The aim of this worksheet is to give an explicit description in term of bases over Z, of some Eichler orders of an indefinite quaternion algebra B defined over Q. Following a work of Hashimoto, we give a procedure which returns a basis of the Eichler orders of level N. This construction provides a very useful tool for working with Eichler orders. Let q be a prime number not dividing the discriminant of B; it is well known that there are two natural inclusions of R(Nq) in R(N). We provide a new procedure in Maple which returns a basis of an Eichler order on level Nq in B and a basis of the other copy of R(Nq) in R(N).
John Ogilvie
Dr. Valery Cyboulko
Dr. Jason Schattman
Richard Baur
Dr. Ahmed Baroudy
Prof. Mark Meyerson
Dr. Miriam Ciavarella
Dr. Robert Lopez
Maplesoft