Аналитический вид производной математического выражения произвольного порядка

//---------------------------------------------------------------------------
 
#include <vcl.h>
#include<math.h>
#pragma hdrstop
 
#include "Unit1.h"
//---------------------------------------------------------------------------
#pragma package(smart_init)
#pragma resource "*.dfm"
TForm1 *Form1;
//---------------------------------------------------------------------------
class Telement {
protected:
Telement *left, *right;
Telement (Telement* L,Telement* R){
left = L; right = R;
}
public:
~Telement(void) {delete left; delete right;}
virtual double rezult(void) = 0;
virtual Telement* copy(void) = 0;
virtual Telement* differ(void) = 0;
virtual void set_var(double X){
if (left)  left -> set_var(X);
if (right) right -> set_var(X);
}
};
//---------------------------------------------------------------------------
class Real : public Telement{
double f;
public:
Real(double F):Telement(NULL,NULL){f=F;}
double rezult(void) {return f; }
Telement* copy (void){return new Real(f);}
Telement* differ(void){return new Real(0);}
};
//---------------------------------------------------------------------------
class Var :public Telement{
double x;
public:
Var(double X = 0):Telement(NULL, NULL){x = X;}
double rezult(void){return x;}
Telement* copy(void){return new Var(x);}
Telement* differ(void){return new Real(1.0);}
void set_var(double X) {x = X;}
};
//---------------------------------------------------------------------------
struct Plus:public Telement{
Plus(Telement* L,Telement* R):Telement(L, R){};
double rezult(void) { return left -> rezult() + right -> rezult();}
Telement* copy(void) {return new Plus(left -> copy(), right -> copy());}
Telement* differ(void) { return new Plus(left -> differ(),right -> differ());}
};
//---------------------------------------------------------------------------
struct Minus:public Telement{
Minus(Telement* L,Telement* R):Telement(L, R){};
double rezult(void) {return left->rezult() - right->rezult();}
Telement* copy(void) {return new Minus(left->copy(), right->copy());}
Telement* differ(void) {return new Minus(left->differ(), right->differ());}
};
//--------------------------------------------------------------------------------
struct Mult:public Telement{
Mult(Telement* L, Telement* R):Telement(L, R){};
double rezult(void){return left->rezult()*right->rezult();}
Telement* copy(void){return new Mult(left->copy(),right->copy());}
Telement* differ(void){return new Plus(new Mult( left->differ(), right->copy()),
new Mult( left->copy(), right->differ()));}
};
//-------------------------------------------------------------------------------
struct Div:public Telement{
Div(Telement* L,Telement* R):Telement(L, R) {};
double rezult(void){return left->rezult() / right->rezult();}
Telement* copy(void){return new Div(left->copy(), right->copy());}
Telement* differ(void){
return new Div( new Minus(new Mult(left->differ(), right->copy()),
new Mult(left->copy(), right->differ())),
new Mult( right->copy(), right->copy()));
}
};
//---------------------------------------------------------------------------
int PosFromEnd(AnsiString s, AnsiString sub);
Telement* form(AnsiString s){
Telement* h;
int i,p,l = s.Length();
AnsiString s1, s2;
// Аналізуємо справа наліво:
    if ((p = PosFromEnd(s,"+")) > 1){   // Якщо натрапляємо на "+"
s1 =s.SubString(1, p - 1);
s2 =s.SubString(p+1, l-p);
        h = new Plus(form(s1), form(s2));   // Створюємо вершину Plus
}
else if ((p = PosFromEnd(s,"-")) > 1){     // Якщо натрапляємо на "-"
s1 =s.SubString(1, p - 1);
s2 = s.SubString(p+1, l-p);
h = new Minus(form(s1), form(s2));      // Створюємо вершину Minus
}
else if ((p = PosFromEnd(s, "*")) > 1){   // Якщо натрапляємо на "*"
s1 = s.SubString(1, p - 1);
s2 = s.SubString(p+1, l-p);
h = new Mult(form(s1), form(s2));    // Створюємо вершину Mult.
}
else if ((p = PosFromEnd(s,"/")) > 1){       // Якщо натрапляємо на "/"
s1 =s.SubString(1, p-1);
s2 = s.SubString(p + 1,l - p);
h = new Div(form(s1), form(s2)); // Створюємо вершину Div
}
else if (s == "x") h = new Var(); // Створюємо вершину Var
else h = new Real(StrToFloat(s)); // Створюємо Real
return h;
}
//---------------------------------------------------------------------------
int PosFromEnd(AnsiString s, AnsiString sub){
int l = s.Length();
AnsiString p;
p.SetLength(l);
for(int i = 1;i<=l;i++)
p[ (l - i) + 1] = s[i];        // Обертаємо рядок
if (p.Pos(sub) > 0)
return l - p.Pos(sub) + 1;
else return 0;
}
//---------------------------------------------------------------------------
__fastcall TForm1::TForm1(TComponent* Owner)
    : TForm(Owner)
{
}
//---------------------------------------------------------------------------
void __fastcall TForm1::Button1Click(TObject *Sender)
{
Telement*x = form(Edit1->Text);
Telement* f = form(Edit2->Text);
Telement* f1 = f -> differ();
Telement* f2 = f1 -> differ();
double X = x -> rezult();
f -> set_var( X);
f1 -> set_var( X);
f2 -> set_var( X);
int precision = 15;
int digits = StrToFloat(ComboBox1->Text);
Edit3 -> Text = FloatToStrF( x -> rezult(), ffFixed, precision, digits);
Edit4 -> Text = FloatToStrF( f -> rezult(), ffFixed, precision, digits);
Edit5 -> Text = FloatToStrF( f1 -> rezult(), ffFixed, precision, digits);
Edit6 -> Text = FloatToStrF( f2 -> rezult(), ffFixed, precision, digits);
}
//---------------------------------------------------------------------------
void __fastcall TForm1::ComboBox1Change(TObject *Sender)
{
Button1Click(Button1);
}
//---------------------------------------------------------------------------
void __fastcall TForm1::Button2Click(TObject *Sender)
{
Form1->Close();
}
//---------------------------------------------------------------------------
void __fastcall TForm1::Edit1KeyPress(TObject *Sender, char &Key)
{
if ((Key>='0')&&(Key<='9'))
    return;
if ((Key=='x'))
    return;
if ((Key=='+')||(Key=='*')||(Key=='-')||(Key=='/'))
    return;
if (Key==VK_BACK)
    return;
if (Key==VK_RETURN) {
    if (((TEdit*)Sender)->Name == "Edit1") Edit2->SetFocus();
return;
}
Key = 0;
if ((Key == '.')||(Key == ',')) {
       Key = DecimalSeparator;
    if ( (((TEdit*)Sender)->Text).Pos(DecimalSeparator) != 0)
            Key = 0; // разделитель уже введен
    }
}
//---------------------------------------------------------------------------
void __fastcall TForm1::Edit3KeyPress(TObject *Sender, char &Key)
{
Key = 0;
}
//---------------------------------------------------------------------------
void __fastcall TForm1::Edit1Change(TObject *Sender)
{
if ((Edit1->Text.Length() == 0 ) || (Edit2->Text.Length() == 0))
    {
        Button1->Enabled = false;
    }
    else
        Button1->Enabled = true;
}
//---------------------------------------------------------------------------