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 sp_norm(alg,var,poly,alglist)

:: Norm computation over an algebraic number field.
 return

polynomial
 var

The main variable of poly
 poly

univariate polynomial
 alg

root
 alglist

root
list

Defined in the file `sp'.

Computes the norm of poly with respect to alg.
Namely, if we write
K = Q(alglist \ {alg}),
The function returns a product of all conjugates of poly,
where the conjugate of polynomial poly is a polynomial
in which the algebraic number alg is substituted
for its conjugate over K.

The result is a polynomial over K.

The method of computation depends on the input. Currently
direct computation of resultant and Chinese remainder theorem
are used but the selection is not necessarily optimal.
By setting the global variable
USE_RES
to 1, the builtin function
res()
is always used.
[0] load("sp")$
[39] A0=newalg(x^2+1)$
[40] A1=newalg(x^2+A0)$
[41] sp_norm(A1,x,x^3+A0*x+A1,[A1,A0]);
x^6+(2*#0)*x^4+(#0^2)*x^2+(#0)
[42] sp_norm(A0,x,@@,[A0]);
x^12+2*x^8+5*x^4+1
 Reference

section
res
, section asq
, af
, af_noalg
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