Hi, > However, I can't figure out a way to do this. Sage doesn't like me > taking logarithms at this point, so I need to embed into RR or CC, > which screams minkowski embedding, but I can't get it to work, because > I don't really know what I'm doing. >
I've only quickly read your email, but there are several functions for number fields you might find helpful here. In particular: sage: L.<b> = NumberField(x^6+3) sage: L.Minkowski_embedding() [ 1.41421356237310 -1.47084137671644 1.01982445132775 0.000000000000000 -1.47084137671644 3.05947335398326] [0.000000000000000 0.849190664782477 -1.76638776450072 2.44948974278318 -2.54757199434743 1.76638776450072] [ 1.41421356237310 0.000000000000000 -2.03964890265551 0.000000000000000 2.94168275343288 0.000000000000000] [0.000000000000000 1.69838132956495 0.000000000000000 -2.44948974278318 0.000000000000000 3.53277552900144] [ 1.41421356237310 1.47084137671644 1.01982445132775 0.000000000000000 -1.47084137671644 -3.05947335398326] [0.000000000000000 0.849190664782477 1.76638776450072 2.44948974278318 2.54757199434743 1.76638776450072] sage: L.real_embeddings() [] sage: L.complex_embeddings() [ Ring morphism: From: Number Field in b with defining polynomial x^6 + 3 To: Complex Double Field Defn: b |--> -1.04004191153 - 0.600468477588*I, Ring morphism: From: Number Field in b with defining polynomial x^6 + 3 To: Complex Double Field Defn: b |--> -1.04004191153 + 0.600468477588*I, Ring morphism: From: Number Field in b with defining polynomial x^6 + 3 To: Complex Double Field Defn: b |--> -1.52661999456e-16 - 1.20093695518*I, Ring morphism: From: Number Field in b with defining polynomial x^6 + 3 To: Complex Double Field Defn: b |--> 4.22939257713e-16 + 1.20093695518*I, Ring morphism: From: Number Field in b with defining polynomial x^6 + 3 To: Complex Double Field Defn: b |--> 1.04004191153 + 0.600468477588*I, Ring morphism: From: Number Field in b with defining polynomial x^6 + 3 To: Complex Double Field Defn: b |--> 1.04004191153 - 0.600468477588*I ] I'm not sure how much you've used sage or ipython -- do you know about ?, ??, and tab completion? Here's the three line summary: you could type L.<TAB><TAB> to see all methods available on L, L.Minkowski_embedding? to see documentation on that method, and L.Minkowski_embedding?? to see the source itself. It's probably confusing that we've got L.Minkowski_embedding and L.minkowski_bound (note the different capitalization) -- we should standardize this. I wrote the one that's capitalized, so it's clear what I vote for. ;) As I said at the top, I only skimmed your email -- if I'm not really answering your question, or you have more questions, feel free to reply again. :) -cc --~--~---------~--~----~------------~-------~--~----~ To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support-unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URLs: http://www.sagemath.org -~----------~----~----~----~------~----~------~--~---
