Supported math and editing features

This is a presentation and editing scope, not a claim of full LaTeX or computer-algebra support. Blank slots remain editable and export as empty groups. All catalog symbols are exercised against KaTeX in unit tests.

Editing / LaTeX parity (0.2.0)

Existing editor capability	Export	Editable import	Acceptance
117 catalog symbols	Yes	Yes	Every symbol round-trips; aliases normalize
Fractions, roots, scripts and three delimiter structures	Yes	Yes	Empty/filled slots and nested pairs
Sums, products and integrals	Yes	Yes	Limits and bodies preserved
All six matrix environments	Yes	Yes	Rectangular cells and environment preserved
Two-column alignment and cases	Yes	Yes	Cell structure preserved
Top-level multiple lines	`gathered`	Yes	Root/additional lines preserved; rejected by inline host
Identity/zero matrices, vectors, formula templates	Yes	Yes	Restored as editable structure, not template IDs
Arbitrary TeX styling, macros and unsupported model nodes	No	No	Fail atomically; source editor fallback

The LaTeX contract defines syntax, limits and normalization. Version 0.2.0 includes the bounded loader described here. UI interaction parity between rich React and native renderers remains a separate concern.

See the LaTeX editing guide for input examples and prioritized additions.

Structural notation

| Family | Implemented input / structure | LaTeX output | Upper/lower limits | Editable condition/body | \limsup, \liminf | Not evaluation | | Limits | |---|---|---|---| | Fractions | Two editable slots; wrap a selection as numerator | \frac{a}{b} | No automatic algebraic simplification | | Upper/lower limits | Editable condition/body | \limsup, \liminf | Not evaluation | | Limits | Editable approach condition and expression | \\lim_{x\\to 0}{x} | One lower condition; \limits accepted, \nolimits supported in workspace | | Binomial coefficients | Two editable terms; selection wrapping | \\binom{n}{k} | Parentheses without a fraction bar | | Square roots | Editable radicand; selection wrapping | \sqrt{x} | Use indexedRoot for an explicit index | | Indexed roots | Index and radicand; selection wrapping | \sqrt[n]{x} | Empty index can be removed to recover a square root | | Additional accents | Fixed wave/bar/dots and wide hat/wave; one editable body | \tilde, \bar, \dot, \ddot, \widehat, \widetilde | Fixed variants do not stretch across a long body | | Accents | Editable body; selection wrapping | \vec{x}, \hat{x}, \overline{AB} | Additional wide accents are separate structures; overset/underset are separate supported structures | | Brace annotations | Editable annotation and body, selection wrapping | \overbrace{a+b}^{n}, \underbrace{a+b}_{n} | No automatic algebraic grouping | | Powers | Base and superscript; automatic parentheses when wrapping a compound base | {x}^{2} | Combined scripts use a separate shared-base node | | Combined scripts | Shared base, lower and upper slots | {x}_{i}^{2} | Explicit grouping can still represent nesting | | Literal text | One editable literal row | \text{otherwise} | No embedded math or text styling | | Named functions | Editable upright name, 19 standard functions and custom names | \sin x, \operatorname{custom} | Arguments remain adjacent math; no evaluation | | Subscripts | Base and lower script | {x}_{i} | No declaration or index semantics | | Parentheses | Editable group | \left(x\right) | Generic group; no function-argument semantics | | Brackets | Editable group | \left[x\right] | Not an interval data type | | Norm | One editable body; selected-expression wrapping | \left\Vert x\right\Vert | Not numerical evaluation | | Absolute value | Editable group | \left|x\right| | No evaluation | | Sum | Lower limit, upper limit, body | \sum_{i=1}^{n}x | No bound-variable resolution | | Product | Lower limit, upper limit, body | \prod_{i=1}^{n}x | No evaluation | | Triple / contour integrals | Three editable slots; side bounds or explicit limits | \iiint, \oint | No computation; \nolimits supported in workspace | | Integral | Lower limit, upper limit, integrand | \int_{a}^{b}x | Differential entered as text; no integration engine | | Matrices / vectors | Editable nested cells; row/column changes | matrix, pmatrix, bmatrix, Bmatrix, vmatrix, Vmatrix | 1–20 rows and columns; workspace rectangular clipboard and full-matrix transpose | | Aligned equations | Two columns, left side right-aligned and right side left-aligned | aligned | 1–20 rows, one alignment point; type the relation explicitly | | Cases | Expression and condition columns, left brace | cases | 1–20 rows; conditions accept math and literal text nodes | | Multiple document lines | Split/join top-level rows | gathered | No wrapping several document lines into one structure |

