论文信息 - A new zero-test for formal power series

A new zero-test for formal power series

In this paper, we present a new zero-test for expressions which are constructed from formal power solutions to algebraic differential equations using the ring operations and differentiation. We also provide a survey of all existing methods that we know of and a detailed comparison of these methods with our approach.

Joris van der Hoeven

[1] Ariane Péladan-Germa,et al. Testing Identities of Series Defined by Algebraic Partial Differential Equations , 1995, AAECC.

[2] H. T. Kung,et al. Fast Algorithms for Manipulating Formal Power Series , 1978, JACM.

[3] James Ax,et al. On Schanuel's Conjectures , 1971 .

[4] Joris van der Hoeven,et al. Fast Evaluation of Holonomic Functions Near and in Regular Singularities , 2001, J. Symb. Comput..

[5] John Shackell. Zero-equivalence in function fields defined by algebraic differential equations , 1993 .

[6] Daniel Richardson,et al. The Uniformity Conjecture , 2000, CCA.

[7] Leonard Lipshitz,et al. Decision problems for differential equations , 1989, Journal of Symbolic Logic.

[8] François Boulier,et al. Étude et implantation de quelques algorithmes en algèbre différentielle. (Study and implementation of some algorithms in differential algebra) , 1994 .

[9] Joris van der Hoeven,et al. Relax, but Don't be Too Lazy , 2002, J. Symb. Comput..

[10] J. Shackle,et al. A differential-equations approach to functional equivalence , 1989, ISSAC '89.

[11] Robert H. Risch. ALGEBRAIC PROPERTIES OF THE ELEMENTARY FUNCTIONS OF ANALYSIS. , 1979 .

[12] Jens Blanck,et al. Computability and complexity in analysis : 4th International Workshop, CCA 2000, Swansea, UK, September 17-19, 2000 : selected papers , 2001 .

[13] L. Lipshitz,et al. Power series solutions of algebraic differential equations , 1984 .