11.9.1 Euclidean quotient
In Xcas mode, Quo is simply the inert form of
quo; namely, it returns the Euclidean quotient of two
polynomials without evaluation. (See Section 11.2.2.)
In Maple mode, the Quo
command can additionally be used in conjunction with
mod to compute the Euclidean quotient of two polynomials with
coefficients in ℤ/pℤ.
-
In Maple mode, Quo takes two arguments:
P and Q, two polynomials with coefficients
in ℤ/pℤ.
- Quo(P,Q) returns the
Euclidean quotient of P divided by Q.
Examples
Input in Xcas mode:
| Quo((x^3+x^2+1) mod 13,(2*x^2+4) mod 13) |
|
| |
quo | ⎛
⎝ | ⎛
⎝ | 1%13 | ⎞
⎠ | x3+ | ⎛
⎝ | 1%13 | ⎞
⎠ | x2+1%13, | ⎛
⎝ | 2%13 | ⎞
⎠ | x2+4%13 | ⎞
⎠ |
| | | | | | | | | | |
|
To get the result of the division:
|
| |
| ⎛
⎝ | ⎛
⎝ | −6 | ⎞
⎠ | %13 | ⎞
⎠ | x+ | ⎛
⎝ | −6 | ⎞
⎠ | %13
|
| | | | | | | | | | |
|
Input in Maple mode:
| Quo(x^3+x^2+1,2*x^2+4) mod 13 |
Input in Maple mode:
| Quo(x^2+2*x,x^2+6*x+5) mod 5 |