Changes between Version 3 and Version 4 of Ticket #17283


Ignore:
Timestamp:
11/11/14 21:35:06 (5 years ago)
Author:
pbruin
Comment:

The previous inconsistencies reported on this ticket were just because there does not exist a Dirichlet character with the values as in the example...

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  • Ticket #17283

    • Property Keywords modular symbols removed
    • Property Priority changed from critical to minor
    • Property Summary changed from Evaluating Dirichlet characters can give wrong results to Check consistency when constructing Dirichlet characters
  • Ticket #17283 – Description

    v3 v4  
    1 Evaluating Dirichlet characters is broken in some cases (the image of 133 is wrong in this example):
     1It is too easy to construct Dirichlet characters with inconsistent values:
    22{{{
    33sage: k.<i> = CyclotomicField(4)
    44sage: G = DirichletGroup(192)
    5 sage: chi = G([i,-1,-1]); chi
     5sage: chi = G([i,-1,-1]); chi  # should raise an error since 127 only has order 2
    66Dirichlet character modulo 192 of conductor 48 mapping 127 |--> zeta16^4, 133 |--> -1, 65 |--> -1
    7 sage: chi(133)
     7sage: chi(133)  # no surprise that this gives an inconsistent answer
    881
    99}}}
    10 Because of this, changing the coefficient field of `chi` is broken as well:
    11 {{{
    12 sage: G0 = DirichletGroup(192, k)
    13 sage: chi0 = G0(chi); chi0
    14 Dirichlet character modulo 192 of conductor 24 mapping 127 |--> i, 133 |--> 1, 65 |--> -1
    15 }}}
    16 
    17 This probably explains the following bug where two ways of computing the dimension of a space of modular symbols do not give the same result:
    18 {{{
    19 sage: M = ModularSymbols(chi);
    20 sage: M.cuspidal_submodule()
    21 AssertionError: According to dimension formulas the cuspidal subspace of "Modular Symbols space of dimension 0 and level 192, weight 2, character [zeta4, 1, -1], sign 0, over Cyclotomic Field of order 4 and degree 2" has dimension 40; however, computing it using modular symbols we obtained 0, so there is a bug (please report!).
    22 }}}
    23 
     10The `check` option (`True` by default) should verify that the images of the generators have the correct orders.