// What language is this???   It's Java 21!

import java.util.Optional;

// interface number defined below
record Int(int x) implements number {}
record Rat(int n, int d) implements number {
    public Rat { assert d != 0 : "zero denominator in rational number"; }
    //assertions trigger error if run with java -ea
}
record Real(double r) implements number {}
record Complex(double r, double i) implements number {}

record pair(number a, number b) {}

interface number {
    
  default boolean equals(number other) {
    var a_and_b = new pair(this,other);
    return
      switch (a_and_b) {
      case pair(Int(int x), Int(int y)) -> x==y;
      case pair(Int(int x), Rat(int n, int d)) -> x*d==n;
      case pair(Int(int x), Real(double r)) -> 1.0*x == r;
      case pair(Int(int x), Complex(double r, double i)) when i==0.0 ->
          1.0*x == r;
      case pair(Rat(int a, int b), Rat(int c, int d)) -> a*d == b*c;
      case pair(Rat(int a, int b), Real(double r)) -> a*1.0 == b*r;
      case pair(Rat(int a,int b), Complex(double r,double i)) when i==0.0 ->
          a*1.0 == b*r;
      case pair(Real(double a),Real(double b)) -> a==b;
      case pair(Real(double a),Complex(double r,double i)) when i==0.0 -> a==r;
      case pair(Complex(double a, double b),Complex(double c,double d)) ->
          a==c && b==d;
      case pair(number a, number b) -> b.equals(a);
      //      default -> false;  // not needed in this case
      };//switch (match)
  }//equal

  default number multiply(number other) {
    var a_and_b = new pair(this,other);
    return
      switch (a_and_b) {
      case pair(Int(int x), Int(int y)) -> new Int(x*y);
      case pair(Int(int x), Rat(int n, int d)) -> new Rat(x*n,d);
      case pair(Int(int x), Real(double r)) -> new Real(x*r);
      case pair(Int(int x), Complex(double r, double i)) ->
          new Complex(x*r,x*i);
      case pair(Rat(int a, int b), Rat(int c, int d)) ->
          new Rat(a*c,b*d);
      case pair(Rat(int a, int b), Real(double r)) ->
          new Real(a*r/b);
      case pair(Rat(int a,int b), Complex(double r,double i)) ->
          new Complex(a*r/b,a*i/b);
      case pair(Real(double a),Real(double b)) -> new Real(a*b);
      case pair(Real(double a),Complex(double r,double i)) ->
          new Complex(a*r,a*i);
      case pair(Complex(double a, double b),Complex(double c,double d)) ->
          new Complex(a*c-b*d,a*d+b*c);
      case pair(number a, number b) -> b.multiply(a);
      };//switch
  }//multiply

  default Optional<number> inverse() { // multiplicative inverse
      switch (this) {
      case Int(int x) when x!=0:
          return Optional.of(new Rat(1,x));
      case Rat(int n, int d) when n!=0:
          return Optional.of(new Rat(d,n));
      case Real(double r) when r!=0.0:
          return Optional.of(new Real(1.0/r));
      case Complex(double r, double i) when r!=0.0 || i!=0.0:
          var d = r*r + i*i;
          return Optional.of(new Complex(r/d,i/d));
      default:
          return Optional.empty();      
      }//switch    
  }//inverse

  // implment division by multiplying with inverse,
  // with monadic error handling
  default Optional<number> divide(number other) {
    return other.inverse().map(inv -> this.multiply(inv));
  }//divide

    static int gcd(int a, int b) {
        while (a!=0 && b!=0) {
            if (a>b) a = a%b; else b = b%a;
        }
        return a+b;
    }//gcd
    
  default String tostr() {  // can't override toString in interface
    switch (this) {
    case Int(int x): return x+"";
    case Rat(int n,int d) when n%d==0: return ""+(n/d);
    case Rat(int n,int d):
        var c = gcd(n,d);
        return (n/c) + "/" + (d/c);
    case Real(double r): return ""+((int)(r*1000+0.5)/1000.0);
    case Complex(double r,double i) when i==0.0:
        return new Real(r).tostr();
    case Complex(double r,double i):
        var rr = (int)(r*1000+0.5)/1000.0;
        var ir = (int)(i*1000+0.5)/1000.0;
        return rr+ "+" + ir + "i";
    default : return "";
    }//switch
  }//tostr
    
}//number interface

public class numbers {
  public static void main(String[] args) {
      number N[] = {
          new Int(4),
          new Real(4.3),
          new Rat(2,7),
          new Complex(2.0,1.0),
          new Rat(1,3),
          new Real(0.2)
      };
      number product = new Int(1);
      for(var n:N) product = product.multiply(n);
      System.out.printf("product: %s\n", product.tostr());
      product.divide(new Real(2.0))
          .ifPresent(x -> System.out.printf("product/2: %s\n",x.tostr()));
      System.out.println("div by zero? " + product.divide(new Rat(0,1)));
  }//main
}