import { Equation, Expression, Fraction, parse, toTex } from 'algebra.js';

{
  let expr = new Expression("x");
  expr = expr.subtract(3);
  expr = expr.add("x");
  expr.toString();
  const eq = new Equation(expr, 4);
  eq.toString();
  const x = eq.solveFor("x");
  x.toString();
}
{
  let frac = new Fraction(1, 2);
  frac.toString();
  frac = frac.add(new Fraction(3, 4));
  frac.toString();
  frac = frac.subtract(2);
  frac.toString();
  frac = frac.multiply(new Fraction(4, 3));
  frac.toString();
  frac = frac.divide(5);
  frac.toString();

  let x = new Expression("x");
  x = x.add(3);
  x.toString();
  x = x.subtract(new Fraction(1, 3));
  x.toString();
  x = x.add("y");
  x.toString();
  const otherExp = new Expression("x").add(6);
  x = x.add(otherExp);
  x.toString();

  let expr1 = new Expression("a").add("b").add("c");
  let expr2 = new Expression("c").subtract("b");
  let expr3 = expr1.subtract(expr2);
  `${expr1.toString()} - (${expr2.toString()}) = ${expr3.toString()}`;

  expr1 = new Expression("x");
  expr1 = expr1.add(2);
  expr1 = expr1.multiply(4);
  expr2 = new Expression("x");
  expr2 = expr2.multiply("y");
  expr2 = expr2.multiply(new Fraction(1, 3));
  expr2 = expr2.add(4);
  expr3 = expr1.multiply(expr2);
  `(${expr1.toString()})(${expr2.toString()}) = ${expr3.toString()}`;

  x = new Expression("x").divide(2).divide(new Fraction(1, 5));
  x.toString();
  let exp = new Expression("x");
  exp = exp.add("y");
  exp = exp.add(3);
  exp.toString();
  const sum = exp.summation("x", 3, 6);
  sum.toString();
  exp = new Expression("x").add(2);
  const exp3 = exp.pow(3);
  `(${exp.toString()})^3 = ${exp3.toString()}`;

  let expr = new Expression("x");
  expr = expr.multiply(2);
  expr = expr.multiply("x");
  expr = expr.add("y");
  expr = expr.add(new Fraction(1, 3));
  expr.toString();
  const answer1 = expr.eval({ x: 2 });
  const answer2 = expr.eval({ x: 2, y: new Fraction(3, 4) });
  answer1.toString();
  answer2.toString();
  expr = new Expression("x").add(2);
  expr.toString();
  const sub = new Expression("y").add(4);
  const answer = expr.eval({ x: sub });
  answer.toString();
  exp = new Expression("x").add(2);
  exp.toString();
  exp = exp.multiply(5, false);
  exp.toString();
  exp = exp.simplify();
  exp.toString();
  exp = exp.add(5, false);
  exp.toString();
  exp = exp.divide(5, false);
  exp.toString();
  exp = exp.simplify();
  exp.toString();
  exp = exp.pow(2, false);
  exp.toString();
  exp = exp.simplify();
  exp.toString();
  const z = new Expression("z");
  const eq1 = new Equation(z.subtract(4).divide(9), z.add(6));
  eq1.toString();
  const eq2 = new Equation(z.add(4).multiply(9), 6);
  eq2.toString();
  const eq3 = new Equation(z.divide(2).multiply(7), new Fraction(1, 4));
  eq3.toString();
}
{
  const x1 = parse("1/5 * x + 2/15");
  const x2 = parse("1/7 * x + 4");
  let eq = new Equation(x1 as Expression, x2 as Expression);
  eq.toString();
  const answer = eq.solveFor("x");
  "x = " + answer.toString();
  const expr1 = parse("1/4 * x + 5/4");
  const expr2 = parse("3 * y - 12/5");
  eq = new Equation(expr1 as Expression, expr2 as Expression);
  eq.toString();
  let xAnswer = eq.solveFor("x");
  let yAnswer = eq.solveFor("y");
  "x = " + xAnswer.toString();
  "y = " + yAnswer.toString();
  let n1 = parse("x + 5") as Expression;
  let n2 = parse("x - 3/4") as Expression;
  const quad = new Equation(n1.multiply(n2), 0);
  quad.toString();
  let answers = quad.solveFor("x");
  "x = " + answers.toString();
  n1 = parse("x + 2") as Expression;
  n2 = parse("x + 3") as Expression;
  const n3 = parse("x + 4") as Expression;
  const cubic = new Equation(n1.multiply(n2).multiply(n3), 0);
  cubic.toString();
  answers = cubic.solveFor("x");
  "x = " + answers.toString();
  let expr = new Expression("x");
  expr = expr.multiply("x");
  expr = expr.add("x");
  expr = expr.add("y");
  eq = new Equation(expr, 3);
  eq.toString();
  xAnswer = eq.solveFor("x");
  yAnswer = eq.solveFor("y");
  "x = " + xAnswer;
  "y = " + yAnswer.toString();
  let exp = parse("2 * x^2 + 4 * x + 4");
  exp.toString();
  exp = parse("x * y + 4");
  exp.toString();
}
{
  const eq = parse("x^2 + 4 * x + 4 = 0") as Equation;
  eq.toString();
  const ans = eq.solveFor("x");
  "x = " + ans.toString();
  const a = new Expression("x").pow(2);
  const b = new Expression("x").multiply(new Fraction(5, 4));
  const c = new Fraction(-21, 4);
  const expr = a.add(b).add(c);
  const quad = new Equation(expr, 0);
  toTex(quad);
  const answers = quad.solveFor("x");
  toTex(answers);
  const lambda = new Expression("lambda").add(3).divide(4);
  const Phi = new Expression("Phi").subtract(new Fraction(1, 5)).add(lambda);
  toTex(lambda);
  toTex(Phi);
}