Render math in chat messages with KaTeX

Add a marked extension that tokenizes math delimiters and renders them
with KaTeX: `$$ ... $$` / `\[ ... \]` as block, `$ ... $` / `\( ... \)`
and mid-paragraph `$$ ... $$` as inline.

Inline `$ ... $` requires a non-space after the opening `$`, no newline
inside, and a non-digit after the closing `$`, so prose like "$100 から
$200" is left alone; `\$` still escapes a literal dollar sign. Parse
errors fall back to KaTeX's red inline message instead of throwing, and
math whose closing delimiter has not streamed in yet stays plain text.

DOMPurify strips `semantics` and `annotation` by default, which would
leak the raw TeX out of KaTeX's MathML output, so both are allowed
explicitly.

Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>

frontend/src/components/MarkdownContent.vue

@@ -2,6 +2,8 @@
 import { computed } from 'vue'
 import { marked } from 'marked'
 import DOMPurify from 'dompurify'
+import 'katex/dist/katex.min.css'
+import { mathExtension, mathSanitizeConfig } from '../utils/math'
 
 const props = defineProps<{
   content: string
@@ -9,6 +11,7 @@ const props = defineProps<{
 }>()
 
 marked.setOptions({ breaks: true, gfm: true })
+marked.use(mathExtension)
 
 function closeOpenFences(src: string): string {
   const fenceCount = (src.match(/^```/gm) ?? []).length
@@ -18,7 +21,7 @@ function closeOpenFences(src: string): string {
 
 const html = computed(() => {
   const raw = props.pending ? closeOpenFences(props.content) : props.content
-  return DOMPurify.sanitize(marked.parse(raw) as string)
+  return DOMPurify.sanitize(marked.parse(raw) as string, mathSanitizeConfig)
 })
 </script>
 
@@ -104,6 +107,15 @@ const html = computed(() => {
 /* 水平線 */
 .md :deep(hr) { border-color: #333; margin: 10px 0; }
 
+/* 数式 (KaTeX) */
+.md :deep(.katex) { font-size: 1.05em; }
+.md :deep(.katex-display) {
+  margin: 10px 0;
+  padding: 2px 0;
+  overflow-x: auto;
+  overflow-y: hidden;
+}
+
 /* リンク */
 .md :deep(a) { color: #60a5fa; text-decoration: none; }
 .md :deep(a:hover) { text-decoration: underline; }