Note that this basis extends to a universal basis, i.e the basis for d is a subset of the basis for n iff d|n.
The rank (number of elements in basis) is 1
See Algorithm 2.4 for details
Note that equality is modulo multiplication by an nth unit root.1: v(12,1) is in basis
Compare with Algorithm 1.2 and 2.2
1: v(12,1) - method B (Case V,i - A12)
2: v(6,1) - method Z-2 (Case IV - A12)
3: v(4,1) - method T (Case II - A22)
4: v(3,1) - method T (Case III, A22)
5: v(12,5) - method Z-3 (Case V,iv - A12)
6: v(2,1) - method T (Case II - A22)
7: v(12,7) - method Z-2 (Case V,iv - A12)
8: v(3,2) - method S (Case III, A22)
9: v(4,3) - method T (Case II - A22)
10: v(6,5) - method Z-2 (Case IV - A12)
11: v(12,11) - method Z-2 (Case V,iv - A12)
Back to the Cyclotomic Unit Resources page
© by: Marc Conrad, 2016. If you want me
to come to your organisation and talk about cyclotomic units please contact me.
The material on this page is presented "as is". There is no warranty implied by presenting this stuff.
Feel free to use and modify the material for your own teaching. When doing so please link to this web site (http://perisic.com/cyclotomic). In acadmic publications cite this page as: Conrad, Marc (2016) Cyclotomic Units - Relations and Computations (online), available at: http://perisic.com/cyclotomic.
The webspace for this project is kindly provided by the Perisic Guesthouse (www.perisic.com).