-- 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.


annaGen command ==
  htInitPage('"AXIOM/NAG Expert System Command",nil)
  string :=
    #command < 50 => STRCONC('"{\centerline{\tt ",command,'" }}")
    STRCONC('"{\tt ",command,'" }")
  htMakePage [
     '(text
        "\center{{\em Here is the AXIOM command}}"
          "\center{{\em you could have issued to compute this result:}}"
            "\vspace{2}\newline "),
      ['text,: string]]
  htMakeDoitButton('"Do It", command)
  htShowPage()

annaInt() ==
  htInitPage('"Integration using AXIOM/NAG Expert System",nil)
  htMakePage '(
    (domainConditions
      (isDomain F (Float))
       (isDomain PI (PositiveInteger))
        (isDomain EM $EmptyMode))
    (text . "\blankline ")
    (text . "Analyses the function for various attributes, chooses and ")
    (text . "then uses a suitable integration routine to ")
    (text . "evaluate the finite, semi-infinite or infinite integral ")
    (text . "\blankline ")
    (text . "\tab{22} \space{1} \vspace{-32} ")
    (text . "\inputbitmap{\htbmdir{}/ing.bitmap} \vspace{-34} f(x) dx ")
    (text . "\blankline ")
    (text . "\newline")
    (text . "\newline \menuitemstyle{} \tab{2} {\em Lower} bound of the interval {\em a}: ")
    (radioButtons lower
        ("" "  Finite" lowerFinite)
        ("" "  Minus Infinity" lowerInfinite))
    (text . "\blankline ")
    (text . "\newline \menuitemstyle{} \tab{2} {\em Upper} bound of the interval {\em b}: ")
    (radioButtons upper
        ("" "  Finite" upperFinite)
        ("" "  Plus Infinity" upperInfinite)))
  htMakeDoneButton('"Continue",'annaIntSolve)
  htShowPage()

annaDan() ==

  page := htInitPage('"Integration using AXIOM/NAG Expert System",nil)
  htMakePage '(
    (domainConditions
      (isDomain F (Float))
       (isDomain PI (PositiveInteger))
        (isDomain EM $EmptyMode))
    (text . "\menuitemstyle{}\tab{2} ")
    (text . "Enter the {\em function} f to be integrated: \newline \tab{2} ")
    (bcStrings (50 "(log(2-x)*log(x))/((2-x)^(2/3)*sqrt(x))" expression EM))
    (text . "\blankline ")
    (text . "\newline \menuitemstyle{}\tab{2} ")
    (text . "\newline {\em Lower} bound of the interval {\em a}: ")
    (text . "\tab{30} \menuitemstyle{}\tab{32} ")
    (text . "{\em Upper} bound of the interval {\em b}:")
    (text . "\newline\tab{2} ")
    (bcStrings (15 "0.0" lower EM))
    (text . "\tab{32} ")
    (bcStrings (15 "2.0" upper EM))
    (text . "\blankline ")
    (text . "\newline ")
    (text . "\menuitemstyle{}\tab{2}")
    (text . "\newline Absolute accuracy required:")
    (text . "\tab{30} \menuitemstyle{}\tab{32}")
    (text . "Relative accuracy required:")
    (text . "\newline\tab{2} ")
    (bcStrings (10 "0.0" epsabs F))
    (text . "\tab{32} ")
    (bcStrings (10 "1.0e-6" epsrel F))
    (text . "\blankline"))
  htMakeDoneButton('"Continue",'annaIntGen)
  htShowPage()

annaBar() ==

  page := htInitPage('"Integration using AXIOM/NAG Expert System",nil)
  htMakePage '(
    (domainConditions
      (isDomain F (Float))
       (isDomain PI (PositiveInteger))
        (isDomain EM $EmptyMode))
    (text . "\menuitemstyle{}\tab{2} ")
    (text . "Enter the {\em function} f to be integrated: \newline \tab{2} ")
    (bcStrings (50 "exp(-y)/sqrt(y)" expression EM))
    (text . "\blankline ")
    (text . "\newline \menuitemstyle{}\tab{2} ")
    (text . "\newline {\em Lower} bound of the interval {\em a}: ")
    (text . "\tab{30} \menuitemstyle{}\tab{32} ")
    (text . "{\em Upper} bound of the interval {\em b}:")
    (text . "\newline\tab{2} ")
    (bcStrings (15 "0.0" lower EM))
    (text . "\tab{32} ")
    (bcStrings (15 "%plusInfinity" upper EM))
    (text . "\blankline ")
    (text . "\newline ")
    (text . "\menuitemstyle{}\tab{2}")
    (text . "\newline Absolute accuracy required:")
    (text . "\tab{30} \menuitemstyle{}\tab{32}")
    (text . "Relative accuracy required:")
    (text . "\newline\tab{2} ")
    (bcStrings (10 "0.0" epsabs F))
    (text . "\tab{32} ")
    (bcStrings (10 "1.0e-6" epsrel F))
    (text . "\blankline"))
  htMakeDoneButton('"Continue",'annaIntGen)
  htShowPage()

annaFoo() ==

  page := htInitPage('"Integration using AXIOM/NAG Expert System",nil)
  htMakePage '(
    (domainConditions
      (isDomain F (Float))
       (isDomain PI (PositiveInteger))
        (isDomain EM $EmptyMode))
    (text . "\menuitemstyle{}\tab{2} ")
    (text . "Enter the {\em function} f to be integrated: \newline \tab{2} ")
    (bcStrings (50 "(exp(-x^3)+exp(-3*x^2))/sqrt(x)" expression EM))
    (text . "\blankline ")
    (text . "\newline \menuitemstyle{}\tab{2} ")
    (text . "\newline {\em Lower} bound of the interval {\em a}: ")
    (text . "\tab{30} \menuitemstyle{}\tab{32} ")
    (text . "{\em Upper} bound of the interval {\em b}:")
    (text . "\newline\tab{2} ")
    (bcStrings (15 "0.0" lower EM))
    (text . "\tab{32} ")
    (bcStrings (15 "%plusInfinity" upper EM))
    (text . "\blankline ")
    (text . "\newline ")
    (text . "\newline ")
    (text . "\menuitemstyle{}\tab{2}")
    (text . "\newline Absolute accuracy required:")
    (text . "\tab{30} \menuitemstyle{}\tab{32}")
    (text . "Relative accuracy required:")
    (text . "\newline\tab{2} ")
    (bcStrings (10 "0.0" epsabs F))
    (text . "\tab{32} ")
    (bcStrings (10 "1.0e-6" epsrel F))
    (text . "\blankline"))
  htMakeDoneButton('"Continue",'annaIntGen)
  htShowPage()

annaBlah() ==

  page := htInitPage('"Integration using AXIOM/NAG Expert System",nil)
  htMakePage '(
    (domainConditions
      (isDomain F (Float))
       (isDomain PI (PositiveInteger))
        (isDomain EM $EmptyMode))
    (text . "\menuitemstyle{}\tab{2} ")
    (text . "Enter the {\em function} f to be integrated: \newline \tab{2} ")
    (bcStrings (50 "exp(-omega)/((omega-5)*(omega-1/2))" expression EM))
    (text . "\blankline ")
    (text . "\newline \menuitemstyle{}\tab{2} ")
    (text . "\newline {\em Lower} bound of the interval {\em a}: ")
    (text . "\tab{30} \menuitemstyle{}\tab{32} ")
    (text . "{\em Upper} bound of the interval {\em b}:")
    (text . "\newline\tab{2} ")
    (bcStrings (15 "0.0" lower EM))
    (text . "\tab{32} ")
    (bcStrings (15 "%plusInfinity" upper EM))
    (text . "\blankline ")
    (text . "\newline ")
    (text . "\newline ")
    (text . "\menuitemstyle{}\tab{2}")
    (text . "\newline Absolute accuracy required:")
    (text . "\tab{30} \menuitemstyle{}\tab{32}")
    (text . "Relative accuracy required:")
    (text . "\newline\tab{2} ")
    (bcStrings (10 "0.0" epsabs F))
    (text . "\tab{32} ")
    (bcStrings (10 "1.0e-6" epsrel F))
    (text . "\blankline"))
  htMakeDoneButton('"Continue",'annaIntGen)
  htShowPage()

