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Sorry not to have actually helped answer your question! John Cremona On 9 May 2014 13:30, Yves Lignac <[email protected]> wrote: > Hello all, > > I am looking for a way to determine if an embedding $\sigma$ of a number > field $L$ into the complex numbers restricts to a given embedding $\tau$ of > a subfield $K$ (asking for equality between $\tau$ and $\sigma \circ i$ > where $i$ is the embedding of $K$ into $L$ does not work). > More specifically, I have a cubic field $K$ of signature (1,1) and a > quadratic extension $L/K$ with $L$ of signature (0,3), and I want to be > able to obtain one of the two complex places of $L$ that does not lie above > the real place of $K$. I have tried to do this by taking a polynomial for > $L$ over $K$, taking one of its (complex) roots at the complex place of $K$ > and using create_embedding_from_approx, but this does not work (on my > computer at least) because the latter seems to work only with real > embeddings > (for completeness, here is the code I used (given the number fields K,L > and the embedding i from K to L : > > L_over_K.<u,t> = L.relativize(i) > g = L_over_K.relative_polynomial() > coef = g.coefficients() > expo = g.exponents() > Q = K.places() ; q = Q[1] > coef2 = [] > for c in coef : > coef2.append(q(c)) > h = 0 > y = polygen(CC) > for i in range(0,len(coef)) : > h = h + coef2[i] * y^(expo[i]) > root = (complex_roots(h)[0][0]).center() > p = create_embedding_from_approx(L, root) > > In any case, if there is a way to test divisibility between archimedean > places of number fields without using the above uncomfortable way I would > be very much happier to use it. > > -- > You received this message because you are subscribed to the Google Groups > "sage-support" group. > To unsubscribe from this group and stop receiving emails from it, send an > email to [email protected]. > To post to this group, send email to [email protected]. > Visit this group at http://groups.google.com/group/sage-support. > For more options, visit https://groups.google.com/d/optout. > -- You received this message because you are subscribed to the Google Groups "sage-support" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To post to this group, send email to [email protected]. Visit this group at http://groups.google.com/group/sage-support. For more options, visit https://groups.google.com/d/optout.
