@article{KANNAN198569,
    Abstract = {We consider a system of linear equations of the form A(x)X(x) = b(x), where A(x), b(x) are given m × n and m × 1 matrices with entries from Q[x], the ring of polynomials in the variable x over the rationals. We provide a polynomial-time algorithm to find the general solution of this system over Q[x]. This is accomplished by devising a polynomial-time algorithm to find the triangular canonical form (Hermite form) of the matrix A(x) using unimodular column operations. As applications we are able to give polynomial-time algorithms for finding the diagonal (Smith canonical) form of a polynomial matrix, testing whether two given matrices of rational entries are similar and for finding the invariant factors of a matrix of rationals.},
    Author = {Kannan, R.},
    File = {Solving systems of linear equations over polynomials - 1-s2.0-0304397585901318-main.pdf},
    ISSN = {0304-3975},
    Journal = {Theoretical Computer Science},
    Note = {Third Conference on Foundations of Software Technology and Theoretical Computer Science},
    Pages = {69-88},
    Title = {Solving systems of linear equations over polynomials},
    URL = {https://www.sciencedirect.com/science/article/pii/0304397585901318},
    Volume = {39},
    Year = {1985},
    bdsk-url-1 = {https://www.sciencedirect.com/science/article/pii/0304397585901318},
    bdsk-url-2 = {https://doi.org/10.1016/0304-3975(85)90131-8},
    date-added = {2023-05-04 13:19:11 +0200},
    date-modified = {2023-05-04 13:19:11 +0200},
    doi = {10.1016/0304-3975(85)90131-8}
}

@article{KANNAN198569, Abstract = {We consider a system of linear equations of the form A(x)X(x) = b(x), where A(x), b(x) are given m × n and m × 1 matrices with entries from Q[x], the ring of polynomials in the variable x over the rationals. We provide a polynomial-time algorithm to find the general solution of this system over Q[x]. This is accomplished by devising a polynomial-time algorithm to find the triangular canonical form (Hermite form) of the matrix A(x) using unimodular column operations. As applications we are able to give polynomial-time algorithms for finding the diagonal (Smith canonical) form of a polynomial matrix, testing whether two given matrices of rational entries are similar and for finding the invariant factors of a matrix of rationals.}, Author = {Kannan, R.}, File = {Solving systems of linear equations over polynomials - 1-s2.0-0304397585901318-main.pdf}, ISSN = {0304-3975}, Journal = {Theoretical Computer Science}, Note = {Third Conference on Foundations of Software Technology and Theoretical Computer Science}, Pages = {69-88}, Title = {Solving systems of linear equations over polynomials}, URL = {https://www.sciencedirect.com/science/article/pii/0304397585901318}, Volume = {39}, Year = {1985}, bdsk-url-1 = {https://www.sciencedirect.com/science/article/pii/0304397585901318}, bdsk-url-2 = {https://doi.org/10.1016/0304-3975(85)90131-8}, date-added = {2023-05-04 13:19:11 +0200}, date-modified = {2023-05-04 13:19:11 +0200}, doi = {10.1016/0304-3975(85)90131-8} }