public CasExpr ToExpr()
{
var p = new CasPolynomial();
p.Terms.Add(this);
return(new CasExpr(p, CasPolynomial.ConstantPoly(1)));
}
public CasExpr(CasPolynomial poly1, CasPolynomial poly2)
{
Poly1 = poly1;
Poly2 = poly2;
if (poly2.Terms.Count == 0)
{
throw new Exception("Attempt to divide by zero.");
}
}
public static CasPolynomial ConstantPoly(int c)
{
var p = new CasPolynomial();
if (c != 0)
{
p.Terms.Add(new CasTerm(c));
}
return(p);
}
public CasExpr VarExpr(CasVar v)
{
var t = new CasTerm(1);
t.Variables[v] = 1;
var p = new CasPolynomial();
p.Terms.Add(t);
return(new CasExpr(p, CasPolynomial.ConstantPoly(1)));
}
public CasExpr Mul(CasExpr expr1, CasExpr expr2)
{
if (expr1.Poly1.PolyEquals(expr2.Poly2))
{
return(new CasExpr(expr2.Poly1, expr1.Poly2));
}
if (expr1.Poly2.PolyEquals(expr2.Poly1))
{
return(new CasExpr(expr1.Poly1, expr2.Poly2));
}
return(new CasExpr(CasPolynomial.PolyProd(expr1.Poly1, expr2.Poly1), CasPolynomial.PolyProd(expr1.Poly2, expr2.Poly1)));
}
public static CasPolynomial PolyProd(CasPolynomial poly1, CasPolynomial poly2)
{
CasPolynomial res = new CasPolynomial();
foreach (var t1 in poly1.Terms)
{
foreach (var t2 in poly2.Terms)
{
res.Terms.Add(CasTerm.TermProduct(t1, t2));
}
}
res.Simplify();
return(res);
}
public static CasPolynomial PolySum(CasPolynomial poly1, CasPolynomial poly2)
{
CasPolynomial res = new CasPolynomial();
foreach (var t in poly1.Terms)
{
res.Terms.Add(t);
}
foreach (var t in poly2.Terms)
{
res.Terms.Add(t);
}
res.Simplify();
return(res);
}
public CasExpr Add(CasExpr expr1, CasExpr expr2)
{
if (expr1.Poly2.PolyEquals(expr2.Poly2))
{
return(new CasExpr(CasPolynomial.PolySum(expr1.Poly1, expr2.Poly1), expr2.Poly2));
}
else
{
var p1 = CasPolynomial.PolyProd(expr1.Poly1, expr2.Poly2);
var p2 = CasPolynomial.PolyProd(expr1.Poly2, expr2.Poly1);
var num = CasPolynomial.PolySum(p1, p2);
var denom = CasPolynomial.PolyProd(expr1.Poly2, expr2.Poly2);
return(new CasExpr(num, denom));
}
}
public bool PolyEquals(CasPolynomial poly)
{
HashSet <string> terms = new HashSet <string>();
foreach (var t in poly.Terms)
{
terms.Add(t.ToString());
}
foreach (var t in Terms)
{
if (!terms.Contains(t.ToString()))
{
return(false);
}
terms.Remove(t.ToString());
}
return(terms.Count == 0);
}
public CasExpr Substitute(CasExpr expr, CasVar forV)
{
if (!ContainsVar(forV))
{
return(new CasExpr(this, CasPolynomial.ConstantPoly(1)));
}
List <CasExpr> exprs = new List <CasExpr>();
foreach (var t in Terms)
{
exprs.Add(t.Substitute(expr, forV));
}
var sum = CasExpr.ConstantExpr(0);
foreach (var e in exprs)
{
sum = CasSystem.Instance.Add(sum, e);
}
return(sum);
}
// Result is null if solver fails
public CasExpr MakeZero(CasExpr expr, CasVar v)
{
List <CasTerm> zeroTerms = new List <CasTerm>();
List <CasTerm> oneTerms = new List <CasTerm>();
