internal virtual Algebraic fzexakt(Zahl x)
{
if (x.smaller(Zahl.ZERO))
{
Algebraic r = fzexakt((Zahl)x.mult(Zahl.MINUS));
if (r != null)
{
return(r.cc());
}
return(r);
}
if (x.integerq())
{
if (x.intval() % 2 == 0)
{
return(Zahl.ONE);
}
else
{
return(Zahl.MINUS);
}
}
Algebraic qs = x.add(new Unexakt(.5));
if (((Zahl)qs).integerq())
{
if (((Zahl)qs).intval() % 2 == 0)
{
return(Zahl.IMINUS);
}
else
{
return(Zahl.IONE);
}
}
qs = x.mult(new Unexakt(4));
if (((Zahl)qs).integerq())
{
Algebraic sq2 = FunctionVariable.create("sqrt", new Unexakt(0.5));
switch (((Zahl)qs).intval() % 8)
{
case 1:
return(Zahl.ONE.add(Zahl.IONE).div(Zahl.SQRT2));
case 3:
return(Zahl.MINUS.add(Zahl.IONE).div(Zahl.SQRT2));
case 5:
return(Zahl.MINUS.add(Zahl.IMINUS).div(Zahl.SQRT2));
case 7:
return(Zahl.ONE.add(Zahl.IMINUS).div(Zahl.SQRT2));
}
}
qs = x.mult(new Unexakt(6));
if (((Zahl)qs).integerq())
{
switch (((Zahl)qs).intval() % 12)
{
case 1:
return(Zahl.SQRT3.add(Zahl.IONE).div(Zahl.TWO));
case 2:
return(Zahl.ONE.add(Zahl.SQRT3.mult(Zahl.IONE)).div(Zahl.TWO));
case 4:
return(Zahl.SQRT3.mult(Zahl.IONE).add(Zahl.MINUS).div(Zahl.TWO));
case 5:
return(Zahl.IONE.sub(Zahl.SQRT3).div(Zahl.TWO));
case 7:
return(Zahl.IMINUS.sub(Zahl.SQRT3).div(Zahl.TWO));
case 8:
return(Zahl.SQRT3.mult(Zahl.IMINUS).sub(Zahl.ONE).div(Zahl.TWO));
case 10:
return(Zahl.SQRT3.mult(Zahl.IMINUS).add(Zahl.ONE).div(Zahl.TWO));
case 11:
return(Zahl.IMINUS.add(Zahl.SQRT3).div(Zahl.TWO));
}
}
return(null);
}
internal override Algebraic f_exakt(Algebraic f)
{
if (f is Rational)
{
Algebraic nom = f_exakt(((Rational)f).nom);
Algebraic den = f_exakt(((Rational)f).den);
if (den is Zahl)
{
return(f_exakt(nom.div(den)));
}
if (den is Exponential && ((Polynomial)den).a[0].Equals(Zahl.ZERO) && ((Polynomial)den).a[1] is Zahl)
{
if (nom is Zahl || nom is Polynomial)
{
Exponential denx = (Exponential)den;
Exponential den_inv = new Exponential(Zahl.ONE.div(denx.a[1]), Zahl.ZERO, denx.expvar, denx.exp_b.mult(Zahl.MINUS));
return(nom.mult(den_inv));
}
}
f = nom.div(den);
return(f);
}
if (f is Exponential)
{
return(f.map(this));
}
if (!(f is Polynomial))
{
return(f.map(this));
}
Polynomial fp = (Polynomial)f;
if (!(fp.v is FunctionVariable) || !((FunctionVariable)fp.v).fname.Equals("exp"))
{
return(f.map(this));
}
Algebraic arg = ((FunctionVariable)fp.v).arg.reduce();
if (arg is Zahl)
{
return(fp.value(FunctionVariable.create("exp", arg)).map(this));
}
if (!(arg is Polynomial) || !(((Polynomial)arg).degree() == 1))
{
return(f.map(this));
}
Algebraic r = Zahl.ZERO;
Algebraic a = ((Polynomial)arg).a[1];
for (int i = 1; i < fp.a.Length; i++)
{
Algebraic b = ((Polynomial)arg).a[0];
Zahl I = new Unexakt((double)i);
Algebraic ebi = Zahl.ONE;
while (b is Polynomial && ((Polynomial)b).degree() == 1)
{
Algebraic f1 = FunctionVariable.create("exp", (new Polynomial(((Polynomial)b).v)).mult(((Polynomial)b).a[1].mult(I)));
