### 2.25.5 Euclidien remainder: `Rem`

`Rem` is the inert form of `rem`.

`Rem` returns the euclidean remainder between two polynomials
(decreasing power division) without evaluation.
It is used when `Xcas` is in Maple mode to compute
the euclidean remainder of the division of two
polynomials with coefficients in ℤ/*p*ℤ using Maple-like syntax.

In `Xcas` mode, input :

`Rem(x``^`

`3-1,x``^`

`2-1)`

Output :

`rem(x``^`

`3-1,x``^`

`2-1)`

In `Maple` mode, input :

`Rem(x``^`

`3+3*x,2*x``^`

`2+6*x+5) mod 5`

Output :

`2*x`

The division was done using modular arithmetic, unlike with

`rem(x``^`

`3+3*x,2*x``^`

`2+6*x+5) mod 5`

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

`12*x`

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

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