11.8.19 Factoring a polynomial with coefficients in a Galois field

The factor command can factor univariate polynomials with coefficients in a Galois field.

• factor takes one mandatory argument and one optional argument:
  • expr, an expression or a list of expressions.
  • Optionally, α, to specify an extension field.
• factor(expr) returns expr factored over the field of its coefficients, with the addition of i in complex mode (see Section 2.5.5). If sqrt is enabled in the CAS configuration (see Section 2.5.7), polynomials of order 2 are factorized in complex mode or in real mode if the discriminant is positive.

  factor(expr,α) returns expr factored over F[α], where F is the field of coefficients of expr.

• cfactor factors like factor, except the field includes i whether in real or complex mode.

Example

The command factor can factorize a univariate polynomial with coefficients in a Galois field. For example, to have G=𝔽₄, input:

Now input, for example: