skewpoly.hpp

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// Copyright 2003 Michael E. Stillman
 
#ifndef _skewpoly_hh_
#define _skewpoly_hh_

 
#include "poly.hpp"


class SkewPolynomialRing : public PolyRing
{
  bool initialize_skew(M2_arrayint skewvars);
 
  SkewPolynomialRing() {}
  virtual ~SkewPolynomialRing();
 
 public:
  static SkewPolynomialRing *create(const Ring *K,
                                    const Monoid *M,
                                    M2_arrayint skewvars);
 
  void text_out(buffer &o) const;
 
  virtual bool has_gcd() const { return false; }
  virtual bool is_skew_commutative_ring() const { return true; }
  virtual bool is_commutative_ring() const { return false; }
  virtual const SkewPolynomialRing *cast_to_SkewPolynomialRing() const
  {
    return this;
  }
  virtual SkewPolynomialRing *cast_to_SkewPolynomialRing() { return this; }
  virtual ring_elem power(const ring_elem f, mpz_srcptr n) const;
  virtual ring_elem power(const ring_elem f, int n) const;
 
  // antipode: implements the isomorphism of R and the opposite of R
  // this is done by multiplying every monomial of f which has degree
  // d (in the skew commuting variables) by (-1)^(d choose 2).
  ring_elem antipode(const ring_elem f) const;
 
 protected:
  virtual ring_elem mult_by_term(const ring_elem f,
                                 const ring_elem c,
                                 const int *m) const;
};
#endif
 
// Local Variables:
// compile-command: "make -C $M2BUILDDIR/Macaulay2/e "
// indent-tabs-mode: nil
// End: