sp_norm

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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