Factoring in ℤ/pℤ[x]: Factor

6.35.4 Factoring in ℤ/pℤ[x]: Factor

In Xcas mode, Factor is simply the inert form of factor; namely, it factors a polynomial without evaluation. (See section Section 6.12.10.) In Maple mode, the Factor command can additionally be used in conjunction with mod to factor a polynomials with coefficients in ℤ/pℤ, where p must be prime.

(In Maple mode.)
Factor takes one argument:
P, a polynomial with coefficients in ℤ/pℤ for prime p.
Factor(P) returns the factored form of P.

Example.
Input (in Xcas mode):

Factor((-3*x^3+5*x^2-5*x+4)%13)

Output:

factor

⎛
⎝

−3

⎞
⎠

%13

⎞
⎠

x³+

⎛
⎝

5%13

⎞
⎠

x²+

⎛
⎝

−5

⎞
⎠

%13

⎞
⎠

x+4%13

⎞
⎠

To get the actual factorization:
Input:

eval(ans())

Output:

⎛
⎝

−3

⎞
⎠

%13

⎞
⎠

⎛
⎝

1%13

⎞
⎠

⎛
⎝

−6

⎞
⎠

%13

⎞
⎠

⎛
⎝

1%13

⎞
⎠

x²+6%13

⎞
⎠

Input (in Maple mode):

Factor(-3*x^3+5*x^2-5*x+4) mod 13

Output:

−3

⎛
⎝

x−6

⎞
⎠

⎛
⎝

x²+6

⎞
⎠