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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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Zero-equivalence in function fields defined by algebraic differential equations
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by John Shackell PDF
Trans. Amer. Math. Soc. 336 (1993), 151-171 Request permission

Abstract:

We consider function fields obtained as towers over the field of rational functions, each extension being by a solution of an algebraic differential equation. On the assumption that an oracle exists for the constants, we present two algorithms for determining whether a given expression is functionally equivalent to zero in such a field. The first, which uses Gröbner bases, has the advantage of theoretical simplicity, but is liable to involve unnecessary computations. The second method is designed with a view to eliminating these.
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Additional Information
  • © Copyright 1993 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 336 (1993), 151-171
  • MSC: Primary 12H05; Secondary 13P10
  • DOI: https://doi.org/10.1090/S0002-9947-1993-1088022-2
  • MathSciNet review: 1088022