11.8.6 Euclidean remainder
The rem command finds the remainder of
the Euclidean division of two polynomials (see also Section 11.2.3).
-
rem takes two mandatory arguments and one optional
argument:
-
P and Q, two polynomials with
coefficients in ℤ/pℤ.
- Optionally x, the variable (by default
x), if P and Q are given as expressions.
- rem(P,Q ⟨,x⟩) returns
the remainder of the Euclidean division of P divided by Q.
Example
| rem((x^3+x^2+1)%13,(2*x^2+4)%13) |
|
| |
| ⎛
⎝ | ⎛
⎝ | −2 | ⎞
⎠ | %13 | ⎞
⎠ | x+ | ⎛
⎝ | −1 | ⎞
⎠ | %13
|
| | | | | | | | | | |
|
Indeed, x3+x2+1=(2x2+4)·x+1/2+5x−4/4
and −3· 4=−6· 2≡ 1(mod 13 ).