internal override Algebraic SymEval(Algebraic x)
{
if (x.Equals(Symbol.ZERO))
{
return(Symbol.ZERO);
}
return(null);
}
internal override Algebraic SymEval(Algebraic x)
{
if (x.Equals(Symbol.ONE))
{
return(Symbol.ZERO);
}
if (x.Equals(Symbol.MINUS))
{
return(Symbol.PI * Symbol.IONE);
}
if (x is Polynomial &&
(( Polynomial )x).Degree() == 1 &&
(( Polynomial )x)[0].Equals(Symbol.ZERO) &&
(( Polynomial )x).Var is FunctionVariable &&
(( FunctionVariable )(( Polynomial )x).Var).Name.Equals("exp"))
{
return((( FunctionVariable )(( Polynomial )x).Var).Var + FunctionVariable.Create("log", (( Polynomial )x)[1]));
}
return(null);
}
internal override Algebraic SymEval(Algebraic x, Algebraic y)
{
if (x.Equals(Symbol.ZERO))
{
if (y.Equals(Symbol.ZERO))
{
return(Symbol.ONE);
}
return(Symbol.ZERO);
}
if (y is Symbol && (( Symbol )y).IsInteger())
{
return(x.Pow((( Symbol )y).ToInt()));
}
return(FunctionVariable.Create("exp", FunctionVariable.Create("log", x) * y));
}
private static void subst(Vector expr, Vector vars, int n)
{
if (n < 0)
{
return;
}
var pa = expr[n];
if (pa is Polynomial)
{
var p = ( Polynomial )pa;
Variable v = null;
Algebraic c1 = null, c0;
for (int k = 0; k < vars.Length(); k++)
{
var va = (( Polynomial )vars[k]).Var;
c1 = p.GetCoeff(va, 1);
if (!c1.Equals(Symbol.ZERO))
{
v = va;
break;
}
}
if (v != null)
{
expr[n] = p / c1;
var val = -p.GetCoeff(v, 0) / c1;
for (int k = 0; k < n; k++)
{
var ps = expr[k];
if (ps is Polynomial)
{
expr.set(k, (( Polynomial )ps).Value(v, val));
}
}
}
}
subst(expr, vars, n - 1);
}
protected override Algebraic Mul(Algebraic x)
{
if (x.Equals(Symbol.ZERO))
{
return(x);
}
if (x is Symbol)
{
return(new Exponential(this[1] * x, this[0] * x, expvar, exp_b));
}
if (x is Exponential && expvar.Equals((( Exponential )x).expvar))
{
var xp = ( Exponential )x;
Algebraic r = Symbol.ZERO;
var nex = exp_b + xp.exp_b;
if (Equals(nex, Symbol.ZERO))
{
r = this[1] * xp[1];
}
else
{
r = new Exponential(this[1] * xp[1], Symbol.ZERO, expvar, nex);
}
r = r + this[0] * xp;
r = r + this * xp[0];
r = r.Reduce();
return(r);
}
return(poly2exp(this * x));
}
internal override Algebraic SymEval(Algebraic x)
{
if (x.Equals(Symbol.ZERO))
{
return(Symbol.ONE);
}
if (x is Polynomial &&
(( Polynomial )x).Degree() == 1 &&
(( Polynomial )x)[0].Equals(Symbol.ZERO))
{
var xp = ( Polynomial )x;
if (xp.Var is SimpleVariable && (( SimpleVariable )xp.Var).name.Equals("pi"))
{
var q = xp[1] / Symbol.IONE;
if (q is Symbol)
{
return(fzexakt(( Symbol )q));
}
}
if (xp[1] is Symbol &&
xp.Var is FunctionVariable &&
(( FunctionVariable )xp.Var).Name.Equals("log"))
{
if ((( Symbol )xp[1]).IsInteger())
{
int n = (( Symbol )xp[1]).ToInt();
return((( FunctionVariable )xp.Var).Var.Pow(n));
}
}
}
return(null);
}
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(Symbol.ZERO) && slope is Symbol)
{
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 SymbolicException("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);
}