangleleft\ \triangleright\ \angle\ \infty\ \prime\ \triangle
|
||||
\end{align*}
|
||||
$$
|
||||
|
||||
*Samples taken from [KaTeX Live Demo](https://sixthform.info/katex/examples/demo.html)*
|
|
@ -84,6 +84,8 @@ global: {
|
|||
dateFormat: 'YYYY-MM-DD' // YYYY-MM-DD, MM-DD-YYYY, DD-MM-YYYY, MONTH DAY YYYY, DAY MONTH YYYY
|
||||
// gap between title and subtitle
|
||||
titleGap: 2 // 1, 2, 3
|
||||
// enable KaTeX for mathematical formulas rendering
|
||||
katex: true // true, false
|
||||
}
|
||||
```
|
||||
|
||||
|
|
|
@ -84,6 +84,8 @@ global: {
|
|||
dateFormat: 'YYYY-MM-DD' // YYYY-MM-DD, MM-DD-YYYY, DD-MM-YYYY, MONTH DAY YYYY, DAY MONTH YYYY
|
||||
// espacio entre título y subtítulo
|
||||
titleGap: 2 // 1, 2, 3
|
||||
// habilitar KaTeX para renderizar fórmulas matemáticas
|
||||
katex: true // true, false
|
||||
}
|
||||
```
|
||||
|
||||
|
|
|
@ -56,7 +56,7 @@ color: {
|
|||
// ダークモード
|
||||
dark: {
|
||||
// プライマリカラー
|
||||
// タイトル、ホバーなどに使用
|
||||
// サイトタイトル、ホバー効果などに使用
|
||||
primary: 'oklch(92% 0.005 298)'
|
||||
// セカンダリカラー
|
||||
// 通常テキストに使用
|
||||
|
@ -84,6 +84,8 @@ global: {
|
|||
dateFormat: 'YYYY-MM-DD' // YYYY-MM-DD, MM-DD-YYYY, DD-MM-YYYY, MONTH DAY YYYY, DAY MONTH YYYY
|
||||
// タイトルとサブタイトルの間隔
|
||||
titleGap: 2 // 1, 2, 3
|
||||
// 数式表示のためのKaTeXを有効化
|
||||
katex: true // true, false
|
||||
}
|
||||
```
|
||||
|
||||
|
|
|
@ -84,6 +84,8 @@ global: {
|
|||
dateFormat: 'YYYY-MM-DD' // YYYY-MM-DD, MM-DD-YYYY, DD-MM-YYYY, MONTH DAY YYYY, DAY MONTH YYYY
|
||||
// промежуток между заголовком и подзаголовком
|
||||
titleGap: 2 // 1, 2, 3
|
||||
// включить KaTeX для отображения математических формул
|
||||
katex: true // true, false
|
||||
}
|
||||
```
|
||||
|
||||
|
@ -192,7 +194,6 @@ preload: {
|
|||
customUmamiAnalyticsJS: 'https://js.radishzz.cc/jquery.min.js'
|
||||
}
|
||||
```
|
||||
|
||||
## Создание Новой Статьи
|
||||
|
||||
Создайте новый файл с расширением `.md` или `.mdx` в директории `src/content/posts/` и добавьте метаданные Front Matter в верхней части файла.
|
||||
|
|
|
@ -56,7 +56,7 @@ color: {
|
|||
// 暗色模式
|
||||
dark: {
|
||||
// 高亮顏色
|
||||
// 用於標題、hover等
|
||||
// 用於站點標題、滑鼠懸停效果等
|
||||
primary: 'oklch(92% 0.005 298)'
|
||||
// 次要顏色
|
||||
// 用於普通文本
|
||||
|
@ -84,6 +84,8 @@ global: {
|
|||
dateFormat: 'YYYY-MM-DD' // YYYY-MM-DD, MM-DD-YYYY, DD-MM-YYYY, MONTH DAY YYYY, DAY MONTH YYYY
|
||||
// 標題與副標題之間的距離
|
||||
titleGap: 2 // 1, 2, 3
|
||||
// 啟用 KaTeX 數學公式渲染
|
||||
katex: true // true, false
|
||||
}
|
||||
```
|
||||
|
||||
|
|
|
@ -56,7 +56,7 @@ color: {
|
|||
// 暗色模式
|
||||
dark: {
|
||||
// 高亮颜色
|
||||
// 用于标题、hover等
|
||||
// 用于站点标题、鼠标悬停效果等
|
||||
primary: 'oklch(92% 0.005 298)'
|
||||
// 次要颜色
|
||||
// 用于普通文本
|
||||
|
@ -84,6 +84,8 @@ global: {
|
|||
dateFormat: 'YYYY-MM-DD' // YYYY-MM-DD, MM-DD-YYYY, DD-MM-YYYY, MONTH DAY YYYY, DAY MONTH YYYY
|
||||
// 标题与副标题之间的距离
|
||||
titleGap: 2 // 1, 2, 3
|
||||
// 启用 KaTeX 数学公式渲染
|
||||
katex: true // true, false
|
||||
}
|
||||
```
|
||||
|
||||
|
|
|
@ -11,6 +11,10 @@ import '@/styles/font.css'
|
|||
import '@/styles/global.css'
|
||||
import '@/styles/heti.css'
|
||||
|
||||
if (themeConfig.global.katex) {
|
||||
await import('katex/dist/katex.min.css')
|
||||
}
|
||||
|
||||
interface Props {
|
||||
postTitle?: string
|
||||
postDescription?: string
|
||||
|
|
1
src/types/index.d.ts
vendored
1
src/types/index.d.ts
vendored
|
@ -34,6 +34,7 @@ export interface ThemeConfig {
|
|||
fontStyle: 'sans' | 'serif'
|
||||
dateFormat: 'YYYY-MM-DD' | 'MM-DD-YYYY' | 'DD-MM-YYYY' | 'MONTH DAY YYYY' | 'DAY MONTH YYYY'
|
||||
titleGap: 1 | 2 | 3
|
||||
katex: boolean
|
||||
}
|
||||
|
||||
comment: {
|
||||
|
|
Loading…
Add table
Add a link
Reference in a new issue