public static Vector 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();
var d = Poly.poly_gcd(q, q.Derive(x));
var b = Poly.polydiv(q, d);
int m = b is Polynomial ? (( Polynomial )b).Degree() : 0;
int n = d is Polynomial ? (( Polynomial )d).Degree() : 0;
var a = new SimpleVariable[m];
var X = new Polynomial(x);
Algebraic A = Symbolic.ZERO;
for (int 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 = Symbolic.ZERO;
for (int 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 (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.Derive(a[k]);
}
for (int k = 0; k < n; k++)
{
aik[i][k + m] = cf.Derive(c[k]);
}
}
var s = LambdaLINSOLVE.Gauss(new Matrix(aik), new Vector(co));
A = Symbolic.ZERO;
for (int i = m - 1; i >= 0; i--)
{
A = A + s[i];
if (i > 0)
{
A = A * X;
}
}
C = Symbolic.ZERO;
for (int 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 }));
}
public override Algebraic Derive(Variable v)
{
return(((nom.Derive(v) * den - den.Derive(v) * nom) / (den * den)).Reduce());
}
//JAVA TO C# CONVERTER WARNING: Method 'throws' clauses are not available in .NET:
//ORIGINAL LINE: Vektor solve(Vector expr, Vector x, int n) throws JasymcaException
internal virtual Vector solve(ArrayList expr, ArrayList x, int n)
{
Algebraic equ = null;
Variable v = null;
int i, k, iv = 0, ke = 0;
for (i = 0; i < n && equ == null; i++)
{
v = (Variable)x[i];
double norm = -1.0;
for (k = 0; k < n; k++)
{
Algebraic exp = (Algebraic)expr[k];
if (exp is Rational)
{
exp = ((Rational)exp).nom;
}
Algebraic slope = exp.Derive(v);
if (!slope.Equals(Symbolic.ZERO) && slope is Symbolic)
{
double nm = slope.Norm() / exp.Norm();
if (nm > norm)
{
norm = nm;
equ = exp;
ke = k;
iv = i;
}
}
}
}
if (equ == null)
{
for (i = 0; i < n && equ == null; i++)
{
v = (Variable)x[i];
for (k = 0; k < n; k++)
{
Algebraic exp = (Algebraic)expr[k];
if (exp is Rational)
{
exp = ((Rational)exp).nom;
}
if (exp.Depends(v))
{
equ = exp;
ke = k;
iv = i;
break;
}
}
}
}
if (equ == null)
{
throw new JasymcaException("Expressions do not depend of Variables.");
}
Vector sol = LambdaSOLVE.solve(equ, v);
expr.RemoveAt(ke);
expr.Insert(n - 1, equ);
x.RemoveAt(iv);
x.Insert(n - 1, v);
return(sol);
}