I am new to sage. I am not scared of reading docs for computer programs. I cannot work out how to answer basic questions I have from the sage docs though :-( and it's so easy just to ask for help, so here I am.
Here's my question. I have a polynomial with coefficients in a cyclotomic field and I want to know how to compute the product of that polynomial with all its Galois conjugates (because I want to run newton_slopes on it but the manual is not, as far as I can see, clear on whether this will work, so I'm going to build a polynomial for which I know it will work). Here's my issue: although I would love to work out how to do this myself by reading the docs, I spent 30 minutes failing and now I have to go and feed my kids :-/ Here is why I failed. 1) I went to http://www.sagemath.org/doc/reference/index.html and typed cyclotomic fields into the quick search box, in an attempt to find a simple page about how to access the Galois group of a cyclotomic field. I got 53 results and none of them seemed to be about cyclotomic fields :-( 2) I gave up on this, created a cyclotomic field K, and typed "K.[tab]" and spotted the answer: K.galois_group() . 3) Now I have my group. Let g be an element. I have my polynomial f. How to hit it with an element of the group? g(f)? No. Probably need to access the coefficients by hand. How do I turn a polynomial into a list of coefficients? How do I turn a list of coefficients into a polynomial? I search the sage docs for "polynomial". Am I being naive here? If I were searching the python docs for something, I would probably find a page about that something, containing explanations of how to create the something and how to manipulate it. The search for polynomial in the sage docs gives me unusable results. I give up with the docs again. 4) f.[tab] tells me that it's f.coefficients() I'm after. 5) I manage to hit the list of coefficients with the element of Galois! 6) Now I have to turn the new list of coefficients back into a polynomial. And now I'm in trouble because I can't use the tab trick any more and I don't understand the docs. Of course I can try and remind myself how python lists work (from the python manual :-/ ) and then just build the conjugate by summing the conjugates of the coefficients and multiplying by powers of x. But surely there is a command which does this and not only do I not know the command, I don't know how to find it out without simply asking. And to be honest I am not 100% confident that I will be able to create sum_i a_i x^i in sage because I am still a bit unsure about x and x^i at this point (although probably more reading the manual will sort this out for me). So the question I actually want to know the answer to is how to compute prod_{g in G}g(f) in sage, G a Galois group, f a polynomial. But the question I should really be told the answer to is how I am supposed to be using the sage manual to answer my questions, because when the tab trick doesn't work I am lost. Kevin -- 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.
