Element.java

import java.math.BigInteger;

public class Element{
    private static final BigInteger minusOne = BigInteger.valueOf(-1);
    private static final BigInteger zero = BigInteger.valueOf(0);
    private static final BigInteger one = BigInteger.valueOf(1);
    private static final BigInteger two = BigInteger.valueOf(2);

    //VB for variable so it doesn't interfere with simple getter names
    private BigInteger iVB;
    private BigInteger jVB;
    private BigInteger aVB;
    private BigInteger bVB;
    private BigInteger cVB;
    private BigInteger dVB;
    private BigInteger eVB;
    private BigInteger fVB;
    private BigInteger nVB;
    private BigInteger xVB;
    private BigInteger tVB;
    private BigInteger xplusnVB;
    private BigInteger dplusnVB;
    private BigInteger xplusnsquaredVB;
    private BigInteger dplusnsquaredVB;
    private BigInteger uVB;
    private BigInteger bignVB;
    private BigInteger naVB;
    private boolean oddxplusnsquaredVB;
    private String descriptionV;

    public Element(String aSend, String bSend){
        this(new BigInteger(aSend), new BigInteger(bSend));
    }

    public Element(String aSend, String bSend, String fSend){
        this(new BigInteger(aSend), new BigInteger(bSend), new BigInteger(fSend));
    }

    public Element(BigInteger aSend, BigInteger bSend){
        aVB = aSend;
        bVB = bSend;
        cVB = aVB.multiply(bVB);
        dVB = sqrt(cVB);
        eVB = cVB.subtract(dVB.multiply(dVB));
        fVB = eVB.subtract((dVB.multiply(two)).add(one));
        if(aSend.compareTo(zero) < 0 && bSend.compareTo(zero) < 0){
            nVB = ((aVB.add(bVB)).divide(two)).add(dVB);
        } else {
            nVB = ((aVB.add(bVB)).divide(two)).subtract(dVB);
        }
        xVB = dVB.subtract(aVB);
        tVB = zero;
        if((eVB.mod(two)).equals(zero)){
            tVB = (xVB.add(two)).divide(two);
        } else {
            tVB = (xVB.add(one)).divide(two);
        }
        iVB = nVB.add(dVB);
        jVB = bVB.subtract(iVB);
        xplusnVB = xVB.add(nVB);
        dplusnVB = dVB.add(nVB);
        xplusnsquaredVB = xplusnVB.multiply(xplusnVB);
        dplusnsquaredVB = dplusnVB.multiply(dplusnVB);
        uVB = zero;
        oddxplusnsquaredVB = true;
        if((xplusnsquaredVB.mod(two)).equals(two)){
            oddxplusnsquaredVB = false;
            uVB = xplusnVB.divide(two);
        } else {
            uVB = (xplusnVB.subtract(one)).divide(two);
        }
        bignVB = ((cVB.add(one)).divide(two)).subtract(dVB);
        descriptionV = "("+eVB+","+nVB+","+tVB+") = {"+eVB+":"+nVB+":"+dVB+":"+xVB+":"+aVB+":"+bVB+"}, f="+fVB+", c="+cVB+", u="+uVB+", i="+iVB+", j="+jVB;
    }

    public Element(BigInteger aSend, BigInteger bSend, BigInteger fSend){
        aVB = aSend;
        bVB = bSend;
        cVB = aVB.multiply(bVB);
        dVB = (sqrt(cVB)).add(one);
        eVB = fSend;
        fVB = ((dVB.multiply(two)).add(one)).subtract(eVB);
        nVB = ((aVB.add(bVB)).divide(two)).subtract(dVB);
        xVB = dVB.subtract(aVB);
        tVB = zero;
        if((eVB.mod(two)).equals(zero)){
            tVB = (xVB.add(two)).divide(two);
        } else {
            tVB = (xVB.add(one)).divide(two);
        }
        iVB = nVB.add(dVB);
        jVB = bVB.subtract(iVB);
        xplusnVB = xVB.add(nVB);
        dplusnVB = dVB.add(nVB);
        xplusnsquaredVB = xplusnVB.multiply(xplusnVB);
        dplusnsquaredVB = dplusnVB.multiply(dplusnVB);
        uVB = zero;
        oddxplusnsquaredVB = true;
        if((xplusnsquaredVB.mod(two)).equals(zero)){
            oddxplusnsquaredVB = false;
            uVB = xplusnVB.divide(two);
        } else {
            uVB = (xplusnVB.subtract(one)).divide(two);
        }
        bignVB = ((cVB.add(one)).divide(two)).subtract(dVB);
        descriptionV = "("+eVB+","+nVB+","+tVB+") = {"+eVB+":"+nVB+":"+dVB+":"+xVB+":"+aVB+":"+bVB+"}, f="+fVB+", c="+cVB+", u="+uVB+", i="+iVB+", j="+jVB;
    }

    public static BigInteger sqrt(BigInteger x) {
        if(x.compareTo(zero) == -1){
            x = x.multiply(minusOne);
        }
        if(x.equals(zero)){
            return zero;
        }
        BigInteger div = zero.setBit(x.bitLength()/2);
        BigInteger div2 = div;
        BigInteger returnvalue = zero;
        for(;;) {
            BigInteger y = div.add(x.divide(div)).shiftRight(1);
            if (y.equals(div) || y.equals(div2)){
                returnvalue = y;
                break;
            }
            div2 = div;
            div = y;
        }

        BigInteger testsquare = returnvalue.multiply(returnvalue);
        BigInteger testp1square = (returnvalue.add(one)).multiply(returnvalue.add(one));
        if((testsquare.equals(x)) || (((testsquare.compareTo(x)) == -1) && ((testp1square.compareTo(x)) == 1))){
            return returnvalue;
        } else {
            return returnvalue.subtract(one);
        }
    }

    public BigInteger a(){
        return aVB;
    }

    public BigInteger b(){
        return bVB;
    }

    public BigInteger c(){
        return cVB;
    }

    public BigInteger d(){
        return dVB;
    }

    public BigInteger e(){
        return eVB;
    }

    public BigInteger f(){
        return fVB;
    }

    public BigInteger n(){
        return nVB;
    }

    public BigInteger x(){
        return xVB;
    }

    public BigInteger t(){
        return tVB;
    }

    public BigInteger i(){
        return iVB;
    }

    public BigInteger j(){
        return jVB;
    }

    public BigInteger xplusn(){
        return xplusnVB;
    }

    public BigInteger dplusn(){
        return dplusnVB;
    }

    public BigInteger xplusnsquared(){
        return xplusnsquaredVB;
    }

    public BigInteger dplusnsquared(){
        return dplusnsquaredVB;
    }

    public BigInteger u(){
        return uVB;
    }

    public BigInteger bign(){
        return bignVB;
    }

    public boolean oddxplusnsquared(){
        return oddxplusnsquaredVB;
    }

    public void print(){
        System.out.println(descriptionV);
    }

    public String description(){
        return descriptionV;
    }
}