public static Vector Horowitz(Algebraic p, Polynomial q, Variable x)
{
if (Poly.Degree(p, x) >= Poly.Degree(q, x))
{
throw new SymbolicException("Degree of p must be smaller than degree of q");
}
p = p.Rat();
q = ( Polynomial )q.Rat();
var d = Poly.poly_gcd(q, q.Derive(x));
var b = Poly.polydiv(q, d);
var m = b is Polynomial ? (( Polynomial )b).Degree() : 0;
var n = d is Polynomial ? (( Polynomial )d).Degree() : 0;
var a = new SimpleVariable[m];
var X = new Polynomial(x);
Algebraic A = Symbol.ZERO;
for (var i = a.Length - 1; i >= 0; i--)
{
a[i] = new SimpleVariable("a" + i);
A = A + new Polynomial(a[i]);
if (i > 0)
{
A = A * X;
}
}
var c = new SimpleVariable[n];
Algebraic C = Symbol.ZERO;
for (var i = c.Length - 1; i >= 0; i--)
{
c[i] = new SimpleVariable("c" + i);
C = C + new Polynomial(c[i]);
if (i > 0)
{
C = C * X;
}
}
var r = Poly.polydiv(C * b * d.Derive(x), d);
r = b * C.Derive(x) - r + d * A;
var aik = Matrix.CreateRectangularArray <Algebraic>(m + n, m + n);
Algebraic cf;
var co = new Algebraic[m + n];
for (var i = 0; i < m + n; i++)
{
co[i] = Poly.Coefficient(p, x, i);
cf = Poly.Coefficient(r, x, i);
for (var k = 0; k < m; k++)
{
aik[i][k] = cf.Derive(a[k]);
}
for (var k = 0; k < n; k++)
{
aik[i][k + m] = cf.Derive(c[k]);
}
}
var s = LambdaLINSOLVE.Gauss(new Matrix(aik), new Vector(co));
A = Symbol.ZERO;
for (var i = m - 1; i >= 0; i--)
{
A = A + s[i];
if (i > 0)
{
A = A * X;
}
}
C = Symbol.ZERO;
for (var i = n - 1; i >= 0; i--)
{
C = C + s[i + m];
if (i > 0)
{
C = C * X;
}
}
return(new Vector(new[] { C / d, A / b }));
}
//JAVA TO C# CONVERTER WARNING: Method 'throws' clauses are not available in .NET:
//ORIGINAL LINE: public static Vektor horowitz(Algebraic p, Polynomial q, Variable x) throws JasymcaException
public static Vektor horowitz(Algebraic p, Polynomial q, Variable x)
{
if (Poly.degree(p, x) >= Poly.degree(q, x))
{
throw new JasymcaException("Degree of p must be smaller than degree of q");
}
p = p.rat();
q = (Polynomial)q.rat();
Algebraic d = Poly.poly_gcd(q, q.deriv(x));
Algebraic b = Poly.polydiv(q, d);
int m = b is Polynomial? ((Polynomial)b).degree():0;
int n = d is Polynomial? ((Polynomial)d).degree():0;
SimpleVariable[] a = new SimpleVariable[m];
Polynomial X = new Polynomial(x);
Algebraic A = Zahl.ZERO;
for (int i = a.Length - 1; i >= 0; i--)
{
a[i] = new SimpleVariable("a" + i);
A = A.add(new Polynomial(a[i]));
if (i > 0)
{
A = A.mult(X);
}
}
SimpleVariable[] c = new SimpleVariable[n];
Algebraic C = Zahl.ZERO;
for (int i = c.Length - 1; i >= 0; i--)
{
c[i] = new SimpleVariable("c" + i);
C = C.add(new Polynomial(c[i]));
if (i > 0)
{
C = C.mult(X);
}
}
Algebraic r = Poly.polydiv(C.mult(b).mult(d.deriv(x)), d);
r = b.mult(C.deriv(x)).sub(r).add(d.mult(A));
//JAVA TO C# CONVERTER NOTE: The following call to the 'RectangularArrays' helper class reproduces the rectangular array initialization that is automatic in Java:
//ORIGINAL LINE: Algebraic[][] aik = new Algebraic[m+n][m+n];
Algebraic[][] aik = RectangularArrays.ReturnRectangularAlgebraicArray(m + n, m + n);
Algebraic cf; Algebraic[] co = new Algebraic[m + n];
for (int i = 0; i < m + n; i++)
{
co[i] = Poly.coefficient(p, x, i);
cf = Poly.coefficient(r, x, i);
for (int k = 0; k < m; k++)
{
aik[i][k] = cf.deriv(a[k]);
}
for (int k = 0; k < n; k++)
{
aik[i][k + m] = cf.deriv(c[k]);
}
}
Vektor s = LambdaLINSOLVE.Gauss(new Matrix(aik), new Vektor(co));
A = Zahl.ZERO;
for (int i = m - 1; i >= 0; i--)
{
A = A.add(s.get(i));
if (i > 0)
{
A = A.mult(X);
}
}
C = Zahl.ZERO;
for (int i = n - 1; i >= 0; i--)
{
C = C.add(s.get(i + m));
if (i > 0)
{
C = C.mult(X);
}
}
co = new Algebraic[2];
co[0] = C.div(d);
co[1] = A.div(b);
return(new Vektor(co));
}