axiom-source 20170501-3 / usr / share / axiom-20170501 / src / algebra / SDVAR.spad

)abbrev domain SDVAR SequentialDifferentialVariable
++ Author:  William Sit
++ Date Created: 19 July 1990
++ Date Last Updated: 13 September 1991
++ References:
++ Kolchin, E.R. "Differential Algebra and Algebraic Groups"
++   (Academic Press, 1973).
++ Description:
++ \spadtype{OrderlyDifferentialVariable} adds a commonly used sequential
++ ranking to the set of derivatives of an ordered list of differential
++ indeterminates.  A sequential ranking is a ranking \spadfun{<} of the
++ derivatives with the property that for any derivative v,
++ there are only a finite number of derivatives u with u \spadfun{<} v.
++ This domain belongs to \spadtype{DifferentialVariableCategory}.  It
++ defines \spadfun{weight} to be just \spadfun{order}, and it
++ defines a sequential ranking \spadfun{<} on derivatives u by the
++ lexicographic order on the pair
++ (\spadfun{variable}(u), \spadfun{order}(u)).

SequentialDifferentialVariable(S) : SIG == CODE where
  S : OrderedSet

  SIG ==> DifferentialVariableCategory(S)

  CODE ==> add

    Rep := Record(var:S, ord:NonNegativeInteger)

    makeVariable(s,n) == [s, n]

    variable v     == v.var

    order v        == v.ord

    v < u ==
      variable v = variable u => order v < order u
      variable v < variable u