public virtual int Degree(Variable v)
{
if (this._v == v)
{
return(Coeffs.Length - 1);
}
int degree = 0;
foreach (var t in Coeffs)
{
int d = Poly.Degree(t, v);
if (d > degree)
{
degree = d;
}
}
return(degree);
}
public static Symbolic exp_gcd(ArrayList v, Variable x)
{
var gcd = Symbolic.ZERO;
int k = 0;
foreach (var t in v)
{
var a = (Algebraic)t;
Algebraic c;
if (Poly.Degree(a, x) == 1 && (c = Poly.Coefficient(a, x, 1)) is Symbolic)
{
k++;
gcd = gcd.gcd(( Symbolic )c);
}
}
return(k > 0 ? gcd : Symbolic.ONE);
}
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 }));
}
internal override Algebraic SymEval(Algebraic f)
{
if (gcd.Equals(Symbolic.ZERO))
{
return(f);
}
if (f is Polynomial)
{
Polynomial p = (Polynomial)f;
if (p._v is FunctionVariable && ((FunctionVariable)p._v).Name.Equals("exp") && Poly.Degree(((FunctionVariable)p._v).Var, @var) == 1)
{
Algebraic arg = ((FunctionVariable)p._v).Var;
Algebraic[] new_coef = new Algebraic[2];
new_coef[1] = gcd.ToComplex();
new_coef[0] = Symbolic.ZERO;
Algebraic new_arg = new Polynomial(@var, new_coef);
Algebraic subst = FunctionVariable.Create("exp", new_arg);
Algebraic exp = Poly.Coefficient(arg, @var, 1) / gcd;
if (!(exp is Symbolic) && !((Symbolic)exp).IsInteger())
{
throw new JasymcaException("Not integer exponent in exponential simplification.");
}
subst = subst ^ (( Symbolic )exp).ToInt();
subst = subst * FunctionVariable.Create("exp", Poly.Coefficient(arg, @var, 0));
int n = p.Coeffs.Length;
Algebraic r = SymEval(p[n - 1]);
for (int i = n - 2; i >= 0; i--)
{
r = r * subst + SymEval(p[i]);
}
return(r);
}
}
return(f.Map(this));
}
internal override Algebraic SymEval(Algebraic x)
{
if (x is Rational)
{
var xr = ( Rational )x;
if (xr.den._v is FunctionVariable &&
(( FunctionVariable )xr.den._v).Name.Equals("exp") &&
(( FunctionVariable )xr.den._v).Var.IsComplex())
{
var fv = ( FunctionVariable )xr.den._v;
int maxdeg = Math.Max(Poly.Degree(xr.nom, fv), Poly.Degree(xr.den, fv));
if (maxdeg % 2 == 0)
{
return(divExponential(xr.nom, fv, maxdeg / 2) / divExponential(xr.den, fv, maxdeg / 2));
}
else
{
var fv2 = new FunctionVariable("exp", (( FunctionVariable )xr.den._v).Var / Symbolic.TWO, (( FunctionVariable )xr.den._v).AlgLambda);
Algebraic ex = new Polynomial(fv2, new Algebraic[] { Symbolic.ZERO, Symbolic.ZERO, Symbolic.ONE });
var xr1 = xr.nom.Value(xr.den._v, ex) / xr.den.Value(xr.den._v, ex);
return(SymEval(xr1));
}
}
}
if (x is Polynomial && (( Polynomial )x)._v is FunctionVariable)
{
var xp = ( Polynomial )x;
Algebraic xf = null;
var fvar = ( FunctionVariable )xp._v;
if (fvar.Name.Equals("exp"))
{
var re = fvar.Var.RealPart();
var im = fvar.Var.ImagPart();
if (im != Symbolic.ZERO)
{
bool _minus = minus(im);
if (_minus)
{
im = -im;
}
var a = FunctionVariable.Create("exp", re);
var b = FunctionVariable.Create("cos", im);
var c = FunctionVariable.Create("sin", im) * Symbolic.IONE;
xf = a * (_minus ? b - c : b + c);
}
}
if (fvar.Name.Equals("log"))
{
var arg = fvar.Var;
Algebraic factor = Symbolic.ONE, sum = Symbolic.ZERO;
if (arg is Polynomial &&
(( Polynomial )arg).Degree() == 1 &&
(( Polynomial )arg)._v is FunctionVariable &&
(( Polynomial )arg)[0].Equals(Symbolic.ZERO) &&
(( FunctionVariable )(( Polynomial )arg)._v).Name.Equals("sqrt"))
{
sum = FunctionVariable.Create("log", (( Polynomial )arg)[1]);
factor = new Complex(0.5);
arg = (( FunctionVariable )(( Polynomial )arg)._v).Var;
xf = FunctionVariable.Create("log", arg);
}
try
{
var re = arg.RealPart();
var im = arg.ImagPart();
if (im != Symbolic.ZERO)
{
bool min_im = minus(im);
if (min_im)
{
im = -im;
}
var a1 = new SqrtExpand().SymEval(arg * arg.Conj());
var a = FunctionVariable.Create("log", a1) / Symbolic.TWO;
var b1 = SymEval(re / im);
var b = FunctionVariable.Create("atan", b1) * Symbolic.IONE;
xf = min_im ? a + b : a - b;
var pi2 = Symbolic.PI * Symbolic.IONE / Symbolic.TWO;
xf = min_im ? xf - pi2 : xf + pi2;
}
}
catch (JasymcaException)
{
}
if (xf != null)
{
xf = xf * factor + sum;
}
}
if (xf == null)
{
return(x.Map(this));
}
Algebraic r = Symbolic.ZERO;
for (int i = xp.Coeffs.Length - 1; i > 0; i--)
{
r = (r + SymEval(xp[i])) * xf;
}
if (xp.Coeffs.Length > 0)
{
r = r + SymEval(xp[0]);
}
return(r);
}
return(x.Map(this));
}