f1 = Exponential.poly2exp(f1);
ebi = ebi.mult(f1);
b = ((Polynomial)b).a[0];
}
ebi = ebi.mult(FunctionVariable.create("exp", b.mult(I)));
Algebraic cf = f_exakt(fp.a[i].mult(ebi));
Algebraic f2 = FunctionVariable.create("exp", (new Polynomial(((Polynomial)arg).v)).mult(a.mult(I)));
f2 = Exponential.poly2exp(f2);
r = r.add(cf.mult(f2));
}
if (fp.a.Length > 0)
{
r = r.add(f_exakt(fp.a[0]));
}
return(Exponential.poly2exp(r));
}
public CollectExp(Algebraic f)
{
v = new ArrayList();
(new GetExpVars(v)).f_exakt(f);
}
//JAVA TO C# CONVERTER WARNING: Method 'throws' clauses are not available in .NET:
//ORIGINAL LINE: Vektor solvesys(Vector expr, Vector x) throws JasymcaException
internal virtual Vector solvesys(ArrayList expr, ArrayList x)
{
int nvars = x.Count;
ArrayList lsg = new ArrayList(), vars = new ArrayList();
lsg.Add(expr);
vars.Add(x);
int n = nvars;
while (n > 0)
{
for (int i = 0; i < lsg.Count; i++)
{
try
{
ArrayList equ = (ArrayList)lsg[i];
ArrayList xv = (ArrayList)vars[i];
Vector sol = solve(equ, xv, n);
lsg.RemoveAt(i);
vars.RemoveAt(i);
Variable v = (Variable)xv[n - 1];
for (int k = 0; k < sol.Length(); k++)
{
ArrayList eq = new ArrayList();
for (int j = 0; j < n - 1; j++)
{
eq.Add(((Algebraic)equ[j]).Value(v, sol[k]));
}
eq.Add(sol[k]);
for (int j = n; j < nvars; j++)
{
eq.Add(equ[j]);
}
lsg.Insert(i, eq);
vars.Insert(i, clonev(xv));
i++;
}
}
catch (JasymcaException)
{
lsg.RemoveAt(i);
vars.RemoveAt(i);
i--;
}
}
if (lsg.Count == 0)
{
throw new JasymcaException("Could not solve equations.");
}
n--;
}
for (int i = 0; i < lsg.Count; i++)
{
ArrayList equ = (ArrayList)lsg[i];
ArrayList xv = (ArrayList)vars[i];
for (n = 1; n < nvars; n++)
{
Algebraic y = (Algebraic)equ[n - 1];
Variable v = (Variable)xv[n - 1];
for (int k = n; k < nvars; k++)
{
Algebraic z = (Algebraic)equ[k];
equ.RemoveAt(k);
equ.Insert(k, z.Value(v, y));
}
}
}
for (int i = 0; i < lsg.Count; i++)
{
ArrayList equ = (ArrayList)lsg[i];
ArrayList xv = (ArrayList)vars[i];
for (n = 0; n < nvars; n++)
{
Variable v = (Variable)xv[n];
Algebraic y = (new Polynomial(v)) - ((Algebraic)equ[n]);
equ.RemoveAt(n);
equ.Insert(n, y);
}
}
Vector[] r = new Vector[lsg.Count];
for (int i = 0; i < lsg.Count; i++)
{
r[i] = Vector.Create((ArrayList)lsg[i]);
}
return(new Vector(r));
}
public virtual Algebraic rational(Algebraic expr)
{
return(ratsubst(expr).div(gcd).div(new Polynomial(t)).reduce());
}
internal override Algebraic f_exakt(Algebraic x)
{
throw new JasymcaException("Usage: ATAN2(y,x).");
}
private static void elim(Vector expr, Vector vars, int n)
{
if (n >= expr.Length())
{
return;
}
double maxc = 0.0;
int iv = 0, ie = 0;
Variable vp = null;
Algebraic f = Symbolic.ONE;
Polynomial pm = null;
for (int i = 0; i < vars.Length(); i++)
{
var v = ((Polynomial)vars[i])._v;
for (int k = n; k < expr.Length(); k++)
{
var pa = expr[k];
