11.8.5 Euclidean quotient
The quo command finds the quotient of
of two polynomials (see also Section 11.2.2).
-
quo takes two mandatory arguments and one optional
argument:
-
P and Q, two polynomials
with coefficients in ℤ/pℤ.
- 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.
Example
| quo((x^3+x^2+1)%13,(2*x^2+4)%13) |
|
| |
| ⎛
⎝ | ⎛
⎝ | −6 | ⎞
⎠ | %13 | ⎞
⎠ | x+ | ⎛
⎝ | −6 | ⎞
⎠ | %13
|
| | | | | | | | | | |
|
Indeed, x3+x2+1=(2x2+4)x+1/2+5x−4/4
and −3· 4=−6· 2≡ 1(mod 13 ).