6.34.6 Euclidean remainder: rem
The rem command finds the remainder of the Euclidean division
of two polynomials (see also Section 6.28.3).
-
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.
Input:
rem((x^3+x^2+1)%13,(2*x^2+4)%13)
Output:
⎛
⎝ | ⎛
⎝ | −2 | ⎞
⎠ | %13 | ⎞
⎠ | x+ | ⎛
⎝ | −1 | ⎞
⎠ | %13
|
Indeed x3+x2+1=(2x2+4)(x+1/2)+5x−4/4
and −3*4=−6*2=1 mod13.