cnum

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Represent rational numbers in comfortably numeric way.

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{"version":3,"file":"index.cjs","sources":["../src/version.ts","../src/Token.ts","../src/Lexer.ts","../src/Parser.ts","../src/bigint.ts","../src/SternBrocotTree.ts","../src/config.ts","../src/Rat.ts","../src/Symbolizer.ts","../src/Polyrat.ts","../src/cnum.ts"],"sourcesContent":["export default '0.1.3'\n","export const enum TokenType {\n identifier,\n keyword,\n separator,\n operator,\n literal,\n comment,\n}\n\n/**\n * @class Token\n * @name Token\n */\nexport class Token {\n type: TokenType\n s: string\n\n /**\n * Initialize a token.\n */\n constructor(type: TokenType, s: string) {\n this.type = type\n this.s = s\n }\n\n /**\n * The text representation.\n */\n toString(): string {\n return `${this.type}(${this.s})`\n }\n}\n\nexport default Token\n","import Token, { TokenType } from './Token'\n\nconst OPERATORS = {\n '+': 'add',\n '-': 'sub',\n '*': 'mul',\n '/': 'div',\n '**': 'pow',\n '^': 'pow',\n '=': 'set',\n '==': 'equals',\n '<': 'isLessThan',\n '>': 'isGreaterThan',\n}\n\n/**\n * @class Lexer\n * @name Lexer\n */\nexport class Lexer {\n s: string\n\n /**\n * Initialize a lexer.\n */\n constructor(input: string) {\n this.s = input\n }\n\n /**\n * Yields tokens as they are lexed.\n *\n */\n *lex(): Generator<Token> {\n let onSpace = false\n let onInteger = false\n let onWord = false\n let onOperator = false\n let buffer = ''\n\n // for each character\n for (let i = 0; i < this.s.length; i++) {\n const char = this.s[i] ?? '?'\n\n // if a space, combine with subsequent spaces into a separator\n if (/^\\s$/.exec(char)) {\n if (onInteger) {\n yield new Token(TokenType.literal, buffer)\n onInteger = false\n buffer = ''\n } else if (onWord) {\n yield new Token(TokenType.identifier, buffer)\n onWord = false\n buffer = ''\n }\n onSpace = true\n buffer += char\n continue\n } else if (onSpace) {\n yield new Token(TokenType.separator, '')\n onSpace = false\n buffer = ''\n }\n\n // if a digit, combine with subsequent digits into a literal\n if (/^\\d$/.exec(char)) {\n if (!onWord) {\n onInteger = true\n }\n buffer += char\n continue\n } else if (onInteger) {\n yield new Token(TokenType.literal, buffer)\n onInteger = false\n buffer = ''\n }\n\n // if a letter, combine with subsequent letters/numbers into an identifier\n if (/^[a-z]$/.exec(char) || (onWord && /^\\d$/.exec(char))) {\n onWord = true\n buffer += char\n continue\n } else if (onWord) {\n yield new Token(TokenType.identifier, buffer)\n onWord = false\n buffer = ''\n }\n\n // if another char, combine with subsequent char and match an operator\n buffer += char\n if (buffer in OPERATORS) {\n yield new Token(TokenType.operator, buffer)\n onOperator = false\n buffer = ''\n continue\n }\n if (onOperator) {\n throw `Invalid operator \"${buffer}\"`\n }\n onOperator = true\n }\n\n if (onSpace) {\n yield new Token(TokenType.separator, '')\n }\n\n if (onInteger) {\n yield new Token(TokenType.literal, buffer)\n }\n\n if (onWord) {\n yield new Token(TokenType.identifier, buffer)\n }\n }\n}\n\nexport default Lexer\n","import { Token, TokenType } from './Token'\n\ninterface Identifiers<T> {\n [Key: string]: T\n}\n\n/**\n * @class Parser\n * @name Parser\n */\nexport class Parser {\n tokens: Generator<Token>\n identifiers: Identifiers<string> = {}\n\n /**\n * Initialize a parser from a token generator.\n */\n constructor(tokens: Generator<Token>) {\n this.tokens = tokens\n }\n\n /**\n * Evaluate the result.\n */\n evaluate(): bigint {\n let n = 0n\n for (const x of this.tokens) {\n if (x.type === TokenType.identifier) {\n if (!(x.s in this.identifiers)) {\n throw `\"${x.s}\" is undefined`\n }\n n += BigInt(this.identifiers[x.s] ?? -1)\n }\n // else if (x.type === TokenType.separator) {\n // }\n // else if (x.type === TokenType.operator) {\n // if (x.s === '=') {\n // }\n // }\n else if (x.type === TokenType.literal) {\n n += BigInt(x.s)\n }\n }\n return n\n }\n\n /**\n * The text representation.\n */\n toString(): string {\n return this.evaluate().toString()\n }\n}\n\nexport default Parser\n","/**\n * Find the greatest common denominator of the two numbers.\n */\nexport const gcd = (a: bigint, b: bigint): bigint => {\n if (b === 1n || a === 1n) {\n return 1n\n }\n while (b !== 0n) {\n //[a, b] = [b, a % b] // not pretty???\n const t = a % b\n a = b\n b = t\n }\n return a < 0n ? -a : a\n}\n\n/**\n * Returns true if the number is prime.\n */\nexport const isPrime = (n: bigint): boolean => {\n if (n === 1n) return false\n for (let i = 2n; i * i <= n; i++) {\n if (n % i === 0n) return false\n }\n return true\n}\n\n/**\n * Yields the prime numbers.\n */\nexport function* primes(): Generator<bigint> {\n for (let n = 2n; true; n++) {\n if (isPrime(n)) {\n yield n\n }\n }\n}\n\n/**\n * Finds the prime factors, returning them in ascending order as arrays with their exponent as the second element.\n */\nexport const primeFactors = (n: bigint): Array<[bigint, bigint]> => {\n const f: Array<[bigint, bigint]> = []\n for (const p of primes()) {\n let e = 0n\n while (n % p === 0n) {\n e++\n n /= p\n }\n if (e) f.push([p, e])\n if (n === 1n) break\n }\n return f\n}\n","import { MAX_LOOPS } from './config'\nimport Rat from './Rat'\n\n/**\n * Find the rational number that best approximates the floating point number.\n */\nexport function rationalApproximation(n: number): Rat {\n let m0 = 1n,\n m1 = 0n,\n m2 = 0n,\n m3 = 1n\n const r = new Rat(1n)\n for (let i = 0; i < MAX_LOOPS; i++) {\n if (r.approximates(n)) break\n if (+r > n) {\n m0 += m1\n m2 += m3\n } else {\n m1 += m0\n m3 += m2\n }\n r.n = m0 + m1\n r.d = m2 + m3\n }\n return r\n}\n\n/**\n * Yield false for each left and true for each right.\n */\nexport function* pathToValue(n: number): Generator<boolean> {\n let m0 = 1n,\n m1 = 0n,\n m2 = 0n,\n m3 = 1n\n const r = new Rat(1n)\n for (let i = 0; i < MAX_LOOPS; i++) {\n if (r.approximates(n)) break\n const direction = n > +r\n yield direction\n if (!direction) {\n m0 += m1\n m2 += m3\n } else {\n m1 += m0\n m3 += m2\n }\n r.n = m0 + m1\n r.d = m2 + m3\n }\n}\n\n/**\n * Yield the values of the continued fraction, ie. the length of runs left/right.\n */\nexport function* continuedFraction(n: number): Generator<number> {\n let last = true\n let run = 0\n for (const direction of pathToValue(n)) {\n if (direction === last) {\n run++\n } else {\n yield run\n run = 1\n last = direction\n }\n }\n yield run + 1\n}\n","/**\n * Machine epsilon gives an upper bound on the relative error due to rounding in floating point arithmetic.\n */\nexport const EPSILON = 1e-16\n// @todo why not Number.EPSILON?\n\n/**\n * Limit on the number of loops in algorithms.\n */\nexport const MAX_LOOPS = 512\n","import { EPSILON } from './config'\nimport { gcd, primeFactors } from './bigint'\nimport { rationalApproximation, continuedFraction } from './SternBrocotTree'\n\n/**\n * @class Rational Number\n * @name Rat\n */\nexport class Rat {\n n: bigint\n d: bigint\n\n /**\n * Initialize a rational number.\n */\n constructor(\n numerator: bigint | number = 0n,\n denominator: bigint | number = 1n,\n ) {\n this.n = BigInt(numerator)\n this.d = BigInt(denominator)\n this.normalize()\n }\n\n /**\n * The decimal approximation.\n */\n valueOf(): number {\n return Number(this.n) / Number(this.d)\n }\n\n /**\n * The text representation.\n */\n toString(): string {\n return this.n.toString() + (this.d === 1n ? '' : `/${ this.d.toString()}`)\n }\n\n /**\n * Returns a text profile of the number in various formats and it's value after common transformations.\n */\n public get profile(): string {\n const p = [`Rat: ${this.toString()} (≈${+this})`]\n p.push(`Mixed: ${this.mixedFractionString()}`)\n p.push(`Continued: ${this.continuedFractionString()}`)\n p.push(`Factorization: ${this.primeFactorizationString()}`)\n p.push(`Egyptian: ${this.egyptianFractionString()}`)\n p.push(`Babylonian: ${this.babylonianFractionString()}`)\n p.push(`psin(t): ${this.psin().toString()}`)\n p.push(`pcos(t): ${this.pcos().toString()}`)\n p.push(`ptan(t): ${this.ptan().toString()}`)\n return p.join('\\n')\n }\n\n /**\n * Clone this.\n */\n clone(): Rat {\n return new Rat(this.n, this.d)\n }\n\n /**\n * Normalize the numerator and denominator by factoring out the common denominators.\n */\n normalize(): void {\n // normalize 0/±1, ±1/0, 0/0\n if (this.n === 0n) {\n if (this.d !== 0n) {\n this.d = 1n\n }\n return\n }\n if (this.d === 0n) {\n this.n = this.n > 0n ? 1n : -1n\n return\n }\n\n // normalize 1/1\n if (this.n === this.d) {\n this.n = this.d = 1n\n return\n }\n\n // remove negative denominator\n if (this.d < 0n) {\n this.n = -this.n\n this.d = -this.d\n }\n\n // reduce numerator and denomitator by the greatest common divisor\n const divisor = gcd(this.n, this.d)\n this.n /= divisor\n this.d /= divisor\n }\n\n /**\n * Add this to that.\n */\n add(that: Rat): Rat {\n const r = new Rat(this.n * that.d + that.n * this.d, this.d * that.d)\n r.normalize()\n return r\n }\n\n /**\n * Subtract this from that.\n */\n sub(that: Rat): Rat {\n return this.add(that.neg())\n }\n\n /**\n * Multiply that by this.\n */\n mul(that: Rat): Rat {\n const r = new Rat(this.n * that.n, this.d * that.d)\n r.normalize()\n return r\n }\n\n /**\n * Divide this by that.\n */\n div(that: Rat): Rat {\n const r = new Rat(this.n * that.d, this.d * that.n)\n r.normalize()\n return r\n }\n\n /**\n * Mediant of this and that.\n */\n mediant(that: Rat): Rat {\n const r = new Rat(this.n + that.n, this.d + that.d)\n r.normalize()\n return r\n }\n\n /**\n * Minimum of this and that.\n */\n min(that: Rat): Rat {\n return this.isLessThan(that) ? this : that\n }\n\n /**\n * Maximum of this and that.\n */\n max(that: Rat): Rat {\n return this.isGreaterThan(that) ? this : that\n }\n\n /**\n * Raise this to the power of that.\n */\n pow(that: Rat): Rat {\n // zero\n if (that.n === 0n) {\n return new Rat(1n)\n }\n // integer\n if (that.d === 1n) {\n return new Rat(Number(this.n) ** Number(that.n), Number(this.d) ** Number(that.n))\n }\n // fraction\n const estimate = Math.pow(+this, +that)\n return floatToRat(estimate)\n }\n\n /**\n * Returns the dot product of this and that.\n */\n dot(that: Rat): bigint {\n return this.n * that.n + this.d * that.d\n }\n\n /**\n * Returns true if this equals that.\n */\n equals(that: Rat): boolean {\n return this.n === that.n && this.d === that.d\n }\n\n /**\n * Returns true if this approximates the number.\n */\n approximates(n: number): boolean {\n return Math.abs(+this - n) < EPSILON\n }\n\n /**\n * Returns true if this is greater than that.\n */\n isGreaterThan(that: Rat): boolean {\n return this.n * that.d > that.n * this.d\n }\n\n /**\n * Returns true if this is less than that.\n */\n isLessThan(that: Rat): boolean {\n return this.n * that.d < that.n * this.d\n }\n\n /**\n * Absolute value of this.\n */\n abs(): Rat {\n const r = this.clone()\n if (r.n < 0) r.n = -r.n\n return r\n }\n\n /**\n * Opposite (negative) of this.\n */\n neg(): Rat {\n const r = this.clone()\n r.n = -r.n\n return r\n }\n\n /**\n * Returns true if this is less than zero.\n */\n isNegative(): boolean {\n return this.n < 0\n }\n\n /**\n * Returns true if this is a finite number.\n */\n isFinite(): boolean {\n return this.d !== 0n\n }\n\n /**\n * The reciprocal, or multiplicative inverse, of this.\n */\n inv(): Rat {\n return new Rat(this.d, this.n)\n }\n\n /**\n * Square root of this.\n */\n sqrt(): Rat {\n return this.root(2)\n }\n\n /**\n * Returns the nth root, a number which approximates this when multiplied by itself n times.\n */\n root(n: number): Rat {\n // Handle 0/±1, ±1/0, 0/0, ±1/1\n if (this.n === 0n || this.d === 0n || this.n === this.d) {\n return this.clone()\n }\n\n if (this.isNegative()) {\n throw `Roots of negative numbers like ${this.toString()} are too complex for this basic library`\n }\n\n return floatToRat(Math.pow(+this, 1 / n))\n // return functionToRat(r => r.pow(n), +this)\n }\n\n /**\n * Return the closest integer approximation.\n */\n round(): bigint {\n return BigInt(Math.round(+this))\n }\n\n /**\n * Returns the largest integer equal to or smaller than.\n */\n floor(): bigint {\n return BigInt(Math.floor(+this))\n }\n\n /**\n * Returns the smallest integer equal to or greater than.\n */\n ceil(): bigint {\n return BigInt(Math.ceil(+this))\n }\n\n /**\n * Parametric sine: 2t / (1 + t²)\n * @see https://youtu.be/Ui8OvmzDn7o?t=245\n */\n psin(): Rat {\n if (this.d === 0n) return new Rat(0n)\n const one = new Rat(1)\n const two = new Rat(2)\n const n = two.mul(this)\n const d = one.add(this.pow(two))\n return n.div(d)\n }\n\n /**\n * Parametric cosine: (1 - t²) / (1 + t²)\n */\n pcos(): Rat {\n if (this.d === 0n) return new Rat(-1n)\n const one = new Rat(1)\n const two = new Rat(2)\n const t2 = this.pow(two)\n const n = one.sub(t2)\n const d = one.add(t2)\n return n.div(d)\n }\n\n /**\n * Parametric tangent: psin() / pcos()\n */\n ptan(): Rat {\n return this.psin().div(this.pcos())\n }\n\n /**\n * Mixed fraction as a string.\n */\n mixedFractionString(): string {\n const integerPart = this.isNegative() ? this.ceil() : this.floor()\n const fractionPart = this.sub(new Rat(integerPart)).toString()\n return integerPart ? `${integerPart} + ${fractionPart}` : fractionPart\n }\n\n /**\n * Returns the integers representing the continued fraction.\n */\n *continuedFraction(): Generator<number> {\n if (this.n === 0n || this.d === 0n) {\n yield +this\n } else {\n for (const n of continuedFraction(+this)) {\n yield n\n }\n }\n }\n\n /**\n * Continued fraction as a string.\n */\n continuedFractionString(): string {\n const a: string[] = []\n for (const r of this.continuedFraction()) {\n a.push(r.toString())\n }\n const n = a.shift()\n if (n !== undefined && this.d !== 0n) {\n let s = n.toString()\n if (a.length) {\n s += `; ${ a.join(', ')}`\n }\n return `[${s}]`\n }\n return '[]'\n }\n\n /**\n * Returns an array of the prime factors with their exponents.\n */\n primeFactorization(): Array<[bigint, bigint]> {\n const f: Array<[bigint, bigint]> = []\n if (this.n !== 1n) {\n f.push(...primeFactors(this.n))\n }\n if (this.d !== 1n) {\n f.push(\n ...primeFactors(this.d).map((f) => {\n f[1] = -f[1]\n return f\n }),\n )\n }\n return f.sort((a, b) => {\n return Number(a[0] - b[0])\n })\n }\n\n /**\n * Prime factorization as a calc string.\n */\n primeFactorizationString(): string {\n const a: string[] = []\n for (const p of this.primeFactorization()) {\n a.push(p[1] === 1n ? p[0].toString() : `${p[0]}^${p[1]}`)\n }\n return a.join(' * ')\n }\n\n /**\n * A list of unit fractions which add up to this number.\n */\n egyptianFraction(): Array<Rat> {\n const r: Rat[] = []\n const f = new Rat(1n)\n let t = this.clone()\n\n // start with the integer part if non-zero\n const integerPart = this.floor()\n if (integerPart) {\n const integerRat = new Rat(integerPart)\n r.push(integerRat)\n t = t.sub(integerRat)\n }\n\n if (t.n === 0n) {\n return r\n }\n\n // increment the denominator of f, substracting it from t when bigger, until t has a numerator of 1\n while (t.n !== 1n) {\n f.d++\n if (t.isGreaterThan(f)) {\n r.push(f.clone())\n t = t.sub(f)\n }\n }\n\n // include the final t\n r.push(t)\n\n return r\n }\n\n /**\n * Egyptian fraction as a calc string.\n */\n egyptianFractionString(): string {\n return this.egyptianFraction().join(' + ')\n }\n\n /**\n * A dictionary with the exponents of 60 and their coefficents, which add up to this number.\n */\n babylonianFraction(): Array<string> {\n const a: string[] = []\n let n = Number(this.floor())\n let r = Math.abs(+this - n)\n let d = 0\n // consume increasing powers until the integer part is divided\n for (let p = 0; n > 0; p++) {\n d = n % 60\n if (d !== 0) {\n a.unshift(`${d} * 60^${p}`)\n }\n n = (n - d) / 60\n }\n // consume decreasing powers until the remainder is accumulated\n // @todo use a more precise calculation to get rid of this abhorrent epsilon\n for (let p = -1; r > 1e-10; p--) {\n r *= 60\n d = Math.floor(r)\n r -= d\n if (d !== 0) {\n a.push(`${d} * 60^${p}`)\n }\n n = (n - d) / 60\n }\n return a\n }\n\n /**\n * Babylonian fraction as a calc string.\n */\n babylonianFractionString(): string {\n const a: string[] = []\n const f = this.babylonianFraction()\n for (const i of f) {\n a.push(`${i}`)\n }\n return a.join(' + ')\n }\n}\n\n/**\n * Find a Rat approximation of the floating point number.\n */\nexport const floatToRat = (n: number): Rat => {\n // Handle special values: 0/0, 1/0, -1/0\n if (isNaN(n)) return new Rat(0, 0)\n if (n === Infinity) return new Rat(1, 0)\n if (n === -Infinity) return new Rat(-1, 0)\n\n // Shortcut for numbers close to an integer or 1/integer\n if (Math.abs(n % 1) < EPSILON) return new Rat(Math.round(n))\n if (Math.abs((1 / n) % 1) < EPSILON) return new Rat(1, Math.round(1 / n))\n\n // Traverse the Stern–Brocot tree until a good approximation is found\n // If negative, search for the positive value and negate the result\n const negative = n < 1\n const r = rationalApproximation(Math.abs(n))\n return negative ? r.neg() : r\n}\n\n/**\n * Parse the string for a numeric value and return it as a Rat.\n */\nexport const parseRat = (s: string): Rat => {\n // Handle special values: 0/0, 1/0, -1/0\n if (s === 'NaN') return new Rat(0, 0)\n if (s === 'Infinity') return new Rat(1, 0)\n if (s === '-Infinity') return new Rat(-1, 0)\n\n const [n, d] = s.split('/', 2)\n if (d === undefined) {\n return floatToRat(Number(n))\n }\n return new Rat(BigInt(n ?? 1), BigInt(d))\n}\n\n/**\n * Pi, an approximation of the ratio between a circle's circumference and it's diameter.\n */\n// export const π = new Rat(3141592653589793238462643383279502884197169399375105820974944592307816406286208998628034825342117067982148086513282306647093844609550582231725359408128481117450284102701938521105559644622948954930381964428810975665933446128475648233786783165271201909145648566923460348610454326648213393607260249141273724587n, 1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000n)\n\nexport default Rat\n","/**\n * @class Symbolizer\n * @name Symbolizer\n */\nexport class Symbolizer {\n symbols: string[] = []\n\n /**\n * Initialize a symbolizer.\n */\n constructor(symbols?: string) {\n if (symbols) this.symbols = symbols.split('')\n }\n\n /**\n * Symbol generator.\n */\n *generator(): Generator<string> {\n for (let i = 0; ; i++) {\n if (i < this.symbols.length) {\n yield this.symbols[i] ?? '?'\n } else {\n yield String.fromCharCode(945 + i - this.symbols.length)\n }\n }\n }\n}\n\nexport default Symbolizer\n","import { Rat } from './Rat'\nimport Symbolizer from './Symbolizer'\n\nexport interface Coefficents {\n [Key: string]: bigint\n}\n\n/**\n * @class Rational polynumber\n * @name Polyrat\n */\nexport class Polyrat {\n // coefficent values are indexed with their the exponents in each dimension, comma-separated, as the key\n coefficents: Coefficents = {}\n\n // the dimension is how many params there are, defined by the length of the exponent keys\n dimension = 0\n\n // unique symbols for each dimension\n latinSymbols = ''\n greekSymbols = ''\n\n /**\n * Initialize a rational polynumber.\n */\n constructor(coefficents?: Coefficents) {\n if (coefficents) {\n this.coefficents = coefficents\n }\n if (Object.keys(this.coefficents).length) {\n const ck = Object.keys(this.coefficents)\n this.dimension = ck[0] ? ck[0].split(',').length : 0\n }\n const lsg = new Symbolizer('xyzw').generator()\n for (let i = 0; i < this.dimension; i++) {\n this.latinSymbols += lsg.next().value\n }\n const gsg = new Symbolizer().generator()\n for (let i = 0; i < this.dimension; i++) {\n this.greekSymbols += gsg.next().value\n }\n }\n\n /**\n * Evaluate the result given the parameters for each dimension.\n */\n evaluate(parameters: Rat[]): Rat {\n let result: Rat = new Rat()\n for (const [exponents, coefficent] of Object.entries(this.coefficents)) {\n let value: Rat = new Rat(coefficent)\n const dimensions = exponents.split(',')\n for (let i = 0; i < dimensions.length; i++) {\n if (i in parameters) {\n const base = parameters[i] ?? new Rat(1)\n const dimension = parseInt(dimensions[i] ?? '1', 10)\n value = value.mul(base.pow(new Rat(dimension)))\n }\n }\n result = result.add(value)\n }\n return result\n }\n\n /**s\n * The text representation.\n */\n toString(): string {\n return `${this.constructor.name}(${this.toJSON()})`\n }\n\n /**\n * The JSON representation.\n */\n toJSON(): string {\n // return JSON.stringify(this.coefficents)\n const r = []\n for (const [exponents, coefficent] of Object.entries(this.coefficents)) {\n r.push(`\"${exponents}\":\"${coefficent.toString()}\"`)\n }\n return `{${r.join(',')}}`\n }\n\n /**\n * The formula in the human way with exponents as HTML sups.\n */\n toHTMLFormula(): string {\n const r: string[] = []\n for (const [exponents, coefficent] of Object.entries(this.coefficents)) {\n const t: string[] = []\n const f = coefficent.toString()\n if (f !== '1') t.push(f)\n const dimensions = exponents.split(',')\n for (let i = 0; i < dimensions.length; i++) {\n if (dimensions[i] !== '0') {\n if (dimensions[i] === '1') {\n t.push(this.latinSymbols[i] ?? '?')\n } else {\n t.push(\n `${this.latinSymbols[i] ?? '?'}${parseInt(\n dimensions[i] ?? '?',\n 10,\n )}`,\n )\n }\n }\n }\n if (t) r.push(t.join(''))\n }\n if (r.length === 0) return '0'\n return r.join(' + ')\n }\n\n /**\n * The formula in the standard alpha form as HTML.\n */\n toStandardAlphaFormHTML(): string {\n const rn: string[] = []\n const rd: string[] = []\n if (!Object.keys(this.coefficents).length) return '0'\n for (const [exponents, coefficent] of Object.entries(this.coefficents)) {\n const tn: string[] = []\n const td: string[] = []\n const f = coefficent.toString()\n if (f !== '1') tn.push(f)\n const dimensions = exponents.split(',')\n for (let i = 0; i < dimensions.length; i++) {\n if (dimensions[i] !== '0') {\n if (dimensions[i] === '1') {\n tn.push(this.greekSymbols[i] ?? '?')\n } else {\n const exponent = parseInt(dimensions[i] ?? '0', 10)\n if (exponent > 0) {\n tn.push(`${this.greekSymbols[i] ?? 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