Euclidean quotient : quo

### 6.34.5 Euclidean quotient : quo

The quo command finds the quotient of of two polynomials (see also Section 6.28.2).

- 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.
Input:

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

Output:

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

Indeed x3+x2+1=(2x2+4)(x+1/2)+5x−4/4 and −3*4=−6*2=1 mod13.