11.2.3 Euclidean remainder
The rem command finds the
remainder of the Euclidean division of two polynomials.
-
rem takes two mandatory arguments and one optional
argument:
-
P and Q, two polynomials.
- Optionally x, the variable (by default
x), if P and Q are given as expressions.
- rem(P,Q ⟨,x⟩) returns
the Euclidean remainder of P divided by Q.
Rem is the inert form
of rem; namely, it evaluates to
rem for later evaluation. It is used when Xcas is in
Maple mode (see Section 2.5.2) to compute the euclidean remainder
of the division of two polynomials with coefficients in
ℤ/pℤ using Maple-like syntax.
Examples
To have the remainder of x2+2x+4 by x2+x+2, you can also do:
i.e. the polynomial x+2.
Input in Xcas mode:
Input in Maple mode:
Rem(x^3+3*x,2*x^2+6*x+5) mod 5 |
This division was done using modular arithmetic, unlike with the
following command, where the division is done in ℤ[X]
and reduction afterwards:
rem(x^3+3*x,2*x^2+6*x+5) mod 5 |
If Xcas is not in Maple mode, polynomial division
in ℤ/pℤ[X] is entered like this:
rem((x^3+3*x)%5,(2x^2+6x+5)%5) |