asq
, af
, af_noalg
root
list
root
list of pairs of an indeterminate and a polynomial
cr_gcda()
is invoked.
af()
requires the specification of base field,
i.e., list of root's for its second argument.
alglist
, root defined last must come
first.
af(F,AL)
, AL
denotes a list of roots
and it
represents an algebraic number field. In AL=[An,...,A1]
each
Ak
should be defined as a root of a defining polynomial
whose coefficients are in Q(A(k+1),...,An)
.
[1] A1 = newalg(x^2+1); [2] A2 = newalg(x^2+A1); [3] A3 = newalg(x^2+A2*x+A1); [4] af(x^2+A2*x+A1,[A2,A1]); [[x^2+(#1)*x+(#0),1]]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.
[1] af_noalg(x^2+a2*x+a1,[[a2,a2^2+a1],[a1,a1^2+1]]); [[x^2+a2*x+a1,1]]
af_noalg
, algebraic numbers in @v{factor} are
replaced by the indeterminates according to defpolylist.
[98] A = newalg(t^2-2); (#0) [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]] [101] af_noalg(-x^2+3*x+a,[[a,x^2-2]]); [[x+a-1,1],[-x+a+2,1]]
cr_gcda
, section fctr
, sqfr
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