113 lines
2.4 KiB
C++
113 lines
2.4 KiB
C++
|
|
template<unsigned p>
|
|
class Zp
|
|
{
|
|
public:
|
|
typedef ::linear_combination<Zp<p> > linear_combination;
|
|
typedef ::linear_combination_const_iter<Zp<p> > linear_combination_const_iter;
|
|
|
|
private:
|
|
unsigned v;
|
|
|
|
public:
|
|
Zp () : v(0) { }
|
|
Zp (unsigned init) : v(init % p) { }
|
|
Zp (int init)
|
|
{
|
|
int i = init % (int)p;
|
|
if (i < 0)
|
|
i += p;
|
|
assert (i >= 0 && i < (int)p);
|
|
v = i;
|
|
}
|
|
|
|
Zp (const Zp &x) : v(x.v) { }
|
|
Zp (copy, const Zp &x) : v(x.v) { }
|
|
~Zp () { }
|
|
|
|
Zp &operator = (const Zp &x) { v = x.v; return *this; }
|
|
Zp &operator = (int x)
|
|
{
|
|
return operator = (Zp (x));
|
|
}
|
|
|
|
bool operator == (const Zp &x) const { return v == x.v; }
|
|
|
|
bool operator == (int x) const { return operator == (Zp (x)); }
|
|
bool operator != (int x) const { return !operator == (x); }
|
|
|
|
bool operator < (const Zp &x) const { return v < x.v; }
|
|
|
|
bool is_unit () const
|
|
{
|
|
return v != 0;
|
|
}
|
|
|
|
Zp operator + (const Zp &x) const { return Zp (v + x.v); }
|
|
Zp operator - (const Zp &x) const { return Zp ((int)v - (int)x.v); }
|
|
Zp operator - () const { return Zp (- (int)v); }
|
|
|
|
Zp operator * (const Zp &x) const { return Zp (v * x.v); }
|
|
|
|
Zp operator / (const Zp &x) const
|
|
{
|
|
return operator * (x.recip ());
|
|
}
|
|
|
|
Zp recip () const
|
|
{
|
|
triple<unsigned, int, int> t = unsigned_extended_gcd (v, p);
|
|
assert (t.first == 1);
|
|
assert ((int)t.first == t.second*(int)v + t.third*(int)p);
|
|
|
|
return Zp (t.second);
|
|
}
|
|
|
|
Zp &operator += (const Zp &x)
|
|
{
|
|
v = (v + x.v) % p;
|
|
return *this;
|
|
}
|
|
|
|
Zp &operator -= (const Zp &x) { return operator = (Zp ((int)v - (int)x.v)); }
|
|
|
|
Zp &operator *= (const Zp &x)
|
|
{
|
|
v = (v * x.v) % p;
|
|
return *this;
|
|
}
|
|
|
|
Zp &operator /= (const Zp &x)
|
|
{
|
|
return operator *= (x.recip ());
|
|
}
|
|
|
|
// d | n, d.divides (n)
|
|
bool divides (const Zp &n) const
|
|
{
|
|
return v || !n.v;
|
|
}
|
|
|
|
bool operator | (const Zp &n) const { return divides (n); }
|
|
|
|
Zp div (const Zp &d) const { return operator / (d); }
|
|
|
|
triple<Zp, Zp, Zp> extended_gcd (const Zp &x) const
|
|
{
|
|
if (v)
|
|
return triple<Zp, Zp, Zp> (v, 1, 0);
|
|
else
|
|
return triple<Zp, Zp, Zp> (x, 0, 1);
|
|
}
|
|
|
|
Zp gcd (const Zp &x) const
|
|
{
|
|
assert (v || x.v);
|
|
return 1;
|
|
}
|
|
|
|
static void show_ring () { printf ("Z%d", p); }
|
|
void show_self () const { printf ("%d (%d)", v, p); }
|
|
void display_self () const { show_self (); newline (); }
|
|
};
|