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Drichlet ring is now included in FriCAS

The Dirichlet Ring

The Dirichlet Ring is the ring of arithmetical functions

 f: \mathbb N_+ \rightarrow R 
(see http://en.wikipedia.org/wiki/Arithmetic_function) together with the Dirichlet convolution (see http://en.wikipedia.org/wiki/Dirichlet_convolution) as multiplication and component-wise addition. Since we can consider the values an arithmetic functions assumes as the coefficients of a Dirichlet generating series, we call R the coefficient ring of a function.

In general we only assume that the coefficient ring R is a ring. If R happens to be commutative, then so is the Dirichlet ring, and in this case it is even an algebra.

Apart from the operations inherited from those categories, we only provide some convenient coercion functions.




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