annaJoe() ==

  page := htInitPage('"Integration using AXIOM/NAG Expert System",nil)
  htMakePage '(
    (domainConditions
      (isDomain F (Float))
       (isDomain PI (PositiveInteger))
        (isDomain EM $EmptyMode))
    (text . "\menuitemstyle{}\tab{2} ")
    (text . "Enter the {\em function} f to be integrated: \newline \tab{2} ")
    (bcStrings (50 "(exp(-x^3)+exp(-3*x^2))/(x^2-2)" expression EM))
    (text . "\blankline ")
    (text . "\newline \menuitemstyle{}\tab{2} ")
    (text . "\newline {\em Lower} bound of the interval {\em a}: ")
    (text . "\tab{30} \menuitemstyle{}\tab{32} ")
    (text . "{\em Upper} bound of the interval {\em b}:")
    (text . "\newline\tab{2} ")
    (bcStrings (15 "0.0" lower EM))
    (text . "\tab{32} ")
    (bcStrings (15 "2.0" upper EM))
    (text . "\blankline ")
    (text . "\newline ")
    (text . "\newline ")
    (text . "\menuitemstyle{}\tab{2}")
    (text . "\newline Absolute accuracy required:")
    (text . "\tab{30} \menuitemstyle{}\tab{32}")
    (text . "Relative accuracy required:")
    (text . "\newline\tab{2} ")
    (bcStrings (10 "0.0" epsabs F))
    (text . "\tab{32} ")
    (bcStrings (10 "1.0e-6" epsrel F))
    (text . "\blankline"))
  htMakeDoneButton('"Continue",'annaIntGen)
  htShowPage()

annaSue() ==

  page := htInitPage('"Integration using AXIOM/NAG Expert System",nil)
  htMakePage '(
    (domainConditions
      (isDomain F (Float))
       (isDomain PI (PositiveInteger))
        (isDomain EM $EmptyMode))
    (text . "\menuitemstyle{}\tab{2} ")
    (text . "Enter the {\em function} f to be integrated: \newline \tab{2} ")
    (bcStrings (50 "1/(x^6-1)" expression EM))
    (text . "\blankline ")
    (text . "\newline \menuitemstyle{}\tab{2} ")
    (text . "\newline {\em Lower} bound of the interval {\em a}: ")
    (text . "\tab{30} \menuitemstyle{}\tab{32} ")
    (text . "{\em Upper} bound of the interval {\em b}:")
    (text . "\newline\tab{2} ")
    (bcStrings (15 "0.0" lower EM))
    (text . "\tab{32} ")
    (bcStrings (15 "2.0" upper EM))
    (text . "\blankline ")
    (text . "\newline ")
    (text . "\newline ")
    (text . "\menuitemstyle{}\tab{2}")
    (text . "\newline Absolute accuracy required:")
    (text . "\tab{30} \menuitemstyle{}\tab{32}")
    (text . "Relative accuracy required:")
    (text . "\newline\tab{2} ")
    (bcStrings (10 "0.0" epsabs F))
    (text . "\tab{32} ")
    (bcStrings (10 "1.0e-6" epsrel F))
    (text . "\blankline"))
  htMakeDoneButton('"Continue",'annaIntGen)
  htShowPage()

annaAnn() ==

  page := htInitPage('"Integration using AXIOM/NAG Expert System",nil)
  htMakePage '(
    (domainConditions
      (isDomain F (Float))
       (isDomain PI (PositiveInteger))
        (isDomain EM $EmptyMode))
    (text . "\menuitemstyle{}\tab{2} ")
    (text . "Enter the {\em function} f to be integrated: \newline \tab{2} ")
    (bcStrings (50 "cos(t^2)+sin(t)+cos(sin(t^3))" expression EM))
    (text . "\blankline ")
    (text . "\newline \menuitemstyle{}\tab{2} ")
    (text . "\newline {\em Lower} bound of the interval {\em a}: ")
    (text . "\tab{30} \menuitemstyle{}\tab{32} ")
    (text . "{\em Upper} bound of the interval {\em b}:")
    (text . "\newline\tab{2} ")
    (bcStrings (15 "-%pi" lower EM))
    (text . "\tab{32} ")
    (bcStrings (15 "%pi" upper EM))
    (text . "\blankline ")
    (text . "\newline ")
    (text . "\newline ")
    (text . "\menuitemstyle{}\tab{2}")
    (text . "\newline Absolute accuracy required:")
    (text . "\tab{30} \menuitemstyle{}\tab{32}")
    (text . "Relative accuracy required:")
    (text . "\newline\tab{2} ")
    (bcStrings (10 "0.0" epsabs F))
    (text . "\tab{32} ")
    (bcStrings (10 "1.0e-6" epsrel F))
    (text . "\blankline"))
  htMakeDoneButton('"Continue",'annaIntGen)
  htShowPage()

annaBab() ==

  page := htInitPage('"Integration using AXIOM/NAG Expert System",nil)
  htMakePage '(
    (domainConditions
      (isDomain F (Float))
       (isDomain PI (PositiveInteger))
        (isDomain EM $EmptyMode))
    (text . "\menuitemstyle{}\tab{2} ")
    (text . "Enter the {\em function} f to be integrated: \newline \tab{2} ")
    (bcStrings (50 "x*product(x-i/10,i=-4..4)" expression EM))
    (text . "\blankline ")
    (text . "\newline \menuitemstyle{}\tab{2} ")
    (text . "\newline {\em Lower} bound of the interval {\em a}: ")
    (text . "\tab{30} \menuitemstyle{}\tab{32} ")
    (text . "{\em Upper} bound of the interval {\em b}:")
    (text . "\newline\tab{2} ")
    (bcStrings (15 "-1" lower EM))
    (text . "\tab{32} ")
    (bcStrings (15 "1" upper EM))
    (text . "\blankline ")
    (text . "\newline ")
    (text . "\newline ")
    (text . "\menuitemstyle{}\tab{2}")
    (text . "\newline Absolute accuracy required:")
    (text . "\tab{30} \menuitemstyle{}\tab{32}")
    (text . "Relative accuracy required:")
    (text . "\newline\tab{2} ")
    (bcStrings (10 "0.0" epsabs F))
    (text . "\tab{32} ")
    (bcStrings (10 "1.0e-6" epsrel F))
    (text . "\blankline"))
  htMakeDoneButton('"Continue",'annaIntGen)
  htShowPage()

annaFnar() ==

  page := htInitPage('"Integration using AXIOM/NAG Expert System",nil)
  htMakePage '(
    (domainConditions
      (isDomain F (Float))
       (isDomain PI (PositiveInteger))
        (isDomain EM $EmptyMode))
    (text . "\menuitemstyle{}\tab{2} ")
    (text . "Enter the {\em function} f to be integrated: \newline \tab{2} ")
    (bcStrings (50 "cos(20*rho)*(sin(rho^2) + cos(rho^2))" expression EM))
    (text . "\blankline ")
    (text . "\newline \menuitemstyle{}\tab{2} ")
    (text . "\newline {\em Lower} bound of the interval {\em a}: ")
    (text . "\tab{30} \menuitemstyle{}\tab{32} ")
    (text . "{\em Upper} bound of the interval {\em b}:")
    (text . "\newline\tab{2} ")
    (bcStrings (15 "0" lower EM))
    (text . "\tab{32} ")
    (bcStrings (15 "1" upper EM))
    (text . "\blankline ")
    (text . "\newline ")
    (text . "\newline ")
    (text . "\menuitemstyle{}\tab{2}")
    (text . "\newline Absolute accuracy required:")
    (text . "\tab{30} \menuitemstyle{}\tab{32}")
    (text . "Relative accuracy required:")
    (text . "\newline\tab{2} ")
    (bcStrings (10 "0.0" epsabs F))
    (text . "\tab{32} ")
    (bcStrings (10 "1.0e-6" epsrel F))
    (text . "\blankline"))
  htMakeDoneButton('"Continue",'annaIntGen)
  htShowPage()

annaTub() ==

  page := htInitPage('"Integration using AXIOM/NAG Expert System",nil)
  htMakePage '(
    (domainConditions
      (isDomain F (Float))
       (isDomain PI (PositiveInteger))
        (isDomain EM $EmptyMode))
    (text . "\menuitemstyle{}\tab{2} ")
    (text . "Enter the {\em function} f to be integrated: \newline \tab{2} ")
    (bcStrings (50 "exp(-z^2/2)/sqrt(2*%pi)" expression EM))
    (text . "\blankline ")
    (text . "\newline \menuitemstyle{}\tab{2} ")
    (text . "\newline {\em Lower} bound of the interval {\em a}: ")
    (text . "\tab{30} \menuitemstyle{}\tab{32} ")
    (text . "{\em Upper} bound of the interval {\em b}:")
    (text . "\newline\tab{2} ")
    (bcStrings (15 "%minusInfinity" lower EM))
    (text . "\tab{32} ")
    (bcStrings (15 "%plusInfinity" upper EM))
    (text . "\blankline ")
    (text . "\menuitemstyle{}\tab{2}")
    (text . "\newline Absolute accuracy required:")
    (text . "\tab{30} \menuitemstyle{}\tab{32}")
    (text . "Relative accuracy required:")
    (text . "\newline\tab{2} ")
    (bcStrings (10 "0.0" epsabs F))
    (text . "\tab{32} ")
    (bcStrings (10 "1.0e-6" epsrel F))
    (text . "\blankline"))
  htMakeDoneButton('"Continue",'annaIntGen)
  htShowPage()

annaRats() ==

  page := htInitPage('"Integration using AXIOM/NAG Expert System",nil)
  htMakePage '(
    (domainConditions
      (isDomain F (Float))
       (isDomain PI (PositiveInteger))
        (isDomain EM $EmptyMode))
    (text . "\menuitemstyle{}\tab{2} ")
    (text . "Enter the {\em function} f to be integrated: \newline \tab{2} ")
    (bcStrings (50 "log(u*u)" expression EM))
    (text . "\blankline ")
    (text . "\newline \menuitemstyle{}\tab{2} ")
    (text . "\newline {\em Lower} bound of the interval {\em a}: ")
    (text . "\tab{30} \menuitemstyle{}\tab{32} ")
    (text . "{\em Upper} bound of the interval {\em b}:")
    (text . "\newline\tab{2} ")
    (bcStrings (15 "-1" lower EM))
    (text . "\tab{32} ")
    (bcStrings (15 "1" upper EM))
    (text . "\blankline ")
    (text . "\menuitemstyle{}\tab{2}")
    (text . "\newline Absolute accuracy required:")
    (text . "\tab{30} \menuitemstyle{}\tab{32}")
    (text . "Relative accuracy required:")
    (text . "\newline\tab{2} ")
    (bcStrings (10 "0.0" epsabs F))
    (text . "\tab{32} ")
    (bcStrings (10 "1.0e-6" epsrel F))
    (text . "\blankline"))
  htMakeDoneButton('"Continue",'annaIntGen)
  htShowPage()

annaIntSolve htPage ==

  l := htpButtonValue(htPage,'lower)
  u := htpButtonValue(htPage,'upper)
  a := 
    l = 'lowerFinite => '"finite"
    '"%minusInfinity"
  b := 
    u = 'upperFinite => '"finite"
    '"%plusInfinity"
  (a = b) => annaDan()
  a = '"finite" => annaFoo()
  b = '"%plusInfinity" => annaTub()
  page := htInitPage('"Integration using AXIOM/NAG Expert System",htPage)
  htMakePage '(
    (domainConditions
      (isDomain F (Float))
       (isDomain PI (PositiveInteger))
        (isDomain EM $EmptyMode))
    (text . "\menuitemstyle{}\tab{2} ")
    (text . "Enter the {\em function} f to be integrated: \newline \tab{2} ")
    (bcStrings (45 "exp(-x^2/2)/sqrt(2*%pi)" expression EM))
    (text . "\blankline ")
    (text . "\newline \menuitemstyle{}\tab{2} ")
    (text . "\newline {\em Lower} bound of the interval {\em a}: ")
    (text . "\tab{30} \menuitemstyle{}\tab{32} ")
    (text . "{\em Upper} bound of the interval {\em b}:")
    (text . "\newline\tab{2} ")
    (bcStrings (15 "%minusInfinity" lower EM))
    (text . "\tab{32} ")
    (bcStrings (15 "0.0" upper EM))
    (text . "\blankline ")
    (text . "\newline ")
    (text . "\menuitemstyle{}\tab{2}")
    (text . "\newline Absolute accuracy required:")
    (text . "\tab{30} \menuitemstyle{}\tab{32}")
    (text . "Relative accuracy required:")
    (text . "\newline\tab{2} ")
    (bcStrings (10 "0.0" epsabs F))
    (text . "\tab{32} ")
    (bcStrings (10 "1.0e-6" epsrel F))
    (text . "\blankline"))
  htMakeDoneButton('"Continue",'annaIntGen)
  htpSetProperty(page,'inputArea, htpInputAreaAlist htPage)
  htShowPage()


annaIntGen htPage ==
  lower := htpLabelInputString(htPage,'lower)
  upper := htpLabelInputString(htPage,'upper)
  expression := htpLabelInputString(htPage,'expression)
  epsabs := htpLabelInputString(htPage,'epsabs)
  epsrel := htpLabelInputString(htPage,'epsrel)
  annaGen STRCONC('"integrate(",expression,", ",lower,"..",upper,", ",epsabs,", ",epsrel,")")

annaMInt() ==
  htInitPage('"Integration using AXIOM/NAG Expert System",nil)
  htMakePage '(
    (domainConditions
       (isDomain PI (PositiveInteger))
        (isDomain EM $EmptyMode))
    (text . "Analyses the function for various attributes, chooses and ")
    (text . "then uses a suitable integration routine ")
    (text . "\blankline ")
    (text . "\menuitemstyle{}\tab{2} ")
    (text . "Enter the {\em function} f of the form: ")
    (text . "\center{\inputbitmap{\htbmdir{}/d01fcf.bitmap}} ")
    (text . "\newline ")
    (text . "to be integrated in terms of subscripted ") 
    (text . "variables e.g. X[1]...X[n]: \newline \tab{2} ")
    (bcStrings (58 "4.0*X[1]*X[3]*X[3]*exp(2.0*X[1]*X[3])/((1.0+X[2]+X[4])**2)" expression EM))
    (text . "\blankline ")
    (text . "\menuitemstyle{}\tab{2} ")
    (text . "Number of dimensions n in the integral, 2 \htbitmap{less=} ")
    (text . "{\it N} \htbitmap{less=} 15: ")
    (text . "\newline\tab{2} ")
    (bcStrings (2 4 n PI))
    (text . "\blankline ")
    (text . "\blankline "))
  htMakeDoneButton('"Continue", 'annaMIntSolve)
  htShowPage()

annaMIntSolve htPage ==
  n :=
    $bcParseOnly => PARSE_-INTEGER htpLabelInputString(htPage, 'n)
    objValUnwrap htpLabelSpadValue(htPage, 'n)
  n = '4 => annaMIntDefaultSolve(htPage)
  expression := htpLabelInputString(htPage,'expression)
  rangeList :=
    "append"/[f(i,n) for i in 1..n] where f(i,n) ==
      prefix := ('"\newline a")
      prefix := STRCONC(prefix,STRINGIMAGE i,'"\space{1}")
      post   := ('"\tab{30} b")
      post   := STRCONC(post,STRINGIMAGE i,'"\space{1}")
      rnam := INTERN STRCONC ('"x",STRINGIMAGE i)
      inam := INTERN STRCONC ('"y",STRINGIMAGE i)
      [['text,:prefix],['bcStrings,[5, 0.0, rnam, 'EM]],
       ['text,:post],['bcStrings,[5, 1.0, inam, 'EM]]]
  errList :=
    errtext := ('"\newline \blankline \menuitemstyle{}\tab{2}")
    errtext := STRCONC(errtext,'"Absolute accuracy required:")
    errtext := STRCONC(errtext,'"\tab{30} \menuitemstyle{}\tab{32}")
    errtext := STRCONC(errtext,'"Relative accuracy required: \newline\tab{2} ")
    [['text,:errtext],['bcStrings,[10, 0.0, 'abserr, 'F]],
     ['text,"\tab{32} "],['bcStrings,[10, 1.0e-4, 'relerr, 'F]]]
  equationPart := [
     '(domainConditions
        (isDomain EM ($EmptyMode))
         (isDomain F (Float))
          (isDomain S (String))
            (isDomain PI (PositiveInteger))),
              :rangeList,:errList]
  page := htInitPage("AXIOM/NAG Multiple Integration", htpPropertyList htPage)
  htSay '"Please enter the limits of integration:-  "
  htSay '"\blankline \menuitemstyle{} \tab{2} "
  htSay '"Lower Limits: \tab{30} \menuitemstyle{} \tab{32} "
  htSay '"Upper Limits: \newline "
  htMakePage equationPart
  htMakeDoneButton('"Continue",'annaMIntGen)
  htpSetProperty(page,'expression,expression)
  htpSetProperty(page,'inputArea, htpInputAreaAlist htPage)
  htShowPage()

annaMIntDefaultSolve (htPage) ==

  page := htInitPage('"AXIOM/NAG Multiple Integration",nil)
  expression := htpLabelInputString(htPage,'expression)
  htMakePage '(
    (domainConditions
       (isDomain F (Float))
        (isDomain EM $EmptyMode))
    (text . "\newline ")
    (text . "Please enter the limits of integration:- ")
    (text . "\blankline ")
    (text . "\newline \menuitemstyle{} \tab{2} ")
    (text . "Lower limits: \tab{30} ")
    (text . "\menuitemstyle{} \tab{32} Upper limits: ")
    (text . "\newline a1 ")
    (bcStrings (10 "0.0" a1 F))
    (text . "\tab{30} b1 ")
    (bcStrings (10 "1.0" b1 F))
    (text . "\newline a2 ")
    (bcStrings (10 "0.0" a2 F))
    (text . "\tab{30} b2 ")
    (bcStrings (10 "1.0" b2 F))
    (text . "\newline a3 ")
    (bcStrings (10 "0.0" a3 F))
    (text . "\tab{30} b3 ")
    (bcStrings (10 "1.0" b3 F))
    (text . "\newline a4 ")
    (bcStrings (10 "0.0" a4 F))
    (text . "\tab{30} b4 ")
    (bcStrings (10 "1.0" b4 F))
    (text . "\newline ")
    (text . "\blankline ")
    (text . "\menuitemstyle{}\tab{2}")
    (text . "\newline Absolute accuracy required:")
    (text . "\tab{30} \menuitemstyle{}\tab{32}")
    (text . "Relative accuracy required:")
    (text . "\newline\tab{2} ")
    (bcStrings (10 "0.0" epsabs F))
    (text . "\tab{32} ")
    (bcStrings (10 "1.0e-4" epsrel F))
    (text . "\blankline"))
  htMakeDoneButton('"Continue",'annaMIntGen)
  htpSetProperty(page,'expression,expression)
  htpSetProperty(page,'inputArea, htpInputAreaAlist htPage)
  htShowPage()


annaMIntGen htPage ==
  expression := htpProperty(htPage,'expression)
  alist := htpInputAreaAlist htPage
  y := alist
  epsrel := STRCONC((first y).1,'"")
  y := rest y
  epsabs := STRCONC((first y).1,'"")
  y := rest y
  while y repeat
    right := STRCONC((first y).1,'"")
    y := rest y
    left := STRCONC((first y).1,"..")
    y := rest y
    rangelist := [STRCONC(left,right),:rangelist]
  rangestring := bcwords2liststring rangelist
  annaGen STRCONC ('"integrate( ",expression,", ",rangestring,", ",epsabs,", ",epsrel,")")

annaOde() ==
  htInitPage('"Solution of Initial Value Problems of Ordinary Differential Equations using AXIOM/NAG Expert System",nil)
  htMakePage '(
    (domainConditions
      (isDomain F (Float))
       (isDomain PI (PositiveInteger))
        (isDomain EM $EmptyMode))
    (text . "Analyses the function for various attributes, chooses and ")
    (text . "then uses a suitable ODE solver to provide a ")
    (text . "solution to the system of n ODEs \center{\htbitmap{d02gaf},}" )
    (text . "for i = 1,2,...,n.")
    (text . "\blankline ")
    (text . "\newline \menuitemstyle{} \tab{2} Is there any stopping criteria (i.e. some function ")
    (text . "G(X,Y) such that the algorithm should stop when G(X,Y) = 0)? ")
    (radioButtons stoppingCriteria
        ("" "  No \space{1} If No, G(X,Y) is set to 1.0" nostop)
        ("" "  Yes" stop))
    (text . "\blankline")
    (text . "\newline \menuitemstyle{} \tab{2} Are intermediate values required? ")
    (radioButtons intermediateValues
        ("" "  No" noint)
        ("" "  Yes" int))
    (text . "\blankline ")
    (text . "\menuitemstyle{}\tab{2} ")
    (text . "\newline Size of the system of equations:\space{1}")
    (bcStrings (3 3 n PI))
    (text . "\newline"))
  htMakeDoneButton('"Continue",'annaOdeSolve)
  htShowPage()

annaOdeSolve htPage ==

  s := htpButtonValue(htPage,'stoppingCriteria)
  i := htpButtonValue(htPage,'intermediateValues)
  stoppingCriteria := 
    s = 'nostop => '"no"
    '"stopping"
  intermediateValues := 
    i = 'noint => '"no"
    '"intervals"
  n :=
    $bcParseOnly => PARSE_-INTEGER htpLabelInputString(htPage, 'n)
    objValUnwrap htpLabelSpadValue(htPage, 'n)
  (n = '3) => 
    (stoppingCriteria = intermediateValues) => annaOdeDefaultSolve()
    (stoppingCriteria = '"stopping") =>
      (intermediateValues = '"intervals") => annaOdeDefaultSolve1() 
      annaOdeDefaultSolve2()
    annaOdeDefaultSolve3()
  expressionList :=
    "append"/[fe(i,n) for i in 1..n] where fe(i,n) ==
      prefix := ('"\blankline \newline Y")
      prefix := STRCONC(prefix,STRINGIMAGE i,'"'\space{1}")
      expression := INTERN STRCONC ('"Y",STRINGIMAGE i)
      [['text,:prefix],
       ['bcStrings,[45, STRCONC ('"Y[",STRINGIMAGE i,'"]"), expression, 'EM]]]
  xList :=
    prefix := ('"\blankline \newline \menuitemstyle{} \tab{2} Initial Value for X: ")
    middle := ('"\tab{24} \menuitemstyle{} \tab{26} Final Value for X: ")
    [['text,:prefix],['bcStrings,[5, "0.0", "xinit", 'EM]],
     ['text,:middle],['bcStrings,[5, "10.0", "xend", 'EM]]]
  middle := ('"\blankline \menuitemstyle{} \tab{2} Initial Value for Y[i]: ")
  middle := STRCONC(middle,"\newline ")
  yinitList := 
    "append"/[fy(i,n) for i in 1..n] where fy(i,n) ==
      prefix := ('"\newline Y")
      prefix := STRCONC(prefix,STRINGIMAGE i,'"\space{1}")
      yinit := INTERN STRCONC ('"y",STRINGIMAGE i)
      [['text,:prefix],['bcStrings,[10, '"0.0", yinit, 'EM]]]
  yinitList := [['text,:middle],:yinitList]
  if stoppingCriteria = '"no" then
    sExpression := []
  else 
    sText := '"\blankline \newline \menuitemstyle{} \tab{2}"
    sText := STRCONC(sText,'"\newline Enter the function G(x,y) (The Stopping Criteria): ")
    sText := STRCONC(sText,'"\newline \tab{2}")
    sExpression := [['bcStrings,[15, '"Y[1]", "stop", 'EM]]]
    sExpression := [['text,sText],:sExpression]
  if intermediateValues = '"no" then
    ilist := []
  else 
    iText := '"\blankline \newline \menuitemstyle{} \tab{2}"
    iText := STRCONC(iText,'"Enter the list of Intermediate Values required: ")
    iText := STRCONC(iText,"\newline \tab{2}")
    iList := [['bcStrings,[15, '"[2,4,6,8]", "ivals", 'EM]]]
    iList := [['text,iText],:iList]
  tolList := 
    tolText := '"\blankline \newline \menuitemstyle{} \tab{2}"
    tolText := STRCONC(tolText,'"Relative accuracy required:\space{1}")
    [['text,tolText],['bcStrings,[10, '"1.0e-4", "relerr", 'F]]]
  expressionPart := [
     '(domainConditions
        (isDomain EM ($EmptyMode))
         (isDomain F (Float))
           (isDomain S (String))
            (isDomain PI (PositiveInteger))),
              :expressionList,:xList,:yinitList,:sExpression,:iList,:tolList]
  page := htInitPage("AXIOM/NAG ODE Solvers", htpPropertyList htPage)
  htSay '"\menuitemstyle{} \tab{2} Enter the list of ODE's (i.e.~the derivatives "
  htSay '"Y[1]'..Y[n]') in terms of Y[1]..Y[n]: "
  htSay '"\newline "
  htMakePage expressionPart
  htMakeDoneButton('"Continue",'annaOdeGen)
  htpSetProperty(page,'n,n)
  htpSetProperty(page,'stoppingCriteria,stoppingCriteria)
  htpSetProperty(page,'intermediateValues,intermediateValues)
  htShowPage()


annaOdeDefaultSolve() ==

  n := '3
  stoppingCriteria := '"no"
  intermediateValues :=  '"no"
  page := htInitPage('"Solution of Initial Value Problems of Ordinary Differential Equations using AXIOM/NAG Expert System",nil)
  htMakePage '(
    (domainConditions
      (isDomain F (Float))
       (isDomain PI (PositiveInteger))
        (isDomain EM $EmptyMode))
    (text . "\menuitemstyle{} \tab{2} Enter the list of ODE's (i.e. the derivatives Y[1]'..Y[n]') ")
    (text . "in terms of Y[1]..Y[n]: ")
    (text . "\blankline ")
    (text . "\newline \tab{2} {\em Y[1]':} \space{1}")
    (bcStrings (42 "tan(Y[3])" Y1 EM))
    (text . "\blankline ")
    (text . "\newline \tab{2} {\em Y[2]':} \space{1}")
    (bcStrings (42 "-0.032*tan(Y[3])/Y[2]-0.02*Y[2]/cos(Y[3])" Y2 EM))
    (text . "\blankline ")
    (text . "\newline \tab{2} {\em Y[3]':} \space{1}")
    (bcStrings (42 "-0.032/(Y[2]**2)" Y3 EM))
    (text . "\blankline ")
    (text . "\newline \menuitemstyle{}\tab{2} ")
    (text . "\newline Initial Value for X: ")
    (text . "\tab{24} \menuitemstyle{}\tab{26} ")
    (text . "Final Value for X:")
    (text . "\newline\tab{2} ")
    (bcStrings (10 "0.0" xinit EM))
    (text . "\tab{26} ")
    (bcStrings (10 "10.0" xend EM))
    (text . "\blankline ")
    (text . "\newline \menuitemstyle{}\tab{2} ")
    (text . "\newline Initial Value for Y[i]: ")
    (text . "\newline \tab{2} {\em Y[1]:} \space{1}")
    (bcStrings (10 "0.5" y1 EM))
    (text . "\newline \tab{2} {\em Y[2]:} \space{1}")
    (bcStrings (10 "0.5" y2 EM))
    (text . "\newline \tab{2} {\em Y[3]:} \space{1}")
    (bcStrings (10 "%pi*0.2" y3 EM))
    (text . "\blankline ")
    (text . "\newline \menuitemstyle{}\tab{2} ")
    (text . "Relative accuracy required:\space{1}")
    (bcStrings (10 "1.0e-4" tol F))
    (text . "\blankline "))
  htMakeDoneButton('"Continue",'annaOdeGen)
  htpSetProperty(page,'stoppingCriteria,stoppingCriteria)
  htpSetProperty(page,'intermediateValues,intermediateValues)
  htpSetProperty(page,'n,n)
  htShowPage()

annaOdeDefaultSolve3() ==

  n := '3
  stoppingCriteria := '"no"
  intermediateValues := '"intervals"
  page := htInitPage('"Solution of Initial Value Problems of Ordinary Differential Equations using AXIOM/NAG Expert System",nil)
  htMakePage '(
    (domainConditions
      (isDomain F (Float))
       (isDomain PI (PositiveInteger))
        (isDomain EM $EmptyMode))
    (text . "\menuitemstyle{} \tab{2} Enter the list of ODE's (i.e. the derivatives Y[1]'..Y[n]') ")
    (text . "in terms of Y[1]..Y[n]:  ")
    (text . "\blankline ")
    (text . "\newline \tab{2} {\em Y[1]':} \space{1}")
    (bcStrings (42 "-0.04*Y[1]+1.0e4*Y[2]*Y[3]" Y1 EM))
    (text . "\blankline ")
    (text . "\newline \tab{2} {\em Y[2]':} \space{1}")
    (bcStrings (42 "0.04*Y[1]-1.0e4*Y[2]*Y[3]-3.0e7*Y[2]*Y[2]" Y2 EM))
    (text . "\blankline ")
    (text . "\newline \tab{2} {\em Y[3]':} \space{1}")
    (bcStrings (42 "3.0e7*Y[2]*Y[2]" Y3 EM))
    (text . "\blankline ")
    (text . "\newline \menuitemstyle{}\tab{2} ")
    (text . "\newline Initial Value for X: ")
    (text . "\tab{24} \menuitemstyle{}\tab{26} ")
    (text . "Final Value for X:")
    (text . "\newline\tab{2} ")
    (bcStrings (10 "0.0" xinit EM))
    (text . "\tab{26} ")
    (bcStrings (10 "10.0" xend EM))
    (text . "\blankline ")
    (text . "\newline \menuitemstyle{}\tab{2} ")
    (text . "\newline Initial Value for Y[i]: ")
    (text . "\newline \tab{2} {\em Y[1]:} \space{1}")
    (bcStrings (10 "1.0" y1 EM))
    (text . "\newline \tab{2} {\em Y[2]:} \space{1}")
    (bcStrings (10 "0.0" y2 EM))
    (text . "\newline \tab{2} {\em Y[3]:} \space{1}")
    (bcStrings (10 "0.0" y3 EM))
    (text . "\blankline ")
    (text . "\newline \menuitemstyle{}\tab{2} ")
    (text . "\newline Enter the list of Intermediate Values required: ")
    (bcStrings (10 "[2,4,6,8]" intvals EM))
    (text . "\blankline ")
    (text . "\newline \menuitemstyle{}\tab{2} ")
    (text . "Relative accuracy required:\space{1}")
    (bcStrings (10 "1.0e-4" tol F))
    (text . "\blankline "))
  htMakeDoneButton('"Continue",'annaOdeGen)
  htpSetProperty(page,'stoppingCriteria,stoppingCriteria)
  htpSetProperty(page,'intermediateValues,intermediateValues)
  htpSetProperty(page,'n,n)
  htShowPage()

annaOdeDefaultSolve2() ==

  n := '3
  stoppingCriteria := '"stopping"
  intermediateValues := '"no"
  page := htInitPage('"Solution of Initial Value Problems of Ordinary Differential Equations using AXIOM/NAG Expert System",nil)
  htMakePage '(
    (domainConditions
      (isDomain F (Float))
       (isDomain PI (PositiveInteger))
        (isDomain EM $EmptyMode))
    (text . "\menuitemstyle{} \tab{2} Enter the list of ODE's (i.e. the derivatives Y[1]'..Y[n]') ")
    (text . "in terms of Y[1]..Y[n]:  ")
    (text . "\blankline ")
    (text . "\newline \tab{2} {\em Y[1]':} \space{1}")
    (bcStrings (42 "tan(Y[3])" Y1 EM))
    (text . "\blankline ")
    (text . "\newline \tab{2} {\em Y[2]':} \space{1}")
    (bcStrings (42 "-0.032*tan(Y[3])/Y[2]-0.02*Y[2]/cos(Y[3])" Y2 EM))
    (text . "\blankline ")
    (text . "\newline \tab{2} {\em Y[3]':} \space{1}")
    (bcStrings (42 "-0.032/(Y[2]**2)" Y3 EM))
    (text . "\blankline ")
    (text . "\newline \menuitemstyle{}\tab{2} ")
    (text . "\newline Initial Value for X: ")
    (text . "\tab{24} \menuitemstyle{}\tab{26} ")
    (text . "Final Value for X:")
    (text . "\newline\tab{2} ")
    (bcStrings (10 "0.0" xinit EM))
    (text . "\tab{26} ")
    (bcStrings (10 "10.0" xend EM))
    (text . "\blankline ")
    (text . "\newline \menuitemstyle{}\tab{2} ")
    (text . "\newline Initial Value for Y[i]: ")
    (text . "\newline \tab{2} {\em Y[1]:} \space{1}")
    (bcStrings (10 "0.5" y1 EM))
    (text . "\newline \tab{2} {\em Y[2]:} \space{1}")
    (bcStrings (10 "0.5" y2 EM))
    (text . "\newline \tab{2} {\em Y[3]:} \space{1}")
    (bcStrings (10 "%pi*0.2" y3 EM))
    (text . "\blankline ")
    (text . "\newline \menuitemstyle{}\tab{2} ")
    (text . "\newline Enter the function G(x,y) (The Stopping Criteria): ")
    (bcStrings (10 "Y[1]" g EM))
    (text . "\blankline ")
    (text . "\newline \menuitemstyle{}\tab{2} ")
    (text . "Relative accuracy required:\space{1}")
    (bcStrings (10 "1.0e-4" tol F))
    (text . "\blankline "))
  htMakeDoneButton('"Continue",'annaOdeGen)
  htpSetProperty(page,'stoppingCriteria,stoppingCriteria)
  htpSetProperty(page,'intermediateValues,intermediateValues)
  htpSetProperty(page,'n,n)
  htShowPage()

annaOdeDefaultSolve1() ==

  n := '3
  stoppingCriteria := '"stopping"
  intermediateValues := '"intervals"
  page := htInitPage('"Solution of Initial Value Problems of Ordinary Differential Equations using AXIOM/NAG Expert System",nil)
  htMakePage '(
    (domainConditions
      (isDomain F (Float))
       (isDomain PI (PositiveInteger))
        (isDomain EM $EmptyMode))
    (text . "\menuitemstyle{} \tab{2} Enter the list of ODE's (i.e. the derivatives Y[1]'..Y[n]') ")
    (text . "in terms of Y[1]..Y[n]:  ")
    (text . "\blankline ")
    (text . "\newline \tab{2} {\em Y[1]':} \space{1}")
    (bcStrings (42 "-0.04*Y[1]+1.0e4*Y[2]*Y[3]" Y1 EM))
    (text . "\blankline ")
    (text . "\newline \tab{2} {\em Y[2]':} \space{1}")
    (bcStrings (42 "0.04*Y[1]-1.0e4*Y[2]*Y[3]-3.0e7*Y[2]*Y[2]" Y2 EM))
    (text . "\blankline ")
    (text . "\newline \tab{2} {\em Y[3]':} \space{1}")
    (bcStrings (42 "3.0e7*Y[2]*Y[2]" Y3 EM))
    (text . "\blankline ")
    (text . "\newline \menuitemstyle{}\tab{2} ")
    (text . "\newline Initial Value for X: ")
    (text . "\tab{24} \menuitemstyle{}\tab{26} ")
    (text . "Final Value for X:")
    (text . "\newline\tab{2} ")
    (bcStrings (10 "0.0" xinit EM))
    (text . "\tab{26} ")
    (bcStrings (10 "10.0" xend EM))
    (text . "\blankline ")
    (text . "\newline \menuitemstyle{}\tab{2} ")
    (text . "\newline Initial Value for Y[i]: ")
    (text . "\newline \tab{2} {\em Y[1]:} \space{1}")
    (bcStrings (10 "1.0" y1 EM))
    (text . "\newline \tab{2} {\em Y[2]:} \space{1}")
    (bcStrings (10 "0.0" y2 EM))
    (text . "\newline \tab{2} {\em Y[3]:} \space{1}")
    (bcStrings (10 "0.0" y3 EM))
    (text . "\blankline ")
    (text . "\newline \menuitemstyle{}\tab{2} ")
    (text . "\newline Enter the function G(x,y) (The Stopping Criteria): ")
    (bcStrings (10 "Y[1]-0.9" g EM))
    (text . "\blankline ")
    (text . "\newline \menuitemstyle{}\tab{2} ")
    (text . "\newline Enter the list of Intermediate Values required: ")
    (bcStrings (10 "[2,4,6,8]" intvals EM))
    (text . "\blankline ")
    (text . "\newline \menuitemstyle{}\tab{2} ")
    (text . "Relative accuracy required:\space{1}")
    (bcStrings (10 "1.0e-4" tol F))
    (text . "\blankline "))
  htMakeDoneButton('"Continue",'annaOdeGen)
  htpSetProperty(page,'stoppingCriteria,stoppingCriteria)
  htpSetProperty(page,'intermediateValues,intermediateValues)
  htpSetProperty(page,'n,n)
  htShowPage()

annaOdeGen htPage ==

  n := htpProperty(htPage,'n)
  stoppingCriteria := htpProperty(htPage,'stoppingCriteria)
  intermediateValues := htpProperty(htPage,'intermediateValues)
  alist := htpInputAreaAlist htPage
  y := alist
  epsrel := STRCONC((first y).1,'"")
  epsrelString := STRCONC(", ",epsrel)
  y := rest y
  if intermediateValues = '"no" then 
    intvalsString := '""
  else 
    intvals := STRCONC((first y).1,'"")
    intvalsString := STRCONC(", ",intvals)
    y := rest y
  if stoppingCriteria = '"no" then
    gString := '""
  else 
    g := STRCONC((first y).1,'"")
    gString := STRCONC(", ",g)
    y := rest y
  for i in 1..n repeat
    yi := STRCONC((first y).1,'"")
    yiList := [yi,:yiList]
    y := rest y
  yiString := bcwords2liststring yiList
  xend := STRCONC((first y).1,'"")
  y := rest y
  xinit := STRCONC((first y).1,'"")
  y := rest y
  for i in 1..n repeat
    fi := STRCONC((first y).1,'"")
    fiList := [fi,:fiList]
    y := rest y
  fiString := bcwords2liststring fiList
  prefix := STRCONC('"solve(",fiString,", ", xinit,", ", xend,", ")
  prefix := STRCONC(prefix,yiString,gString,intvalsString,epsrelString)
  prefix := STRCONC(prefix,")")
  annaGen prefix

--d03fafVariables() ==
--  htInitPage('"Helmholtz Equation in 3-D, Cartesian Coordinates",nil)
--  htMakePage '(
--    (domainConditions
--      (isDomain F (Float))
--        (isDomain S (String)))
--    (text . "Descretizing the PDE:")
--    (text . "\newline\centerline{\inputbitmap{\htbmdir{}/d03faf.xbm}}")
--    (text . "\newline and solving the resulting seven-diagonal finite ") 
--    (text . "difference equations using a method based on the Fast ")
--    (text . "Fourier Transform.\blankline Entering the names of pre-prepared ")
--    (text . "variables for xCond, yCond, zCond and f(x,y,z)")
--    (text . "\blankline Please enter the names of the condition variables")
--    (text . "\blankline \menuitemstyle{}\tab{2} xCond:\space{1} ")
--    (bcStrings (10 "xCond" x S))
--    (text . "\newline \menuitemstyle{}\tab{2} yCond:\space{1} ")
--    (bcStrings (10 "yCond" y S))
--    (text . "\newline \menuitemstyle{}\tab{2} zCond:\space{1} ")
--    (bcStrings (10 "zCond" z S))
--    (text . "\blankline \menuitemstyle{}\tab{2} Please enter the value of lambda:\space{1} ")
--    (bcStrings (8 "-1.0" lambda F))
--    (text . "\blankline \menuitemstyle{}\tab{2} Please enter the name of the variable for f(x,y,z):")
--    (text . "\space{1} ")
--    (bcStrings (10 "foo" f S))
--    (text . "\blankline "))
--  htMakeDoneButton('"Continue",'annaOptSolve)
--  htShowPage()

