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Comparison of two polynomials in Brent's method of factoring

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  • Kermit Rose
    I compare the efficiency of x**2 + 2 with the efficiency of 4 x**6 + 4 x**4 - x**2 - 1 = (2 x**2 -1 ) * (2 x**2 + 1) * (x**2 + 1) for number of iterations
    Message 1 of 1 , Sep 13, 2008
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      I compare the efficiency of

      x**2 + 2 with the efficiency of

      4 x**6 + 4 x**4 - x**2 - 1 = (2 x**2 -1 ) * (2 x**2 + 1) * (x**2 + 1)

      for number of iterations needed under Brent's method of factoring.

      Almost always the degree 6 polynomial found the factors first.

      >>> FactorSix(p7[0])
      Factored z = 617999 in 8 steps by Brent Method Two Algorithm.
      [409L, 1511L]

      >>> FactorSix(p20[0])
      Factored z = 62940134090320320101 in 18354 steps by Brent Method Six
      Algorithm.
      [9942857383L, 6330185747L]


      >>> FactorSix(p20[1])
      Factored z = 20769381218777181113 in 14216 steps by Brent Method Six
      Algorithm.
      [2173609013L, 9555251701L]


      >>> FactorSix(p20[2])
      Factored z = 18692365700052053077 in 36541 steps by Brent Method Six
      Algorithm.
      [2659137737L, 7029483821L]


      >>> FactorSix(p20[3])
      Factored z = 24020594249838967723 in 35579 steps by Brent Method Six
      Algorithm.
      [3027670697L, 7933687859L]


      >>> FactorSix(p20[4])
      Factored z = 47537628000771577759 in 41656 steps by Brent Method Six
      Algorithm.
      [5134093499L, 9259205741L]
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