if (pa is Polynomial)
{
var p = (Polynomial)pa;
var c = p.coefficient(v, 1);
double nm = c.Norm();
if (nm > maxc)
{
maxc = nm;
vp = v;
ie = k;
iv = i;
f = c;
pm = p;
}
}
}
}
if (maxc == 0.0)
{
return;
}
expr.set(ie, expr[n]);
expr.set(n, pm);
for (int i = n + 1; i < expr.Length(); i++)
{
var p = expr[i];
if (p is Polynomial)
{
var fc = ((Polynomial)p).coefficient(vp, 1);
if (!fc.Equals(Symbolic.ZERO))
{
p = p - pm * fc / f;
}
}
expr.set(i, p);
}
elim(expr, vars, n + 1);
}
internal override Algebraic SymEval(Algebraic x)
{
if (!(x is Polynomial))
{
return(x.Map(this));
}
var xp = ( Polynomial )x;
var item = xp._v;
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._v);
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(Symbolic.ONE))
{
issquare = false;
}
}
if (issquare)
{
xf = Symbolic.ONE;
for (int i = 1; i < sqfr.Length; i += 2)
{
if (!sqfr[i].Equals(Symbolic.ZERO))
{
xf = xf * sqfr[i] ^ ((i + 1) / 2);
}
}
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);
}
}
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 = Symbolic.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));
}
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));
}
//JAVA TO C# CONVERTER WARNING: Method 'throws' clauses are not available in .NET:
//ORIGINAL LINE: public int lambda(Stack st) throws ParseException, JasymcaException
public override int lambda(Stack st)
{
int narg = getNarg(st);
if (narg != 4)
{
throw new ParseException("Usage: ROMBERG (exp,var,ll,ul)");
}
Algebraic exp = getAlgebraic(st);
Variable v = getVariable(st);
Algebraic ll = getAlgebraic(st);
Algebraic ul = getAlgebraic(st);
LambdaAlgebraic xc = new ExpandConstants();
exp = xc.f_exakt(exp);
ll = xc.f_exakt(ll);
ul = xc.f_exakt(ul);
if (!(ll is Zahl) || !(ul is Zahl))
{
throw new ParseException("Usage: ROMBERG (exp,var,ll,ul)");
}
double rombergtol = 1.0e-4;
int rombergit = 11;
Zahl a1 = pc.env.getnum("rombergit");
if (a1 != null)
{
rombergit = a1.intval();
}
a1 = pc.env.getnum("rombergtol");
if (a1 != null)
{
rombergtol = a1.unexakt().real;
}
double a = ((Zahl)ll).unexakt().real;
double b = ((Zahl)ul).unexakt().real;
//JAVA TO C# CONVERTER NOTE: The following call to the 'RectangularArrays' helper class reproduces the rectangular array initialization that is automatic in Java:
//ORIGINAL LINE: double[][] I = new double[rombergit][rombergit];
double[][] I = RectangularArrays.ReturnRectangularDoubleArray(rombergit, rombergit);
int i = 0, n = 1;
Algebraic t = trapez(exp, v, n, a, b);
if (!(t is Zahl))
{
throw new ParseException("Expression must evaluate to number");
}
I[0][0] = ((Zahl)t).unexakt().real;
double epsa = 1.1 * rombergtol;
while (epsa > rombergtol && i < rombergit - 1)
{
i++;
n *= 2;
t = trapez(exp, v, n, a, b);
I[0][i] = ((Zahl)t).unexakt().real;
double f = 1.0;
for (int k = 1; k <= i; k++)
{
f *= 4;
