Euclidean quotient

### 11.8.5 Euclidean quotient

The quo command finds the quotient of of two polynomials (see also Section 11.2.2).

- quo 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.
- quo(P,Q ⟨,x⟩) returns the Euclidean quotient of P divided by Q.

#### Example

quo((x^3+x^2+1)%13,(2*x^2+4)%13)

| ⎛ ⎝ | ⎛ ⎝ | −6 | ⎞ ⎠ | %13 | ⎞ ⎠ | x+ | ⎛ ⎝ | −6 | ⎞ ⎠ | %13

Indeed, x3+x2+1=(2x2+4)x+1/2+5x−4/4 and −3· 4=−6· 2≡ 1(mod 13 ).