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D.8.10.1 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
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- Assume:
- basering = Q[x] or Q(a)[x]
- Note:
- This procedure is outdated, and should no longer be used. Use div and mod
instead.
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
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