Bill Allombert on Mon, 8 Sep 2003 18:26:57 +0200 |
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Decomposition of ideals in hard case. |
Hello PARI dev, I would like to compute the decomposition of a prime number in a number field, in hard case. Hard case mean the prime number divide the index of the defining polynomial, I don't have the nfinit() around, and probably I cannot factor the discriminant of the polynomial. I use the code below: decomp(P,p)= { d=poldisc(P); B=nfbasis(P,,Mat([p,valuation(d,p)])); /*B is a basis of a p-maximal order*/ K=nfinit([G.pol,B],1); idealprimedec(K,p) } As an example try P=x^54 + 796392*x^36 + 292918032*x^18 + 1259712. I don't neccessarily need all the info given by idealprimedec. The ramification and residual degrees can be enough in some case. Can it be done faster? The call to nfinit() seems to waste time doing too much things. Cheers, Bill.