Changes between Version 9 and Version 11 of Ticket #30518


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Timestamp:
Mar 25, 2021, 12:52:31 PM (18 months ago)
Author:
Vincent Delecroix
Comment:

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  • Ticket #30518

    • Property Status changed from needs_review to needs_work
    • Property Dependencies changed from to #31558
    • Property Branch changed from u/vdelecroix/30518 to
    • Property Authors changed from Vincent Delecroix to
    • Property Commit changed from cf668005799173205566b30be5bf0559752f14c9 to
    • Property Summary changed from homomorphism of extension fields do not preserve canonical embeddings of the base to eigenvectors over QQbar are incorrectly conjugated
  • Ticket #30518 – Description

    v9 v11  
    1 {{{
    2 sage: K.<i> = QuadraticField(-1)
    3 sage: L = K.extension(x^2 - 6*x - 4, 'a1')
    4 sage: eigval = L.gen()
    5 sage: eigval_conj = eigval.galois_conjugates(QQbar)
    6 sage: f0 = hom(eigval.parent(), QQbar, eigval_conj[0])
    7 sage: f1 = hom(eigval.parent(), QQbar, eigval_conj[1])
    8 sage: f0(i)  # wrong embedding!!
    9 0.?e-54 - 1.000000000000000?*I
    10 sage: f1(i)  # wrong embedding!!
    11 0.?e-54 - 1.000000000000000?*I
    12 }}}
    13 
    14 As the consequence eigenvectors over QQbar could get incorrectly conjugated. In the following example from [https://groups.google.com/g/sage-devel/c/9Ss98-XKR9c devel], the eigenvectors of a matrix over `QuadraticField(-1)` are computed in two ways, one of which incorrectly returns the conjugate of some eigenvectors.
     1Eigenvectors over QQbar could get incorrectly conjugated. In the following example from [https://groups.google.com/g/sage-devel/c/9Ss98-XKR9c devel], the eigenvectors of a matrix over `QuadraticField(-1)` are computed in two ways, one of which incorrectly returns the conjugate of some eigenvectors.
    152
    163By converting the matrix to `QQbar` first: