Twisted Polynomial Ring(Construct new Class)

asked 2015-12-15 08:06:27 -0600

Nick123 gravatar image

I would like to implement a class of twisted polynomial rings, which assigns to ring $K$ in characterstic $p$ a ring $K[\tau]$, whose underlying additive structure is just an ordinary polynomial ring in $\tau$, but with the multiplication defined by $\tau x=x^p \tau$. Is it possible to construct this as a usual polynomial ring and modify the multiplication in some way?

I am totally new to Sage and Python, and I couldn't even figure out the parent/element dynamics, i.e. what exactly I have to specify for my object to fit with the usual Sage classes. The thematic tutorials on the documentation page don't really specify a general way to deal with this, so I am lost where to start.

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