internal override Algebraic SymEval(Algebraic x)
{
throw new SymbolicException("Usage: ATAN2(y,x).");
}
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));
}
internal override Algebraic SymEval(Algebraic x)
{
return(Equals(x, Symbol.ZERO) ? Symbol.ZERO : null);
}
public FunctionVariable(string fname, Algebraic fvar, LambdaAlgebraic flambda)
{
Name = fname;
Var = fvar;
Body = flambda;
}
internal override Algebraic SymEval(Algebraic x)
{
if (!(x is Polynomial))
{
return(x.Map(this));
}
var xp = ( Polynomial )x;
var item = xp.Var;
if (item is Root)
{
var cr = (( Root )item).poly;
if (cr.Length() == xp.Degree() + 1)
{
var xr = new Algebraic[xp.Degree() + 1];
Algebraic ratio = null;
for (int i = xr.Length - 1; i >= 0; i--)
{
xr[i] = xp[i].Map(this);
if (i == xr.Length - 1)
{
ratio = xr[i];
}
else if (i > 0 && ratio != null)
{
if (!Equals(cr[i] * ratio, xr[i]))
{
ratio = null;
}
}
}
if (ratio != null)
{
return(xr[0] - ratio * cr[0]);
}
else
{
return(new Polynomial(item, xr));
}
}
}
Algebraic xf = null;
if (item is FunctionVariable && (( FunctionVariable )item).Name.Equals("sqrt") && (( FunctionVariable )item).Var is Polynomial)
{
var arg = ( Polynomial )(( FunctionVariable )item).Var;
var sqfr = arg.square_free_dec(arg.Var);
var issquare = !(sqfr.Length > 0 && !sqfr[0].Equals(arg[arg.Coeffs.Length - 1]));
for (int i = 2; i < sqfr.Length && issquare; i++)
{
if ((i + 1) % 2 == 1 && !sqfr[i].Equals(Symbol.ONE))
{
issquare = false;
}
}
if (issquare)
{
xf = Symbol.ONE;
for (int i = 1; i < sqfr.Length; i += 2)
{
if (!sqfr[i].Equals(Symbol.ZERO))
{
xf = xf * sqfr[i] ^ ((i + 1) / 2);
}
}
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);
}
}
if (item is FunctionVariable && (( FunctionVariable )item).Name.Equals("sqrt") && xp.Degree() > 1)
{
xf = (( FunctionVariable )item).Var;
var sq = new Polynomial(item);
var r = SymEval(xp[0]);
Algebraic xv = Symbol.ONE;
for (int i = 1; i < xp.Coeffs.Length; i++)
{
if (i % 2 == 1)
{
r = r + SymEval(xp[i]) * xv * sq;
}
else
{
xv = xv * xf;
r = r + SymEval(xp[i]) * xv;
}
}
return(r);
}
return(x.Map(this));
}
public CollectExp(Algebraic f)
{
v = new ArrayList();
new GetExpVars(v).SymEval(f);
}
internal override Algebraic SymEval(Algebraic f)
{
if (f is Rational)
{
var r = ( Rational )f;
var nom = SymEval(r.nom);
var den = SymEval(r.den);
if (den is Symbol)
{
return(SymEval(nom / den));
}
if (den is Exponential && (( Polynomial )den)[0].Equals(Symbol.ZERO) && (( Polynomial )den)[1] is Symbol)
{
if (nom is Symbol || nom is Polynomial)
{
var denx = ( Exponential )den;
var den_inv = new Exponential(Symbol.ONE / denx[1], Symbol.ZERO, denx.expvar, -denx.exp_b);
return(nom * den_inv);
}
}
f = nom / den;
return(f);
}
if (f is Exponential)
{
return(f.Map(this));
}
if (!(f is Polynomial))
{
return(f.Map(this));
}
var fp = ( Polynomial )f;
if (!(fp.Var is FunctionVariable) || !(( FunctionVariable )fp.Var).Name.Equals("exp"))
{
return(f.Map(this));
}
var arg = (( FunctionVariable )fp.Var).Var.Reduce();
if (arg is Symbol)
{
return(fp.value(FunctionVariable.Create("exp", arg)).Map(this));
}
if (!(arg is Polynomial) || (( Polynomial )arg).Degree() != 1)
{
return(f.Map(this));
}
Algebraic z = Symbol.ZERO;
var a = (( Polynomial )arg)[1];
for (int i = 1; i < fp.Coeffs.Length; i++)
{
var b = (( Polynomial )arg)[0];
Symbol I = new Complex(( double )i);
Algebraic ebi = Symbol.ONE;
while (b is Polynomial && (( Polynomial )b).Degree() == 1)
{
var p = ( Polynomial )b;
var f1 = FunctionVariable.Create("exp", new Polynomial(p.Var) * p[1] * I);
f1 = Exponential.poly2exp(f1);
ebi = ebi * f1;
b = (( Polynomial )b)[0];
}
ebi = ebi * FunctionVariable.Create("exp", b * I);
var cf = SymEval(fp[i] * ebi);
var f2 = FunctionVariable.Create("exp", new Polynomial((( Polynomial )arg).Var) * a * I);
f2 = Exponential.poly2exp(f2);
z = z + cf * f2;
}
if (fp.Coeffs.Length > 0)
{
z = z + SymEval(fp[0]);
}
return(Exponential.poly2exp(z));
}
public virtual Algebraic rational(Algebraic expr)
{
return((ratsubst(expr) / gcd / new Polynomial(t)).Reduce());
}
public Exponential(Polynomial x) : base(x.Var, x.Coeffs)
{
expvar = (( Polynomial )(( FunctionVariable )Var).Var).Var;
exp_b = (( Polynomial )(( FunctionVariable )Var).Var)[1];
}
internal virtual Algebraic SymEval(Algebraic ax, Algebraic ay)
{
return(null);
}