6.28.2 Euclidean quotient: quo Quo
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.
Examples.
-
Input:
quo(x^2+2*x +1,x)
Output:
- Input:
quo(y^2+2*y +1,y,y)
Output:
- In list representation, to get the quotient of x2+2x+4 by x2+x+2
you can also input:
quo([1,2,4],[1,1,2])
Output:
that is to say, the polynomial 1.
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 3.5.2) to compute the euclidean quotient
of the division of two polynomials with coefficients in
ℤ/pℤ using Maple-like syntax.
Examples.
-
Input (in Xcas mode):
Quo(x^2+2*x+1,x)
Output:
- Input (in Maple mode):
Quo(x^3+3*x,2*x^2+6*x+5) mod 5
Output:
This 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:
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)