Euclidean quotient : Quo

### 5.30.3 Euclidean quotient : Quo

Quo is the inert form of quo.
Quo returns the euclidean quotient between two polynomials (decreasing power division) without evaluation. It is used when Xcas is in Maple mode to compute the euclidean quotient of the division of two polynomials with coefficients in ℤ/pℤ using Maple-like syntax.
In Xcas mode, input :

Quo(x`^`2+2*x+1,x)

Output :

quo(x`^`2+2*x+1,x)

In Maple mode, input :

Quo(x`^`3+3*x,2*x`^`2+6*x+5) mod 5

Output :

-(2)*x+1

The division was done using modular arithmetic, unlike with

quo(x`^`3+3*x,2*x`^`2+6*x+5) mod 5

where the division is done in ℤ[X] and reduced after to:

3*x-9

If Xcas is not in Maple mode, polynomial division in ℤ/pℤ[X] is done e.g. by :

`quo((x^3+3*x)% 5,(2x^2+6x+5)%5)`