feature requests for lazy Dirichlet series welcome!

[Martin R]

Here, or at https://trac.sagemath.org/ticket/32309.

Martin

[Martin R]

Last call, especially to number theorists :-)

The ticket is almost ready.  It would be great to get some hints about desirable features and interesting examples!

You can do things like:

sage: D = LazyDirichletSeriesRing(QQ, "s")
sage: L.<z> = LazyLaurentSeriesRing(D)
sage: zeta = D(constant=1)
sage: (1/(1-zeta*z))[6]
1 + 6/2^s + 6/3^s + 21/4^s + 6/5^s + 36/6^s + 6/7^s + O(1/(8^s))

or

sage: D = LazyDirichletSeriesRing(QQ, "s")
sage: L.<z> = LazyLaurentSeriesRing(QQ)
sage: e = L(lambda n: 1/factorial(n), valuation=0)

sage: zeta = D(constant=1)

sage: g = D(None, valuation=2)
sage: g.define((zeta-1) * e(g))
sage: g
1/(2^s) + 1/(3^s) + 2/4^s + 1/(5^s) + 3/6^s + 1/(7^s) + 9/2/8^s + O(1/(9^s))

Martin