Cyclotomic Unit Calculator


Cyclotomic Unit Calculation

Basis for Cyclotomic Units for n = 9 = 3^2 (relative mode)

Note that the union of all bases over all n extends to a universal basis

v(9,4), v(9,7)

The rank (number of elements in basis) is 2

Cyclotomic Units Base Representations for n = 9 = 3^2 (relative mode)

v(9,2) 1

Cyclotomic Units Base Representations for n = 9 = 3^2 (relative mode)

See Algorithm 2.4 for details

Note that equality is modulo multiplication by an nth unit root and modulo dth cyclotomic units where d is a proper divisor of n.

1: v(9,1) = 1
2: v(9,2) = v(9,7)
4: v(9,4) is in basis
5: v(9,5) = v(9,4)
7: v(9,7) is in basis
8: v(9,8) = 1
The rank is: 2

Cyclotomic Units - Methods for First Development for n = 9 = 3^2

Compare with Algorithm 2.2

1: v(9,1) - method T (Case IV,iii - A22)
2: v(9,2) - method S (Case IV,i - A22)
4: v(9,4) - method B (Case IV,ii - A22)
5: v(9,5) - method S (Case IV,i - A22)
7: v(9,7) - method B (Case IV,ii - A22)
8: v(9,8) - method S (Case IV,i - A22)

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