64 lines
1.9 KiB
C
64 lines
1.9 KiB
C
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class Q
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{
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public:
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typedef linear_combination<Q> linear_combination;
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// typedef linear_combination_iter<Q> linear_combination_iter;
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typedef linear_combination_const_iter<Q> linear_combination_const_iter;
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private:
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int n;
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unsigned d;
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void reduce ();
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public:
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Q () : n(0), d(1) { }
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Q (int x) : n(x), d(1) { }
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Q (int n_, unsigned d_) : n(n_), d(d_) { assert (d != 0); reduce (); }
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Q (const Q &q) : n(q.n), d(q.d) { }
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~Q () { }
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Q &operator = (const Q &q) { n = q.n; d = q.d; return *this; }
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Q &operator = (int x) { n = x; d = 1; return *this; }
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bool operator == (const Q &q) const { return n == q.n && d == q.d; }
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bool operator == (int x) const { return n == x && d == 1; }
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bool operator != (int x) const { return !operator == (x); }
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bool is_unit () const { return n != 0; }
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Q operator + (const Q &x) const { return Q (n*x.d + x.n*d, d*x.d); }
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Q operator - (const Q &x) const { return Q (n*x.d - x.n*d, d*x.d); }
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Q operator * (const Q &x) const { return Q (n*x.n, d*x.d); }
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Q operator / (const Q &x) const { return operator * (x.recip ()); }
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Q recip () const
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{
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assert (is_unit ());
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if (n < 0)
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return Q (-d, -n);
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else
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return Q (d, n);
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}
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Q &operator += (const Q &x) { n = n*x.d + x.n*d; d *= x.d; reduce (); return *this; }
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Q &operator -= (const Q &x) { n = n*x.d - x.n*d; d *= x.d; reduce (); return *this; }
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Q &operator *= (const Q &x) { n *= x.n; d *= x.d; reduce (); return *this; }
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Q &operator /= (const Q &x) { return operator *= (x.recip ()); }
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bool divides (const Q &q) const { return (n != 0) || (q.n == 0); }
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bool operator | (const Q &q) const { return divides (q); }
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Q gcd (const Q &q) const
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{
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assert (n != 0 && q.n != 0);
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return Q (1);
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}
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static void show_ring () { printf ("Q"); }
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void show_self () const;
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void display_self () const { show_self (); newline (); }
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};
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