MathAction Jet BaseFunctionCategory

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BaseFunctionCategory (BFC)

axiom

)lib JBC

   JetBundleCategory is now explicitly exposed in frame initial
   JetBundleCategory will be automatically loaded when needed from
      /var/zope2/var/LatexWiki/JBC.NRLIB/code

axiom

)lib SEM

   SparseEchelonMatrix is now explicitly exposed in frame initial
   SparseEchelonMatrix will be automatically loaded when needed from
      /var/zope2/var/LatexWiki/SEM.NRLIB/code

axiom

)lib JBFC

   JetBundleFunctionCategory is now explicitly exposed in frame initial

   JetBundleFunctionCategory will be automatically loaded when needed
      from /var/zope2/var/LatexWiki/JBFC.NRLIB/code

spad

)abb category     BFC      BaseFunctionCategory

M    ==> Matrix
Sy   ==> Symbol
PI   ==> PositiveInteger
NNI  ==> NonNegativeInteger
I    ==> Integer
B    ==> Boolean
L    ==> List
OUT  ==> OutputForm
JBC  ==> JetBundleCategory
JBFC ==> JetBundleFunctionCategory JB
SEM  ==> SparseEchelonMatrix(JB,$)

SIMPREC ==> Record(Sys:L $, JM:SEM, Depend:Union("failed",L L NNI))
LDREC   ==> Record(LD:JB, Fake?:B, Dep:L NNI, Fun:$)

errmsg ==> "cannot simplify"

++ Description:
++ \axiomType{BaseFunctionCategory} defines the category of functions
++ (local sections) of the base space of a jet bundle, i.e. functions
++ depending only on the independent variables. Such a category is needed
++ e.g. for the representation of solutions.

BaseFunctionCategory(JB:JBC) : Category == Def where

  errmsg ==> "Only functions of independent variables allowed"

  Def ==> JBFC add

    U(i:PI):$ == error errmsg

    U():$ == error errmsg

    P(i:PI,l:L NNI):$ == error errmsg

    P(l:L NNI):$ == error errmsg

    P(i:PI,l:NNI):$ == error errmsg

    P(i:NNI):$ == error errmsg

spad

   Compiling FriCAS source code from file 
      /var/zope2/var/LatexWiki/2606282796454758026-25px002.spad using 
      old system compiler.
   BFC abbreviates category BaseFunctionCategory 
   processing macro definition M ==> Matrix 

   processing macro definition Sy ==> Symbol 

   processing macro definition PI ==> PositiveInteger 

   processing macro definition NNI ==> NonNegativeInteger 

   processing macro definition I ==> Integer 

   processing macro definition B ==> Boolean 

   processing macro definition L ==> List 

   processing macro definition OUT ==> OutputForm 

   processing macro definition JBC ==> JetBundleCategory 

   processing macro definition JBFC ==> JetBundleFunctionCategory JB 

   processing macro definition SEM ==> SparseEchelonMatrix(JB,$) 

   processing macro definition SIMPREC ==> Record(Sys: L $,JM: SEM,Depend: Union(failed,L L NNI)) 

   processing macro definition LDREC ==> Record(LD: JB,Fake?: B,Dep: L NNI,Fun: $) 

   processing macro definition errmsg ==> cannot simplify 

   processing macro definition cannot simplify ==> Only functions of independent variables allowed 
   processing macro definition Def ==> -- the constructor capsule 
------------------------------------------------------------------------
   initializing NRLIB BFC for BaseFunctionCategory 
   compiling into NRLIB BFC 

;;;     ***       |BaseFunctionCategory| REDEFINED
Time: 0 SEC.

   BFC- abbreviates domain BaseFunctionCategory& 
------------------------------------------------------------------------
   initializing NRLIB BFC- for BaseFunctionCategory& 
   compiling into NRLIB BFC- 
   compiling exported U : PositiveInteger -> S
      BFC-;U;PiS;1 is replaced by errorOnly functions of independent variables allowed 
Time: 0.03 SEC.

   compiling exported U : () -> S
      BFC-;U;S;2 is replaced by errorOnly functions of independent variables allowed 
Time: 0 SEC.

   compiling exported P : (PositiveInteger,List NonNegativeInteger) -> S
      BFC-;P;PiLS;3 is replaced by errorOnly functions of independent variables allowed 
Time: 0.01 SEC.

   compiling exported P : List NonNegativeInteger -> S
      BFC-;P;LS;4 is replaced by errorOnly functions of independent variables allowed 
Time: 0.06 SEC.

   compiling exported P : (PositiveInteger,NonNegativeInteger) -> S
      BFC-;P;PiNniS;5 is replaced by errorOnly functions of independent variables allowed 
Time: 0.01 SEC.

   compiling exported P : NonNegativeInteger -> S
      BFC-;P;NniS;6 is replaced by errorOnly functions of independent variables allowed 
Time: 0 SEC.

(time taken in buildFunctor:  0)

;;;     ***       |BaseFunctionCategory&| REDEFINED
Time: 0 SEC.

   Cumulative Statistics for Constructor BaseFunctionCategory&
      Time: 0.11 seconds

   finalizing NRLIB BFC- 
   Processing BaseFunctionCategory& for Browser database:
--------constructor---------
------------------------------------------------------------------------
   BaseFunctionCategory& is now explicitly exposed in frame initial 
   BaseFunctionCategory& will be automatically loaded when needed from 
      /var/zope2/var/LatexWiki/BFC-.NRLIB/code
   finalizing NRLIB BFC 
   Processing BaseFunctionCategory for Browser database:
--------constructor---------
------------------------------------------------------------------------
   BaseFunctionCategory is now explicitly exposed in frame initial 
   BaseFunctionCategory will be automatically loaded when needed from 
      /var/zope2/var/LatexWiki/BFC.NRLIB/code

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