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3.3.5 Polynomials Modulo Primes

Mathematica can work with polynomials whose coefficients are in the finite field of integers modulo a prime


Functions for manipulating polynomials over finite fields.

  • Here is an ordinary polynomial.
  • In[1]:= Expand[ (1 + x)^6 ]


  • This reduces the coefficients modulo 2.
  • In[2]:= PolynomialMod[%, 2]


  • Here are the factors of the resulting polynomial over the integers.
  • In[3]:= Factor[%]


  • If you work modulo 2, further factoring becomes possible.
  • In[4]:= Factor[%, Modulus->2]