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2021-03-30 19:32:53 +0200 marked best answer How to build a generating series

Hello. Forgive me, I'm still a bit new to coding. I want to create a generating q-series for functions I've already defined, which have complex number outputs. These functions are denoted g(k, n, z), where k, n are integers and z in a complex input. I'd like the series sum([g(k, n, z)*q^n for n in range(1, 100)]) or something along those lines. The error code is:

`---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
<ipython-input-35-5dc58c06413b> in <module>
      5     return sum([g(k, n, z)*q**n for n in range(Integer(1), Integer(100))])
      6 
----> 7 G(Integer(2), Integer(1)+i)

<ipython-input-35-5dc58c06413b> in G(k, z)
      3 def G(k, z):
      4     var('q')
----> 5     return sum([g(k, n, z)*q**n for n in range(Integer(1), Integer(100))])
      6 
      7 G(Integer(2), Integer(1)+i)
<ipython-input-35-5dc58c06413b> in <listcomp>(.0)
      3 def G(k, z):
      4     var('q')
----> 5     return sum([g(k, n, z)*q**n for n in range(Integer(1), Integer(100))])
      6 
      7 G(Integer(2), Integer(1)+i)
TypeError: unsupported operand type(s) for *: 'NoneType' and 'sage.symbolic.expression.Expression`

I apologize I cannot make the above formatting more clear. Perhaps someone could help me! Edit: Thank you for editing above error code!

2021-03-30 19:32:51 +0200 commented answer How to build a generating series

I added var('q') in the def of G and also used your advice about return. This seemed to work! Thank you!

2021-03-30 17:57:56 +0200 edited question How to build a generating series

How to build a generating series Hello. Forgive me, I'm still a bit new to coding. I want to create a generating q-serie

2021-03-30 17:26:09 +0200 asked a question How to build a generating series

How to build a generating series Hello. Forgive me, I'm still a bit new to coding. I want to create a generating q-serie

2021-01-20 00:33:57 +0200 commented answer Print scaling factors in eta-products

Very nice. Did not know this function. Thank you!

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2021-01-19 01:03:30 +0200 asked a question Print scaling factors in eta-products

I have the useful command:

EtaGroup(8).basis()[0].r(2)

which will return the first exponent in (eta_2)^-4 (eta_4)^12 (eta_8)^-8; namely -4. Similarly

EtaGroup(8).basis()[0].r(4)

will return 12 etc. I want to extract the scaling factors though. That is, I want to print 2 or 4 or 8 in the expression (eta_2)^-4 (eta_4)^12 (eta_8)^-8 How??

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2020-03-27 00:52:59 +0200 commented answer How to do arithmetic with a basis element from modular forms space

It worked!!! So when I do print(g.q_expansion()*L.q_expansion) something goes wrong, but leaving out "print" seems to fix this... weird.

2020-03-25 16:21:06 +0200 commented answer How to do arithmetic with a basis element from modular forms space

Yes, but if I try something like g*L.q_expansion() or g*L.qexp(20) or things like that I get that error.

2020-03-25 16:19:19 +0200 commented question How to do arithmetic with a basis element from modular forms space

Yes, sorry. It's L = EtaProduct(7, {1:4, 7:-4}). I also mixed up the level on accident but edited to fix. It's 7.

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2020-03-23 20:08:30 +0200 asked a question How to do arithmetic with a basis element from modular forms space

Hi, I'm new to Sage and coding in general. I want to look at the 1-dim'l space CuspForms(Gamma0(7), 3) but with character. Here's my code for that

S = G = DirichletGroup(7, QQ)
list(G)
G.gens()
e = G.0
S = CuspForms(e, 3, prec=20)
print(S)
print(Gamma0(7).cusps())
print(S.basis())
g = S.0

Here, g is the only basis element for S. I want to do F = g*(L+4) where L is some eta-quotient of level 7. However, I get a long error with 'NoneType' object is not iterable at the end. So I'm thinking I need to define g in a different way, since it seems to be that g is not a q-series type object the way I've defined it?