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)abbrev domain ODEPROB NumericalODEProblem
++ Author: Brian Dupee
++ Date Created: December 1997
++ Date Last Updated: December 1997
++ References:
++ Dupe95 Using Computer Algebra to Choose and Apply Numerical Routines
++ Dewa92 Using Computer Algebra to Select Numerical Algorithms
++ Description:
++ \axiomType{NumericalODEProblem} is a \axiom{domain}
++ for the representation of Numerical ODE problems for use
++ by ANNA. 
++
++ The representation is of type: 
++
++ \axiomType{Record}(xinit:\axiomType{DoubleFloat},\br
++ xend:\axiomType{DoubleFloat},\br
++ fn:\axiomType{Vector Expression DoubleFloat},\br
++ yinit:\axiomType{List DoubleFloat},intvals:\axiomType{List DoubleFloat},\br
++ g:\axiomType{Expression DoubleFloat},abserr:\axiomType{DoubleFloat},\br
++ relerr:\axiomType{DoubleFloat})
++

NumericalODEProblem() : SIG == CODE where

  DFB   ==> DoubleFloat
  VEDFB ==> Vector Expression DoubleFloat
  LDFB  ==> List DoubleFloat
  EDFB  ==> Expression DoubleFloat
  ODEAB ==> Record(xinit:DFB,xend:DFB,fn:VEDFB,yinit:LDFB,intvals:LDFB,
                   g:EDFB,abserr:DFB,relerr:DFB)

  SIG ==> SetCategory with

    coerce : ODEAB -> %
      ++ coerce(x) is not documented

    coerce : % -> OutputForm
      ++ coerce(x) is not documented

    retract : % -> ODEAB
      ++ retract(x) is not documented

  CODE ==> add

      Rep := ODEAB
 
      coerce(s:ODEAB) == s

      coerce(x:%):OutputForm ==
        (retract(x))::OutputForm

      retract(x:%):ODEAB == x :: Rep