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/**
* Best-effort LaTeX math to Unicode plain text conversion for terminal display.
*
* The goal is readable math in a monospace grid, not faithful typesetting:
* symbols map to their Unicode equivalents (\sum → ∑, \alpha → α), scripts use
* Unicode sub/superscript characters when every character is available
* (x_{t-k} → xₜ₋ₖ) and stay in TeX notation otherwise (x_\theta → x_θ), and
* structural commands degrade to linear notation (\frac{a}{b} → a/b).
* Unknown commands keep their name with the backslash dropped, so output is
* never worse than the raw source.
*/
const SYMBOLS: Record<string, string> = {
alpha: "α",
beta: "β",
gamma: "γ",
delta: "δ",
epsilon: "ε",
varepsilon: "ε",
zeta: "ζ",
eta: "η",
theta: "θ",
vartheta: "ϑ",
iota: "ι",
kappa: "κ",
lambda: "λ",
mu: "μ",
nu: "ν",
xi: "ξ",
pi: "π",
varpi: "ϖ",
rho: "ρ",
varrho: "ϱ",
sigma: "σ",
varsigma: "ς",
tau: "τ",
upsilon: "υ",
phi: "ϕ",
varphi: "φ",
chi: "χ",
psi: "ψ",
omega: "ω",
Gamma: "Γ",
Delta: "Δ",
Theta: "Θ",
Lambda: "Λ",
Xi: "Ξ",
Pi: "Π",
Sigma: "Σ",
Upsilon: "Υ",
Phi: "Φ",
Psi: "Ψ",
Omega: "Ω",
sum: "∑",
prod: "∏",
coprod: "∐",
int: "∫",
iint: "∬",
iiint: "∭",
oint: "∮",
bigcup: "⋃",
bigcap: "⋂",
bigoplus: "⨁",
bigotimes: "⨂",
bigodot: "⨀",
bigvee: "⋁",
bigwedge: "⋀",
bigsqcup: "⨆",
pm: "±",
mp: "∓",
times: "×",
div: "÷",
cdot: "·",
ast: "∗",
star: "⋆",
circ: "∘",
bullet: "•",
oplus: "⊕",
ominus: "⊖",
otimes: "⊗",
oslash: "⊘",
odot: "⊙",
wedge: "∧",
land: "∧",
vee: "∨",
lor: "∨",
cap: "∩",
cup: "∪",
setminus: "∖",
sqcap: "⊓",
sqcup: "⊔",
uplus: "⊎",
dagger: "†",
ddagger: "‡",
leq: "≤",
le: "≤",
geq: "≥",
ge: "≥",
neq: "≠",
ne: "≠",
equiv: "≡",
sim: "∼",
simeq: "≃",
approx: "≈",
cong: "≅",
propto: "∝",
ll: "≪",
gg: "≫",
subset: "⊂",
supset: "⊃",
subseteq: "⊆",
supseteq: "⊇",
sqsubseteq: "⊑",
sqsupseteq: "⊒",
in: "∈",
ni: "∋",
notin: "∉",
models: "⊨",
vdash: "⊢",
dashv: "⊣",
perp: "⊥",
parallel: "∥",
mid: "∣",
asymp: "≍",
doteq: "≐",
prec: "≺",
succ: "≻",
preceq: "⪯",
succeq: "⪰",
triangleq: "≜",
coloneqq: "≔",
coloneq: "≔",
to: "→",
rightarrow: "→",
leftarrow: "←",
gets: "←",
leftrightarrow: "↔",
Rightarrow: "⇒",
Leftarrow: "⇐",
Leftrightarrow: "⇔",
iff: "⇔",
implies: "⇒",
impliedby: "⇐",
mapsto: "↦",
longrightarrow: "⟶",
longleftarrow: "⟵",
Longrightarrow: "⟹",
Longleftarrow: "⟸",
longmapsto: "⟼",
uparrow: "↑",
downarrow: "↓",
updownarrow: "↕",
Uparrow: "⇑",
Downarrow: "⇓",
hookrightarrow: "↪",
hookleftarrow: "↩",
rightharpoonup: "⇀",
leftharpoonup: "↼",
rightrightarrows: "⇉",
rightleftarrows: "⇄",
leadsto: "⇝",
nearrow: "↗",
searrow: "↘",
nwarrow: "↖",
swarrow: "↙",
infty: "∞",
partial: "∂",
nabla: "∇",
forall: "∀",
exists: "∃",
nexists: "∄",
emptyset: "∅",
varnothing: "∅",
neg: "¬",
lnot: "¬",
angle: "∠",
triangle: "△",
square: "□",
Box: "□",
blacksquare: "■",
diamond: "⋄",
Diamond: "◇",
aleph: "ℵ",
hbar: "ℏ",
ell: "ℓ",
Re: "ℜ",
Im: "ℑ",
wp: "℘",
top: "⊤",
bot: "⊥",
flat: "♭",
sharp: "♯",
natural: "♮",
checkmark: "✓",
degree: "°",
prime: "′",
therefore: "∴",
because: "∵",
dots: "…",
ldots: "…",
dotsc: "…",
dotso: "…",
cdots: "⋯",
dotsb: "⋯",
vdots: "⋮",
ddots: "⋱",
langle: "⟨",
rangle: "⟩",
lceil: "⌈",
rceil: "⌉",
lfloor: "⌊",
rfloor: "⌋",
lvert: "|",
rvert: "|",
vert: "|",
lVert: "‖",
rVert: "‖",
Vert: "‖",
};
/** Operator names render as plain words (\log → log). */
const OPERATOR_NAMES = new Set([
"log",
"ln",
"lg",
"exp",
"sin",
"cos",
"tan",
"cot",
"sec",
"csc",
"arcsin",
"arccos",
"arctan",
"sinh",
"cosh",
"tanh",
"coth",
"min",
"max",
"argmin",
"argmax",
"arg",
"sup",
"inf",
"lim",
"limsup",
"liminf",
"det",
"dim",
"ker",
"deg",
"gcd",
"hom",
"Pr",
"tr",
"Tr",
"rank",
"diag",
"sgn",
"softmax",
"mod",
"bmod",
]);
/** Single-character escapes (\{ → {) and spacing commands. */
const ESCAPES: Record<string, string> = {
"{": "{",
"}": "}",
"%": "%",
$: "$",
"&": "&",
"#": "#",
_: "_",
"|": "‖",
"\\": "\n",
" ": " ",
",": " ",
";": " ",
":": " ",
"!": "",
};
const SPACING_COMMANDS: Record<string, string> = {
quad: " ",
qquad: " ",
thinspace: " ",
enspace: " ",
medspace: " ",
thickspace: " ",
};
/** Accent commands → combining character appended to each character. */
const ACCENTS: Record<string, string> = {
hat: "̂",
widehat: "̂",
bar: "̄",
overline: "̅",
underline: "̲",
vec: "⃗",
tilde: "̃",
widetilde: "̃",
dot: "̇",
ddot: "̈",
breve: "̆",
check: "̌",
acute: "́",
grave: "̀",
mathring: "̊",
};
const SUPERSCRIPTS: Record<string, string> = {
"0": "⁰",
"1": "¹",
"2": "²",
"3": "³",
"4": "⁴",
"5": "⁵",
"6": "⁶",
"7": "⁷",
"8": "⁸",
"9": "⁹",
"+": "⁺",
"-": "⁻",
"−": "⁻",
"=": "⁼",
"(": "⁽",
")": "⁾",
"*": "*",
a: "ᵃ",
b: "ᵇ",
c: "ᶜ",
d: "ᵈ",
e: "ᵉ",
f: "ᶠ",
g: "ᵍ",
h: "ʰ",
i: "ⁱ",
j: "ʲ",
k: "ᵏ",
l: "ˡ",
m: "ᵐ",
n: "ⁿ",
o: "ᵒ",
p: "ᵖ",
r: "ʳ",
s: "ˢ",
t: "ᵗ",
u: "ᵘ",
v: "ᵛ",
w: "ʷ",
x: "ˣ",
y: "ʸ",
z: "ᶻ",
A: "ᴬ",
B: "ᴮ",
D: "ᴰ",
E: "ᴱ",
G: "ᴳ",
H: "ᴴ",
I: "ᴵ",
J: "ᴶ",
K: "ᴷ",
L: "ᴸ",
M: "ᴹ",
N: "ᴺ",
O: "ᴼ",
P: "ᴾ",
R: "ᴿ",
T: "ᵀ",
U: "ᵁ",
V: "ⱽ",
W: "ᵂ",
β: "ᵝ",
γ: "ᵞ",
δ: "ᵟ",
θ: "ᶿ",
ϕ: "ᵠ",
φ: "ᵠ",
χ: "ᵡ",
};
const SUBSCRIPTS: Record<string, string> = {
"0": "₀",
"1": "₁",
"2": "₂",
"3": "₃",
"4": "₄",
"5": "₅",
"6": "₆",
"7": "₇",
"8": "₈",
"9": "₉",
"+": "₊",
"-": "₋",
"−": "₋",
"=": "₌",
"(": "₍",
")": "₎",
a: "ₐ",
e: "ₑ",
h: "ₕ",
i: "ᵢ",
j: "ⱼ",
k: "ₖ",
l: "ₗ",
m: "ₘ",
n: "ₙ",
o: "ₒ",
p: "ₚ",
r: "ᵣ",
s: "ₛ",
t: "ₜ",
u: "ᵤ",
v: "ᵥ",
x: "ₓ",
β: "ᵦ",
γ: "ᵧ",
ρ: "ᵨ",
ϕ: "ᵩ",
φ: "ᵩ",
χ: "ᵪ",
};
const COMMON_FRACTIONS: Record<string, string> = {
"1/2": "½",
"1/3": "⅓",
"2/3": "⅔",
"1/4": "¼",
"3/4": "¾",
"1/5": "⅕",
"2/5": "⅖",
"3/5": "⅗",
"4/5": "⅘",
"1/6": "⅙",
"5/6": "⅚",
"1/8": "⅛",
};
interface AlphabetStyle {
/** Code point of the styled "A" in the Mathematical Alphanumeric block. */
upper?: number;
/** Code point of the styled "a". */
lower?: number;
/** Code point of the styled "0". */
digit?: number;
/** Letters whose styled forms predate the block and live elsewhere in the BMP. */
