 
 
 
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 ).
 
 
