D.7.5.3 Quotient

Procedure from library zeroset.lib (see zeroset_lib).

Usage:

Quotient(f, g); where f,g are polynomials;

Purpose:

compute the quotient q and remainder r s.t. f = g*q + r, deg(r) < deg(g)

Return:

list of polynomials

_[1] = quotient q _[2] = remainder r

Assume:

basering = Q[x] or Q(a)[x]

Example:

LIB "zeroset.lib";
ring R = (0,a), x, lp;
minpoly = a2+1;
poly f =  x4 - 2;
poly g = x - a;
list qr = Quotient(f, g);
qr;
→ [1]:
→    x3+(a)*x2-x+(-a)
→ [2]:
→    0
qr[1]*g + qr[2] - f;
→ 1