foreach (var t in expr.Poly1.Terms)
{
if (!t.Variables.ContainsKey(v))
{
zeroTerms.Add(t);
}
else if (t.Variables[v] == 1)
{
oneTerms.Add(t);
}
else
{
return(null);
}
}
if (oneTerms.Count == 0)
{
return(null);
}
CasPolynomial poly1 = new CasPolynomial();
CasPolynomial poly2 = new CasPolynomial();
foreach (var t in zeroTerms)
{
poly1.Terms.Add(t.CopyWithCoefficient(-1 * t.Coefficient));
}
foreach (var t in oneTerms)
{
poly2.Terms.Add(t.CopyWithCoefficient(t.Coefficient));
}
foreach (var t in poly2.Terms)
{
t.Variables.Remove(v);
}
return(new CasExpr(poly1, poly2));
}
public static CasExpr ConstantExpr(int c)
{
return(new CasExpr(CasPolynomial.ConstantPoly(c), CasPolynomial.ConstantPoly(1)));
}
// Result is null if solver fails
public Tuple <CasExpr, CasVar> Solve(CasExpr expr, CasVar forV)
{
if (expr.Poly1.ContainsVar(forV) && expr.Poly2.ContainsVar(forV))
{
return(null);
}
if (!expr.Poly1.ContainsVar(forV) && !expr.Poly2.ContainsVar(forV))
{
return(null);
}
if (expr.Poly1.ContainsVar(forV) && !expr.Poly2.ContainsVar(forV))
{
List <CasTerm> zeroTerms = new List <CasTerm>();
List <CasTerm> oneTerms = new List <CasTerm>();
foreach (var t in expr.Poly1.Terms)
{
if (!t.Variables.ContainsKey(forV))
{
zeroTerms.Add(t);
}
else if (t.Variables[forV] == 1)
{
oneTerms.Add(t);
}
else
{
return(null);
}
}
if (oneTerms.Count == 0)
{
return(null);
}
CasPolynomial polyZeros = new CasPolynomial();
CasPolynomial polyOnes = new CasPolynomial();
foreach (var t in zeroTerms)
{
polyZeros.Terms.Add(t.CopyWithCoefficient(-1 * t.Coefficient));
}
foreach (var t in oneTerms)
{
polyOnes.Terms.Add(t.CopyWithCoefficient(t.Coefficient));
t.Variables.Remove(forV);
}
var newVar = NewVar();
var newTerm = new CasTerm(1);
newTerm.Variables[newVar] = 1;
polyZeros.Terms.Add(newTerm);
var resExpr = new CasExpr(CasPolynomial.PolyProd(polyZeros, expr.Poly2), polyOnes);
return(new Tuple <CasExpr, CasVar>(resExpr, newVar));
}
else
{
List <CasTerm> zeroTerms = new List <CasTerm>();
List <CasTerm> oneTerms = new List <CasTerm>();
foreach (var t in expr.Poly2.Terms)
{
if (!t.Variables.ContainsKey(forV))
{
zeroTerms.Add(t);
}
else if (t.Variables[forV] == 1)
{
oneTerms.Add(t);
}
else
{
return(null);
}
}
if (oneTerms.Count == 0)
{
return(null);
}
CasPolynomial polyZeros = new CasPolynomial();
CasPolynomial polyOnes = new CasPolynomial();
var newVar = NewVar();
foreach (var t in zeroTerms)
{
polyZeros.Terms.Add(t.CopyWithCoefficient(-1 * t.Coefficient));
t.Variables[newVar] = 1;
}
foreach (var t in oneTerms)
{
polyOnes.Terms.Add(t.CopyWithCoefficient(t.Coefficient));
t.Variables.Remove(forV);
t.Variables[newVar] = 1;
}
var resExpr = new CasExpr(CasPolynomial.PolySum(polyZeros, expr.Poly2), polyOnes);
return(new Tuple <CasExpr, CasVar>(resExpr, newVar));
}
}
