 
 
 
11.9.4  Factoring in ℤ/pℤ[x]
In Xcas mode, Factor is simply the inert form of
factor; namely, it factors a polynomial without evaluation.
(See Section 9.1.10.)
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
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) | 
|  | | | factor | ⎛ ⎝
 | ⎛ ⎝
 | ⎛ ⎝
 | −3 | ⎞ ⎠
 | %13 | ⎞ ⎠
 | x3+ | ⎛ ⎝
 | 5%13 | ⎞ ⎠
 | x2+ | ⎛ ⎝
 | ⎛ ⎝
 | −5 | ⎞ ⎠
 | %13 | ⎞ ⎠
 | x+4%13 | ⎞ ⎠
 | 
 |  |  |  |  |  |  |  |  |  |  | 
 | 
To get the actual factorization:
|  | | |  | ⎛ ⎝
 | ⎛ ⎝
 | −3 | ⎞ ⎠
 | %13 | ⎞ ⎠
 | ⎛ ⎝
 | ⎛ ⎝
 | 1%13 | ⎞ ⎠
 | x+ | ⎛ ⎝
 | −6 | ⎞ ⎠
 | %13 | ⎞ ⎠
 | ⎛ ⎝
 | ⎛ ⎝
 | 1%13 | ⎞ ⎠
 | x2+6%13 | ⎞ ⎠
 | 
 |  |  |  |  |  |  |  |  |  |  | 
 | 
Input in Maple mode:
| Factor(-3*x^3+5*x^2-5*x+4) mod 13 | 
 
 
