# Dedekind eta function in sage

Anonymous

I would like to use the dedekind eta function, $q^{\frac{1}{24}}\prod_{n=1}(1-q^n)$, in my code. However when I do

N=20 R. = PowerSeriesRing(QQ,default_prec=p*N+1)

eta = q^(1/24)*prod([(1-q^n) for n in range(1,N)]) eta =R(eta.truncate(N))

I get "ValueError: power series valuation is not a multiple of 24". I would like to know how I can implement the formula above or if there is some inbuilt eta function I can use somehow (I couldn't find anything in the documentation).

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1

Not a SageMath way but you can try some Python libraries (and you can use them directly in SageMath): https://mpmath.org/doc/current/functions/qfunctions.html

( 2024-07-28 06:10:42 +0200 )edit

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It's a always a good idea using the existing functionality rather than reinventing the wheel. Without the factor $q^{1/24}$ the expansion of eta function in Sage can be computed as follows:

from sage.modular.etaproducts import qexp_eta
N=20
qexp_eta(ZZ[['q']], N)

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