public poly substitudeY(poly y_x)
{
for (int i = 0; i < y_x.count; i++)
{
if (y_x.terms[i].yp > 0)
{
throw new Exception("y_x is not a function of x!");
}
}
poly temp = new poly();
temp.addTerm(this);
for (int i = 0; i < yp; i++)
{
for (int j = 0; j < temp.count; j++)
{
temp.terms[j].yp--;
}
temp *= y_x;
}
for (int i = 0; i < temp.count; i++)
{
if (temp.terms[i].yp > 0)
{
throw new Exception("yp > 0 after substitude!");
}
}
return(temp);
}
public poly substitudeX(poly x_y)
{
for (int i = 0; i < x_y.count; i++)
{
if (x_y.terms[i].xp > 0)
{
throw new Exception("x_y is not a function of x!");
}
}
poly temp = new poly();
temp.addTerm(this);
for (int i = 0; i < xp; i++)
{
for (int j = 0; j < temp.count; j++)
{
temp.terms[j].xp--;
}
temp *= x_y;
}
for (int i = 0; i < temp.count; i++)
{
if (temp.terms[i].xp > 0)
{
throw new Exception("xp > 0 after substitude!");
}
}
return(temp);
}
public void extend(poly p)
{
for (int i = 0; i < p.count; i++)
{
this.addTerm(p.terms[i]);
}
}
public static poly operator +(poly p1, poly p2)
{
poly a = new poly();
a.extend(p1);
a.extend(p2);
return(a);
}
public poly(poly p)
{
count = p.count;
for (int i = 0; i < count; i++)
{
terms[i] = new term(p.terms[i]);
}
}
public static poly operator -(poly p1, poly p2)
{
poly a = new poly();
term neg = new term(-1);
a.extend(p1);
a.extend(neg * p2);
return(a);
}
public static poly operator *(poly p1, poly p2)
{
poly result = new poly();
for (int i = 0; i < p1.count; i++)
{
result += p1.terms[i] * p2;
}
return(result);
}
public static poly operator *(poly p, term t)
{
poly result = new poly(p);
for (int i = 0; i < p.count; i++)
{
result.terms[i] *= t;
}
return(result);
}
public poly integralY()
{
poly temp = new poly();
for (int i = 0; i < count; i++)
{
temp.addTerm(terms[i].integralY());
}
return(temp);
}
public poly substitudeX(poly x_y)
{
poly temp = new poly();
for (int i = 0; i < count; i++)
{
temp += terms[i].substitudeX(x_y);
}
return(temp);
}
public poly substitudeY(poly y_x)
{
poly temp = new poly();
for (int i = 0; i < count; i++)
{
temp += terms[i].substitudeY(y_x);
}
return(temp);
}
static poly pol(int[,] termData)
{
poly p = new poly();
for (int i = 0; i < termData.GetLength(0); i++)
{
p.addTerm(ter(termData[i, 0], termData[i, 1], termData[i, 2]));
}
return(p);
}
static void test2()
{
poly f = pol(ter(2, 2, 1));
poly z = pol(new int[, ] {
{ 4, 0, 0 }, { -1, 2, 0 }, { -1, 0, 2 }
});
f.extend(pol(ter(2, 0, 2)) * z);
f.extend(pol(ter(1, 1, 0)) * z);
doubleItgYX(f, pol(ter(0)), pol(ter(1)), fra(0), fra(1)).print();
}
static void test()
{
poly f = pol(new int[, ] {
{ 1, 1, 0 }, { 1, 0, 1 }
});
poly x = new poly(ter(fra(1, 6), 1));
poly y_x1 = pol(new int[, ] {
{ 3, 0, 0 }, { -1, 1, 0 }
});
poly y_x0 = new poly(ter(fra(1, 2), 1));
doubleItgYX(x * f, y_x0, y_x1, fra(0), fra(2)).print();
}
static frac doubleItgYX(poly f, poly y_x0, poly y_x1, frac x0, frac x1)
{
frac res = new frac(0);
f.print();
poly iy_f = f.integralY();
iy_f.print();
poly f_x = iy_f.substitudeY(y_x1) - iy_f.substitudeY(y_x0);
f_x.print();
poly F = f_x.integralX();
F.print();
res = F.value(x1, new frac(0)) - F.value(x0, new frac(0));
return(res);
}
