ring.cpp

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// Copyright 1995-2020 Michael E. Stillman
 
#include "ring.hpp"
 
#include "ZZ.hpp"          // for RingZZ
#include "coeffrings.hpp"  // for CoefficientRingR
#include "exceptions.hpp"  // for exc::engine_error
#include "freemod.hpp"     // for FreeModule
#include "monoid.hpp"      // for Monoid
#include "poly.hpp"        // for PolyRing
#include "polyring.hpp"    // for PolynomialRing
 
const Monoid *Ring::degree_monoid() const { return degree_ring->getMonoid(); }
#if 1
RingZZ *makeIntegerRing() { return new RingZZ; }
#endif
#if 0
ARingZZ* makeIntegerRing()
{
  return new M2::ConcreteRing<M2::ARingZZ>;
}
#endif
 
const CoefficientRingR *Ring::getCoefficientRingR() const
{
  if (cR == nullptr) cR = new CoefficientRingR(this);
  return cR;
}
 
void Ring::initialize_ring(long P0,
                           const PolynomialRing *DR,
                           const std::vector<int> &heft_vector)
{
  // Remember: if this is a poly ring, the ring is K[M].
  // If this is a basic routine, K = this, M = trivial monoid.
  // If this is a frac field, K = R, M = trivial monoid.
  mCharacteristic = P0;
  if (DR == nullptr)
    degree_ring = PolyRing::get_trivial_poly_ring();
  else
    degree_ring = DR;
  mHeftVector = heft_vector;
 
  _non_unit = ZERO_RINGELEM;
  _isfield = 0;
 
  zeroV = ZERO_RINGELEM;
  oneV = ZERO_RINGELEM;
  minus_oneV = ZERO_RINGELEM;
}
 
Ring::~Ring() {}
FreeModule *Ring::make_FreeModule() const
{
  return new FreeModule(this, 0, false);
}
 
FreeModule *Ring::make_Schreyer_FreeModule() const
{
  return new FreeModule(this, 0, true);
}
 
FreeModule *Ring::make_FreeModule(int n) const
{
  return new FreeModule(this, n, false);
}
 
bool Ring::is_field() const { return _isfield == 1; }
bool Ring::declare_field()
{
  if (_isfield >= 0)
    {
      _isfield = 1;
      return true;
    }
  else
    {
      ERROR("attempting to declare a ring with known non-units to be a field");
      return false;
    }
}
ring_elem Ring::get_non_unit() const
{
  if (_isfield >= 0) return zero();
  return copy(_non_unit);
}
 
void Ring::set_non_unit(ring_elem non_unit) const
{
  bool was_field = (_isfield == 1);
  const_cast<Ring *>(this)->_isfield = -1;
  const_cast<Ring *>(this)->_non_unit = non_unit;
  if (was_field)
    throw exc::engine_error("a non unit was found in a ring declared to be a field");
}
 
ring_elem Ring::var(int v) const
{
  (void) v;
  // The default behavior is to just return 0.
  return zeroV;
}

//
//  The method used is successive squaring.
//  Which classes actually use this?
ring_elem Ring::power(const ring_elem gg, mpz_srcptr m) const
{
  ring_elem ff = gg;
  int cmp = mpz_sgn(m);  // the sign of m, <0, ==0, >0
  if (cmp == 0) return one();
  mpz_t n;
  mpz_init_set(n, m);
  // @TODO MES: rewrite this so it inverts before creating n.
  // That way we don't have to catch any exceptions here.
  // e.g. as
#if 0  
  if (cmp < 0)
    ff = invert(ff);
  mpz_init_set(n, m);
  mpz_t n;
  if (cmp < 0)
    mpz_neg(n, n);
#endif
  if (cmp < 0)
    {
      mpz_neg(n, n);
      ff = invert(
          ff);  // this can raise an exception, in which case we need to free n.
      if (is_zero(ff))
        {
          ERROR(
              "either element not invertible, or no method available to "
              "compute its inverse");
          mpz_clear(n);
          return ff;
        }
    }
  ring_elem prod = from_long(1);
  ring_elem base = copy(ff);
  ring_elem tmp;
 
  for (;;)
    {
      if (RingZZ::mod_ui(n, 2) == 1)
        {
          tmp = mult(prod, base);
          prod = tmp;
        }
      mpz_tdiv_q_2exp(n, n, 1);
      if (mpz_sgn(n) == 0)
        {
          mpz_clear(n);
          return prod;
        }
      else
        {
          tmp = mult(base, base);
          base = tmp;
        }
    }
}
 
ring_elem Ring::power(const ring_elem gg, int n) const
{
  // TODO: reorganize to match the above routine (but using an int).
  ring_elem ff = gg;
  if (n == 0) return one();
  if (n < 0)
    {
      n = -n;
      ff = invert(ff);
      if (is_zero(ff))
        {
          ERROR("negative power of noninvertible element requested");
          return ff;
        }
    }
 
  // The exponent 'n' should be > 0 here.
  ring_elem prod = from_long(1);
  ring_elem base = copy(ff);
  ring_elem tmp;
 
  for (;;)
    {
      if ((n % 2) != 0)
        {
          tmp = mult(prod, base);
          prod = tmp;
        }
      n >>= 1;
      if (n == 0) { return prod; }
      else
        {
          tmp = mult(base, base);
          base = tmp;
        }
    }
}
 
void Ring::mult_to(ring_elem &f, const ring_elem g) const { f = mult(f, g); }
void Ring::add_to(ring_elem &f, const ring_elem &g) const { f = add(f, g); }
void Ring::subtract_to(ring_elem &f, const ring_elem &g) const
{
  f = subtract(f, g);
}
void Ring::negate_to(ring_elem &f) const { f = negate(f); }
ring_elem Ring::remainder(const ring_elem f, const ring_elem g) const
{
  if (is_zero(g)) return f;
  return zero();
}
 
ring_elem Ring::quotient(const ring_elem f, const ring_elem g) const
{
  if (is_zero(g)) return g;
  return divide(f, g);
}
 
ring_elem Ring::remainderAndQuotient(const ring_elem f,
                                     const ring_elem g,
                                     ring_elem &quot) const
{
  if (is_zero(g))
    {
      quot = g;  // zero
      return f;
    }
  quot = divide(f, g);
  return zero();
}
 
std::pair<bool, long> Ring::coerceToLongInteger(ring_elem a) const
{
  (void) a;
  return std::pair<bool, long>(false,
                               0);  // the default is that it cannot be lifted.
}
 
bool Ring::from_BigComplex(gmp_CC z, ring_elem &result) const
{
  (void) z;
  result = from_long(0);
  return false;
}
 
bool Ring::from_BigReal(gmp_RR z, ring_elem &result) const
{
  (void) z;
  result = from_long(0);
  return false;
}
 
bool Ring::from_Interval(gmp_RRi z, ring_elem &result) const
{
  (void) z;
  result = from_long(0);
  return false;
}
 
bool Ring::from_ComplexInterval(gmp_CCi z, ring_elem &result) const
{
  result = from_long(0);
  return false;
}
 
bool Ring::from_double(double a, ring_elem &result) const
{
  (void) a;
  result = from_long(0);
  return false;
}
bool Ring::from_complex_double(double re, double im, ring_elem &result) const
{
  (void) re;
  (void) im;
  result = from_long(0);
  return false;
}
 
ring_elem Ring::random() const
{
  ERROR("random scalar elements for this ring are not implemented");
  return 0;
}
 
ring_elem Ring::preferred_associate(ring_elem f) const
{
  // Here we assume that 'this' is a field:
  if (is_zero(f)) return from_long(1);
  return invert(f);
}
 
bool Ring::lower_associate_divisor(ring_elem &f, const ring_elem g) const
// Implementation for a basic ring
{
  if (is_zero(f))
    {
      f = g;
      return !is_zero(f);
    }
  return true;
}
 
void Ring::lower_content(ring_elem &result, ring_elem g) const
// default implementation
{
  // The default implementation here ASSUMES that result and g are in the same
  // ring!
  if (is_zero(result)) result = g;
}
 
ring_elem Ring::content(ring_elem f) const
// default implementation
{
  return f;
}
 
ring_elem Ring::content(ring_elem f, ring_elem g) const
// default implementation
{
  lower_content(f, g);
  return f;
}
 
ring_elem Ring::divide_by_given_content(ring_elem f, ring_elem c) const
// default implementation
{
  // The default implementation here ASSUMES that f and c are in the same ring!
  return divide(f, c);
}
 
ring_elem Ring::divide_by_content(ring_elem f) const
{
  ring_elem c = content(f);
  return divide_by_given_content(f, c);
}
 
ring_elem Ring::split_off_content(ring_elem f, ring_elem &result) const
{
  ring_elem c = content(f);
  result = divide_by_given_content(f, c);
  return c;
}
 
void Ring::monomial_divisor(const ring_elem a, exponents_t exp) const
{
  (void) a;
  (void) exp;
}
 
ring_elem Ring::diff(ring_elem a, ring_elem b, int use_coeff) const
{
  (void) use_coeff;
  return mult(a, b);
}
 
bool Ring::in_subring(int nslots, const ring_elem a) const
{
  (void) nslots;
  (void) a;
  return true;
}
 
void Ring::degree_of_var(int n, const ring_elem a, int &lo, int &hi) const
{
  (void) n;
  (void) a;
  lo = 0;
  hi = 0;
}
 
ring_elem Ring::divide_by_var(int n, int d, const ring_elem a) const
{
  (void) n;
  if (d == 0) return a;
  return from_long(0);
}
 
ring_elem Ring::divide_by_expvector(const_exponents exp, const ring_elem a) const
{
  (void) exp;
  return a;
}
 
ring_elem Ring::homogenize(const ring_elem f,
                           int,
                           int deg,
                           const std::vector<int> &) const
{
  if (deg != 0) ERROR("homogenize: no homogenization exists");
  return f;
}
 
ring_elem Ring::homogenize(const ring_elem f,
                           int,
                           const std::vector<int> &) const
{
  return f;
}
 
bool Ring::is_homogeneous(const ring_elem) const { return true; }
 
bool Ring::multi_degree(const ring_elem f, monomial d) const
// returns true iff f is homogeneous
{
  (void) f;
  degree_monoid()->one(d);
  return true;
}
 
void Ring::degree_weights(const ring_elem,
                          const std::vector<int> &,
                          int &lo,
                          int &hi) const
{
  lo = hi = 0;
}
 
int Ring::index_of_var(const ring_elem a) const
{
  (void) a;
  return -1;
}
 
M2_arrayint Ring::support(const ring_elem a) const
{
  (void) a;
  M2_arrayint result = M2_makearrayint(0);
  return result;
}
 
// These next three routines are only overridden by RRR,CCC,polynomial rings,
// and quotient rings
unsigned long Ring::get_precision() const { return 0; }
ring_elem Ring::zeroize_tiny(gmp_RR epsilon, const ring_elem f) const
// Default is to return f itself.
{
  (void) epsilon;
  return f;
}
 
void Ring::increase_maxnorm(gmp_RRmutable norm, const ring_elem f) const
// If any real number appearing in f has larger absolute value than norm,
// replace norm.
{
  // Default for rings not over RRR or CCC is to do nothing.
  (void) norm;
  (void) f;
}

// SumCollector: default version //
class SumCollectorDefault : public SumCollector
{
  const Ring *R;
  ring_elem result;
 
 public:
  SumCollectorDefault(const Ring *R0) : R(R0), result(R->zero()) {}
  virtual ~SumCollectorDefault() {}
  virtual void add(ring_elem f) { R->add_to(result, f); }
  virtual ring_elem getValue()
  {
    ring_elem val = result;
    result = R->zero();
    return val;
  }
};
 
SumCollector *Ring::make_SumCollector() const
{
  return new SumCollectorDefault(this);
}
 
// Local Variables:
// compile-command: "make -C $M2BUILDDIR/Macaulay2/e "
// indent-tabs-mode: nil
// End: