@Article{         kar20672,
  Author        = "Shackell, John",
  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 Grobner 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.",
  date-added    = "2023-02-03 07:22:00 +0100",
  date-modified = "2023-02-03 07:22:00 +0100",
  Journal       = "Transactions of the American Mathematical Society",
  Keywords      = "zero equivalence; functional equivalence; symbolic computation; computer algebra",
  Month         = "March",
  Number        = "1",
  Pages         = "151--171",
  Publisher     = "American Mathematical Society",
  Title         = "Zero-equivalence in function-fields defined by algebraic differential-equations",
  URL           = "https://kar.kent.ac.uk/20672/",
  Volume        = "336",
  Year          = "1993",
  bdsk-url-1    = "https://kar.kent.ac.uk/20672/",
  File          = "Zero-equivalence in function-fields defined by algebraic differential-equations - S0002-9947-1993-1088022-2 - a.pdf"
}

@Article{ kar20672, Author = "Shackell, John", 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 Grobner 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.", date-added = "2023-02-03 07:22:00 +0100", date-modified = "2023-02-03 07:22:00 +0100", Journal = "Transactions of the American Mathematical Society", Keywords = "zero equivalence; functional equivalence; symbolic computation; computer algebra", Month = "March", Number = "1", Pages = "151--171", Publisher = "American Mathematical Society", Title = "Zero-equivalence in function-fields defined by algebraic differential-equations", URL = "https://kar.kent.ac.uk/20672/", Volume = "336", Year = "1993", bdsk-url-1 = "https://kar.kent.ac.uk/20672/", File = "Zero-equivalence in function-fields defined by algebraic differential-equations - S0002-9947-1993-1088022-2 - a.pdf" }