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/pℤ using Maple-like syntax.
In Xcas mode, input :
^
3-1,x^
2-1)Output :
^
3-1,x^
2-1)In Maple mode, input :
^
3+3*x,2*x^
2+6*x+5) mod 5Output :
The division was done using modular arithmetic, unlike with
^
3+3*x,2*x^
2+6*x+5) mod 5where the division is done in ℤ[X] and reduced after to:
If Xcas is not in Maple mode, polynomial division in ℤ/pℤ[X] is done e.g. by :
rem((x^3+3*x)% 5,(2x^2+6x+5)%5)