I[k][i] = I[k - 1][i] + (I[k - 1][i] - I[k - 1][i - 1]) / (f - 1.0);
}
epsa = Math.Abs((I[i][i] - I[i - 1][i - 1]) / I[i][i]);
}
st.Push(new Unexakt(I[i][i]));
return(0);
}
public FunctionVariable(string fname, Algebraic fvar, LambdaAlgebraic flambda)
{
this.Name = fname;
this.Var = fvar;
this.AlgLambda = flambda;
}
//JAVA TO C# CONVERTER WARNING: Method 'throws' clauses are not available in .NET:
//ORIGINAL LINE: Algebraic makelog(Algebraic c, Variable x, Algebraic a) throws JasymcaException
internal virtual Algebraic makelog(Algebraic c, Variable x, Algebraic a)
{
Algebraic arg = (new Polynomial(x)).sub(a);
return(FunctionVariable.create("log", arg).mult(c));
}
//JAVA TO C# CONVERTER WARNING: Method 'throws' clauses are not available in .NET:
//ORIGINAL LINE: public static Vektor horowitz(Algebraic p, Polynomial q, Variable x) throws JasymcaException
public static Vektor horowitz(Algebraic p, Polynomial q, Variable x)
{
if (Poly.degree(p, x) >= Poly.degree(q, x))
{
throw new JasymcaException("Degree of p must be smaller than degree of q");
}
p = p.rat();
q = (Polynomial)q.rat();
Algebraic d = Poly.poly_gcd(q, q.deriv(x));
Algebraic b = Poly.polydiv(q, d);
int m = b is Polynomial? ((Polynomial)b).degree():0;
int n = d is Polynomial? ((Polynomial)d).degree():0;
SimpleVariable[] a = new SimpleVariable[m];
Polynomial X = new Polynomial(x);
Algebraic A = Zahl.ZERO;
for (int i = a.Length - 1; i >= 0; i--)
{
a[i] = new SimpleVariable("a" + i);
A = A.add(new Polynomial(a[i]));
if (i > 0)
{
A = A.mult(X);
}
}
SimpleVariable[] c = new SimpleVariable[n];
Algebraic C = Zahl.ZERO;
for (int i = c.Length - 1; i >= 0; i--)
{
c[i] = new SimpleVariable("c" + i);
C = C.add(new Polynomial(c[i]));
if (i > 0)
{
C = C.mult(X);
}
}
Algebraic r = Poly.polydiv(C.mult(b).mult(d.deriv(x)), d);
r = b.mult(C.deriv(x)).sub(r).add(d.mult(A));
//JAVA TO C# CONVERTER NOTE: The following call to the 'RectangularArrays' helper class reproduces the rectangular array initialization that is automatic in Java:
//ORIGINAL LINE: Algebraic[][] aik = new Algebraic[m+n][m+n];
Algebraic[][] aik = RectangularArrays.ReturnRectangularAlgebraicArray(m + n, m + n);
Algebraic cf; Algebraic[] co = new Algebraic[m + n];
for (int i = 0; i < m + n; i++)
{
co[i] = Poly.coefficient(p, x, i);
cf = Poly.coefficient(r, x, i);
for (int k = 0; k < m; k++)
{
aik[i][k] = cf.deriv(a[k]);
}
for (int k = 0; k < n; k++)
{
aik[i][k + m] = cf.deriv(c[k]);
}
}
Vektor s = LambdaLINSOLVE.Gauss(new Matrix(aik), new Vektor(co));
A = Zahl.ZERO;
for (int i = m - 1; i >= 0; i--)
{
A = A.add(s.get(i));
if (i > 0)
{
A = A.mult(X);
}
}
C = Zahl.ZERO;
for (int i = n - 1; i >= 0; i--)
{
C = C.add(s.get(i + m));
if (i > 0)
{
C = C.mult(X);
}
}
co = new Algebraic[2];
co[0] = C.div(d);
co[1] = A.div(b);
return(new Vektor(co));
}
//JAVA TO C# CONVERTER WARNING: Method 'throws' clauses are not available in .NET:
//ORIGINAL LINE: public Algebraic value(Variable var, Algebraic x) throws JasymcaException
public override Algebraic value(Variable @var, Algebraic x)
{
return(nom.value(@var, x).div(den.value(@var, x)));
}
internal override Algebraic f_exakt(Algebraic x)
{
if (!(x is Polynomial))
{
return(x.map(this));
}
var xp = ( Polynomial )x;
var item = xp.v;
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.a[i].map(this);
if (i == xr.Length - 1)
{
ratio = xr[i];
}
else if (i > 0 && ratio != null)
{
if (!cr.get(i).mult(ratio).Equals(xr[i]))
{
ratio = null;
}
}
}
if (ratio != null)
{
return(xr[0].sub(ratio.mult(cr.get(0))));
}
else
{
return(new Polynomial(item, xr));
}
}
}
Algebraic xf = null;
if (item is FunctionVariable && (( FunctionVariable )item).fname.Equals("sqrt") && (( FunctionVariable )item).arg is Polynomial)
{
var arg = ( Polynomial )(( FunctionVariable )item).arg;
var sqfr = arg.square_free_dec(arg.v);
var issquare = !(sqfr.Length > 0 && !sqfr[0].Equals(arg.a[arg.a.Length - 1]));
for (int i = 2; i < sqfr.Length && issquare; i++)
{
if ((i + 1) % 2 == 1 && !sqfr[i].Equals(Zahl.ONE))
{
issquare = false;
}
}
if (issquare)
{
xf = Zahl.ONE;
for (int i = 1; i < sqfr.Length; i += 2)
{
if (!sqfr[i].Equals(Zahl.ZERO))
{
xf = xf.mult(sqfr[i].pow_n((i + 1) / 2));
}
}
Algebraic r = Zahl.ZERO;
for (int i = xp.a.Length - 1; i > 0; i--)
{
r = r.add(f_exakt(xp.a[i])).mult(xf);
}
if (xp.a.Length > 0)
{
r = r.add(f_exakt(xp.a[0]));
}
return(r);
}
}
if (item is FunctionVariable && (( FunctionVariable )item).fname.Equals("sqrt") && xp.degree() > 1)
{
xf = (( FunctionVariable )item).arg;
var sq = new Polynomial(item);
var r = f_exakt(xp.a[0]);
Algebraic xv = Zahl.ONE;
for (int i = 1; i < xp.a.Length; i++)
{
if (i % 2 == 1)
{
r = r.add(f_exakt(xp.a[i]).mult(xv).mult(sq));
}
else
{
xv = xv.mult(xf);
r = r.add(f_exakt(xp.a[i]).mult(xv));
}
}
return(r);
}
return(x.map(this));
}
internal override Algebraic SymEval(Algebraic x)
{
return(Equals(x, Symbolic.ZERO) ? Symbolic.ZERO : null);
}
internal override Algebraic f_exakt(Algebraic x)
{
if (x is Rational)
{
var xr = ( Rational )x;
if (xr.den.v is FunctionVariable &&
(( FunctionVariable )xr.den.v).fname.Equals("exp") &&
(( FunctionVariable )xr.den.v).arg.komplexq())
{
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).div(divExponential(xr.den, fv, maxdeg / 2)));
}
else
{
var fv2 = new FunctionVariable("exp", (( FunctionVariable )xr.den.v).arg.div(Zahl.TWO), (( FunctionVariable )xr.den.v).la);
Algebraic ex = new Polynomial(fv2, new Algebraic[] { Zahl.ZERO, Zahl.ZERO, Zahl.ONE });
var xr1 = xr.nom.value(xr.den.v, ex).div(xr.den.value(xr.den.v, ex));
return(f_exakt(xr1));
}
}
}
if (x is Polynomial && (( Polynomial )x).v is FunctionVariable)
{
var xp = ( Polynomial )x;
Algebraic xf = null;
var fvar = ( FunctionVariable )xp.v;
if (fvar.fname.Equals("exp"))
{
var re = fvar.arg.realpart();
