Asir - asq af af

asq(poly): :: Square-free factorization of polynomial poly over an algebraic number field.
af(poly,alglist)
af_noalg(poly,defpolylist): :: Factorization of polynomial poly over an algebraic number field.

Both defined in the file `sp'.
If the inputs contain no root's, these functions run fast since they invoke functions over the integers. In contrast to this, if the inputs contain root's, they sometimes take a long time, since cr_gcda() is invoked.
Function af() requires the specification of base field, i.e., list of root's for its second argument.
In the second argument alglist, root defined last must come first.
To call sp_noalg, one should replace each algebraic number ai in poly with an indeterminate vi. defpolylist is a list [[vn,dn(vn,...,v1)],...,[v1,d(v1)]]. In this expression di(vi,...,v1) is a defining polynomial of ai represented as a multivariate polynomial.
The result is a list, as a result of usual factorization, whose elements is of the form [factor, multiplicity]. In the result of af_noalg, algebraic numbers in @v{factor} are replaced by the indeterminates according to defpolylist.
The product of all factors with multiplicities counted may differ from the input polynomial by a constant.

[99] asq(-x^4+6*x^3+(2*alg(0)-9)*x^2+(-6*alg(0))*x-2);
[[-x^2+3*x+(#0),2]]
[100] af(-x^2+3*x+alg(0),[alg(0)]);
[[x+(#0-1),1],[-x+(#0+2),1]]