annaPDESolve() ==
  htInitPage('"Second Order Elliptic Partial Differential Equation",nil)
  htMakePage '(
    (domainConditions
      (isDomain F (Float))
        (isDomain S (String))
          (isDomain EM $EmptyMode))
    (text . "Descretizing the PDE:")
    (text . "\newline\centerline{\inputbitmap{\htbmdir{}/d03eef.xbm}}")
    (text . "\newline defined on a rectangular region with boundary conditions of the form ")
    (text . "\centerline{\inputbitmap{\htbmdir{}/d03eef1.bitmap}} ")
    (text . " and solving the resulting seven-diagonal finite ") 
    (text . "difference equations using a multigrid technique. \blankline ")
    (text . "\menuitemstyle{} \tab{2} Enter the rectangle on which to discretize the PDE : \newline ")
    (text . "\tab{11} Start \tab{20} Number of grid lines \tab{41} End ")
    (text . " \newline \tab{6} X : \space{1} " ) 
    (bcStrings(7 "0.0" xmin F))
    (text . "\space{7} ")
    (bcStrings(3 "9" ngx I))
    (text . "\space{7} ")
    (bcStrings(7 "1.0" xmax F))
    (text . "\newline \tab{6} Y : \space{1} " )
    (bcStrings(7 "0.0" ymin F))
    (text . "\space{7} ")
    (bcStrings(3 "9" ngy I))
    (text . "\space{7} ")
    (bcStrings(7 "1.0" ymax F))
    (text . "\blankline \menuitemstyle{} Enter the values of the expressions\space{1}")
    (text . " \inputbitmap{\htbmdir{}/alpha.xbm}(X,Y) to\space{1}")
    (text . " \inputbitmap{\htbmdir{}/psi.xbm}(X,Y) : ")
    (text . "\blankline \tab{3} \inputbitmap{\htbmdir{}/alpha.xbm}(X,Y) : ")
    (bcStrings (36 "1" alpha EM))
    (text . "\newline \tab{3} \inputbitmap{\htbmdir{}/beta.xbm}(X,Y) : ")
    (bcStrings (36 "0" beta EM))
    (text . "\newline \tab{3} \inputbitmap{\htbmdir{}/gamma.xbm}(X,Y) : ")
    (bcStrings (36 "1" gamma EM))
    (text . "\newline \tab{3} \inputbitmap{\htbmdir{}/delta.xbm}(X,Y) : ")
    (bcStrings (36 "50" delta EM))
    (text . "\newline \tab{3} \inputbitmap{\htbmdir{}/epsilon.xbm}(X,Y) : ")
    (bcStrings (36 "50" epsilon EM))
    (text . "\newline \tab{3} \inputbitmap{\htbmdir{}/phi.xbm}(X,Y) : ")
    (bcStrings (36 "0" phi EM))
    (text . "\newline \tab{3} \inputbitmap{\htbmdir{}/psi.xbm}(X,Y) : ")
    (bcStrings (36 "-2*sin(X)*sin(Y) + 50*cos(X)*sin(Y) + 50*sin(X)*cos(Y)" psi EM))
    (text . "\blankline \menuitemstyle{} Enter the values of the boundary ")
    (text . " condition expressions for the bottom, top, left and right sides : ")
    (text . " \blankline \tab{2} \menuitemstyle{} Bottom boundary conditions :")
    (text . " (Y := \inputbitmap{\htbmdir{}/ys.xbm})")
    (text . "\newline \tab{4} a(X,Y) : ")
    (bcStrings (34 "0" ba EM))
    (text . "\newline \tab{4} b(X,Y) : ")
    (bcStrings (34 "1" bb EM))
    (text . "\newline \tab{4} c(X,Y) : ")
    (bcStrings (34 "-sin(X)" bc EM))
    (text . " \blankline \tab{2} \menuitemstyle{} Top boundary conditions :")
    (text . " (Y := \inputbitmap{\htbmdir{}/ye.xbm})")
    (text . "\newline \tab{4} a(X,Y) : ")
    (bcStrings (34 "1" ta EM))
    (text . "\newline \tab{4} b(X,Y) : ")
    (bcStrings (34 "0" tb EM))
    (text . "\newline \tab{4} c(X,Y) : ")
    (bcStrings (34 "sin(X)*sin(Y)" tc EM))
    (text . " \blankline \tab{2} \menuitemstyle{} Left boundary conditions :")
    (text . " (X := \inputbitmap{\htbmdir{}/xs.xbm})")
    (text . "\newline \tab{4} a(X,Y) : ")
    (bcStrings (34 "0" la EM))
    (text . "\newline \tab{4} b(X,Y) : ")
    (bcStrings (34 "1" lb EM))
    (text . "\newline \tab{4} c(X,Y) : ")
    (bcStrings (34 "-sin(Y)" lc EM))
    (text . " \blankline \tab{2} \menuitemstyle{} Right boundary conditions :")
    (text . " (Y := \inputbitmap{\htbmdir{}/xe.xbm})")
    (text . "\newline \tab{4} a(X,Y) : ")
    (bcStrings (34 "1" ra EM))
    (text . "\newline \tab{4} b(X,Y) : ")
    (bcStrings (34 "0" rb EM))
    (text . "\newline \tab{4} c(X,Y) : ")
    (bcStrings (34 "sin(X)*sin(Y)" rc EM))
    (text . "\blankline \menuitemstyle{} Do you know that the PDE described is elliptic? \space{2}")
    (text . "\newline \tab{6} ")
    (bcRadioButtons ell
        ("" " Yes \space{2} " yes)
        ("" " Unknown" no))
    (text . "\blankline \menuitemstyle{} Required Tolerance : ")
    (bcStrings (10 "1.0e-4" tol F))
    (text . " \newline "))
  htMakeDoneButton('"Continue",'annaPDESolve2)
  htShowPage()

annaPDESolve2 htPage ==
  e := htpButtonValue(htPage,'ell)
  ell := 
    e = 'yes => '"elliptic"
    '"unknown"
  xmin := htpLabelInputString(htPage,'xmin)
  ngx := htpLabelInputString(htPage,'ngx)
  xmax := htpLabelInputString(htPage,'xmax)
  ymin := htpLabelInputString(htPage,'ymin)
  ngy := htpLabelInputString(htPage,'ngy)
  ymax := htpLabelInputString(htPage,'ymax)
  alpha := htpLabelInputString(htPage,'alpha)
  beta := htpLabelInputString(htPage,'beta)
  gamma := htpLabelInputString(htPage,'gamma)
  delta := htpLabelInputString(htPage,'delta)
  epsilon := htpLabelInputString(htPage,'epsilon)
  phi := htpLabelInputString(htPage,'phi)
  psi := htpLabelInputString(htPage,'psi)
  ba := htpLabelInputString(htPage,'ba)
  bb := htpLabelInputString(htPage,'bb)
  bc := htpLabelInputString(htPage,'bc)
  ta := htpLabelInputString(htPage,'ta)
  tb := htpLabelInputString(htPage,'tb)
  tc := htpLabelInputString(htPage,'tc)
  la := htpLabelInputString(htPage,'la)
  lb := htpLabelInputString(htPage,'lb)
  lc := htpLabelInputString(htPage,'lc)
  ra := htpLabelInputString(htPage,'ra)
  rb := htpLabelInputString(htPage,'rb)
  rc := htpLabelInputString(htPage,'rc)
  tol := htpLabelInputString(htPage,'tol)
  bCond := STRCONC('"[[ ", ba, '", ", bb, '", ", bc, '"],")
  bCond := STRCONC(bCond, '"[ ", ra, '", ", rb, '", ", rc, '"],")
  bCond := STRCONC(bCond, '"[ ", ta, '", ", tb, '", ", tc, '"],")
  bCond := STRCONC(bCond, '"[ ", la, '", ", lb, '", ", lc, '"]]")
  pde := STRCONC('"[", alpha, '", ", beta, '", ", gamma, '", ", delta)
  pde := STRCONC( pde, '", ", epsilon, '", ", phi, '", ", psi, '"]")
  outputString := STRCONC('"solve(", xmin, '", ", xmax, '", ", ymin, '", ", ymax, '", ")
  outputString := STRCONC(outputString , ngx, '", ", ngy, '", ", pde, '", ")
  outputString := STRCONC(outputString , bCond, '", _"", ell ,'"_", ", tol, " )")
  annaGen outputString

annaOpt() ==
  htInitPage('"Minimization of a Multivariate Function using AXIOM/NAG Expert System",nil)
  htMakePage '(
    (domainConditions
      (isDomain F (Float))
       (isDomain NNI (NonNegativeInteger))
        (isDomain S (String))
         (isDomain PI (PositiveInteger))
          (isDomain I (Integer))
           (isDomain EM $EmptyMode))
    (text . "Analyses the function for various attributes, chooses and ")
    (text . "then uses a suitable optimization routine for finding the ")
    (text . "minimum of a nonlinear function {\it F(x)} of {\it n} variables.")
    (text . "\newline {\bf Minimize F(x)} where \center{\htbitmap{e04fdf1}} possibly subject to linear or non-linear ")
    (text . "constraints on the variables. ")
    (text . "\blankline ")
    (text . "\menuitemstyle{}\tab{2}")
    (text . "Number of variables \htbitmap{xj}, {\it n}:")
    (text . "\space{1} ")
    (bcStrings (2 4 n PI))
    (text . "\blankline ")
    (text . "\newline \menuitemstyle{} \tab{2} Are there any constraints ")
    (text . "on the function?")
    (radioButtons constraints
        (" " "  No" nocons)
        (" " "  Yes" cFunctions))
    (text . "\blankline \menuitemstyle{}")
    (text . "Number of linear and/or non-linear constraint functions:\space{1}")
    (bcStrings (2 "0" cons NNI))
    (text . "\blankline "))
  htMakeDoneButton('"Continue",'annaOptSolve)
  htShowPage()

