Cyclotomic Unit Calculator


Cyclotomic Unit Calculation

Basis for Cyclotomic Units for n = 13 (prime)

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.

v(13,2), v(13,3), v(13,4), v(13,5), v(13,6)

The rank (number of elements in basis) is 5

Cyclotomic Units Base Representations for n = 13 (prime)

v(13,7)    1
v(13,8)   1 
v(13,9)  1  
v(13,10) 1   

Cyclotomic Units Base Representations for n = 13 (prime)

See Algorithm 2.4 for details

Note that equality is modulo multiplication by an nth unit root.

1: v(13,1) = 1
2: v(13,2) is in basis
3: v(13,3) is in basis
4: v(13,4) is in basis
5: v(13,5) is in basis
6: v(13,6) is in basis
7: v(13,7) = v(13,6)
8: v(13,8) = v(13,5)
9: v(13,9) = v(13,4)
10: v(13,10) = v(13,3)
11: v(13,11) = v(13,2)
12: v(13,12) = 1
The rank is: 5

Cyclotomic Units - Methods for First Development for n = 13 (prime)

Compare with Algorithm 2.2

1: v(13,1) - method T (Case III, A22)
2: v(13,2) - method B (Case III, A22)
3: v(13,3) - method B (Case III, A22)
4: v(13,4) - method B (Case III, A22)
5: v(13,5) - method B (Case III, A22)
6: v(13,6) - method B (Case III, A22)
7: v(13,7) - method S (Case III, A22)
8: v(13,8) - method S (Case III, A22)
9: v(13,9) - method S (Case III, A22)
10: v(13,10) - method S (Case III, A22)
11: v(13,11) - method S (Case III, A22)
12: v(13,12) - method S (Case III, A22)

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