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);
}
public virtual Algebraic divExponential(Algebraic x, FunctionVariable fv, int n)
{
var a = new Algebraic[2];
a[1] = x;
Algebraic xk = Symbol.ZERO;
for (int i = n; i >= 0; i--)
{
var kf = FunctionVariable.Create("exp", fv.Var).Pow(i);
a[0] = a[1];
a[1] = kf;
Poly.polydiv(a, fv);
if (!a[0].Equals(Symbol.ZERO))
{
var kfi = FunctionVariable.Create("exp", -fv.Var) ^ (n - i);
xk = xk + a[0] * kfi;
}
if (Equals(a[1], Symbol.ZERO))
{
break;
}
}
return(SymEval(xk));
}
internal override Algebraic SymEval(Algebraic f)
{
if (gcd.Equals(Symbol.ZERO))
{
return(f);
}
if (f is Polynomial)
{
Polynomial p = ( Polynomial )f;
if (p.Var is FunctionVariable && (( FunctionVariable )p.Var).Name.Equals("exp") && Poly.Degree((( FunctionVariable )p.Var).Var, vr) == 1)
{
var arg = (( FunctionVariable )p.Var).Var;
var new_coef = new Algebraic[2];
new_coef[1] = gcd.ToComplex();
new_coef[0] = Symbol.ZERO;
Algebraic new_arg = new Polynomial(vr, new_coef);
var subst = FunctionVariable.Create("exp", new_arg);
var exp = Poly.Coefficient(arg, vr, 1) / gcd;
if (!(exp is Symbol) && !(( Symbol )exp).IsInteger())
{
throw new SymbolicException("Not integer exponent in exponential simplification.");
}
subst = subst ^ (( Symbol )exp).ToInt();
subst = subst * FunctionVariable.Create("exp", Poly.Coefficient(arg, vr, 0));
var len = p.Coeffs.Length;
var r = SymEval(p[len - 1]);
for (var n = len - 2; n >= 0; n--)
{
r = r * subst + SymEval(p[n]);
}
return(r);
}
}
return(f.Map(this));
}
public static Symbol exp_gcd(ArrayList v, Variable x)
{
var gcd = Symbol.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 Symbol)
{
k++;
gcd = gcd.gcd(( Symbol )c);
}
}
return(k > 0 ? gcd : Symbol.ONE);
}
internal static Algebraic remove_constant(Algebraic expr, Variable x)
{
if (!expr.Depends(x))
{
return(Symbol.ZERO);
}
if (expr is Polynomial)
{
(( Polynomial )expr)[0] = remove_constant((( Polynomial )expr)[0], x);
return(expr);
}
if (expr is Rational)
{
var den = (( Rational )expr).den;
var nom = (( Rational )expr).nom;
if (!den.Depends(x))
{
return(remove_constant(nom, x) / den);
}
if (nom is Polynomial)
{
var a = new[] { nom, den };
Poly.polydiv(a, den.Var);
if (!a[0].Depends(x))
{
return(a[1] / den);
}
}
}
return(expr);
}
public Vector(Algebraic item)
{
_items = item is Vector?Poly.Clone(( Vector )item) : new[] { item };
}
internal override Algebraic SymEval(Algebraic x)
{
if (x is Rational)
{
var xr = ( Rational )x;
if (xr.den.Var is FunctionVariable &&
(( FunctionVariable )xr.den.Var).Name.Equals("exp") &&
(( FunctionVariable )xr.den.Var).Var.IsComplex())
{
var fv = ( FunctionVariable )xr.den.Var;
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.Var).Var / Symbol.TWO, (( FunctionVariable )xr.den.Var).Body);
Algebraic ex = new Polynomial(fv2, new Algebraic[] { Symbol.ZERO, Symbol.ZERO, Symbol.ONE });
var xr1 = xr.nom.Value(xr.den.Var, ex) / xr.den.Value(xr.den.Var, ex);
return(SymEval(xr1));
}
}
}
if (x is Polynomial && (( Polynomial )x).Var is FunctionVariable)
{
var xp = ( Polynomial )x;
Algebraic xf = null;
var fvar = ( FunctionVariable )xp.Var;
if (fvar.Name.Equals("exp"))
{
var re = fvar.Var.RealPart();
var im = fvar.Var.ImagPart();
if (im != Symbol.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) * Symbol.IONE;
xf = a * (_minus ? b - c : b + c);
}
}
if (fvar.Name.Equals("log"))
{
var arg = fvar.Var;
Algebraic factor = Symbol.ONE, sum = Symbol.ZERO;
if (arg is Polynomial &&
(( Polynomial )arg).Degree() == 1 &&
(( Polynomial )arg).Var is FunctionVariable &&
(( Polynomial )arg)[0].Equals(Symbol.ZERO) &&
(( FunctionVariable )(( Polynomial )arg).Var).Name.Equals("sqrt"))
{
sum = FunctionVariable.Create("log", (( Polynomial )arg)[1]);
factor = new Complex(0.5);
arg = (( FunctionVariable )(( Polynomial )arg).Var).Var;
xf = FunctionVariable.Create("log", arg);
}
try
{
var re = arg.RealPart();
var im = arg.ImagPart();
if (im != Symbol.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) / Symbol.TWO;
var b1 = SymEval(re / im);
var b = FunctionVariable.Create("atan", b1) * Symbol.IONE;
xf = min_im ? a + b : a - b;
var pi2 = Symbol.PI * Symbol.IONE / Symbol.TWO;
xf = min_im ? xf - pi2 : xf + pi2;
}
}
catch (SymbolicException)
{
}
if (xf != null)
{
xf = xf * factor + sum;
}
}
if (xf == null)
{
return(x.Map(this));
}
Algebraic r = Symbol.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));
}
