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9.4.11 sp, sp_noalg

sp(poly)
sp_noalg(poly)
:: Finds the splitting field of polynomial poly and splits.

return
list
poly
polynomial

 
[101] L=sp(x^9-54);
[[x+(-#2),-54*x+(#1^6*#2^4),54*x+(#1^6*#2^4+54*#2),
54*x+(-#1^8*#2^2),-54*x+(#1^5*#2^5),54*x+(#1^5*#2^5+#1^8*#2^2),
-54*x+(-#1^7*#2^3-54*#1),54*x+(-#1^7*#2^3),x+(-#1)],
[[(#2),t#2^6+t#1^3*t#2^3+t#1^6],[(#1),t#1^9-54]]]
[102] for(I=0,M=1;I<9;I++)M*=L[0][I];
[111] M=simpalg(M);
-1338925209984*x^9+72301961339136
[112] ptozp(M);
-x^9+54

Reference
9.4.10 asq, af, af_noalg, 9.4.2 defpoly, 9.4.6 algptorat, 9.4.9 sp_norm.



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