exceptions?: Record<string, string>;
}
const ALPHABETS: Record<string, AlphabetStyle> = {
mathbb: {
upper: 0x1d538,
lower: 0x1d552,
digit: 0x1d7d8,
exceptions: { C: "ℂ", H: "ℍ", N: "ℕ", P: "ℙ", Q: "ℚ", R: "ℝ", Z: "ℤ" },
},
mathbf: { upper: 0x1d400, lower: 0x1d41a, digit: 0x1d7ce },
boldsymbol: { upper: 0x1d400, lower: 0x1d41a, digit: 0x1d7ce },
bm: { upper: 0x1d400, lower: 0x1d41a, digit: 0x1d7ce },
textbf: { upper: 0x1d400, lower: 0x1d41a, digit: 0x1d7ce },
mathcal: {
upper: 0x1d49c,
lower: 0x1d4b6,
exceptions: {
B: "ℬ",
E: "ℰ",
F: "ℱ",
H: "ℋ",
I: "ℐ",
L: "ℒ",
M: "ℳ",
R: "ℛ",
e: "ℯ",
g: "ℊ",
o: "ℴ",
},
},
mathscr: {
upper: 0x1d49c,
lower: 0x1d4b6,
exceptions: {
B: "ℬ",
E: "ℰ",
F: "ℱ",
H: "ℋ",
I: "ℐ",
L: "ℒ",
M: "ℳ",
R: "ℛ",
e: "ℯ",
g: "ℊ",
o: "ℴ",
},
},
mathfrak: {
upper: 0x1d504,
lower: 0x1d51e,
exceptions: { C: "ℭ", H: "ℌ", I: "ℑ", R: "ℜ", Z: "ℨ" },
},
};
/** Text-mode commands: their argument is literal text, so ^ and _ stay as-is. */
const TEXT_COMMANDS = new Set(["text", "textrm", "textit", "textsf", "texttt", "mbox", "hbox"]);
/** Math-mode font commands rendered unstyled; scripts inside still apply. */
const MATH_FONT_COMMANDS = new Set(["mathrm", "mathit", "mathsf", "mathtt", "mathnormal", "operatorname"]);
/** Size/style commands that take no argument and render as nothing. */
const IGNORED_COMMANDS = new Set([
"left",
"right",
"big",
"Big",
"bigg",
"Bigg",
"bigl",
"bigr",
"bigm",
"Bigl",
"Bigr",
"Bigm",
"biggl",
"biggr",
"Biggl",
"Biggr",
"displaystyle",
"textstyle",
"scriptstyle",
"limits",
"nolimits",
"middle",
"allowbreak",
"nonumber",
"notag",
]);
function styleAlphabet(text: string, style: AlphabetStyle): string {
let result = "";
for (const ch of text) {
const exception = style.exceptions?.[ch];
if (exception) {
result += exception;
} else if (ch >= "A" && ch <= "Z" && style.upper !== undefined) {
result += String.fromCodePoint(style.upper + ch.charCodeAt(0) - 0x41);
} else if (ch >= "a" && ch <= "z" && style.lower !== undefined) {
result += String.fromCodePoint(style.lower + ch.charCodeAt(0) - 0x61);
} else if (ch >= "0" && ch <= "9" && style.digit !== undefined) {
result += String.fromCodePoint(style.digit + ch.charCodeAt(0) - 0x30);
} else {
result += ch;
}
}
return result;
}
/** Map every character through a sub/superscript table, or return undefined if any character is missing. */
function mapScript(text: string, table: Record<string, string>): string | undefined {
let result = "";
for (const ch of text) {
const mapped = table[ch];
if (mapped === undefined) {
return undefined;
}
result += mapped;
}
return result;
}
/** True when a fraction/sqrt operand reads unambiguously without parentheses. */
function isSimpleOperand(text: string): boolean {
return [...text].length === 1 || /^[\p{L}\p{N}\p{M}]+$/u.test(text);
}
function parenthesize(text: string): string {
return isSimpleOperand(text) ? text : `(${text})`;
}
class LatexParser {
private readonly src: string;
private pos = 0;
private textMode = false;
constructor(src: string) {
this.src = src;
}
parse(): string {
return this.parseSequence();
}
/** Render atoms (with attached scripts) until a closing brace or end of input. */
private parseSequence(): string {
let result = "";
while (this.pos < this.src.length) {
const ch = this.src[this.pos];
if (ch === "}") {
break;
}
if ((ch === "^" || ch === "_") && !this.textMode) {
this.pos++;
result += this.parseScript(ch === "^" ? SUPERSCRIPTS : SUBSCRIPTS, ch);
continue;
}
if (ch === "&") {
// Alignment marker: becomes a separating space unless one is there.
this.pos++;
if (!/\s$/.test(result)) {
result += " ";
}
continue;
}
result += this.parseAtom() ?? "";
}
return result;
}
/** Render the next atom: a group, a command, or a single character. */
private parseAtom(): string | undefined {
if (this.pos >= this.src.length) {
return undefined;
}
const ch = this.src[this.pos];
if (ch === "{") {
return this.parseGroup();
}
if (ch === "\\") {
return this.parseCommand();
}
this.pos++;
return ch;
}
/** Consume "{...}" and render its contents. Assumes "{" at the current position. */
private parseGroup(): string {
this.pos++; // consume "{"
const content = this.parseSequence();
if (this.src[this.pos] === "}") {
this.pos++;
}
return content;
}
/** Consume "[...]" and render its contents, or return undefined when absent. */
private parseOptionalBracket(): string | undefined {
if (this.src[this.pos] !== "[") {
return undefined;
}
const end = this.src.indexOf("]", this.pos + 1);
if (end === -1) {
return undefined;
}
const content = new LatexParser(this.src.slice(this.pos + 1, end)).parse();
this.pos = end + 1;
return content;
}
/** Render the next required argument: a braced group, or a single atom (TeX allows \frac12). */
private parseArgument(): string {
while (this.pos < this.src.length && /\s/.test(this.src[this.pos])) {
this.pos++;
}
if (this.src[this.pos] === "{") {
return this.parseGroup();
}
return this.parseAtom() ?? "";
}
/** Render a ^ or _ script. The operator character itself is already consumed. */
private parseScript(table: Record<string, string>, operator: string): string {
const content = this.parseArgument();
const mapped = mapScript(content, table);
if (mapped !== undefined) {
return mapped;
}
// No Unicode form for every character: keep lossless TeX notation (x_θ).
return [...content].length === 1 ? `${operator}${content}` : `${operator}{${content}}`;
}
/** Render a command. Assumes "\" at the current position. */
private parseCommand(): string {
this.pos++; // consume "\"
if (this.pos >= this.src.length) {
return "";
}
const ch = this.src[this.pos];
if (!/[a-zA-Z]/.test(ch)) {
this.pos++;
return ESCAPES[ch] ?? ch;
}
let name = "";
while (this.pos < this.src.length && /[a-zA-Z]/.test(this.src[this.pos])) {
name += this.src[this.pos];
this.pos++;
}
if (this.src[this.pos] === "*") {
this.pos++; // operatorname*, section* etc.
