Adapted IntegerEuclids to print LaTeX

IntegerEuclidsToLaTeX.kt

import java.math.BigInteger

/**
 * The extended euclidian algorithm for two numbers (BigIntegers included). Also prints a LaTeX tabular of all the steps.
 *
 * Looks for `ax + by = gcd(a, b)` where `a` and `b` are the input variables.
 * [gcd] contains the gcd, [x] and [y] contain `x` and `y` as seen in the previous expression.
 *
 * @author Ruben Schellekens
 * @author Thomas Schouten
 */
open class IntegerEuclidsToLaTeX(val a: Number, val b: Number, val extended: Boolean = true) {

    var x: BigInteger? = null
        private set(value) {
            field = value
        }

    var y: BigInteger? = null
        private set(value) {
            field = value
        }

    var gcd: BigInteger? = null
        private set(value) {
            field = value
        }

    /**
     * Executes the extended euclidean algorithm.
     *
     * @return A triple of form `(x, y, gcd(a,b))` (see class documentation of [IntegerEuclidsToLaTeX]).
     */
    fun execute(): Triple<BigInteger, BigInteger, BigInteger> {
        // Implementation of Algorithm 2.2 of the lecture notes.

        val aBig = BigInteger("$a")
        val bBig = BigInteger("$b")

        // Step 1: Init
        var aPrime = if(aBig >= BigInteger("0")) aBig else -aBig
        var bPrime = if(bBig >= BigInteger("0")) bBig else -bBig
        var x1 = BigInteger("1")
        var x2 = BigInteger("0")
        var y1 = BigInteger("0")
        var y2 = BigInteger("1")

        // Extended version uses two extra columns
        if (extended) {
            println("\\begin{tabular}{ccccc}")
            println("     & \$Q\$ & \$R\$ & \$x\$ & \$y\$ \\\\")
            println("    \$$aPrime\$ & & & \$1\$ & \$0\$ \\\\")
        } else {
            println("\\begin{tabular}{ccc}")
            println("     & \$Q\$ & \$R\$ \\\\")
            println("    \$$aPrime\$ & & \\\\")
        }


        // Step 2: Loop
        while (bPrime > BigInteger.valueOf(0)) {
            val q = BigInteger.valueOf(Math.floor(aPrime.toDouble() / bPrime.toDouble()).toLong())
            val r = aPrime - q * bPrime
            aPrime = bPrime
            bPrime = r
            val x3 = x1 - q * x2
            val y3 = y1 - q * y2

            if (extended) {
                // Print remainder of previous step, quotient, remainder, and x and y
                println("    \$$aPrime\$ & \$$q\$ & \$$r\$ & \$$x2\$ & \$$y2\$ \\\\")
            } else {
                // Print no x and y
                println("    \$$aPrime\$ & \$$q\$ & \$$r\$ \\\\")
            }


            x1 = x2
            y1 = y2
            x2 = x3
            y2 = y3
        }

        // Step 3: Finalise
        gcd = aPrime
        x = if (aBig >= BigInteger("0") ) x1 else -x1
        y = if (bBig >= BigInteger("0") ) y1 else -y1

        println("\\end{tabular}")

        return Triple(x!!, y!!, gcd!!)
    }
}

testIntegerEuclidsToLaTeX.kt

import java.math.BigInteger

fun main(args: Array<String>) {

       IntegerEuclidsToLaTeX(262063, 117963).execute()
       IntegerEuclidsToLaTeX(62857, 64541, extended = false).execute()
       IntegerEuclidsToLaTeX(BigInteger("33177078799790592463"), BigInteger("62857")).execute()
       
}