Euclidean quotient: Quo

### 5.35.1 Euclidean quotient: Quo

In Xcas mode, Quo is simply the inert form of quo; namely, it returns the Euclidean quotient of two polynomials without evaluation. (See Section 5.28.2.) In Maple mode, the Quo command can additionally be used in conjunction with mod to compute the Euclidean quotient of two polynomials with coefficients in ℤ/pℤ.

- (In Maple mode.)
  Quo takes two arguments:
  P and Q, two polynomials with coefficients in ℤ/pℤ.
- Quo(P,Q) returns the Euclidean quotient of P divided by Q.

#### Examples

- Input (in Xcas mode):
  Quo((x^3+x^2+1) mod 13,(2*x^2+4) mod 13)
  Output:

  quo | ⎛ ⎝ | ⎛ ⎝ | 1%13 | ⎞ ⎠ | x3+ | ⎛ ⎝ | 1%13 | ⎞ ⎠ | x2+1%13, | ⎛ ⎝ | 2%13 | ⎞ ⎠ | x2+4%13 | ⎞ ⎠

  To get the result of the division:
  Input:
  eval(ans())

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

  Input (in Maple mode):
  Quo(x^3+x^2+1,2*x^2+4) mod 13
  Output:

  −6x−6

- Input (in Maple mode):
  Quo(x^2+2*x,x^2+6*x+5) mod 5
  Output:

  1