}
const symbol = SYMBOLS[name];
if (symbol !== undefined) {
return symbol;
}
if (OPERATOR_NAMES.has(name)) {
return name;
}
const spacing = SPACING_COMMANDS[name];
if (spacing !== undefined) {
return spacing;
}
if (IGNORED_COMMANDS.has(name)) {
if (name === "left" || name === "right") {
return this.parseDelimiter();
}
return "";
}
if (TEXT_COMMANDS.has(name)) {
const wasTextMode = this.textMode;
this.textMode = true;
const content = this.parseArgument();
this.textMode = wasTextMode;
return content;
}
if (MATH_FONT_COMMANDS.has(name)) {
return this.parseArgument();
}
const alphabet = ALPHABETS[name];
if (alphabet !== undefined) {
return styleAlphabet(this.parseArgument(), alphabet);
}
const accent = ACCENTS[name];
if (accent !== undefined) {
const content = this.parseArgument();
return [...content].map((c) => (/\s/.test(c) ? c : c + accent)).join("");
}
switch (name) {
case "frac":
case "dfrac":
case "tfrac":
case "cfrac": {
const numerator = this.parseArgument();
const denominator = this.parseArgument();
const common = COMMON_FRACTIONS[`${numerator}/${denominator}`];
if (common !== undefined) {
return common;
}
return `${parenthesize(numerator)}/${parenthesize(denominator)}`;
}
case "binom": {
const top = this.parseArgument();
const bottom = this.parseArgument();
return `C(${top},${bottom})`;
}
case "sqrt": {
const index = this.parseOptionalBracket();
const radicand = this.parseArgument();
const operand = isSimpleOperand(radicand) ? radicand : `(${radicand})`;
if (index === undefined) {
return `√${operand}`;
}
if (index === "3") {
return `∛${operand}`;
}
if (index === "4") {
return `∜${operand}`;
}
return `${mapScript(index, SUPERSCRIPTS) ?? `^${index}`}√${operand}`;
}
case "not": {
const negated = this.parseAtom() ?? "";
return `${negated}̸`;
}
case "begin":
case "end": {
this.parseArgument(); // environment name
return "";
}
case "stackrel":
case "overset": {
const above = this.parseArgument();
const base = this.parseArgument();
const mapped = mapScript(above, SUPERSCRIPTS);
return mapped !== undefined ? base + mapped : `${base}^{${above}}`;
}
case "underset": {
const below = this.parseArgument();
const base = this.parseArgument();
const mapped = mapScript(below, SUBSCRIPTS);
return mapped !== undefined ? base + mapped : `${base}_{${below}}`;
}
default:
// Unknown command: drop the backslash, keep the name.
return name;
}
}
/** Render the delimiter following \left or \right ("." means invisible). */
private parseDelimiter(): string {
while (this.pos < this.src.length && /\s/.test(this.src[this.pos])) {
this.pos++;
}
const ch = this.src[this.pos];
if (ch === undefined) {
return "";
}
if (ch === ".") {
this.pos++;
return "";
}
if (ch === "\\") {
return this.parseCommand();
}
this.pos++;
return ch;
}
}
/**
* Convert LaTeX math source to Unicode plain text.
*
* Newlines in the source are preserved and "\\" becomes a newline, so
* multi-line display math (aligned environments) renders on multiple lines.
* Runs of spaces collapse to one — TeX treats source whitespace as
* insignificant, and spacing commands otherwise leave double gaps.
*/
export function latexToUnicode(tex: string): string {
return new LatexParser(tex)
.parse()
.replace(/[^\S\n]{2,}/g, " ")
.replace(/\n\s*\n/g, "\n");
}