public static Polynomial <XTerm> AddRoots(this Polynomial <XTerm> poly1, Polynomial <XTerm> poly2)
{
var deg1 = poly1.Degree();
var deg2 = poly2.Degree();
Polynomial <XYTerm> X = new XYTerm(1, 0);
Polynomial <XYTerm> Y = new XYTerm(0, 1);
var powersOfXPlusY = CollectionUtil.Naturals.Select(e => (X + Y).RaisedTo(e));
var maxDegreeOfResult = deg1 * deg2;
if (maxDegreeOfResult == 0)
{
return(1);
}
var reducedPowersOfX =
PolyBasisWithHighPowersReducedUsing(poly1).Select(p => p.ToPolynomialOverVariable1Of2()).Take(maxDegreeOfResult + 1).ToArray();
var reducedPowersOfY =
PolyBasisWithHighPowersReducedUsing(poly2).Select(p => p.ToPolynomialOverVariable2Of2()).Take(maxDegreeOfResult + 1).ToArray();
var reducedPowersOfXPlusY =
powersOfXPlusY
.Select(e =>
e.Coefficients
.Select(r => reducedPowersOfX[(int)r.Key.XPower] * reducedPowersOfY[(int)r.Key.YPower] * r.Value)
.Sum())
.Take(maxDegreeOfResult + 1)
.ToArray();
var linearSystem = Matrix.FromColumns(
from col in reducedPowersOfXPlusY
select from row in maxDegreeOfResult.Range()
let exponentForX = row / deg2
let exponentForY = row % deg2
select col.Coefficient(new XYTerm(exponentForX, exponentForY)));
var solvedSystem = linearSystem.Reduced();
var degreeOfSolution = solvedSystem.Rows.Count(row => row.Any(cell => cell != 0));
var lowCoefficients = solvedSystem.Columns[degreeOfSolution].Take(degreeOfSolution);
return(XToThe(degreeOfSolution) - lowCoefficients.TimesPolynomialBasis());
}
public override string ToString()
{
return(XYTerm.PowerFactorString("x", XPower));
}