Editing, discovery and integration

Area	Supported	Remaining boundary
Languages	Korean and English UI, demo, accessible names, hints and suggestions	Custom host labels require host translation
Recent / favorites	Shared UI preference store for known symbols/templates, up to 12 recent and 100 favorites	Optional host persistence; no effect on formula JSON or Undo
Presentation changes	Fence type, fraction/binomial size and operator limits from the contextual toolbar	Existing notation only; no arbitrary fonts or dimensions
Discovery	All-symbol grid with English/Korean/glyph/LaTeX search, click to insert	Scroll through the complete 117-symbol catalog
Line numbers	UI gutter for multiple top-level rows, optional prop	Excluded from math output and clipboard
Aliases	English and Korean in both locales; longest symbolic trigger first	Substring matching with exact matches first; no natural-language parsing
Native input	Active token only; composition draft held stable	Real OS IME validation deferred
Roles	Variables, numeric literals, symbols, spaces	Lexical colors are not semantic declarations
Selection	Partial text, drag across tokens/structures, whole document in preview	Shift+arrow model ranges and workspace rectangular cell selection; touch/OS clipboard validation remains
Wrapping	Fraction, root, power, subscript, parentheses, brackets, absolute value	One balanced row; cross-slot range expands to common structure
Clipboard	Structured internal fragment plus LaTeX text; cut/paste replacement	Ordinary paste is literal; explicit LaTeX insertion parses at the caret/range; nested multiline paste rejected
History	Undo/redo of model changes and caret, up to 100 prior states	Shared host adapters commit one formula edit; per-host history support varies
Deletion	Text boundaries, line join, structure unwrap, two-step filled-grid deletion	General structural deletion rules are still limited
Serialization	Version-1 JSON document and change callback	`parseMathDocument` validates shape and IDs; persistence and future version migrations remain host work
Preview	Demo-only KaTeX view	Library renders its own editable presentation
Accessibility	Localized labels, combobox suggestions, keyboard slot navigation	Not a complete mathematical screen-reader implementation
Computation	None	No solving, simplification, units engine or collaboration

Editable templates and presets

Template / preset	Sizes	Discovery	Behavior
Empty matrix	1–20 rows × 1–20 columns via size shortcuts; 2×2/3×3/4×4 menu presets	`matrix`, `행`, `행렬`; matrix menu	Editable empty cells
Identity matrix	Square sizes 1–20 via size shortcuts; 2×2/3×3/4×4 menu presets	`identity`, `단위`, `단위행렬`; matrix menu	Diagonal 1, other entries 0
Zero matrix	1–20 rows × 1–20 columns via size shortcuts; 2×2/3×3/4×4 templates	`zero`, `영행렬`; template menu	All entries 0, editable
Column vector	2×1, 3×1	`vector`, `column`, `벡터`, `열벡터`; template menu	Empty editable column; existing generic matrix candidates may also match
Quadratic formula	One expression	`quadratic`, `근의공식`; template menu	`x=(-b±√(b²−4ac))/(2a)` using fraction/root/power nodes; assumes a≠0 mathematically, does not enforce it
Pythagorean theorem	One expression	`pythagorean`, `피타고라스`; template menu	`a²+b²=c²` using editable power nodes

Template insertion uses fresh IDs and is undoable. Template search aliases do not include spaces as a complete multiword query parser: use the compact aliases shown above. A template is not a solver.

Symbol catalog

For the compact three-column reference, see Symbol names.

The table below is generated from src/symbols.ts. Aliases are space-separated alternative names. Korean labels are also searchable. LaTeX control words receive separating whitespace during export. Literal Latin names and numbers remain ordinary text; typing a LaTeX command does not imply general LaTeX parsing.

Catalog size: 117 symbols.

