Some new GP features
polsubcyclofast
polsubcyclofast(n,d) returns polynomials defining the
subfields of Q(ζn) with cyclic Galois groups of order d. When d
is small, it is faster than polsubcyclo but return larger
polynomials. Usually the polynomials returned by
polsubcyclo can be recovered by polredabs up to sign.
? polsubcyclo(10^7+19,7)
%79 = x^7+x^6-4285722*x^5-941022196*x^4+178129181010
? P=polsubcyclofast(10^7+19,7)[1]
%80 = x^7-210000399*x^5+321720611268*x^4+42781706185
? polredabs(P)
%81 = x^7-x^6-4285722*x^5+941022196*x^4+178129181010