126 lines
2.5 KiB
C++
126 lines
2.5 KiB
C++
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#include <knotkit.h>
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polynomial<Z2>
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polynomial<Z2>::operator * (polynomial<Z2> p) const
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{
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set<unsigned> r_coeffs;
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for (set_const_iter<unsigned> i = coeffs; i; i ++)
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for (set_const_iter<unsigned> j = p.coeffs; j; j ++)
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r_coeffs.toggle (i.val () + j.val ());
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return polynomial<Z2> (r_coeffs);
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}
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pair<polynomial<Z2>, polynomial<Z2> >
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polynomial<Z2>::divide_with_remainder (polynomial d) const
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{
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assert (d != 0);
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polynomial<Z2> r (COPY, *this);
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polynomial<Z2> q;
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unsigned d_leading_exponent = d.coeffs.tail ();
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for (;;)
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{
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if (r == 0)
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break;
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unsigned r_leading_exponent = r.coeffs.tail ();
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if (r_leading_exponent < d_leading_exponent)
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break;
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for (set_const_iter<unsigned> i = d.coeffs; i; i ++)
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r.coeffs.toggle (r_leading_exponent - d_leading_exponent + i.val ());
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q.coeffs.toggle (r_leading_exponent - d_leading_exponent);
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}
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assert (r == 0 || r.degree () < d.degree ());
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// assert (*this == q*d + r);
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return pair<polynomial<Z2>, polynomial<Z2> > (q, r);
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}
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polynomial<Z2>
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polynomial<Z2>::mod (polynomial d) const
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{
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assert (d != 0);
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polynomial<Z2> r (COPY, *this);
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unsigned d_leading_exponent = d.coeffs.tail ();
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for (;;)
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{
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if (r == 0)
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break;
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unsigned r_leading_exponent = r.coeffs.tail ();
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if (r_leading_exponent < d_leading_exponent)
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break;
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for (set_const_iter<unsigned> i = d.coeffs; i; i ++)
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r.coeffs.toggle (r_leading_exponent - d_leading_exponent + i.val ());
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}
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assert (r == 0 || r.degree () < d.degree ());
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return r;
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}
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bool
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polynomial<Z2>::divides (polynomial d) const
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{
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return mod (d) == 0;
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}
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polynomial<Z2>
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polynomial<Z2>::divide_exact (polynomial d) const
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{
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pair<polynomial<Z2>, polynomial<Z2> > qr = divide_with_remainder (d);
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assert (qr.second == 0);
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return qr.first;
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}
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polynomial<Z2>
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polynomial<Z2>::gcd (polynomial b) const
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{
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// ??? can return *this
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polynomial a = *this;
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while (b != 0)
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{
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pair<polynomial<Z2>, polynomial<Z2> > a_qr = a.divide_with_remainder (b);
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a = b;
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b = a_qr.second;
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}
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return a;
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}
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void
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polynomial<Z2>::show_self () const
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{
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unsigned first = 1;
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for (set_const_iter<unsigned> i = coeffs; i; i ++)
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{
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unsigned e = i.val ();
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if (first)
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first = 0;
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else
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printf (" + ");
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if (e == 0)
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printf ("1");
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else
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{
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if (e == 1)
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printf ("x");
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else
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printf ("x^%d", e);
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}
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}
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if (first)
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printf ("0");
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}
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