Glyph	English label	Korean label	English aliases	Symbolic triggers	LaTeX
↑	Up arrow	위쪽 화살표	uparrow arrow 화살표	- ->	`\\uparrow`
↕	Up-down arrow	상하 화살표	updownarrow arrow 화살표	- ->	`\\updownarrow`
⇐	Double left arrow	왼쪽 이중 화살표	Leftarrow arrow 화살표	- ->	`\\Leftarrow`
⇑	Double up arrow	위쪽 이중 화살표	Uparrow arrow 화살표	- ->	`\\Uparrow`
⇓	Double down arrow	아래쪽 이중 화살표	Downarrow arrow 화살표	- ->	`\\Downarrow`
⇕	Double up-down arrow	상하 이중 화살표	Updownarrow arrow 화살표	- ->	`\\Updownarrow`
↗	Northeast arrow	오른쪽 위 대각선 화살표	nearrow arrow 화살표	- ->	`\\nearrow`
↘	Southeast arrow	오른쪽 아래 대각선 화살표	searrow arrow 화살표	- ->	`\\searrow`
↙	Southwest arrow	왼쪽 아래 대각선 화살표	swarrow arrow 화살표	- ->	`\\swarrow`
↖	Northwest arrow	왼쪽 위 대각선 화살표	nwarrow arrow 화살표	- ->	`\\nwarrow`
⟶	Long right arrow	긴 오른쪽 화살표	longrightarrow arrow 화살표	- ->	`\\longrightarrow`
⟵	Long left arrow	긴 왼쪽 화살표	longleftarrow arrow 화살표	- ->	`\\longleftarrow`
⟷	Long left-right arrow	긴 양방향 화살표	longleftrightarrow arrow 화살표	-	`\\longleftrightarrow`
⟹	Long double right arrow	긴 오른쪽 이중 화살표	Longrightarrow arrow 화살표	- ->	`\\Longrightarrow`
⟸	Long double left arrow	긴 왼쪽 이중 화살표	Longleftarrow arrow 화살표	- ->	`\\Longleftarrow`
⟺	Long double left-right arrow	긴 양방향 이중 화살표	Longleftrightarrow arrow	—	`\\Longleftrightarrow`
↪	Hook right arrow	갈고리 오른쪽 화살표	hookrightarrow arrow 화살표	- ->	`\\hookrightarrow`
↩	Hook left arrow	갈고리 왼쪽 화살표	hookleftarrow arrow 화살표	- ->	`\\hookleftarrow`
⇀	Right harpoon up	오른쪽 위 반쪽 화살표	rightharpoonup arrow 화살표	- ->	`\\rightharpoonup`
↼	Left harpoon up	왼쪽 위 반쪽 화살표	leftharpoonup arrow 화살표	- ->	`\\leftharpoonup`
⇁	Right harpoon down	오른쪽 아래 반쪽 화살표	rightharpoondown arrow 화살표	- ->	`\\rightharpoondown`
↽	Left harpoon down	왼쪽 아래 반쪽 화살표	leftharpoondown arrow 화살표	- ->	`\\leftharpoondown`
⇌	Equilibrium right-left arrows	평형 오른쪽 왼쪽 화살표	rightleftharpoons arrow 화살표	- ->	`\\rightleftharpoons`
⇋	Equilibrium left-right arrows	평형 왼쪽 오른쪽 화살표	leftrightharpoons arrow 화살표	- ->	`\\leftrightharpoons`
↓	Down arrow	아래쪽 화살표	downarrow down 아래화살표 아래쪽화살표	- ->	`\\downarrow`
∋	Contains as an element	원소를 포함	ni contains	—	`\ni`
⊃	Superset	상위집합	supset superset	—	`\supset`
⊇	Superset or equal	상위집합 또는 같음	supseteq	—	`\supseteq`
⊈	Not a subset or equal	부분집합 아님	nsubseteq	—	`\nsubseteq`
∖	Set difference	차집합	setminus difference	—	`\setminus`
ℕ	Natural numbers	자연수 집합	naturals natural	—	`\mathbb{N}`
ℤ	Integers	정수 집합	integers integer	—	`\mathbb{Z}`
ℚ	Rational numbers	유리수 집합	rationals rational	—	`\mathbb{Q}`
ℝ	Real numbers	실수 집합	reals real	—	`\mathbb{R}`
ℂ	Complex numbers	복소수 집합	complexes complex	—	`\mathbb{C}`
⊥	Perpendicular	수직	perp perpendicular	—	`\perp`
∥	Parallel	평행	parallel	—	`\parallel`
≅	Congruent	합동	cong congruent	—	`\cong`
∼	Similar	닮음	sim similar	—	`\sim`
↦	Maps to	대응	mapsto maps arrow 화살표	\|-> - ->	`\\mapsto`
