ASKSAGE: Sage Q&A Forum - RSS feedhttps://ask.sagemath.org/questions/Q&A Forum for SageenCopyright Sage, 2010. Some rights reserved under creative commons license.Fri, 14 Jul 2017 12:29:00 +0200Declaring a vector space map of ringshttps://ask.sagemath.org/question/38258/declaring-a-vector-space-map-of-rings/ Hello sage community!
I am new to sage and have a question which is originally motivated from my tries to implement Berlekamp's algorithm. One is working over a finite field $K=GF(q)$ and wants to factor a polynomial $f\in K[x]$. To do so one considers the ring $R=K[x]/f$ and the map $\beta\colon g\mapsto g^q-g$ from $R$ to itself and wants to compute its kernel. The problem for me is that the definition of $\beta$ <i>uses</i> the ring multiplication of of $R$ but <i>is</i> only a map of $K$-vector spaces, not a ring homomorphism. I am wondering how I can declare this map using sage.
I know I can find a standard $K$-basis of $R$ and I know I can describe $\beta$ by describing its matrix corresponding to this base and I know how to compute the kernel of that matrix and how to translate its elements back to elements of $R$. But still I am interested in wether it is possible to declare a <i>vector space</i> homomorphism of <i>rings</i> in sage and how to work with it.
Thank you!ILikeAlgebraFri, 14 Jul 2017 12:29:00 +0200https://ask.sagemath.org/question/38258/