protected bool Equals(BinaryPolynomial other)
{
if (other == null)
{
return(false);
}
return
(this.Polynomial == other.Polynomial);
}
/// <summary>
/// Implements division through recursion.
/// </summary>
public static Tuple <BinaryPolynomial, BinaryPolynomial> Division(BinaryPolynomial left, BinaryPolynomial right, int currentDegreeForLeft, StringBuilder aggregatedResult)
{
left.Should().NotBeNull();
right.Should().NotBeNull();
var isCurrentLeadingNumberOne = left[currentDegreeForLeft];
if (currentDegreeForLeft < right.Degree)
{
return(Tuple.Create(new BinaryPolynomial(aggregatedResult.ToString()), left.Copy()));
}
if (isCurrentLeadingNumberOne)
{
left = left ^ right.RiseDegree(currentDegreeForLeft - right.Degree);
aggregatedResult.Append("1");
}
else
{
aggregatedResult.Append("0");
}
return(Division(left, right, currentDegreeForLeft - 1, aggregatedResult));
}
/*
* The values for the sum and hasCarriage are calculated by a boolean function using Veitch diagram.
* A = left, B = right, C1 = hasCarriage (current),
* R = sum, C2 = hasCarriage (new)
+---+---+---++---+ ---+
| A | B | C || R | C2 |
|---+---+----++---+---|
| 0 | 0 | 0 || 0 | 0 |
| 0 | 0 | 1 || 1 | 0 |
| 0 | 1 | 0 || 1 | 0 |
| 0 | 1 | 1 || 0 | 1 |
| 1 | 0 | 0 || 1 | 0 |
| 1 | 0 | 1 || 0 | 1 |
| 1 | 1 | 0 || 0 | 1 |
| 1 | 1 | 1 || 1 | 1 |
|---+---+---++---+----|
|
| Veitch table for the sum:
| A
| ___
+-------+
| B ||0|1|0|1|
|-------|
|1|0|1|0|
+-------+
| ___
| C
| Boolean function for the sum: R = A*!B*!C + A*B*C + !A*!B*C + !A*B*!C
|
| Veitch table for hasCarriage:
| A
| ___
+-------+
| B ||1|1|1|0|
|-------|
|0|1|0|0|
+-------+
| ___
| C
| Boolean function for hasCarriage: C2 = A*B + A*C + B*C
*/
public static BinaryPolynomial operator +(BinaryPolynomial left, BinaryPolynomial right)
{
left.Should().NotBeNull();
right.Should().NotBeNull();
var hasCarriage = false;
var sum = new BinaryPolynomial();
for (var degree = 1; degree <= MaxDegree; degree++)
{
sum[degree] =
left[degree] && !right[degree] && !hasCarriage ||
left[degree] && right[degree] && hasCarriage ||
!left[degree] && !right[degree] && hasCarriage ||
!left[degree] && right[degree] && !hasCarriage;
hasCarriage =
left[degree] && right[degree] ||
left[degree] && hasCarriage ||
right[degree] && hasCarriage;
}
return(sum);
}
/// <summary>
/// Constructs a polynomial from an existing polynomial.
/// </summary>
public BinaryPolynomial(BinaryPolynomial copySource)
{
this.Polynomial = copySource.Polynomial;
}
/// <summary>
/// Divides left polynomial with right and returns a tuple (result, rest).
/// </summary>
public static Tuple <BinaryPolynomial, BinaryPolynomial> Division(BinaryPolynomial left, BinaryPolynomial right)
{
return(Division(left.Copy(), right, left.Degree, new StringBuilder()));
}