var im = fvar.arg.imagpart();
if (!im.Equals(Zahl.ZERO))
{
bool _minus = minus(im);
if (_minus)
{
im = im.mult(Zahl.MINUS);
}
var a = FunctionVariable.create("exp", re);
var b = FunctionVariable.create("cos", im);
var c = FunctionVariable.create("sin", im).mult(Zahl.IONE);
xf = a.mult(_minus ? (b.sub(c)) : b.add(c));
}
}
if (fvar.fname.Equals("log"))
{
var arg = fvar.arg;
Algebraic factor = Zahl.ONE, sum = Zahl.ZERO;
if (arg is Polynomial &&
(( Polynomial )arg).degree() == 1 &&
(( Polynomial )arg).v is FunctionVariable &&
(( Polynomial )arg).a[0].Equals(Zahl.ZERO) &&
(( FunctionVariable )(( Polynomial )arg).v).fname.Equals("sqrt"))
{
sum = FunctionVariable.create("log", (( Polynomial )arg).a[1]);
factor = new Unexakt(0.5);
arg = (( FunctionVariable )(( Polynomial )arg).v).arg;
xf = FunctionVariable.create("log", arg);
}
try
{
var re = arg.realpart();
var im = arg.imagpart();
if (!im.Equals(Zahl.ZERO))
{
bool min_im = minus(im);
if (min_im)
{
im = im.mult(Zahl.MINUS);
}
var a1 = (new SqrtExpand()).f_exakt(arg.mult(arg.cc()));
var a = FunctionVariable.create("log", a1).div(Zahl.TWO);
var b1 = f_exakt(re.div(im));
var b = FunctionVariable.create("atan", b1).mult(Zahl.IONE);
xf = min_im ? a.add(b) : a.sub(b);
var pi2 = Zahl.PI.mult(Zahl.IONE).div(Zahl.TWO);
xf = min_im ? xf.sub(pi2) : xf.add(pi2);
}
}
catch (JasymcaException)
{
}
if (xf != null)
{
xf = xf.mult(factor).add(sum);
}
}
if (xf == null)
{
return(x.map(this));
}
Algebraic r = Zahl.ZERO;
for (int i = xp.a.Length - 1; i > 0; i--)
{
r = r.add(f_exakt(xp.a[i])).mult(xf);
}
if (xp.a.Length > 0)
{
r = r.add(f_exakt(xp.a[0]));
}
return(r);
}
return(x.map(this));
}
public static Algebraic reduce_exp(Algebraic p)
{
Algebraic[] a = new Algebraic[] { p };
a = reduce_exp(a);
return(a[0]);
}
public static Vector solve(Algebraic expr, Variable item)
{
Debug("Solve: " + expr + " = 0, Variable: " + item);
expr = (new ExpandUser()).SymEval(expr);
expr = (new TrigExpand()).SymEval(expr);
Debug("TrigExpand: " + expr);
expr = (new NormExp()).SymEval(expr);
Debug("Norm: " + expr);
expr = (new CollectExp(expr)).SymEval(expr);
Debug("Collect: " + expr);
expr = (new SqrtExpand()).SymEval(expr);
Debug("SqrtExpand: " + expr);
if (expr is Rational)
{
expr = (new LambdaRAT()).SymEval(expr);
if (expr is Rational)
{
expr = (( Rational )expr).nom;
}
}
Debug("Canonic Expression: " + expr);
if (!(expr is Polynomial) || !(( Polynomial )expr).Depends(item))
{
throw new JasymcaException("Expression does not depend of variable.");
}
var p = ( Polynomial )expr;
Vector sol = null;
var dep = depvars(p, item);
if (dep.Count == 0)
{
throw new JasymcaException("Expression does not depend of variable.");
}
if (dep.Count == 1)
{
var dvar = ( Variable )dep[0];
Debug("Found one Variable: " + dvar);
sol = p.solve(dvar);
Debug("Solution: " + dvar + " = " + sol);
if (!dvar.Equals(item))
{
var s = new ArrayList();
for (int i = 0; i < sol.Length(); i++)
{
Debug("Invert: " + sol[i] + " = " + dvar);
var sl = finvert(( FunctionVariable )dvar, sol[i]);
Debug("Result: " + sl + " = 0");
var t = solve(sl, item);
Debug("Solution: " + item + " = " + t);
for (int k = 0; k < t.Length(); k++)
{
var tn = t[k];
if (!s.Contains(tn))
{
s.Add(tn);
}
}
}
sol = Vector.Create(s);
}
}
else if (dep.Count == 2)
{
Debug("Found two Variables: " + dep[0] + ", " + dep[1]);
if (dep.Contains(item))
{
var f = ( FunctionVariable )(dep[0].Equals(item) ? dep[1] : dep[0]);
if (f.Name.Equals("sqrt"))
{
Debug("Solving " + p + " for " + f);
sol = p.solve(f);
Debug("Solution: " + f + " = " + sol);
var s = new ArrayList();
for (int i = 0; i < sol.Length(); i++)
{
Debug("Invert: " + sol[i] + " = " + f);
var sl = finvert(f, sol[i]);
Debug("Result: " + sl + " = 0");
if (sl is Polynomial && depvars((( Polynomial )sl), item).Count == 1)
{
Debug("Solving " + sl + " for " + item);
var t = solve(sl, item);
Debug("Solution: " + item + " = " + t);
for (int k = 0; k < t.Length(); k++)
{
var tn = t[k];
if (!s.Contains(tn))
{
s.Add(tn);
}
}
}
else
{
throw new JasymcaException("Could not solve equation.");
}
}
sol = Vector.Create(s);
}
else
{
throw new JasymcaException("Can not solve equation.");
}
}
else
{
throw new JasymcaException("Can not solve equation.");
}
}
else
{
throw new JasymcaException("Can not solve equation.");
}
return(sol);
}
public Exponential(Polynomial x) : base(x.v, x.a)
{
this.expvar = ((Polynomial)((FunctionVariable)this.v).arg).v;
this.exp_b = ((Polynomial)((FunctionVariable)this.v).arg).a[1];
}
public virtual int rank_decompose(Matrix B, Matrix P)
{
int m = nrow(), n = ncol(), perm = 0;
Matrix C = eye(m, m);
Matrix D = eye(m, m);
for (int k = 0; k < m - 1; k++)
{
int _pivot = pivot(k);
if (_pivot != k)
{
Matrix E = elementary(m, k, _pivot);
C = (Matrix)C.mult(E);
D = (Matrix)D.mult(E);
perm++;
}
int p = k;
for (p = k; p < n; p++)
{
if (!a[k][p].Equals(Zahl.ZERO))
{
break;
}
}
if (p < n)
{
for (int i = k + 1; i < m; i++)
{
if (!a[i][p].Equals(Zahl.ZERO))
{
Algebraic f = a[i][p].div(a[k][p]);
a[i][p] = Zahl.ZERO;
for (int j = p + 1; j < n; j++)
{
a[i][j] = a[i][j].sub(f.mult(a[k][j]));
}
C = (Matrix)C.mult(elementary(m, i, k, f));
}
}
}
}
int nm = Math.Max(n, m);
for (int i = nm - 1; i >= 0; i--)
{
if (row_zero(i))
{
remove_row(i);
C.remove_col(i);
}
}
if (B != null)
{
B.a = C.a;
}
if (P != null)
{
P.a = D.a;
}
return(perm);
}
//JAVA TO C# CONVERTER WARNING: Method 'throws' clauses are not available in .NET:
//ORIGINAL LINE: Vektor solve(Vector expr, Vector x, int n) throws JasymcaException
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(Symbolic.ZERO) && slope is Symbolic)
{
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 JasymcaException("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);
}
