power() [1/2]

ring_elem Ring::power ( const ring_elem f, int n ) const

virtual

Reimplemented in FractionField, GF, LocalRing, M2::ConcreteRing< RingType >, M2::ConcreteRing< M2::ARingCCC >, M2::ConcreteRing< M2::ARingRRR >, M2FreeAlgebra, M2FreeAlgebraQuotient, PolyRing, PolyRingQuotient, RingZZ, SchurRing, SkewPolynomialRing, SolvableAlgebra, WeylAlgebra, and Z_mod.

Definition at line 166 of file ring.cpp.

{
  // 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;
        }
    }
}

References base, copy(), ERROR, from_long(), invert(), is_zero(), mult(), and one().