path: root/src/algebra/newdata.spad.pamphlet

\documentclass{article}
\usepackage{axiom}
\begin{document}
\title{\$SPAD/src/algebra newdata.spad}
\author{Themos Tsikas, Marc Moreno Maza}
\maketitle
\begin{abstract}
\end{abstract}
\eject
\tableofcontents
\eject
\section{package IPRNTPK InternalPrintPackage}
<<package IPRNTPK InternalPrintPackage>>=
)abbrev package IPRNTPK InternalPrintPackage
++ Author: Themos Tsikas
++ Date Created: 09/09/1998
++ Date Last Updated: 09/09/1998
++ Basic Functions:
++ Related Constructors:
++ Also See: 
++ AMS Classifications:
++ Keywords:
++ References:
++ Description: A package to print strings without line-feed 
++ nor carriage-return.

InternalPrintPackage(): Exports == Implementation where

  Exports ==  with
     iprint: String -> Void
       ++ \axiom{iprint(s)} prints \axiom{s} at the current position 
       ++ of the cursor.

  Implementation == add
     iprint(s:String) == 
          PRINC(coerce(s)@Symbol)$Lisp
          FLUSH()$Lisp

@
\section{package TBCMPPK TabulatedComputationPackage}
<<package TBCMPPK TabulatedComputationPackage>>=
)abbrev package TBCMPPK TabulatedComputationPackage
++ Author: Marc Moreno Maza
++ Date Created: 09/09/1998
++ Date Last Updated: 12/16/1998
++ Basic Functions:
++ Related Constructors:
++ Also See: 
++ AMS Classifications:
++ Keywords:
++ References:
++ Description: 
++   \axiom{TabulatedComputationPackage(Key ,Entry)} provides some modest support
++   for dealing with operations with type \axiom{Key -> Entry}. The result of
++   such operations can be stored and retrieved with this package by using
++   a hash-table. The user does not need to worry about the management of
++   this hash-table. However, onnly one hash-table is built by calling
++   \axiom{TabulatedComputationPackage(Key ,Entry)}. 
++ Version: 2.

TabulatedComputationPackage(Key ,Entry): Exports == Implementation where
  Key: SetCategory
  Entry: SetCategory
  N ==> NonNegativeInteger
  H ==> HashTable(Key, Entry, "UEQUAL")
  iprintpack ==> InternalPrintPackage()

  Exports ==  with
     initTable!: () -> Void
       ++ \axiom{initTable!()} initializes the hash-table.
     printInfo!: (String, String) -> Void
       ++ \axiom{printInfo!(x,y)} initializes the mesages to be printed 
       ++ when manipulating items from the hash-table. If 
       ++ a key is retrieved then \axiom{x} is displayed. If an item is 
       ++ stored then \axiom{y} is displayed.
     startStats!: (String) -> Void
       ++ \axiom{startStats!(x)} initializes the statisitics process and
       ++ sets the comments to display when statistics are printed
     printStats!: () -> Void
       ++ \axiom{printStats!()} prints the statistics.
     clearTable!: () -> Void
       ++ \axiom{clearTable!()} clears the hash-table and assumes that
       ++ it will no longer be used.
     usingTable?: () -> Boolean
       ++ \axiom{usingTable?()} returns true iff the hash-table is used
     printingInfo?: () -> Boolean
       ++ \axiom{printingInfo?()} returns true iff messages are printed
       ++ when manipulating items from the hash-table.
     makingStats?: () -> Boolean
       ++ \axiom{makingStats?()} returns true iff the statisitics process
       ++ is running.
     extractIfCan: Key -> Union(Entry,"failed")
       ++ \axiom{extractIfCan(x)} searches the item whose key is \axiom{x}.
     insert!: (Key, Entry) -> Void
       ++ \axiom{insert!(x,y)} stores the item whose key is \axiom{x} and whose
       ++ entry is \axiom{y}.

  Implementation == add
     table?: Boolean := false
     t: H := empty()
     info?: Boolean := false
     stats?: Boolean := false
     used: NonNegativeInteger := 0
     ok: String := "o"
     ko: String := "+"
     domainName: String := empty()$String
     
     initTable!(): Void ==
       table? := true
       t := empty()
       void()
     printInfo!(s1: String, s2: String): Void ==
       (empty? s1) or (empty? s2) => void()
       not usingTable? =>
         error "in printInfo!()$TBCMPPK: not allowed to use hashtable"
       info? := true
       ok := s1
       ko := s2
       void()
     startStats!(s: String): Void == 
       empty? s => void()
       not table? =>
         error "in startStats!()$TBCMPPK: not allowed to use hashtable"
       stats? := true
       used := 0
       domainName := s
       void()
     printStats!(): Void == 
       not table? =>
         error "in printStats!()$TBCMPPK: not allowed to use hashtable"
       not stats? =>
         error "in printStats!()$TBCMPPK: statistics not started"
       output(" ")$OutputPackage
       title: String := concat("*** ", concat(domainName," Statistics ***"))
       output(title)$OutputPackage
       n: N := #t
       output("   Table     size: ", n::OutputForm)$OutputPackage
       output("   Entries reused: ", used::OutputForm)$OutputPackage
     clearTable!(): Void == 
       not table? =>
         error "in clearTable!()$TBCMPPK: not allowed to use hashtable"
       t := empty()
       table? := false
       info? := false
       stats? := false
       domainName := empty()$String
       void()
     usingTable?() == table?
     printingInfo?() == info?
     makingStats?() == stats?
     extractIfCan(k: Key): Union(Entry,"failed") ==
       not table? => "failed" :: Union(Entry,"failed")
       s: Union(Entry,"failed") := search(k,t)
       s case Entry => 
         if info? then iprint(ok)$iprintpack
         if stats? then used := used + 1
         return s
       "failed" :: Union(Entry,"failed")
     insert!(k: Key, e:Entry): Void ==
       not table? => void()
       t.k := e
       if info? then iprint(ko)$iprintpack
       void()

@
\section{domain SPLNODE SplittingNode}
<<domain SPLNODE SplittingNode>>=
)abbrev domain SPLNODE SplittingNode
++ Author: Marc Moereno Maza
++ Date Created: 07/05/1996
++ Date Last Updated:  07/19/1996
++ Basic Functions:
++ Related Constructors:
++ Also See: 
++ AMS Classifications:
++ Keywords:
++ References:
++ References:
++ Description: 
++    This domain exports a modest implementation for the
++    vertices of splitting trees. These vertices are called
++    here splitting nodes. Every of these nodes store 3 informations. 
++    The first one is its value, that is the current expression 
++    to evaluate. The second one is its condition, that is the 
++    hypothesis under which the value has to be evaluated. 
++    The last one is its status, that is a boolean flag
++    which is true iff the value is the result of its
++    evaluation under its condition. Two splitting vertices
++    are equal iff they have the sane values and the same
++    conditions (so their status do not matter).

SplittingNode(V,C) : Exports == Implementation where

  V:Join(SetCategory,Aggregate)
  C:Join(SetCategory,Aggregate)
  Z ==> Integer
  B ==> Boolean
  O ==> OutputForm
  VT ==> Record(val:V, tower:C)
  VTB ==> Record(val:V, tower:C, flag:B)

  Exports ==  SetCategory with

     empty : () -> %
       ++ \axiom{empty()} returns the same as 
       ++ \axiom{[empty()$V,empty()$C,false]$%}
     empty? : % -> B
       ++ \axiom{empty?(n)} returns true iff the node n is \axiom{empty()$%}.
     value : % -> V
       ++ \axiom{value(n)} returns the value of the node n.
     condition : % -> C
       ++ \axiom{condition(n)} returns the condition of the node n.
     status : % -> B
       ++ \axiom{status(n)} returns the status of the node n.
     construct : (V,C,B) -> %
       ++ \axiom{construct(v,t,b)} returns the non-empty node with
       ++ value v, condition t and flag b
     construct : (V,C) -> %
       ++ \axiom{construct(v,t)} returns the same as
       ++ \axiom{construct(v,t,false)}
     construct : VT ->  %
       ++ \axiom{construct(vt)} returns the same as
       ++ \axiom{construct(vt.val,vt.tower)}
     construct : List VT ->  List %
       ++ \axiom{construct(lvt)} returns the same as
       ++ \axiom{[construct(vt.val,vt.tower) for vt in lvt]}
     construct : (V, List C) -> List %
       ++ \axiom{construct(v,lt)} returns the same as
       ++ \axiom{[construct(v,t) for t in lt]}
     copy : % -> %
       ++ \axiom{copy(n)} returns a copy of n.
     setValue! : (%,V) -> %
       ++ \axiom{setValue!(n,v)} returns n whose value
       ++ has been replaced by v if it is not 
       ++ empty, else an error is produced.
     setCondition! : (%,C) -> %
       ++ \axiom{setCondition!(n,t)} returns n whose condition
       ++ has been replaced by t if it is not 
       ++ empty, else an error is produced.
     setStatus!: (%,B) -> %
       ++ \axiom{setStatus!(n,b)} returns n whose status
       ++ has been replaced by b if it is not 
       ++ empty, else an error is produced.
     setEmpty! : % -> %
       ++ \axiom{setEmpty!(n)} replaces n by \axiom{empty()$%}.
     infLex? : (%,%,(V,V) -> B,(C,C) -> B) -> B
       ++ \axiom{infLex?(n1,n2,o1,o2)} returns true iff
       ++ \axiom{o1(value(n1),value(n2))} or
       ++ \axiom{value(n1) = value(n2)} and
       ++ \axiom{o2(condition(n1),condition(n2))}.
     subNode? : (%,%,(C,C) -> B) -> B
       ++ \axiom{subNode?(n1,n2,o2)} returns true iff
       ++ \axiom{value(n1) = value(n2)} and
       ++ \axiom{o2(condition(n1),condition(n2))}

  Implementation == add

     Rep ==> VTB

     rep(n:%):Rep == n pretend Rep
     per(r:Rep):% == r pretend %

     empty() == per [empty()$V,empty()$C,false]$Rep
     empty?(n:%) == empty?((rep n).val)$V and  empty?((rep n).tower)$C
     value(n:%) == (rep n).val
     condition(n:%) == (rep n).tower
     status(n:%) == (rep n).flag
     construct(v:V,t:C,b:B) ==  per [v,t,b]$Rep
     construct(v:V,t:C) == [v,t,false]$%
     construct(vt:VT) == [vt.val,vt.tower]$%
     construct(lvt:List VT) == [[vt]$% for vt in lvt]
     construct(v:V,lt: List C) == [[v,t]$% for t in lt]
     copy(n:%) == per copy rep n
     setValue!(n:%,v:V) == 
        (rep n).val := v
        n
     setCondition!(n:%,t:C) ==
        (rep n).tower := t
        n
     setStatus!(n:%,b:B) ==
        (rep n).flag := b
        n
     setEmpty!(n:%) ==
        (rep n).val := empty()$V
        (rep n).tower := empty()$C
        n
     infLex?(n1,n2,o1,o2) ==
        o1((rep n1).val,(rep n2).val) => true
        (rep n1).val = (rep n2).val => 
           o2((rep n1).tower,(rep n2).tower)
        false
     subNode?(n1,n2,o2) ==
        (rep n1).val = (rep n2).val => 
           o2((rep n1).tower,(rep n2).tower)
        false
     -- sample() == empty()
     n1:% = n2:% ==
        (rep n1).val ~= (rep n2).val => false
        (rep n1).tower = (rep n2).tower
     n1:% ~= n2:% ==
        (rep n1).val = (rep n2).val => false
        (rep n1).tower ~= (rep n2).tower
     coerce(n:%):O ==
        l1,l2,l3,l : List O
        l1 := [message("value == "), ((rep n).val)::O]
        o1 : O := blankSeparate l1
        l2 := [message(" tower == "), ((rep n).tower)::O]
        o2 : O := blankSeparate l2
        if ((rep n).flag)
          then
            o3 := message(" closed == true")
          else 
            o3 := message(" closed == false")
        l := [o1,o2,o3]
        bracket commaSeparate l

@
\section{domain SPLTREE SplittingTree}
<<domain SPLTREE SplittingTree>>=
)abbrev domain SPLTREE SplittingTree
++ Author: Marc Moereno Maza
++ Date Created: 07/05/1996
++ Date Last Updated:  07/19/1996
++ Basic Functions:
++ Related Constructors:
++ Also See: 
++ AMS Classifications:
++ Keywords:
++ References:
++      M. MORENO MAZA "Calculs de pgcd au-dessus des tours
++      d'extensions simples et resolution des systemes d'equations
++      algebriques" These, Universite P.etM. Curie, Paris, 1997.
++ Description: 
++    This domain exports a modest implementation of splitting 
++    trees. Spliiting trees are needed when the 
++    evaluation of some quantity under some hypothesis
++    requires to split the hypothesis into sub-cases.
++    For instance by adding some new hypothesis on one
++    hand and its negation on another hand. The computations
++    are terminated is a splitting tree \axiom{a} when
++    \axiom{status(value(a))} is \axiom{true}. Thus,
++    if for the splitting tree \axiom{a} the flag
++    \axiom{status(value(a))} is \axiom{true}, then
++    \axiom{status(value(d))} is \axiom{true} for any
++    subtree \axiom{d} of \axiom{a}. This property
++    of splitting trees is called the termination
++    condition. If no vertex in a splitting tree \axiom{a}
++    is equal to another, \axiom{a} is said to satisfy
++    the no-duplicates condition. The splitting 
++    tree \axiom{a} will satisfy this condition 
++    if nodes are added to \axiom{a} by mean of 
++    \axiom{splitNodeOf!} and if \axiom{construct}
++    is only used to create the root of \axiom{a}
++    with no children.

SplittingTree(V,C) : Exports == Implementation where

  V:Join(SetCategory,Aggregate)
  C:Join(SetCategory,Aggregate)
  B ==> Boolean
  O ==> OutputForm
  NNI ==> NonNegativeInteger
  VT ==> Record(val:V, tower:C)
  VTB ==> Record(val:V, tower:C, flag:B)
  S ==> SplittingNode(V,C)
  A ==> Record(root:S,subTrees:List(%))

  Exports ==  RecursiveAggregate(S) with
     shallowlyMutable
     finiteAggregate
     extractSplittingLeaf : % -> Union(%,"failed")
       ++ \axiom{extractSplittingLeaf(a)} returns the left
       ++ most leaf (as a tree) whose status is false
       ++ if any, else "failed" is returned.
     updateStatus! : % -> %
       ++ \axiom{updateStatus!(a)} returns a where the status
       ++ of the vertices are updated to satisfy 
       ++ the "termination condition".
     construct : S -> %
       ++ \axiom{construct(s)} creates a splitting tree
       ++ with value (i.e. root vertex) given by
       ++ \axiom{s} and no children. Thus, if the
       ++ status of \axiom{s} is false, \axiom{[s]}
       ++ represents the starting point of the 
       ++ evaluation \axiom{value(s)} under the 
       ++ hypothesis \axiom{condition(s)}.
     construct : (V,C, List %) -> %
       ++ \axiom{construct(v,t,la)} creates a splitting tree
       ++ with value (i.e. root vertex) given by
       ++ \axiom{[v,t]$S} and with \axiom{la} as 
       ++ children list.
     construct : (V,C,List S) -> %
       ++ \axiom{construct(v,t,ls)} creates a splitting tree
       ++ with value (i.e. root vertex) given by
       ++ \axiom{[v,t]$S} and with children list given by
       ++ \axiom{[[s]$% for s in ls]}.
     construct : (V,C,V,List C) -> %
       ++ \axiom{construct(v1,t,v2,lt)} creates a splitting tree
       ++ with value (i.e. root vertex) given by
       ++ \axiom{[v,t]$S} and with children list given by
       ++ \axiom{[[[v,t]$S]$% for s in ls]}.
     conditions : % -> List C
       ++ \axiom{conditions(a)} returns the list of the conditions
       ++ of the leaves of a 
     result : % -> List VT
       ++ \axiom{result(a)} where \axiom{ls} is the leaves list of \axiom{a}
       ++ returns \axiom{[[value(s),condition(s)]$VT for s in ls]}
       ++ if the computations are terminated in \axiom{a} else
       ++ an error is produced.
     nodeOf? : (S,%) -> B
       ++ \axiom{nodeOf?(s,a)} returns true iff some node of \axiom{a}
       ++ is equal to \axiom{s}
     subNodeOf? : (S,%,(C,C) -> B) -> B
       ++ \axiom{subNodeOf?(s,a,sub?)} returns true iff for some node
       ++ \axiom{n} in \axiom{a} we have \axiom{s = n} or
       ++ \axiom{status(n)} and \axiom{subNode?(s,n,sub?)}.
     remove : (S,%) -> %
       ++ \axiom{remove(s,a)} returns the splitting tree obtained 
       ++ from a by removing every sub-tree \axiom{b} such
       ++ that \axiom{value(b)} and \axiom{s} have the same
       ++ value, condition and status.
     remove! : (S,%) -> %
       ++ \axiom{remove!(s,a)} replaces a by remove(s,a)
     splitNodeOf! : (%,%,List(S)) -> %
       ++ \axiom{splitNodeOf!(l,a,ls)} returns \axiom{a} where the children
       ++ list of \axiom{l} has been set to
       ++ \axiom{[[s]$% for s in ls | not nodeOf?(s,a)]}.
       ++ Thus, if \axiom{l} is not a node of \axiom{a}, this
       ++ latter splitting tree is unchanged.
     splitNodeOf! : (%,%,List(S),(C,C) -> B) -> %
       ++ \axiom{splitNodeOf!(l,a,ls,sub?)} returns \axiom{a} where the children
       ++ list of \axiom{l} has been set to
       ++ \axiom{[[s]$% for s in ls | not subNodeOf?(s,a,sub?)]}.
       ++ Thus, if \axiom{l} is not a node of \axiom{a}, this
       ++ latter splitting tree is unchanged.


  Implementation == add

     Rep ==> A

     rep(n:%):Rep == n pretend Rep
     per(r:Rep):% == r pretend %

     construct(s:S) == 
        per [s,[]]$A
     construct(v:V,t:C,la:List(%)) ==
        per [[v,t]$S,la]$A
     construct(v:V,t:C,ls:List(S)) ==
        per [[v,t]$S,[[s]$% for s in ls]]$A
     construct(v1:V,t:C,v2:V,lt:List(C)) ==
        [v1,t,([v2,lt]$S)@(List S)]$%

     empty?(a:%) == empty?((rep a).root) and empty?((rep a).subTrees)
     empty() == [empty()$S]$%

     remove(s:S,a:%) ==
       empty? a => a
       (s = value(a)) and (status(s) = status(value(a))) => empty()$%
       la := children(a)
       lb : List % := []
       while (not empty? la) repeat
          lb := cons(remove(s,first la), lb)
          la := rest la
       lb := reverse remove(empty?,lb)
       [value(value(a)),condition(value(a)),lb]$%

     remove!(s:S,a:%) ==
       empty? a => a
       (s = value(a)) and (status(s) = status(value(a))) =>
         (rep a).root := empty()$S
         (rep a).subTrees := []
         a
       la := children(a)
       lb : List % := []
       while (not empty? la) repeat
          lb := cons(remove!(s,first la), lb)
          la := rest la
       lb := reverse remove(empty()$%,lb)
       setchildren!(a,lb)

     value(a:%) == 
        (rep a).root
     children(a:%) == 
        (rep a).subTrees
     leaf?(a:%) == 
        empty? a => false
        empty? (rep a).subTrees
     setchildren!(a:%,la:List(%)) == 
        (rep a).subTrees := la
        a
     setvalue!(a:%,s:S) ==
        (rep a).root := s
        s
     cyclic?(a:%) == false
     map(foo:(S -> S),a:%) ==
       empty? a => a
       b : % := [foo(value(a))]$%
       leaf? a => b
       setchildren!(b,[map(foo,c) for c in children(a)])
     map!(foo:(S -> S),a:%) ==
       empty? a => a
       setvalue!(a,foo(value(a)))
       leaf? a => a
       setchildren!(a,[map!(foo,c) for c in children(a)])
     copy(a:%) == 
       map(copy,a)
     eq?(a1:%,a2:%) ==
       error"in eq? from SPLTREE : la vache qui rit est-elle folle?"
     nodes(a:%) == 
       empty? a => []
       leaf? a => [a]
       cons(a,concat([nodes(c) for c in children(a)]))
     leaves(a:%) ==
       empty? a => []
       leaf? a => [value(a)]
       concat([leaves(c) for c in children(a)])
     members(a:%) ==
       empty? a => []
       leaf? a => [value(a)]
       cons(value(a),concat([members(c) for c in children(a)]))
     #(a:%) ==
       empty? a => 0$NNI
       leaf? a => 1$NNI
       reduce("+",[#c for c in children(a)],1$NNI)$(List NNI)
     a1:% = a2:% ==
       empty? a1 => empty? a2
       empty? a2 => false
       leaf? a1 =>
         not leaf? a2 => false
         value(a1) =$S value(a2)
       leaf? a2 => false
       value(a1) ~=$S value(a2) => false
       children(a1) = children(a2)
     -- sample() == [sample()$S]$%
     localCoerce(a:%,k:NNI):O ==
       s : String
       if k = 1 then  s := "* " else s := "-> "
       for i in 2..k repeat s := concat("-+",s)$String
       ro : O := left(hconcat(message(s)$O,value(a)::O)$O)$O
       leaf? a => ro
       lo : List O := [localCoerce(c,k+1) for c in children(a)]
       lo := cons(ro,lo)
       vconcat(lo)$O
     coerce(a:%):O ==
       empty? a => vconcat(message(" ")$O,message("* []")$O)
       vconcat(message(" ")$O,localCoerce(a,1))
       
     extractSplittingLeaf(a:%) ==
       empty? a => "failed"::Union(%,"failed")
       status(value(a))$S => "failed"::Union(%,"failed")
       la := children(a)
       empty? la => a
       while (not empty? la) repeat
          esl := extractSplittingLeaf(first la)
          (esl case %) => return(esl)
          la := rest la
       "failed"::Union(%,"failed")
       
     updateStatus!(a:%) ==
       la := children(a)
       (empty? la) or (status(value(a))$S) => a
       done := true
       while (not empty? la) and done repeat
          done := done and status(value(updateStatus! first la))
          la := rest la
       setStatus!(value(a),done)$S
       a
     
     result(a:%) ==
       empty? a => []
       not status(value(a))$S => 
          error"in result from SLPTREE : mad cow!"
       ls : List S := leaves(a)
       [[value(s),condition(s)]$VT for s in ls]

     conditions(a:%) ==
       empty? a => []
       ls : List S := leaves(a)
       [condition(s) for s in ls]

     nodeOf?(s:S,a:%) ==
       empty? a => false
       s =$S value(a) => true
       la := children(a)
       while (not empty? la) and (not nodeOf?(s,first la)) repeat
          la := rest la
       not empty? la

     subNodeOf?(s:S,a:%,sub?:((C,C) -> B)) ==
       empty? a => false
       -- s =$S value(a) => true
       status(value(a)$%)$S and subNode?(s,value(a),sub?)$S => true
       la := children(a)
       while (not empty? la) and (not subNodeOf?(s,first la,sub?)) repeat
          la := rest la
       not empty? la

     splitNodeOf!(l:%,a:%,ls:List(S)) ==
       ln := removeDuplicates ls
       la : List % := []
       while not empty? ln repeat
          if not nodeOf?(first ln,a)
            then
              la := cons([first ln]$%, la)
          ln := rest ln
       la := reverse la
       setchildren!(l,la)$%
       if empty? la then (rep l).root := [empty()$V,empty()$C,true]$S
       updateStatus!(a)

     splitNodeOf!(l:%,a:%,ls:List(S),sub?:((C,C) -> B)) ==
       ln := removeDuplicates ls
       la : List % := []
       while not empty? ln repeat
          if not subNodeOf?(first ln,a,sub?)
            then
              la := cons([first ln]$%, la)
          ln := rest ln
       la := reverse la
       setchildren!(l,la)$%
       if empty? la then (rep l).root := [empty()$V,empty()$C,true]$S
       updateStatus!(a)

@
\section{License}
<<license>>=
--Copyright (c) 1991-2002, The Numerical ALgorithms Group Ltd.
--All rights reserved.
--
--Redistribution and use in source and binary forms, with or without
--modification, are permitted provided that the following conditions are
--met:
--
--    - Redistributions of source code must retain the above copyright
--      notice, this list of conditions and the following disclaimer.
--
--    - Redistributions in binary form must reproduce the above copyright
--      notice, this list of conditions and the following disclaimer in
--      the documentation and/or other materials provided with the
--      distribution.
--
--    - Neither the name of The Numerical ALgorithms Group Ltd. nor the
--      names of its contributors may be used to endorse or promote products
--      derived from this software without specific prior written permission.
--
--THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS
--IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED
--TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A
--PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER
--OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
--EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
--PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
--PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
--LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
--NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
--SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
@
<<*>>=
<<license>>

<<package IPRNTPK InternalPrintPackage>>
<<package TBCMPPK TabulatedComputationPackage>>
<<domain SPLNODE SplittingNode>>
<<domain SPLTREE SplittingTree>>
@
\eject
\begin{thebibliography}{99}
\bibitem{1} nothing
\end{thebibliography}
\end{document}