…	Ellipsis	말줄임표	ldots ellipsis	—	`\ldots`
⋯	Centered dots	가로 점	cdots	—	`\cdots`
⋮	Vertical dots	세로 점	vdots	—	`\vdots`
⋱	Diagonal dots	대각 점	ddots	—	`\ddots`
°	Degree	도	degree degrees 각도	—	`{}^{\circ}`
∠	Angle	각 기호	angle	—	`\angle`
+	Plus	더하기	plus sum	+	`+`
−	Minus	빼기	minus	-	`-`
±	Plus or minus	플러스 마이너스	plusminus sum	+- +	`\pm`
∓	Minus or plus	마이너스 플러스	minusplus	-+ -	`\mp`
×	Times	곱하기	times multiply	*	`\times`
·	Dot	가운데 점	dot multiply	*	`\cdot`
÷	Divide	나누기	divide division	/	`\div`
=	Equal	같음	equal	=	`=`
≠	Not equal	같지 않음	neq unequal	!= /= =	`\ne`
≈	Approximately equal	근삿값	approx	~ ~~ =	`\approx`
≡	Equivalent	동치	equiv	=== =	`\equiv`
<	Less than	작음	less	<	`<`
>	Greater than	큼	greater	>	`>`
≤	Less than or equal	작거나 같음	leq less	<= <- <	`\le`
≥	Greater than or equal	크거나 같음	geq greater	>= >- >	`\ge`
∝	Proportional	비례	proportional	~	`\propto`
→	Right arrow	오른쪽 화살표	rightarrow arrow	-> -	`\\to`
←	Left arrow	왼쪽 화살표	leftarrow arrow	<- < - ->	`\\leftarrow`
↔	Left-right arrow	양방향 화살표	leftrightarrow arrow	<-> - ->	`\\leftrightarrow`
⇒	Implies	함의	implies arrow 화살표	=> = - ->	`\\Rightarrow`
⇔	If and only if	필요충분	iff arrow 화살표	<=> - ->	`\\Leftrightarrow`
∈	Element of	원소	in element	E	`\in`
∉	Not an element of	원소 아님	notin element	E/	`\notin`
∀	For all	모든	forall	A	`\forall`
∃	There exists	존재	exists	E	`\exists`
∪	Union	합집합	union	U	`\cup`
∩	Intersection	교집합	intersection	—	`\cap`
⊂	Subset	부분집합	subset	<	`\subset`
⊆	Subset or equal	부분집합 또는 같음	subseteq	<=	`\subseteq`
∅	Empty set	공집합	emptyset	—	`\emptyset`
∞	Infinity	무한대	infinity infty	—	`\infty`
∂	Partial derivative	편미분	partial derivative	—	`\partial`
∇	Nabla	나블라	nabla gradient	—	`\nabla`
∧	Logical and	논리곱	and wedge	^	`\wedge`
∨	Logical or	논리합	or vee	—	`\vee`
¬	Logical not	부정	not neg	!	`\neg`
α	Alpha	알파	alpha	—	`\alpha`
β	Beta	베타	beta	—	`\beta`
γ	Gamma	감마	gamma	—	`\gamma`
δ	Delta	델타	delta	—	`\delta`
ε	Epsilon	엡실론	epsilon	—	`\epsilon`
ζ	Zeta	제타	zeta	—	`\zeta`
η	Eta	에타	eta	—	`\eta`
θ	Theta	세타	theta	—	`\theta`
ι	Iota	이오타	iota	—	`\iota`
κ	Kappa	카파	kappa	—	`\kappa`
λ	Lambda	람다	lambda	—	`\lambda`
μ	Mu	뮤	mu	—	`\mu`
ν	Nu	뉴	nu	—	`\nu`
ξ	Xi	크시	xi	—	`\xi`
π	Pi	파이	pi	—	`\pi`
ρ	Rho	로	rho	—	`\rho`
σ	Sigma	시그마	sigma	—	`\sigma`
τ	Tau	타우	tau	—	`\tau`
υ	Upsilon	입실론	upsilon	—	`\upsilon`
φ	Phi	파이 / 피	phi	—	`\phi`
χ	Chi	카이	chi	—	`\chi`
ψ	Psi	프사이	psi	—	`\psi`
ω	Omega	오메가	omega	—	`\omega`
Γ	Uppercase Gamma	대문자 감마	Gamma	—	`\Gamma`
Δ	Uppercase Delta	대문자 델타	Delta	—	`\Delta`
Θ	Uppercase Theta	대문자 세타	Theta	—	`\Theta`
Λ	Uppercase Lambda	대문자 람다	Lambda	—	`\Lambda`
Ξ	Uppercase Xi	대문자 크시	Xi	—	`\Xi`
Π	Uppercase Pi	대문자 파이	Pi	—	`\Pi`
Σ	Uppercase Sigma	대문자 시그마	Sigma	—	`\Sigma`
Φ	Uppercase Phi	대문자 파이 / 피	Phi	—	`\Phi`
Ψ	Uppercase Psi	대문자 프사이	Psi	—	`\Psi`
Ω	Uppercase Omega	대문자 오메가	Omega	—	`\Omega`

