Fractions to LaTeX expressions

Requirements

Given we now have a functional class that represents fractions well, we can now design a function that returns the LaTeX code. Our goal is:

new Frac(3, -7).tex() // -\frac{3}{7}

This seems as straightforward as `\\frac\{${this.n}\}\{${this.d}\}`, there are some issues when writing this function:

• If the instance is an integer (e.g. new Frac(3, 1)), it should not print something like \frac{3}{1}, but just 3.
• If the instance is a negative fraction, we need to pull the negative sign from this.n or this.d to the front.

Implementation

Below is the code that reflects these issues.

class Frac {
  ...
  function tex() {
    let isNeg = this < 0;             // fraction is negative
    let isInt = this.n % this.d == 0; // fraction is a whole number
    let base = "";
    if (isInt) {
      base = `${this.n / this.d}`;
    } else {
      // attach its sign in front of the fraction
      base =
        (isNeg ? "-" : "+") +
        `\\frac\{${Math.abs(this.n)}\}\{${Math.abs(this.d)}\}`;
    }
    return base;
  }
}

It looks complete, but there is yet another problem: we often drop a lot of details when we write an expression. For example, \begin{align*} & \hl{+\dfrac{2}{3}}x+4 = \dfrac{2}{3}x + 4, \\ & \hl{-1}x - 7 = -x - 7. \end{align*}

To deal with this mess, I feed in a string that tells the location of the fraction:

• "c" if the fraction is a coefficient: $\hl{-}x^3 \hl{+ \frac{2}{3}}x^2 \hl{-\frac{1}{4}}x - 1 $.
  When writing a coefficient, you can omit $1$.
• "s" if the fraction needs a sign: $-x^3 \hl{+ \frac{2}{3}}x^2 \hl{-\frac{1}{4}}x \hl{- 1} $.
  You explicitly need a $+$ sign.
• "b" if the fraction follows an operator: $\frac{1}{4}\times\hl{\left(-\frac{2}{3}\right)}$.
  You need to enclose the fraction with a bracket if it has a negative sign in front.

Then, we update the code:

class Frac {
  ...
  function tex(op = "") {
    let isNeg = this < 0;
    let wholeNum = this.n % this.d === 0;
    let base = "";
    if (wholeNum) {
      base = `${this.n / this.d}`;
    } else {
      base =
        (isNeg ? "-" : "") +
        `\\frac\{${Math.abs(this.n)}\}\{${Math.abs(this.d)}\}`;
    }
    let out =
      // add + symbol if sign is required
      (/s/.test(op) && !isNeg ? "+" : "") +
      // reduce 1 to nothing and -1 to - if it is a coefficient
      (/c/.test(op) ? (base == "1" ? "" : base == "-1" ? "-" : base) : base);
    // put the fraction in bracket if bracket is needed
    out = /b/.test(op) && isNeg ? "\\left(" + out + "\\right)" : out;
    return out;
  }
}

The example polynomial can be written as follows:

let polyTex = [
  `${new Frac(-1).tex("c")} x^3 `,
  `${new Frac(2, 3).tex("cs")} x^2 `,
  `${new Frac(-1,4).tex("cs")} x `,
  `${new Frac(-1).tex("s")}`
].join(''); // - x^3 +\frac{2}{3} x^2 -\frac{1}{4} x -1

which, when rendered with MathJax or Katex, becomes: $ - x^3 +\frac{2}{3} x^2 -\frac{1}{4} x -1. $