public override int Eval(Stack st)
{
int narg = GetNarg(st);
var dgl = GetAlgebraic(st);
var y = GetVariable(st);
var x = GetVariable(st);
var p = Poly.Coefficient(dgl, y, 1);
var q = Poly.Coefficient(dgl, y, 0);
var pi = LambdaINTEGRATE.Integrate(p, x);
if (pi is Rational && !pi.IsNumber())
{
pi = (new LambdaRAT()).SymEval(pi);
}
Variable vexp = new FunctionVariable("exp", pi, new LambdaEXP());
Algebraic dn = new Polynomial(vexp);
var qi = LambdaINTEGRATE.Integrate(q / dn, x);
if (qi is Rational && !qi.IsNumber())
{
qi = (new LambdaRAT()).SymEval(qi);
}
Algebraic cn = new Polynomial(new SimpleVariable("C"));
var res = (qi + cn) * dn;
res = (new ExpandUser()).SymEval(res);
Debug("User Function expand: " + res);
res = (new TrigExpand()).SymEval(res);
Debug("Trigexpand: " + res);
res = (new NormExp()).SymEval(res);
Debug("Norm: " + res);
if (res is Rational)
{
res = (new LambdaRAT()).SymEval(res);
}
res = (new TrigInverseExpand()).SymEval(res);
Debug("Triginverse: " + res);
res = (new SqrtExpand()).SymEval(res);
st.Push(res);
return(0);
}
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));
}
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 }));
}