Renderer availability

This formula catalog describes the shared model and the existing rich React editor. Native DOM/framework surfaces share the notation model, token editing, discovery and presentation utilities; host integration policies remain separate. See the renderer parity table before choosing an adapter.

Combined scripts (workspace)

x_i^2 and x^2_i load into one scripts node with slots [base, subscript, superscript]. In either renderer, enter ^ at the end of a subscript and choose Exponent, or _ at the end of an exponent and choose Subscript. The other script is added to the same base. Tab / Shift+Tab move between slots; Backspace in an empty script removes only that side. Explicit grouping such as {x_i}^2 still represents nesting. Repeated scripts without grouping remain syntax errors. Available in 0.2.0.

Selecting a range opens wrapping actions beside the selection in both renderers, including toolbar-free inline surfaces. Actions include fraction, square root, superscript, subscript, parentheses, brackets and absolute value. A multi-line selection keeps the actions disabled. Applying an action preserves the selected model content and supports Undo. React also respects the host's excluded structure list.

Literal text and functions (workspace)

Type text or 텍스트 and select Text to write a description, then Tab to resume math. Type sin, cos, log and choose the corresponding function suggestion; operatorname opens an editable custom name. Function arguments remain ordinary neighboring math. LaTeX import supports \text{otherwise}, the 19 names listed in LaTeX scope, and \operatorname{custom}. Imported names and text can be edited in React and native adapters. Mixed math inside text and text styling remain unsupported.

Spacing, explicit limits and upright math (workspace)

Input	Model / export policy
`\quad`, `\qquad`	Zero-slot spacing structures, one/two em; original command preserved
`\sum\limits_{i=1}^n`, `\prod\limits`, `\int\limits`, `\lim\limits`	Operator with `limits: true`; explicit directive preserved
`\mathrm{dx}`	One-slot `roman` math group; same command exported
`{\rm dx}`	Scoped upright declaration; normalizes to `\mathrm{dx}`

Type quad / qquad (or 간격 / 큰간격) for an explicit gap. The caret resumes after the gap; Backspace there removes it and Undo restores it. Type mathrm / 직립체 for an editable upright group. Math inside a roman group keeps semantic colors and structure editing. It is not a literal text group.

\limits is accepted immediately after the supported operator, before its scripts. Arbitrary TeX dimensions (\hspace, \kern) and other font declarations remain unsupported. These additions are included in 0.2.0.

