Dear Michael,
The error message that you get here is very misleading. The problem is
nothing to do with precision limits in Pari; it's because the Sage
interface to the Dokchitser calculator is very rudimentary (it hangs on
just about every natural-looking input, and it always blames Pari for its
mistakes!). As far as I can tell from the examples in the manual, there
seems to be no choice but to pass the coefficients as a *string*. This is
definitely a bug -- the init_coeffs function clearly *should* accept a list
as input.
Until it gets fixed, here's how to work around it, adapted from one of the
examples in the manual. This horrible piece of code constructs a Sage list
of the coefficients of the weight 12 modular form Delta, then feeds them to
the Dokchitser calculator. You will want to replace S with your list of
COEFFS, and use your own values for the conductor, weight, etc, of course.
┌────────────────────────────────────────────────────────────────────┐
│ Sage Version 6.5, Release Date: 2015-02-17 │
│ Type "notebook()" for the browser-based notebook interface. │
│ Type "help()" for help. │
└────────────────────────────────────────────────────────────────────┘
sage: S=delta_qexp(30).list()[1:] # coefficients (as a Sage list of
integers)
sage: S_pari_cmd = 'S_pari=' + str(S) + ';' # a string which, when
evaluated as a Pari/GP command, stores the contents of the list S in a Pari
variable called S_pari
sage: L=Dokchitser(conductor=1, gammaV=[0,1], weight=12, eps=1) # launch
the Dokchitser calculator
sage: L.init_coeffs('S_pari[k]', pari_precode=S_pari_cmd) # after
S_pari_cmd has been executed, 'S_pari[k]' returns the coefficient of k^{-s}
in our series
sage: L.check_functional_equation() # hopefully a very small number!
3.17637355220363e-22
David
On 16 March 2015 at 18:54, Michael Lipnowski <[email protected]>
wrote:
> Hi Sage NT.
>
> I'm trying to compute special values of symmetric square L-functions of
> cusp forms of weight > 2 in Sage. Dokchitser's L-function calculator seems
> like my best bet.
>
> I've computed all the Dirichlet coefficients I want in the form of a Sage
> list, call it COEFFS. I've initialized a Dokchitser L-function, call it L,
> using known weight, gamma factor, and sign parameters. But my attempts to
> then feed in the Dirichlet coefficients, like
>
> L.init_coeffs(COEFFS),
>
> all lead to the error message "Unable to create L-series, due to precision
> or other limits in PARI." Do you know of a straightforward way to set the
> Dirichlet coefficients of L using the already-computed Sage list COEFFS?
>
> Thanks,
> ~Mike
>
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