#!/usr/bin/env perl
# -*-Perl-*-
##
## @file    createExampleSBML.pl
## @brief   Creates example SBML $models presented in the SBML specification.
## @author  Akiya Jouraku
## @author  Michael Hucka
## @author  Sarah Keating
## 
## <!--------------------------------------------------------------------------
## This sample program is distributed under a different license than the rest
## of libSBML.  This program uses the open-source MIT license, as follows:
##
## Copyright (c) 2013-2018 by the California Institute of Technology
## (California, USA), the European Bioinformatics Institute (EMBL-EBI, UK)
## and the University of Heidelberg (Germany), with support from the National
## Institutes of Health (USA) under grant R01GM070923.  All rights reserved.
##
## Permission is hereby granted, free of charge, to any person obtaining a
## copy of this software and associated documentation files (the "Software"),
## to deal in the Software without restriction, including without limitation
## the rights to use, copy, modify, merge, publish, distribute, sublicense,
## and/or sell copies of the Software, and to permit persons to whom the
## Software is furnished to do so, subject to the following conditions:
##
## The above copyright notice and this permission notice shall be included in
## all copies or substantial portions of the Software.
##
## THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
## IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
## FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
## THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
## LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
## FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER
## DEALINGS IN THE SOFTWARE.
##
## Neither the name of the California Institute of Technology (Caltech), nor
## of the European Bioinformatics Institute (EMBL-EBI), nor of the University
## of Heidelberg, nor the names of any contributors, may be used to endorse
## or promote products derived from this software without specific prior
## written permission.
## ------------------------------------------------------------------------ -->
## 


use LibSBML;
no strict;


#
# These variables are used in writeExampleSBML when writing an SBML
# document.  They are handed to libSBML functions in order to include
# the program information into comments within the SBML file.
#
$ProgramName = "createExampleModels";
$ProgramVersion = "1.0.0";

#
# The SBML Level and Version of the example SBML $models.
#
$Level = 2;
$Version = 4;

sub trim($)
{
	my $string = shift;
	$string =~ s/^\s+//;
	$string =~ s/\s+$//;
	return $string;
}


#===============================================================================
#
#
# Functions for creating the Example SBML documents.
#
#
#===============================================================================


# 
# 
# Creates an SBML $model represented in "7.1 A Simple example application of SBML"
# in the SBML Level 2 Version 4 Specification.
# 
# 

sub createExampleEnzymaticReaction() {
    $level = $Level;
    $version = $Version;

    #---------------------------------------------------------------------------
    #
    # Creates an SBMLDocument object 
    #
    #---------------------------------------------------------------------------

    $sbmlDoc = new LibSBML::SBMLDocument($level, $version);

    #---------------------------------------------------------------------------
    #
    # Creates a Model object inside the SBMLDocument object.
    #
    #---------------------------------------------------------------------------

    $model = $sbmlDoc->createModel();
    $model->setId("EnzymaticReaction");

    #---------------------------------------------------------------------------
    #
    # Creates UnitDefinition objects inside the Model object.
    #
    #---------------------------------------------------------------------------
    
    #---------------------------------------------------------------------------  
    # (UnitDefinition1) Creates an UnitDefinition object ("per_second")
    #---------------------------------------------------------------------------

    $unitdef = $model->createUnitDefinition();
    $unitdef->setId("per_second");

    #  Creates an Unit inside the UnitDefinition object 

    $unit = $unitdef->createUnit();
    $unit->setKind($LibSBML::UNIT_KIND_SECOND);
    $unit->setExponent(-1);

    #--------------------------------------------------------------------------------
    # (UnitDefinition2) Creates an UnitDefinition object ("litre_per_mole_per_second") 
    #--------------------------------------------------------------------------------

    # Note that we can reuse the pointers '$unitdef' and 'unit' because the
    # actual UnitDefinition object (along with the Unit objects within it)
    # is already attached to the Model object.

    $unitdef = $model->createUnitDefinition();
    $unitdef->setId("litre_per_mole_per_second");

    #  Creates an Unit inside the UnitDefinition object ("litre_per_mole_per_second")

    $unit = $unitdef->createUnit();
    $unit->setKind($LibSBML::UNIT_KIND_MOLE);
    $unit->setExponent(-1);

    #  Creates an Unit inside the UnitDefinition object ("litre_per_mole_per_second")

    $unit = $unitdef->createUnit();
    $unit->setKind($LibSBML::UNIT_KIND_LITRE);
    $unit->setExponent(1);

    #  Creates an Unit inside the UnitDefinition object ("litre_per_mole_per_second")

    $unit = $unitdef->createUnit();
    $unit->setKind($LibSBML::UNIT_KIND_SECOND);
    $unit->setExponent(-1);


    #---------------------------------------------------------------------------
    #
    # Creates a Compartment object inside the Model object.
    #
    #---------------------------------------------------------------------------

    $compName = "cytosol";

    # Creates a Compartment object ("cytosol")

    $comp = $model->createCompartment();
    $comp->setId($compName);

    # Sets the "size" attribute of the Compartment object.
    #
    # We are not setting the units on the compartment size explicitly, so
    # the units of this Compartment object will be the default SBML units of
    # volume, which are liters.
    #
    $comp->setSize(1e-14);


    #---------------------------------------------------------------------------
    #
    # Creates Species objects inside the Model object.
    #
    #---------------------------------------------------------------------------
    
    #---------------------------------------------------------------------------
    # (Species1) Creates a Species object ("ES")
    #---------------------------------------------------------------------------

    # Create the Species objects inside the Model object.

    $sp = $model->createSpecies();
    $sp->setId("ES");
    $sp->setName("ES");

    # Sets the "compartment" attribute of the Species object to identify the 
    # compartment in which the Species object is located.

    $sp->setCompartment($compName);

    # Sets the "initialAmount" attribute of the Species object.
    #
    #  In SBML, the units of a Species object's initial quantity are
    #  determined by two attributes, "substanceUnits" and
    #  "hasOnlySubstanceUnits", and the "spatialDimensions" attribute
    #  of the Compartment object ("cytosol") in which the species
    #  object is located.  Here, we are using the default values for
    #  "substanceUnits" (which is "mole") and "hasOnlySubstanceUnits"
    #  (which is "False").  The compartment in which the species is
    #  located uses volume units of liters, so the units of these
    #  species (when the species appear in numerical formulas in the
    #  $model) will be moles/liters.
    #
    $sp->setInitialAmount(0);

    #---------------------------------------------------------------------------
    # (Species2) Creates a Species object ("P")
    #---------------------------------------------------------------------------

    $sp = $model->createSpecies();
    $sp->setCompartment($compName);
    $sp->setId("P");
    $sp->setName("P");
    $sp->setInitialAmount(0);

    #---------------------------------------------------------------------------
    # (Species3) Creates a Species object ("S")
    #---------------------------------------------------------------------------

    $sp = $model->createSpecies();
    $sp->setCompartment($compName);
    $sp->setId("S");
    $sp->setName("S");
    $sp->setInitialAmount(1e-20);

    #---------------------------------------------------------------------------
    # (Species4) Creates a Species object ("E")
    #---------------------------------------------------------------------------

    $sp = $model->createSpecies();
    $sp->setCompartment($compName);
    $sp->setId("E");
    $sp->setName("E");
    $sp->setInitialAmount(5e-21);


    #---------------------------------------------------------------------------
    #
    # Creates Reaction objects inside the Model object.
    #
    #---------------------------------------------------------------------------

    #---------------------------------------------------------------------------
    # (Reaction1) Creates a Reaction object ("veq").
    #---------------------------------------------------------------------------

    $reaction = $model->createReaction();
    $reaction->setId("veq");

    # (Reactant1) Creates a Reactant object that references Species "E"
    # in the model.  The object will be created within the reaction in the
    # SBML <listOfReactants>.

    $spr = $reaction->createReactant();
    $spr->setSpecies("E");

    # (Reactant2) Creates a Reactant object that references Species "S"
    # in the $model->

    $spr = $reaction->createReactant();
    $spr->setSpecies("S");

    #---------------------------------------------------------------------------
    # (Product1) Creates a Product object that references Species "ES" in
    # the $model.
    #---------------------------------------------------------------------------

    $spr = $reaction->createProduct();
    $spr->setSpecies("ES");

    #---------------------------------------------------------------------------
    # Creates a KineticLaw object inside the Reaction object ("veq"). 
    #---------------------------------------------------------------------------

    $kl = $reaction->createKineticLaw();

    #---------------------------------------------------------------------------
    # Creates an object which represents the following math of the
    # KineticLaw.
    #
    #      <math xmlns="http://www.w3.org/1998/Math/MathML">
    #        <apply>
    #          <times/>
    #          <ci> cytosol </ci>
    #          <apply>
    #            <minus/>
    #            <apply>
    #              <times/>
    #              <ci> kon </ci>
    #              <ci> E </ci>
    #              <ci> S </ci>
    #            </apply>
    #            <apply>
    #              <times/>
    #              <ci> koff </ci>
    #              <ci> ES </ci>
    #            </apply>
    #          </apply>
    #        </apply>
    #      </math>
    #
    #---------------------------------------------------------------------------

    #------------------------------------------
    #
    # create nodes representing the variables
    #
    #------------------------------------------

    $astCytosol = new LibSBML::ASTNode($LibSBML::AST_NAME);
    $astCytosol->setName("cytosol");

    $astKon = new LibSBML::ASTNode($LibSBML::AST_NAME);
    $astKon->setName("kon");

    $astKoff = new LibSBML::ASTNode($LibSBML::AST_NAME);
    $astKoff->setName("koff");

    $astE = new LibSBML::ASTNode($LibSBML::AST_NAME);
    $astE->setName("E");

    $astS = new LibSBML::ASTNode($LibSBML::AST_NAME);
    $astS->setName("S");

    $astES = new LibSBML::ASTNode($LibSBML::AST_NAME);
    $astES->setName("ES");


    #--------------------------------------------
    #
    # create node representing
    #            <apply>
    #              <times/>
    #              <ci> koff </ci>
    #              <ci> ES </ci>
    #            </apply>
    #
    #--------------------------------------------

    $astTimes1 = new LibSBML::ASTNode($LibSBML::AST_TIMES);
    $astTimes1->addChild($astKoff);
    $astTimes1->addChild($astES);

    #--------------------------------------------
    #
    # create node representing
    #            <apply>
    #              <times/>
    #              <ci> kon </ci>
    #              <ci> E </ci>
    #              <ci> S </ci>
    #            </apply>
    #
    #
    # (NOTES)
    #
    #  Since there is a restriction with an of "<times/>" operation
    #  such that the is a binary class and thus only two operands can
    #  be directly added, the following code in this comment block is invalid
    #  because the code directly adds three <ci> ASTNodes to <times/> ASTNode.
    #
    #    *astTimes = ASTNode(AST_TIMES);
    #    astTimes->addChild(astKon);
    #    astTimes->addChild(astE);
    #    astTimes->addChild(astS);
    #
    # The following valid code after this comment block creates the ASTNode
    # as a binary tree.
    #
    # Please see "Converting between ASTs and text strings" described
    # at http://sbml.org/Software/libSBML/docs/cpp-api/class_a_s_t_node.html
    # for the detailed information.
    #
    #--------------------------------------------

    $astTimes2 = new LibSBML::ASTNode($LibSBML::AST_TIMES);
    $astTimes2->addChild($astE);
    $astTimes2->addChild($astS);

    $astTimes = new LibSBML::ASTNode($LibSBML::AST_TIMES);
    $astTimes->addChild($astKon);
    $astTimes->addChild($astTimes2);

    #--------------------------------------------
    #
    # create node representing
    #          <apply>
    #            <minus/>
    #            <apply>
    #              <times/>
    #              <ci> kon </ci>
    #              <ci> E </ci>
    #              <ci> S </ci>
    #            </apply>
    #            <apply>
    #              <times/>
    #              <ci> koff </ci>
    #              <ci> ES </ci>
    #            </apply>
    #          </apply>
    #
    #--------------------------------------------

    $astMinus = new LibSBML::ASTNode($LibSBML::AST_MINUS);
    $astMinus->addChild($astTimes);
    $astMinus->addChild($astTimes1);


    #--------------------------------------------
    #
    # create node representing
    #        <apply>
    #          <times/>
    #          <ci> cytosol </ci>
    #          <apply>
    #            <minus/>
    #            <apply>
    #              <times/>
    #              <ci> kon </ci>
    #              <ci> E </ci>
    #              <ci> S </ci>
    #            </apply>
    #            <apply>
    #              <times/>
    #              <ci> koff </ci>
    #              <ci> ES </ci>
    #            </apply>
    #          </apply>
    #        </apply>
    #
    #--------------------------------------------

    $astMath = new LibSBML::ASTNode($LibSBML::AST_TIMES);
    $astMath->addChild($astCytosol);
    $astMath->addChild($astMinus);

    #---------------------------------------------
    #
    # set the Math element
    #
    #------------------------------------------------

    $kl->setMath($astMath);

    #---------------------------------------------------------------------------
    # Creates local Parameter objects inside the KineticLaw object.
    #---------------------------------------------------------------------------

    # Creates a Parameter ("kon")

    $para = $kl->createParameter();
    $para->setId("kon");
    $para->setValue(1000000);
    $para->setUnits("litre_per_mole_per_second");

    # Creates a Parameter ("koff")

    $para = $kl->createParameter();
    $para->setId("koff");
    $para->setValue(0.2);
    $para->setUnits("per_second");



    #---------------------------------------------------------------------------
    # (Reaction2) Creates a Reaction object ("vcat") .
    #---------------------------------------------------------------------------

    $reaction = $model->createReaction();
    $reaction->setId("vcat");
    $reaction->setReversible(0);

    #---------------------------------------------------------------------------
    # Creates Reactant objects inside the Reaction object ("vcat").
    #---------------------------------------------------------------------------

    # (Reactant1) Creates a Reactant object that references Species "ES" in the
    # $model.

    $spr = $reaction->createReactant();
    $spr->setSpecies("ES");

    #---------------------------------------------------------------------------
    # Creates a Product object inside the Reaction object ("vcat").
    #---------------------------------------------------------------------------

    # (Product1) Creates a Product object that references Species "E" in the $model.

    $spr = $reaction->createProduct();
    $spr->setSpecies("E");

    # (Product2) Creates a Product object that references Species "P" in the $model.

    $spr = $reaction->createProduct();
    $spr->setSpecies("P");

    #---------------------------------------------------------------------------
    # Creates a KineticLaw object inside the Reaction object ("vcat").
    #---------------------------------------------------------------------------

    $kl = $reaction->createKineticLaw();

    #---------------------------------------------------------------------------
    # Sets a math (object) to the KineticLaw object.
    #---------------------------------------------------------------------------

    # To create mathematical expressions, one would typically construct
    # an tree as the above example code which creates a math of another
    # KineticLaw object.  Here, to save some space and illustrate another approach 
    # of doing it, we will write out the formula in MathML form and then use a 
    # libSBML convenience function to create the tree for us.
    # (This is a bit dangerous; it's very easy to make mistakes when writing MathML 
    # by hand, so in a real program, we would not really want to do it this way.)

    $mathXMLString = '<?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
      <apply>
        <times/>
        <ci> cytosol </ci>
        <ci> kcat </ci>
        <ci> ES </ci>
      </apply>
    </math>';
 
    $astMath = LibSBML::readMathMLFromString($mathXMLString);
    $kl->setMath($astMath);

    #---------------------------------------------------------------------------
    # Creates local Parameter objects inside the KineticLaw object.
    #---------------------------------------------------------------------------

    # Creates a Parameter ("kcat")

    $para = $kl->createParameter();
    $para->setId("kcat");
    $para->setValue(0.1);
    $para->setUnits("per_second");


    # Returns the created SBMLDocument object.
    # The returned object must be explicitly deleted by the caller,
    # otherwise a memory leak will happen.

    return $sbmlDoc;
}

# 
# 
# Creates an SBML $model represented in "7.2 Example involving units"
# in the SBML Level 2 Version 4 Specification.
# 
# 

sub createExampleInvolvingUnits() {
    $level = $Level;
    $version = $Version;

    #---------------------------------------------------------------------------
    #
    # Creates an SBMLDocument object 
    #
    #---------------------------------------------------------------------------

    $sbmlDoc = new LibSBML::SBMLDocument($level, $version);

    # Adds the namespace for XHTML to the SBMLDocument object.  We need this
    # because we will add notes to the model.  (By default, the SBML document
    # created by SBMLDocument only declares the SBML XML namespace.)

    $sbmlDoc->getNamespaces()->add("http://www.w3.org/1999/xhtml", "xhtml");

    #---------------------------------------------------------------------------
    #
    # Creates a Model object inside the SBMLDocument object.
    #
    #---------------------------------------------------------------------------

    $model = $sbmlDoc->createModel();
    $model->setId("unitsExample");

    #---------------------------------------------------------------------------
    #
    # Creates UnitDefinition objects inside the Model object.
    #
    #---------------------------------------------------------------------------

    #---------------------------------------------------------------------------  
    # (UnitDefinition1) Creates an UnitDefinition object ("substance").
    #
    # This has the effect of redefining the default unit of subtance for the
    # whole model.
    #---------------------------------------------------------------------------

    $unitdef = $model->createUnitDefinition();
    $unitdef->setId("substance");

    #  Creates an Unit inside the UnitDefinition object 

    $unit = $unitdef->createUnit();
    $unit->setKind($LibSBML::UNIT_KIND_MOLE);
    $unit->setScale(-3);

    #--------------------------------------------------------------------------------
    # (UnitDefinition2) Creates an UnitDefinition object ("mmls") 
    #--------------------------------------------------------------------------------

    # Note that we can reuse the pointers '$unitdef' and 'unit' because the
    # actual UnitDefinition object (along with the Unit objects within it)
    # is already attached to the Model object.

    $unitdef = $model->createUnitDefinition();
    $unitdef->setId("mmls");

    #  Creates an Unit inside the UnitDefinition object ("mmls")

    $unit = $unitdef->createUnit();
    $unit->setKind($LibSBML::UNIT_KIND_MOLE);
    $unit->setScale(-3);

    #  Creates an Unit inside the UnitDefinition object ("mmls")

    $unit = $unitdef->createUnit();
    $unit->setKind($LibSBML::UNIT_KIND_LITRE);
    $unit->setExponent(-1);

    #  Creates an Unit inside the UnitDefinition object ("mmls")

    $unit = $unitdef->createUnit();
    $unit->setKind($LibSBML::UNIT_KIND_SECOND);
    $unit->setExponent(-1);

    #--------------------------------------------------------------------------------
    # (UnitDefinition3) Creates an UnitDefinition object ("mml") 
    #--------------------------------------------------------------------------------

    $unitdef = $model->createUnitDefinition();
    $unitdef->setId("mml");

    #  Creates an Unit inside the UnitDefinition object ("mml")

    $unit = $unitdef->createUnit();
    $unit->setKind($LibSBML::UNIT_KIND_MOLE);
    $unit->setScale(-3);

    #  Creates an Unit inside the UnitDefinition object ("mml")

    $unit = $unitdef->createUnit();
    $unit->setKind($LibSBML::UNIT_KIND_LITRE);
    $unit->setExponent(-1);


    #---------------------------------------------------------------------------
    #
    # Creates a Compartment object inside the Model object.
    #
    #---------------------------------------------------------------------------

    $compName = "cell";

    # Creates a Compartment object ("cell")

    $comp = $model->createCompartment();
    $comp->setId($compName);

    # Sets the "size" attribute of the Compartment object.
    #
    #   The units of this Compartment object is the default SBML 
    #   units of volume (litre), and thus we don't have to explicitly invoke 
    #   setUnits("litre") function to set the default units.
    #
    $comp->setSize(1);


    #---------------------------------------------------------------------------
    #
    # Creates Species objects inside the Model object.
    #
    #---------------------------------------------------------------------------

    
    #---------------------------------------------------------------------------
    # (Species1) Creates a Species object ("x0")
    #---------------------------------------------------------------------------

    $sp = $model->createSpecies();
    $sp->setId("x0");

    # Sets the "compartment" attribute of the Species object to identify the 
    # compartnet in which the Species object located.

    $sp->setCompartment($compName);

    # Sets the "initialConcentration" attribute of the Species object.
    #
    #  The units of this Species object is determined by two attributes of this 
    #  Species object ("substanceUnits" and "hasOnlySubstanceUnits") and the
    #  "spatialDimensions" attribute of the Compartment object ("cytosol") in which 
    #  this species object is located.
    #  Since the default values are used for "substanceUnits" (substance (mole)) 
    #  and "hasOnlySubstanceUnits" (False) and the value of "spatialDimension" (3) 
    #  is greater than 0, the units of this Species object is  moles/liters.
    #
    $sp->setInitialConcentration(1);

    #---------------------------------------------------------------------------
    # (Species2) Creates a Species object ("x1")
    #---------------------------------------------------------------------------

    $sp = $model->createSpecies();
    $sp->setId("x1");
    $sp->setCompartment($compName);
    $sp->setInitialConcentration(1);

    #---------------------------------------------------------------------------
    # (Species3) Creates a Species object ("s1")
    #---------------------------------------------------------------------------

    $sp = $model->createSpecies();
    $sp->setCompartment($compName);
    $sp->setId("s1");
    $sp->setInitialConcentration(1);

    #---------------------------------------------------------------------------
    # (Species4) Creates a Species object ("s2")
    #---------------------------------------------------------------------------

    $sp = $model->createSpecies();
    $sp->setCompartment($compName);
    $sp->setId("s2");
    $sp->setInitialConcentration(1);

    #---------------------------------------------------------------------------
    #
    # Creates global Parameter objects inside the Model object.
    #
    #---------------------------------------------------------------------------

    # Creates a Parameter ("vm")  

    $para = $model->createParameter();
    $para->setId("vm");
    $para->setValue(2);
    $para->setUnits("mmls");

    # Creates a Parameter ("km")  

    $para = $model->createParameter();
    $para->setId("km");
    $para->setValue(2);
    $para->setUnits("mml");


    #---------------------------------------------------------------------------
    #
    # Creates Reaction objects inside the Model object.
    #
    #---------------------------------------------------------------------------

    #---------------------------------------------------------------------------
    # (Reaction1) Creates a Reaction object ("v1").
    #---------------------------------------------------------------------------

    $reaction = $model->createReaction();
    $reaction->setId("v1");

    #---------------------------------------------------------------------------
    # Creates Reactant objects inside the Reaction object ("v1").
    #---------------------------------------------------------------------------

    # (Reactant1) Creates a Reactant object that references Species "x0"
    # in the model.

    $spr = $reaction->createReactant();
    $spr->setSpecies("x0");

    #---------------------------------------------------------------------------
    # Creates a Product object inside the Reaction object ("v1").
    #---------------------------------------------------------------------------

    # Creates a Product object that references Species "s1" in the model.

    $spr = $reaction->createProduct();
    $spr->setSpecies("s1");

    #---------------------------------------------------------------------------
    # Creates a KineticLaw object inside the Reaction object ("v1").
    #---------------------------------------------------------------------------

    $kl = $reaction->createKineticLaw();

    # Creates a <notes> element in the KineticLaw object.
    # Here we illustrate how to do it using a literal string.  This requires
    # known the required syntax of XHTML and the requirements for SBML <notes>
    # elements.  Later below, we show how to create notes using objects instead
    # of strings.

    $notesString = "<xhtml:p> ((vm * s1)/(km + s1)) * cell </xhtml:p>";
    $kl->setNotes($notesString);

    #---------------------------------------------------------------------------
    # Creates an object which represents the following KineticLaw object.
    #
    #  <math xmlns="http://www.w3.org/1998/Math/MathML">
    #   <apply>
    #     <times/>
    #     <apply>
    #       <divide/>
    #       <apply>
    #         <times/>
    #           <ci> vm </ci>
    #           <ci> s1 </ci>
    #       </apply>
    #       <apply>
    #         <plus/>
    #           <ci> km </ci>
    #           <ci> s1 </ci>
    #       </apply>
    #     </apply>
    #     <ci> cell </ci>
    #    </apply>
    #  </math>
    #---------------------------------------------------------------------------

    #
    # In the following code, objects, which construct an tree 
    # of the above math, are created and added in the order of preorder traversal 
    # of the tree (i.e. the order corresponds to the nested structure of the above 
    # MathML elements), and thus the following code maybe a bit more efficient but 
    # maybe a bit difficult to read.
    #

    $astMath = new LibSBML::ASTNode($LibSBML::AST_TIMES);

    $astMath->addChild(new LibSBML::ASTNode($LibSBML::AST_DIVIDE));
    $astDivide = $astMath->getLeftChild();

    $astDivide->addChild(new LibSBML::ASTNode($LibSBML::AST_TIMES));
    $astTimes = $astDivide->getLeftChild();

    $astTimes->addChild(new LibSBML::ASTNode($LibSBML::AST_NAME));
    $astTimes->getLeftChild()->setName("vm");

    $astTimes->addChild(new LibSBML::ASTNode($LibSBML::AST_NAME));
    $astTimes->getRightChild()->setName("s1");

    $astDivide->addChild(new LibSBML::ASTNode($LibSBML::AST_PLUS));
    $astPlus = $astDivide->getRightChild();

    $astPlus->addChild(new LibSBML::ASTNode($LibSBML::AST_NAME));
    $astPlus->getLeftChild()->setName("km");

    $astPlus->addChild(new LibSBML::ASTNode($LibSBML::AST_NAME));
    $astPlus->getRightChild()->setName("s1");


    $astMath->addChild(new LibSBML::ASTNode($LibSBML::AST_NAME));
    $astMath->getRightChild()->setName("cell");

    #---------------------------------------------
    #
    # set the Math element
    #
    #------------------------------------------------

    $kl->setMath($astMath);

    #---------------------------------------------------------------------------
    # (Reaction2) Creates a Reaction object ("v2").
    #---------------------------------------------------------------------------

    $reaction = $model->createReaction();
    $reaction->setId("v2");

    #---------------------------------------------------------------------------
    # Creates Reactant objects inside the Reaction object ("v2").
    #---------------------------------------------------------------------------

    # (Reactant2) Creates a Reactant object that references Species "s1"
    # in the $model.

    $spr = $reaction->createReactant();
    $spr->setSpecies("s1");

    #---------------------------------------------------------------------------
    # Creates a Product object inside the Reaction object ("v2").
    #---------------------------------------------------------------------------

    # Creates a Product object that references Species "s2" in the model.

    $spr = $reaction->createProduct();
    $spr->setSpecies("s2");

    #---------------------------------------------------------------------------
    # Creates a KineticLaw object inside the Reaction object ("v2").
    #---------------------------------------------------------------------------

    $kl = $reaction->createKineticLaw();

    # Sets a notes (by XMLNode) to the KineticLaw object.
    #
    # The following code is an alternative to using setNotes(const string&).
    # The equivalent code would be like this:
    #   
    #     notesString = "<xhtml:p>((vm * s2)/(km + s2))*cell</xhtml:p>";
    #     kl->setNotes(notesString);

    # Creates an of start element (<xhtml:p>) without attributes.

    $notesXMLNode = new LibSBML::XMLNode(
        new LibSBML::XMLTriple("p", "", "xhtml"),
        new LibSBML::XMLAttributes());

    # Adds a text element to the start element.

    $notesXMLNode->addChild(new LibSBML::XMLNode(" ((vm * s2)/(km + s2)) * cell "));

    # Adds it to the kineticLaw object.

    $kl->setNotes($notesXMLNode);

    #---------------------------------------------------------------------------
    # Sets a math (object) to the KineticLaw object.
    #---------------------------------------------------------------------------

    # To create mathematical expressions, one would typically construct
    # an tree as the above example code which creates a math of another
    # KineticLaw object.  Here, to save some space and illustrate another approach 
    # of doing it, we will write out the formula in MathML form and then use a 
    # libSBML convenience function to create the tree for us.
    # (This is a bit dangerous; it's very easy to make mistakes when writing MathML 
    # by hand, so in a real program, we would not really want to do it this way.)

    $mathXMLString = '<?xml version="1.0" encoding="UTF-8"?>
  <math xmlns="http://www.w3.org/1998/Math/MathML">
    <apply>
      <times/>
      <apply>
        <divide/>
        <apply>
          <times/>
          <ci> vm </ci>
          <ci> s2 </ci>
        </apply>
        <apply>
          <plus/>
            <ci> km </ci>
            <ci> s2 </ci>
        </apply>
      </apply>
      <ci> cell </ci>
    </apply>
    </math>';
	
    $astMath = LibSBML::readMathMLFromString($mathXMLString);
    $kl->setMath($astMath);
    

    #---------------------------------------------------------------------------
    # (Reaction3) Creates a Reaction object ("v3").
    #---------------------------------------------------------------------------

    $reaction = $model->createReaction();
    $reaction->setId("v3");

    #---------------------------------------------------------------------------
    # Creates Reactant objects inside the Reaction object ("v3").
    #---------------------------------------------------------------------------

    # (Reactant2) Creates a Reactant object that references Species "s2"
    # in the $model.

    $spr = $reaction->createReactant();
    $spr->setSpecies("s2");

    #---------------------------------------------------------------------------
    # Creates a Product object inside the Reaction object ("v3").
    #---------------------------------------------------------------------------

    # Creates a Product object that references Species "x1" in the $model.

    $spr = $reaction->createProduct();
    $spr->setSpecies("x1");


    #---------------------------------------------------------------------------
    # Creates a KineticLaw object inside the Reaction object ("v3").
    #---------------------------------------------------------------------------

    $kl = $reaction->createKineticLaw();

    # Sets a notes (by string) to the KineticLaw object.

    $notesString = "<xhtml:p> ((vm * x1)/(km + x1)) * cell </xhtml:p>";
    $kl->setNotes($notesString);

    #---------------------------------------------------------------------------
    # Sets a math (object) to the KineticLaw object.
    #---------------------------------------------------------------------------

    $mathXMLString = '<math xmlns="http://www.w3.org/1998/Math/MathML">
      <apply>
        <times/>
        <apply>
          <divide/>
          <apply>
            <times/>
            <ci> vm </ci>
            <ci> x1 </ci>
          </apply>
          <apply>
            <plus/>
              <ci> km </ci>
              <ci> x1 </ci>
          </apply>
        </apply>
        <ci> cell </ci>
      </apply>
    </math>';

    $astMath = LibSBML::readMathMLFromString($mathXMLString);
    $kl->setMath($astMath);


    # Returns the created SBMLDocument object.
    # The returned object must be explicitly deleted by the caller,
    # otherwise memory leak will happen.   
    return $sbmlDoc;
}


# 
# 
# Creates an SBML $model represented in "7.8 Example involving function definitions"
# in the SBML Level 2 Version 4 Specification->
# 
# 

sub createExampleInvolvingFunctionDefinitions {
    $level = $Level;
    $version = $Version;

    #---------------------------------------------------------------------------
    #
    # Creates an SBMLDocument object 
    #
    #---------------------------------------------------------------------------

    $sbmlDoc = new LibSBML::SBMLDocument($level, $version);

    #---------------------------------------------------------------------------
    #
    # Creates a Model object inside the SBMLDocument object.
    #
    #---------------------------------------------------------------------------

    $model = $sbmlDoc->createModel();
    $model->setId("functionExample");

    #---------------------------------------------------------------------------
    #
    # Creates a FunctionDefinition object inside the Model object.
    #
    #---------------------------------------------------------------------------

    $fdef = $model->createFunctionDefinition();
    $fdef->setId("f");

    # Sets a math (object) to the FunctionDefinition object.

    $mathXMLString = '<math xmlns="http://www.w3.org/1998/Math/MathML">
      <lambda>
        <bvar>
          <ci> x </ci>
        </bvar>
        <apply>
          <times/>
          <ci> x </ci>
          <cn> 2 </cn>
        </apply>
      </lambda>
    </math>';

    $astMath = LibSBML::readMathMLFromString($mathXMLString);
    $fdef->setMath($astMath);

    #---------------------------------------------------------------------------
    #
    # Creates a Compartment object inside the Model object.
    #
    #---------------------------------------------------------------------------

    $compName = "compartmentOne";

    # Creates a Compartment object ("compartmentOne")

    $comp = $model->createCompartment();
    $comp->setId($compName);

    # Sets the "size" attribute of the Compartment object.
    #
    #   The units of this Compartment object is the default SBML 
    #   units of volume (litre), and thus we don't have to explicitly invoke 
    #   setUnits("litre") function to set the default units.
    #
    $comp->setSize(1);


    #---------------------------------------------------------------------------
    #
    # Creates Species objects inside the Model object.
    #
    #---------------------------------------------------------------------------

    #---------------------------------------------------------------------------
    # (Species1) Creates a Species object ("S1")
    #---------------------------------------------------------------------------

    $sp = $model->createSpecies();
    $sp->setId("S1");

    # Sets the "compartment" attribute of the Species object to identify the 
    # compartnet in which the Species object located.

    $sp->setCompartment($compName);

    # Sets the "initialConcentration" attribute of the Species object.
    #
    #  The units of this Species object is determined by two attributes of this 
    #  Species object ("substanceUnits" and "hasOnlySubstanceUnits") and the
    #  "spatialDimension" attribute of the Compartment object ("cytosol") in which 
    #  this species object located.
    #  Since the default values are used for "substanceUnits" (substance (mole)) 
    #  and "hasOnlySubstanceUnits" (False) and the value of "spatialDimension" (3) 
    #  is greater than 0, the units of this Species object is  mole/litre.
    #

    $sp->setInitialConcentration(1);

    #---------------------------------------------------------------------------
    # (Species2) Creates a Species object ("S2")
    #---------------------------------------------------------------------------

    $sp = $model->createSpecies();
    $sp->setId("S2");
    $sp->setCompartment($compName);
    $sp->setInitialConcentration(0);


    #---------------------------------------------------------------------------
    #
    # Creates a global Parameter object inside the Model object.
    #
    #---------------------------------------------------------------------------

    # Creates a Parameter ("t")  

    $para = $model->createParameter();
    $para->setId("t");
    $para->setValue(1);
    $para->setUnits("second");


    #---------------------------------------------------------------------------
    #
    # Creates Reaction objects inside the Model object.
    #
    #---------------------------------------------------------------------------

    #---------------------------------------------------------------------------
    # (Reaction1) Creates a Reaction object ("reaction_1").
    #---------------------------------------------------------------------------

    $reaction = $model->createReaction();
    $reaction->setId("reaction_1");
    $reaction->setReversible(0);

    #---------------------------------------------------------------------------
    # Creates Reactant objects inside the Reaction object ("reaction_1")
    #---------------------------------------------------------------------------

    # (Reactant1) Creates a Reactant object that references Species "S1"
    # in the model.

    $spr = $reaction->createReactant();
    $spr->setSpecies("S1");

    #---------------------------------------------------------------------------
    # Creates a Product object inside the Reaction object ("reaction_1")
    #---------------------------------------------------------------------------

    # Creates a Product object that references Species "S2" in the model 

    $spr = $reaction->createProduct();
    $spr->setSpecies("S2");


    #---------------------------------------------------------------------------
    # Creates a KineticLaw object inside the Reaction object ("reaction_1")
    #---------------------------------------------------------------------------

    $kl = $reaction->createKineticLaw();

    #---------------------------------------------------------------------------
    # Sets a math (object) to the KineticLaw object
    #---------------------------------------------------------------------------

    $mathXMLString = '<math xmlns="http://www.w3.org/1998/Math/MathML">
      <apply>
      <divide/>
        <apply>
          <times/>
          <apply>
            <ci> f </ci>
            <ci> S1 </ci>
          </apply>
          <ci> compartmentOne </ci>
        </apply>
        <ci> t </ci>
      </apply>
    </math>';

    $astMath = LibSBML::readMathMLFromString($mathXMLString);
    $kl->setMath($astMath);

    # Returns the created SBMLDocument object.
    # The returned object must be explicitly deleted by the caller,
    # otherwise memory leak will happen.

    return $sbmlDoc;
}
#===============================================================================
#
#
# Helper functions for writing/validating the given SBML documents.
# 
#
#===============================================================================

#
# 
# Validates the given SBMLDocument.
#
#  This function is based on validateSBML.pl implemented by
#  Sarah Keating, Ben Bornstein, and Michael Hucka.
#
#

sub validateExampleSBML {
    $sbmlDoc = shift();
    if ($sbmlDoc == undef) {
        print("validateExampleSBML: given a None SBML Document");
        return 0;
    }
 
    $consistencyMessages = "";
    $validationMessages = "";
    $noProblems = True;
    $numCheckFailures = 0;
    $numConsistencyErrors = 0;
    $numConsistencyWarnings = 0;
    $numValidationErrors = 0;
    $numValidationWarnings = 0;

    # LibSBML is lenient when generating models from scratch using the
    # API for creating objects.  Once the whole model is done and before it
    # gets written out, it's important to check that the whole model is in
    # fact complete, consistent and valid.

    $numCheckFailures = $sbmlDoc->checkInternalConsistency();
    if ($numCheckFailures > 0) {
        $noProblems = 0;
        for ($i=0; $i<$numCheckFailures;$i++) {
            $sbmlErr = $sbmlDoc->getError($i);
            if ($sbmlErr->isFatal() or $sbmlErr->isError()) {
                $numConsistencyErrors = 1 + $numConsistencyErrors; 
            }
            else {
                $numConsistencyWarnings = 1+$numConsistencyWarnings; 
            }
        }
        $sbmlDoc->printErrors();
    }
    # If the internal checks fail, it makes little sense to attempt
    # further validation, because the $model may be too compromised to
    # be properly interpreted->

    if ($numConsistencyErrors > 0) {
        $consistencyMessages = $consistencyMessages  + "Further validation aborted.";
    }
    else {
        $numCheckFailures = $sbmlDoc->checkConsistency();
        if (numCheckFailures > 0) {
            $noProblems = 0;
            for ($i=0; $i < numCheckFailures;$i++) {
                $sbmlErr = $sbmlDoc->getError($i);
                if ($sbmlErr->isFatal() || $sbmlErr->isError()) {
                    $numValidationErrors = 1+$numValidationErrors;
                }
                else {
                    $numValidationWarnings = 1+$numValidationWarnings;
                }
            }
            $sbmlDoc->printErrors();
        }
    }

    if ($noProblems) {
        return 1;
    }
    # problem
    if ($numConsistencyErrors > 0) {
      $tmp = "";
      if ($numConsistencyErrors > 1) {
        $tmp = "s";
      }
      print("ERROR: encountered ", $numConsistencyErrors, " consistency error", $tmp," in model '", $sbmlDoc->getModel()->getId(),  "'.\n");
    }
    if ($numConsistencyWarnings > 0) {
      $tmp = "";
      if ($numConsistencyWarnings > 1) {
        $tmp = "s";
      }
      print("Notice: encountered ", $numConsistencyWarnings, " consistency warning", $tmp, " in model '", $sbmlDoc->getModel()->getId(), "'.");
    }
    print($consistencyMessages);
    
    if ($numValidationErrors > 0) {
      $tmp = "";
      if ($numValidationErrors > 1) {
        $tmp = "s";
      }
      print("ERROR: encountered ",$numValidationErrors," validation error" + $tmp, " in model '", $sbmlDoc->getModel()->getId(), "'.");
    }
    if ($numValidationWarnings > 0) {
      $tmp = "";
      if ($numValidationWarnings > 1) {
        $tmp = "s";
      }
      print("Notice: encountered ",$numValidationWarnings, " validation warning", $tmp, " in model '", $sbmlDoc->getModel()->getId() , "'.");
    }
    print(validationMessages);
    return ($numConsistencyErrors == 0 and $numValidationErrors == 0);
}

# 
# 
# Writes the given SBMLDocument to the given file.
# 
# 
sub writeExampleSBML {
    $sbmlDoc = $_[0];
    $filename = $_[1];
    $result = LibSBML::writeSBML($sbmlDoc, $filename);
    if ($result == 1) {
        print("Wrote file '",$filename,"'\n");
        return 1;
    }
    else {
        print("Failed to write '",$filename,"'\n");
        return 0;
    }
}

#===============================================================================
#
# Main routine
#
#  Creates SBML $models represented in "Example $models expressed in XML using
#  SBML" in Section 7 of the SBML Level 2 Version 4 specification(*).
#
#   (*) The specification document is available at the following URL:
#       http://sbml.org/Documents/Specifications
#
#===============================================================================
#
$sbmlDoc = undef;
$SBMLok = 0;

try {
  #-------------------------------------------------
  # 7.1 A Simple example application of SBML
  #-------------------------------------------------
  
  $sbmlDoc = createExampleEnzymaticReaction();
  $SBMLok = validateExampleSBML($sbmlDoc);
  if ($SBMLok) {
  	writeExampleSBML($sbmlDoc, "enzymaticreaction.xml");
  } else {
  	exit 1;
  }
  #-------------------------------------------------
  # 7.2 Example involving units
  #-------------------------------------------------
  
  $sbmlDoc = createExampleInvolvingUnits();
  $SBMLok = validateExampleSBML($sbmlDoc);
  if ($SBMLok) {
  	writeExampleSBML($sbmlDoc, "units.xml");
  } else {
  	exit 1;
  }
  #-------------------------------------------------
  # 7.8 Example involving function definitions
  #-------------------------------------------------
  
  $sbmlDoc = createExampleInvolvingFunctionDefinitions();
  $SBMLok = validateExampleSBML($sbmlDoc);
  if ($SBMLok) {
  	writeExampleSBML($sbmlDoc, "functiondef.xml");
  } else {
  	exit 1;
  }
  exit 0;
} 
catch {
  print("Unexpected exceptional condition encountered.\n");
  exit 1;
}
# A 0 return status is the standard Unix/Linux way to say "all ok".
exit 0;