public static CasTerm TermProduct(CasTerm term1, CasTerm term2)
{
var res = new CasTerm(term1.Coefficient * term2.Coefficient);
foreach (var v in term1.Variables.Keys)
{
if (res.Variables.ContainsKey(v))
{
res.Variables[v] += term1.Variables[v];
}
else
{
res.Variables[v] = term1.Variables[v];
}
}
foreach (var v in term2.Variables.Keys)
{
if (res.Variables.ContainsKey(v))
{
res.Variables[v] += term2.Variables[v];
}
else
{
res.Variables[v] = term2.Variables[v];
}
}
res.Simplify();
return(res);
}
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 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 CasTerm CopyWithCoefficient(int c)
{
if (c == Coefficient)
{
return(this);
}
var copy = new CasTerm(c);
foreach (var v in Variables)
{
copy.Variables[v.Key] = v.Value;
}
return(copy);
}
// 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));
}
}
