We extend the definition of the discriminant of unary polynomial equations to give a complete description of the multiplicities of the roots of the equations. The method based on Ritt-Wu's decomposition algorithm ...We extend the definition of the discriminant of unary polynomial equations to give a complete description of the multiplicities of the roots of the equations. The method based on Ritt-Wu's decomposition algorithm is constructive. We have given the explicit formulas of all the disciminant systems of polynomial equations whose degrees range from three to five. We also give a description of the invariants of unary equations in terms of the discriminant systems.展开更多
基金The work reported here is supported by NSFC Grant Ji 85312.
文摘We extend the definition of the discriminant of unary polynomial equations to give a complete description of the multiplicities of the roots of the equations. The method based on Ritt-Wu's decomposition algorithm is constructive. We have given the explicit formulas of all the disciminant systems of polynomial equations whose degrees range from three to five. We also give a description of the invariants of unary equations in terms of the discriminant systems.
