#ifndef __FIELD_ARITHMETIC_H__
#define __FIELD_ARITHMETIC_H__
#include <vector>
#include <gmpxx.h>
class ZpField
{
public:
typedef int Element;
ZpField(Element p = 2);
Element id() const { return 1; }
Element zero() const { return 0; }
Element neg(Element a) const { return p_ - a; }
Element add(Element a, Element b) const { return (a+b) % p_; }
Element inv(Element a) const { return inverses_[a]; }
Element mul(Element a, Element b) const { return (a*b) % p_; }
Element div(Element a, Element b) const { return mul(a, inv(b)); }
bool is_zero(Element a) const { return (a % p_) == 0; }
private:
Element p_;
std::vector<Element> inverses_;
};
ZpField::
ZpField(Element p):
p_(p), inverses_(p_)
{
for (Element i = 1; i < p_; ++i)
for (Element j = 1; j < p_; ++j)
if (mul(i,j) == 1)
{
inverses_[i] = j;
break;
}
}
class QField
{
public:
typedef mpq_class Element;
QField() {}
Element id() const { return 1; }
Element zero() const { return 0; }
Element neg(Element a) const { return -a; }
Element add(Element a, Element b) const { return (a+b); }
Element inv(Element a) const { return id()/a; }
Element mul(Element a, Element b) const { return (a*b); }
Element div(Element a, Element b) const { return a/b; }
bool is_zero(Element a) const { return a == 0; }
};
#endif // __FIELD_ARITHMETIC_H__