Additional fences and annotations (workspace)

Input	Model	Editing
`\left\{x\right\}`	`braces`, one body slot	Search `braces` or `중괄호`
`\langle u,v\rangle` or `\left\langle u,v\right\rangle`	`angle`, one body slot	Search `angle`, `내적` or `꺾쇠괄호`
`\left(a,b\right]`	`openClosed`, one body slot	Search `openclosed` or `열린닫힌구간`
`\left[a,b\right)`	`closedOpen`, one body slot	Search `closedopen` or `닫힌열린구간`
Other `\left…\right…` pairs, including `\left.x\right	`	`fenced`, one body slot and independent `left`/`right`
`\overset{a}{b}`	`overset`, `[annotation, body]`	Search `overset` or `위주석`; Tab moves from annotation to body
`\underset{a}{b}`	`underset`, `[annotation, body]`	Search `underset` or `아래주석`; Tab follows model order, even though the annotation is below

Select an expression and choose a fence or annotation in the regular suggestion menu. Fences wrap the expression and resume after it. Annotations keep the selected expression in the body and focus the empty annotation slot. Nested fractions, scripts and other editable structures are allowed in both annotation slots. Backspace after a structure removes its wrapper while preserving its content; Undo restores it.

All structured fences scale with their contents. Short angle notation normalizes to scalable \left\langle…\right\rangle on export. Supported physical ends are (, ), [, ], {, }, ⟨, ⟩, | and .. Plain punctuation stays literal unless imported with a structural command. Double norm bars and brace annotations are supported. Explicit \big/\Big sizing remains unsupported.

Double integrals (workspace)

\iint_R f(x,y) imports as doubleIntegral with exactly three slots: [lower/domain, upper, body], matching integral navigation. Missing bounds remain editable empty slots. \iint\limits preserves the explicit placement directive. Export uses \iint_{lower}^{upper}{body}. Search iint, 이중적분 or ∬ to insert; Tab visits the domain, upper bound and body in order. The reported expression with \rm dx \rm dy, \xi, \eta and \text{Area} is covered by import/round-trip and browser editing fixtures. This is notation support, not numerical integration. Triple and contour integrals are also supported.

Fine spacing: \,, \:, \;, \! are preserved as zero-slot structures. Positive spacing expands and negative thin spacing contracts the next boundary; these are not editable text spaces.

Explicit sizes (0.2.0)

\dfrac, \tfrac, \dbinom and \tbinom can be imported and edited without losing their size choice on export. Type dfrac, tfrac, dbinom or tbinom and select the matching suggestion, then edit the two slots with Tab. See JSON size mapping. General \displaystyle and \textstyle declarations remain unsupported.

Math alphabet support (workspace)

\mathbf, \mathcal and multi-letter \mathbb now support import, suggestions, range wrapping, editing and export. See alphabet scope and examples. Available in 0.2.0.

Labeled arrows (workspace)

\xrightarrow[below]{above} and \xleftarrow[below]{above} support parsing, suggestions, editable math labels and export. See label syntax and slot order. Available in 0.2.0.

Keyboard ranges and brace discovery (0.2.1)

Shift+Left/Right extends or shrinks the same model range used by dragging. Structures are crossed as balanced units; copied and deleted ranges use existing model normalization. Shift+Up/Down extends to an adjacent top-level document line, using a logical text offset rather than pixel-based column matching; an active matrix-cell selection instead uses Shift+arrows to move its rectangular focus corner. Copy, cut, wrapping, deletion and Undo use the existing range behavior. IME composition and modifier shortcuts retain their existing handling.

After a model selection, plain Left/Up restores the caret at its document-ordered start; Right/Down restores it at the end. The same rule applies to reverse drags and Shift+arrow selections, without consuming another character or changing the formula. Alt+Up/Down browses the wrapping suggestions while retaining the range; Enter applies a candidate. Ordinary input suggestions still use Up/Down.

Typing { offers both paired braces and cases. Paired braces remain the first candidate; choose Cases explicitly to insert its editable grid.

Presentation customization

CSS variables support scoped palettes, token colors, slot focus/selection, toolbar density and menu chrome in both renderers and all framework adapters. Portaled suggestions follow their owning editor. See Styling & themes; host integrations retain their own persisted formula-size attributes.