id: 06107901
dt: j
an: 06107901
au: Bruno, A.D.; Batkhin, A.B.
ti: Resolution of an algebraic singularity by power geometry algorithms.
so: Program. Comput. Softw. 38, No. 2, 57-72 (2012); translation from
    Programmirovanie 38, No. 2 (2012).
py: 2012
pu: MAIK Nauka/Interperiodica Publishing, Moskva; Springer, New York
la: EN
cc: 
ut: 
ci: 
li: doi:10.1134/S036176881202003X
ab: Summary: A polynomial in three variables is considered near a singular
    point where the polynomial itself and its partial derivatives vanish. A
    method for calculating asymptotic expansions in parameters for all
    branches of the set of roots of the polynomial near the singular point
    is proposed. The method is based on spatial power geometry and uses
    modern computer algebra algorithms: for calculating Gröbner bases and
    for work with algebraic curves. The implementation of the method is
    demonstrated on the example of a sixth-degree polynomial in three
    variables considered near infinity and near a degenerate singular
    point.
rv: