Closed drewitz closed 4 years ago
I'll look into this, hopefully later on this week.
Thanks for raising this issue.
Hey Simon, So we have the minimal polynomial of the growth rate which is
x^10 - x^9 - x^6 + x^5 - x^4 - x + 1
The repartition of its roots is the following:
If I'm not mistaken, all the complex roots lie on the unit circle and not inside (reason why it is a Salem number but not a Pisot number).
What do you think?
Hi Rafael, yes, you're right. I had learned a wrong "definition" of Pisot numbers which implied that every Salem number is a Pisot number and trusted the source so that I didn't double check the definition. Sorry about that.
For the [3,5,3] orthoscheme, CoxIter says the growth rate is a Salem number but not a Pisot number. This is not possible and afaik, it is indeed both: