6.34.5 Euclidean quotient : quo
The quo command finds the quotient of
of two polynomials (see also Section 6.28.2).
-
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.
Input:
quo((x^3+x^2+1)%13,(2*x^2+4)%13)
Output:
⎛
⎝ | ⎛
⎝ | −6 | ⎞
⎠ | %13 | ⎞
⎠ | x+ | ⎛
⎝ | −6 | ⎞
⎠ | %13
|
Indeed x3+x2+1=(2x2+4)(x+1/2)+5x−4/4
and −3*4=−6*2=1 mod13.