skew.cpp

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#include "skew.hpp"
 
#include "monoid.hpp"
 
SkewMultiplication::SkewMultiplication()
    : _n_vars(0), _n_skew(0), _skew_list(nullptr), _skew_exp(nullptr), skew_byte_size(0)
{
}
 
SkewMultiplication::SkewMultiplication(int nvars, int nskew, int *skew_list)
    : _n_vars(nvars), _n_skew(nskew), _skew_list(skew_list), _skew_exp(nullptr)
{
  _skew_exp = newarray_atomic_clear(bool, nvars);
  for (int v = 0; v < nskew; v++) _skew_exp[skew_list[v]] = true;
 
  skew_byte_size = EXPONENT_BYTE_SIZE(nskew);
}
 
static int sort_sign(int a, int *v1, int b, int *v2)
{
  if (a == 0 || b == 0) return 1;
  int result = 0;  // number of sign switches
  a--;
  b--;
  for (;;)
    {
      if (v1[a] < v2[b])
        {
          b--;
          if (b < 0)
            {
              return (result % 2 == 0 ? 1 : -1);
            }
        }
      else if (v1[a] > v2[b])
        {
          result += b + 1;
          a--;
          if (a < 0)
            {
              return (result % 2 == 0 ? 1 : -1);
            }
        }
      else
        return 0;
    }
}
 
int SkewMultiplication::skew_degree(const int *exp) const
// Returns the number of skew commuting variables appearing in 'exp'.n
{
  int deg = 0;
  for (int i = 0; i < _n_skew; i++)
    {
      int v = _skew_list[i];
      if (exp[v] > 0) deg++;
    }
  return deg;
}
 
int SkewMultiplication::skew_vars(const int *exp, int *result) const
// The number s of skew variables in 'exp' is returned, and their
// indices are placed in result[0], ..., result[s-1].
// The space that 'result' points to MUST hold at least n_skew ints
{
  int i;
  int next = 0;
  for (i = 0; i < _n_skew; i++)
    {
      int v = _skew_list[i];
      if (exp[v] > 0) result[next++] = v;
    }
  return next;
}
 
int SkewMultiplication::skew_vars(const long *exp, int *result) const
// The number s of skew variables in 'exp' is returned, and their
// indices are placed in result[0], ..., result[s-1].
// The space that 'result' points to MUST hold at least n_skew ints
{
  int i;
  int next = 0;
  for (i = 0; i < _n_skew; i++)
    {
      int v = _skew_list[i];
      if (exp[v] > 0) result[next++] = v;
    }
  return next;
}
 
int SkewMultiplication::mult_sign(const int *exp1, const int *exp2) const
{
  exponents_t SKEW1 = ALLOCATE_EXPONENTS(skew_byte_size);
  exponents_t SKEW2 = ALLOCATE_EXPONENTS(skew_byte_size);
  int a = skew_vars(exp1, SKEW1);
  int b = skew_vars(exp2, SKEW2);
  return sort_sign(a, SKEW1, b, SKEW2);
}
 
int SkewMultiplication::mult_sign(const long *exp1, const long *exp2) const
{
  exponents_t SKEW1 = ALLOCATE_EXPONENTS(skew_byte_size);
  exponents_t SKEW2 = ALLOCATE_EXPONENTS(skew_byte_size);
  int a = skew_vars(exp1, SKEW1);
  int b = skew_vars(exp2, SKEW2);
  return sort_sign(a, SKEW1, b, SKEW2);
}
 
int SkewMultiplication::diff(const int *exp1,
                             const int *exp2,
                             int *result) const
// exp1 acting as a differential operator on exp2 is s * result, s = 0, 1, or
// -1.
{
  for (int i = 0; i < _n_vars; i++)
    {
      int cmp = exp2[i] - exp1[i];
      if (cmp < 0) return 0;
      result[i] = cmp;
    }
  exponents_t SKEW1 = ALLOCATE_EXPONENTS(skew_byte_size);
  exponents_t SKEW2 = ALLOCATE_EXPONENTS(skew_byte_size);
  int a = skew_vars(result, SKEW1);
  int b = skew_vars(exp1, SKEW2);
  int sign = sort_sign(a, SKEW1, b, SKEW2);
  int c = b % 4;
  if (c == 2 || c == 3) sign = -sign;
  return sign;
}
 
int SkewMultiplication::divide(const int *exp1,
                               const int *exp2,
                               int *result) const
// If the result is s (1,or -1), then exp1 = s * result * exp2
{
  for (int i = 0; i < _n_vars; i++)
    {
      int cmp = exp1[i] - exp2[i];
      if (cmp < 0) return 0;
      result[i] = cmp;
    }
  int sign = mult_sign(result, exp2);
  return sign;
}
 
bool SkewMultiplication::exp_is_zero(const int *exp) const
// Return whether any skew variable in the exponent vector has exponent >= 2
{
  for (int i = 0; i < _n_skew; i++)
    {
      int v = _skew_list[i];
      if (exp[v] >= 2) return true;
    }
  return false;
}
 
// Local Variables:
// compile-command: "make -C $M2BUILDDIR/Macaulay2/e "
// indent-tabs-mode: nil
// End: