testPower()

template<typename T>

void testPower	(	const T &	R,
		int	ntrials )

Definition at line 397 of file ARingTest.hpp.

{
  // test the following: (x=generator of the finite field, q = card of field)
  // check: x^i != x, for 2 <= i <= characteristic-??
  // x^q == x
  // x^(q-1) == 1
  // x^(-1) * x == 1
  // x^(-2) * x^2 == 1
 
  // a^2 == a*a, for various a
  // a^3 == a*a*a
  // a^0 == 1, what if a == 0?
  // 1^n == 1, various n
  ARingElementGenerator<T> gen(R);
  typename T::ElementType a, b, c, d, one;
  int q = static_cast<int>(R.cardinality());
  R.init(one);
  R.init(a);
  R.init(b);
  R.init(c);
  R.init(d);
  R.set_from_long(one, 1);
  for (int i = 0; i < ntrials; i++)
    {
      gen.nextElement(a);
      gen.nextElement(b);
 
      R.power(c, a, q);
      EXPECT_TRUE(R.is_equal(c, a));  // test a^q == a
 
      if (R.is_zero(a)) continue;
 
      R.power(c, a, q - 1);
      EXPECT_TRUE(R.is_equal(c, one));  // test a^(q-1) == 1
 
      R.power(c, a, -1);  // test a^-1 * a == 1
      R.mult(c, a, c);
      EXPECT_TRUE(R.is_equal(c, one));
 
      R.power(c, a, -2);  // test a^-2 * a^3 == a
      R.power(d, a, 3);
      R.mult(d, c, d);
      EXPECT_TRUE(R.is_equal(d, a));
    }
  R.clear(a);
  R.clear(b);
  R.clear(c);
  R.clear(d);
  R.clear(one);
}

References ARingElementGenerator< RingType >::nextElement(), ntrials, and T.

Referenced by TEST(), TEST(), TEST(), TEST(), TEST(), TEST(), and testFiniteField().