Symbolic Differentiator V1

symbolic-differentiator.js

// I wrote about this at https://reeds.website/project-symbolic-differentiator
function Unexpected(character) {
  return new Error("Unexpected character '" + character + "'");
}

function parse(text) {
  // Array of all the text without whitespace
  const characters = Array.from(text.replaceAll(/\s/g, ""));

  const terms = [];
  const freshTerm = {
    coefficient: "",
    variable: null,
    exponent: "",
  };

  function finishTerm() {
    if (term.coefficient === "") term.coefficient = "1";
    if (term.variable === null && term.exponent === "") term.exponent = "0";
    if (term.variable !== null && term.exponent === "") term.exponent = "1";
    terms.push(term);
    term = { ...freshTerm };
    state = "beginning";
  }

  let term = { ...freshTerm };
  let state = "beginning";

  let lastCoefficient = "";
  for (c of characters) {
    switch (state) {
      case "beginning":
        if (c.match(/[0-9]/)) {
          term.coefficient += c;
          state = "coefficient";
        } else if (c.match(/[a-zA-Z]/)) {
          term.variable = c;
          state = "variable";
        } else {
          throw new Unexpected(c);
        }
        break;
      case "coefficient":
        if (c.match(/[0-9]/)) {
          term.coefficient += c;
          state = "coefficient";
        } else if (c.match(/[a-zA-Z]/)) {
          term.variable = c;
          state = "variable";
        } else if (c === "+") {
          finishTerm();
        } else {
          throw new Unexpected(c);
        }
        break;
      case "variable":
        if (c === "^") {
          state = "exponent";
        } else if (c === "+") {
          finishTerm();
        } else {
          throw new Unexpected(c);
        }
        break;
      case "exponent":
        if (c.match(/[0-9]/)) {
          term.exponent += c;
        } else if (c === "+") {
          finishTerm();
        } else {
          throw new Unexpected(c);
        }
        break;
    }
  }

  finishTerm();
  return terms;
}

function differentiate(terms) {
  return terms
    .filter(({ exponent }) => Number(exponent) > 0)
    .map(({ coefficient, variable, exponent }) => ({
      coefficient: String(Number(coefficient) * Number(exponent)),
      variable: Number(exponent) === 1 ? null : variable,
      exponent: String(Number(exponent) - 1),
    }));
}

const expectedParsed = [
  {
    coefficient: "30",
    variable: "x",
    exponent: "52",
  },
  {
    coefficient: "29",
    variable: "x",
    exponent: "1",
  },
  {
    coefficient: "1",
    variable: "x",
    exponent: "2",
  },
  {
    coefficient: "5",
    variable: null,
    exponent: "0",
  },
];

const expectedDifferentiated = [
  {
    coefficient: "1560",
    variable: "x",
    exponent: "51",
  },
  {
    coefficient: "29",
    variable: null,
    exponent: "0",
  },
  {
    coefficient: "2",
    variable: "x",
    exponent: "1",
  },
];

const input = "30x^52+29x+x^2+5";
const resultParsed = parse(input);
console.log("\nInput:\n");
console.log(input);
console.log("\nParsed:");
console.log(resultParsed);
console.log(
  JSON.stringify(expectedParsed) === JSON.stringify(resultParsed)
    ? "Does match expected!"
    : "Does NOT match expected!"
);

const resultDifferentiated = differentiate(resultParsed);
console.log("\nDifferentiated:");
console.log(resultDifferentiated);
console.log(
  JSON.stringify(expectedDifferentiated) ===
    JSON.stringify(resultDifferentiated)
    ? "Does match expected!"
    : "Does NOT match expected!"
);