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 |