public override RingElement <BigInteger> GetMultiplicativeInverse(RingElement <BigInteger> g)
{
if (g.Identifier == 1 || g.Identifier == -1)
{
return(g);
}
throw new DivideByZeroException();
}
public override RingElement <R[]> GetMultiplicativeInverse(RingElement <R[]> g)
{
var polyg = (Polynomial)g;
if (polyg.degree() == 1)
{
return(new Polynomial(new [] { (R)(1 / polyg[0]) }, this));
}
throw new DivideByZeroException();
}
public override RingElement <R[]> GetAdditiveInverse(RingElement <R[]> g)
{
var polyg = (Polynomial)g;
var coeffs = new R[polyg.degree() + 1];
for (var i = 0; i < coeffs.Length; ++i)
{
coeffs[i] = (R)(-polyg[i]);
}
return(new Polynomial(coeffs, this));
}
public override RingElement <R[]> AddElements(RingElement <R[]> g, RingElement <R[]> h)
{
var polyg = (Polynomial)g;
var polyh = (Polynomial)h;
var len = System.Math.Max(polyg.degree() + 1, polyh.degree() + 1);
var coeffs = new List <R>();
for (var i = 0; i < len; ++i)
{
coeffs.Add((R)(polyg[i] + polyh[i]));
}
return(new Polynomial(coeffs.ToArray(), this));
}
public override RingElement <R[]> MultiplyElements(RingElement <R[]> g, RingElement <R[]> h)
{
var polyg = (Polynomial)g;
var polyh = (Polynomial)h;
var len = polyg.degree() + polyh.degree() + 2;
var coeffs = new R[len];
for (var pow = 0; pow < len; ++pow)
{
coeffs[pow] = (R)Ring.getZero();
for (var gi = 0; gi <= pow; ++gi)
{
var hi = pow - gi;
coeffs[pow] = (R)(coeffs[pow] + polyg[gi] * polyh[hi]);
}
}
return(new Polynomial(coeffs.ToArray(), this));
}
public RingElement <I> dividedBy(RingElement <I> d)
{
return(this / d);
}
public RingElement <I> minus(RingElement <I> r)
{
return(this - r);
}
public virtual RingElement <I> plus(RingElement <I> a)
{
return(this + a);
}
public virtual RingElement <I> times(RingElement <I> a)
{
return(this * a);
}
/// <summary> /// Find the multiplicative inverse of the given element in the ring. /// </summary> /// <param name="g">The element to find the inverse of</param> /// <returns>The element g^-1</returns> /// <exception> If element has no inverse </exception> public abstract RingElement <I> GetMultiplicativeInverse(RingElement <I> g);
/// <summary> /// Find the additive inverse of the given element in the ring. /// </summary> /// <param name="g">The element to find the inverse of</param> /// <returns>The element -g</returns> public abstract RingElement <I> GetAdditiveInverse(RingElement <I> g);
/// <summary> /// Find the sum of two elements in the group. /// </summary> /// <param name="g">The first element to add.</param> /// <param name="h">The second element to add.</param> /// <returns>The element g+h.</returns> public abstract RingElement <I> AddElements(RingElement <I> g, RingElement <I> h);
/// <summary> /// Find the product of two elements in the group. /// </summary> /// <param name="g">The first element to multiply.</param> /// <param name="h">The second element to multiply.</param> /// <returns>The element gh.</returns> public abstract RingElement <I> MultiplyElements(RingElement <I> g, RingElement <I> h);
public override RingElement <BigInteger> GetAdditiveInverse(RingElement <BigInteger> g)
{
return(new IntElement(-g.Identifier, this));
}
public override RingElement <BigInteger> AddElements(RingElement <BigInteger> g, RingElement <BigInteger> h)
{
return(new IntElement(((IntElement)g).Identifier + ((IntElement)h).Identifier, this));
}