On the theory of graded structures
Journal of Symbolic Computation
Admissible orders and linear forms
ACM SIGSAM Bulletin
Computer algebra handbook
Standard bases for local rings of branches and their modules of differentials
Journal of Symbolic Computation
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We prove the existence of standard bases and unique remainder for ideals in power series rings with respect to arbitrary admissible term order. Several characterizations of standard bases are shown to be equivalent. We give an algorithm that computes the unique remainder of a power series modulo a principal ideal with respect to the lexicographical term order. The algorithm applies to the Weierstrass preparation theorem.