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D.8.10.4 sqfrNorm
Procedure from library zeroset.lib (see zeroset_lib).
- Usage:
- sqfrNorm(f); where f is a polynomial in Q(a)[x]
- Purpose:
- compute the norm of the squarefree polynomial f in Q(a)[x].
- Return:
- list with 3 entries
| | _[1] = squarefree norm of g (poly)
_[2] = g (= f(x - s*a)) (poly)
_[3] = s (int)
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- Assume:
- f must be squarefree, basering = Q(a)[x] and minpoly != 0.
- Note:
- the norm is an element of Q[x]
Example:
| | LIB "zeroset.lib";
ring R = (0,a), x, lp;
minpoly = a2+1;
poly f = x4 - 2*x + 1;
sqfrNorm(f);
==> [1]:
==> x8+4*x6-4*x5+8*x4+8*x3-4*x2+8*x+8
==> [2]:
==> x4+(-4a)*x3-6*x2+(4a-2)*x+(2a+2)
==> [3]:
==> 1
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