GF.hpp

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// Copyright 1995 Michael E. Stillman.
#ifndef _GF_hh_
#define _GF_hh_
 
#include "relem.hpp"


class GF : public Ring
{
  // int P; // this is defined in class Ring
  const PolynomialRing *_originalR;  // This should be the ring ((Z/p)[t])/f(t).
 
  const RingElement *_primitive_element;  // An element of K
  int _x_exponent;  // (primitive_element)^(x_exponent) = x,
                    // the given generator of K.
  int Q_;           // this is GF(Q) = GF(P^Qexp)
  int Qexp_;        // P^Qexp = Q
  int Q1_;          // Q1 = Q-1
  int _ZERO;        // = 0   is our representation of 0.
  int _ONE;         // = Q-1 is our representation of 1.
  int _MINUS_ONE;   // = (Q-1)/2 if Q odd, = ONE if Q even.
 
  int *_one_table;  // Indexed from 0..Q1
  int *_from_int_table;
 
  //  GF(const RingElement *prim);
 protected:
  GF();
  virtual ~GF();
  bool initialize_GF(const RingElement *prim);
 
 public:
  const PolynomialRing *originalR() const { return _originalR; }
  static GF *create(const RingElement *prim);
 
  int extension_degree() const { return Qexp_; }
  GF *cast_to_GF() { return this; }
  const GF *cast_to_GF() const { return this; }
  virtual bool isGaloisField() const { return true; }
  const RingElement *getMinimalPolynomial() const;
  // returns the polynomial f(t) mentioned in the def of _originalR above.
  // this is the minimal polynomial of the given generator of this ring
  // (which is not necessarily the primitive element)
  virtual const RingElement *getGenerator() const;
  virtual const RingElement *getRepresentation(const ring_elem &a) const;
 
  ring_elem get_rep(ring_elem f) const;
  // takes an element of this ring, and returns an element of _originalR->XXX()
 
  int discrete_log(ring_elem a) const;
 
  // The following are all the routines required by 'ring'
  unsigned int computeHashValue(const ring_elem a) const { return a.get_int(); }
  virtual void text_out(buffer &o) const;
 
  virtual ring_elem from_long(long n) const;
  virtual ring_elem from_int(mpz_srcptr n) const;
  virtual ring_elem var(int v) const;
  virtual bool from_rational(mpq_srcptr q, ring_elem &result) const;
  virtual bool promote(const Ring *R,
                       const ring_elem f,
                       ring_elem &result) const;
  virtual bool lift(const Ring *R, const ring_elem f, ring_elem &result) const;
 
  virtual bool is_unit(const ring_elem f) const;
  virtual bool is_zero(const ring_elem f) const;
  virtual bool is_equal(const ring_elem f, const ring_elem g) const;
  virtual int compare_elems(const ring_elem f, const ring_elem g) const;
 
  virtual ring_elem copy(const ring_elem f) const;
  virtual void remove(ring_elem &f) const;
 
private:  
  int internal_negate(int f) const;
  int internal_add(int f, int g) const;
  int internal_subtract(int f, int g) const;
 
public:  
  virtual ring_elem negate(const ring_elem f) const;
  virtual ring_elem add(const ring_elem f, const ring_elem g) const;
  virtual ring_elem subtract(const ring_elem f, const ring_elem g) const;
  virtual ring_elem mult(const ring_elem f, const ring_elem g) const;
  virtual ring_elem power(const ring_elem f, mpz_srcptr n) const;
  virtual ring_elem power(const ring_elem f, int n) const;
  virtual ring_elem invert(const ring_elem f) const;
  virtual ring_elem divide(const ring_elem f, const ring_elem g) const;
 
  virtual void syzygy(const ring_elem a,
                      const ring_elem b,
                      ring_elem &x,
                      ring_elem &y) const;
 
  virtual ring_elem random() const;
 
  virtual void elem_text_out(buffer &o,
                             const ring_elem f,
                             bool p_one = true,
                             bool p_plus = false,
                             bool p_parens = false) const;
 
  virtual ring_elem eval(const RingMap *map,
                         const ring_elem f,
                         int first_var) const;
};
 
#endif
 
// Local Variables:
// compile-command: "make -C $M2BUILDDIR/Macaulay2/e "
// indent-tabs-mode: nil
// End: