Changes between Initial Version and Version 9 of Ticket #30518


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Timestamp:
Mar 25, 2021, 12:46:19 PM (18 months ago)
Author:
Vincent Delecroix
Comment:

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  • Ticket #30518

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

    initial v9  
    1 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.
     1{{{
     2sage: K.<i> = QuadraticField(-1)
     3sage: L = K.extension(x^2 - 6*x - 4, 'a1')
     4sage: eigval = L.gen()
     5sage: eigval_conj = eigval.galois_conjugates(QQbar)
     6sage: f0 = hom(eigval.parent(), QQbar, eigval_conj[0])
     7sage: f1 = hom(eigval.parent(), QQbar, eigval_conj[1])
     8sage: f0(i)  # wrong embedding!!
     90.?e-54 - 1.000000000000000?*I
     10sage: f1(i)  # wrong embedding!!
     110.?e-54 - 1.000000000000000?*I
     12}}}
     13
     14As 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.
    215
    316By converting the matrix to `QQbar` first: