11.2.2 Euclidean quotient
The quo command finds the quotient
of the Euclidean division of two polynomials.
-
quo 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.
- quo(P,Q ⟨,x⟩) returns
the Euclidean quotient of P divided by Q.
Quo is the inert form of
quo; namely, it evaluates to
quo for later evaluation. It is used when Xcas is in
Maple mode (see Section 2.5.2) to compute the euclidean quotient
of the division of two polynomials with coefficients in
ℤ/pℤ using Maple-like syntax.
Examples
In list representation, to get the quotient of x2+2x+4 by x2+x+2
you can also input:
that is to say, the polynomial 1.
Input in Xcas mode:
Input in Maple mode:
| Quo(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:
| quo(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 done e.g. by:
| quo((x^3+3*x)%5,(2x^2+6x+5)%5) |