annaOptSolve htPage ==
  n :=
    $bcParseOnly => PARSE_-INTEGER htpLabelInputString(htPage, 'n)
    objValUnwrap htpLabelSpadValue(htPage, 'n)
  c := htpButtonValue(htPage,'constraints)
  constraints := 
    c = 'nocons => '"none"
    '"cf"
  cons :=
    $bcParseOnly => PARSE_-INTEGER htpLabelInputString(htPage, 'cons)
    objValUnwrap htpLabelSpadValue(htPage, 'cons)
  constraints = '"none" => annaOptSolve1(n)
  ((n = '4) and (cons = '0)) => annaOptDefaultSolve2()
  ((n = '4) and (cons = '3)) => annaOptDefaultSolve3()
  ((n = '7) and (cons = '7)) => annaOptDefaultSolve4()
  cText := ('"\blankline \menuitemstyle{}\tab{2} Enter lower and upper ")
  cText := STRCONC(cText,'"boundary conditions {\it bl(n)} and {\it bu(n)}: ")
  cText := STRCONC(cText,'"\newline \tab{5} Lower \tab{25} Constraint ")
  cText := STRCONC(cText,'"\tab{45} Upper ")
  cList := 
    "append"/[fc(i) for i in 1..n] where fc(i) ==
      prefix := ('"\newline \tab{2}")
      xn := INTERN STRCONC ("\tab{27}",'"X",STRINGIMAGE i,"\tab{42}")
      blnam := INTERN STRCONC ('"bl",STRINGIMAGE i)
      bunam := INTERN STRCONC ('"bu",STRINGIMAGE i)
      [['text,:prefix],['bcStrings,[8, '"-1.0", blnam, 'F]],['text,:xn],
       ['bcStrings,[8, '"1.0", bunam, 'F]]]
  consList := 
    "append"/[fe(i) for i in n+1..n+cons] where fe(i) ==
      lineEnd := ('"\newline\tab{2}")
      space := ('"\space{1}")
      space2 := ('"\tab{42}")
      cnam := INTERN STRCONC ('"c",STRINGIMAGE i)
      blnam := INTERN STRCONC ('"bl",STRINGIMAGE i)
      bunam := INTERN STRCONC ('"bu",STRINGIMAGE i)
      [['text,:lineEnd],['bcStrings,[8, '"-1.0", blnam, 'F]],['text,:space],
       ['bcStrings,[26, '"X[1]", cnam, 'EM]],['text,:space2],
        ['bcStrings,[8, '"1.0", bunam, 'F]]]
  cList := [['text,:cText],:cList,:consList]
  funcList := [['bcStrings,[48, '"X[1]", 'f, 'EM]]]
  xmiddle := ('"\blankline \menuitemstyle{}\tab{2} Enter initial guess of the")
  xmiddle := STRCONC(xmiddle,'" solution vector {\it x(n)}: ")
  xList := 
    "append"/[fg(i) for i in 1..n] where fg(i) ==
      xnam := INTERN STRCONC ('"x",STRINGIMAGE i)
      [['text,'"\newline\tab{2}"],['bcStrings,[8, '"0.0", xnam, 'F]]]
  xList := [['text,:xmiddle],:xList]
  equationPart := [
     '(domainConditions 
        (isDomain EM $EmptyMode)
          (isDomain F (Float))),
              :funcList,:cList,:xList]
  page := htInitPage('"Minimization of a Multivariate Function using AXIOM/NAG Expert System", nil)
  htSay '"\menuitemstyle{}\tab{2} "
  htSay '"Enter the objective function, {\it F(x)} in terms of X[1]...X[n]: "
  htSay '"\newline \tab{2} "
  htMakePage equationPart
  htMakeDoneButton('"Continue",'annaOptGen)
  htpSetProperty(page,'constraints,constraints)
  htpSetProperty(page,'cons,cons)
  htpSetProperty(page,'n,n)
  htShowPage()

annaOptSolve1(n) ==

  n = '2 => annaOptDefaultSolve1()
  constraints := '"none"
  cons := '0
  funcList := [['bcStrings,[48, "X[1]", 'f, 'EM]]]
  xmiddle := ('"\blankline \menuitemstyle{}\tab{2} Enter initial guess of the")
  xmiddle := STRCONC(xmiddle,'" solution vector {\it x(n)}: ")
  xList := 
    "append"/[fg(i) for i in 1..n] where fg(i) ==
      xnam := INTERN STRCONC ('"x",STRINGIMAGE i)
      [['text,'"\newline\tab{2}"],['bcStrings,[8, '"0.0", xnam, 'F]]]
  xList := [['text,:xmiddle],:xList]
  equationPart := [
     '(domainConditions 
        (isDomain EM $EmptyMode)
           (isDomain F (Float))),
                  :funcList,:xList]
  page := htInitPage('"Minimization of a Multivariate Function using AXIOM/NAG Expert System", nil)
  htSay '"\menuitemstyle{}\tab{2} "
  htSay '"Enter the objective function, {\it F(x)} in terms of X[1]...X[n]: "
  htSay '"\newline \tab{2} "
  htMakePage equationPart
  htMakeDoneButton('"Continue",'annaOptGen)
  htpSetProperty(page,'constraints,constraints)
  htpSetProperty(page,'cons,cons)
  htpSetProperty(page,'n,n)
  htShowPage()

annaOptDefaultSolve5() ==
  n := '7
  constraints := '"cf"
  cons := '7
  page := htInitPage('"Minimization of a Multivariate Function using AXIOM/NAG Expert System", nil)
  htMakePage '(
    (domainConditions
      (isDomain F (Float))
       (isDomain EM $EmptyMode))
    (text . "\menuitemstyle{}\tab{2} ")
    (text . "Enter the objective function, {\it F(x)} in terms of X[1]...X[n]: ")
    (text . "\newline \tab{2} ")
    (bcStrings (51 "(X[1]-0.02)*X[1]+(X[2]-0.2)*X[2]+(X[3]-0.2)*X[3]+(X[4]+2*X[3]-0.2)*X[4]+(X[5]-0.2)*X[5]+(0.04-X[6])*X[6]+(0.04-2*X[6]-X[7])*X[7]" f EM))
    (text . "\blankline \menuitemstyle{}\tab{2} Enter lower and upper ")
    (text . "boundary conditions {\it bl(n)} and {\it bu(n)}: ")
    (text . "\newline \tab{5} Lower \tab{25} Constraint \tab{45} Upper ")
    (text . "\newline \tab{2}")
    (bcStrings (8 "-0.01" bl1 F))
    (text . "\tab{27} X1 \tab{42}")
    (bcStrings (8 "0.01" bu1 F))
    (text . "\newline \tab{2}")
    (bcStrings (8 "-0.1" bl2 F))
    (text . "\tab{27} X2 \tab{42}")
    (bcStrings (8 "0.15" bu2 F))
    (text . "\newline \tab{2}")
    (bcStrings (8 "-0.01" bl3 F))
    (text . "\tab{27} X3 \tab{42}")
    (bcStrings (8 "0.03" bu3 F))
    (text . "\newline \tab{2}")
    (bcStrings (8 "-0.04" bl4 F))
    (text . "\tab{27} X4 \tab{42}")
    (bcStrings (8 "0.04" bu4 F))
    (text . "\newline \tab{2}")
    (bcStrings (8 "-0.1" bl5 F))
    (text . "\tab{27} X5 \tab{42}")
    (bcStrings (8 "0.05" bu5 F))
    (text . "\newline \tab{2}")
    (bcStrings (8 "-0.01" bl6 F))
    (text . "\tab{27} X6 \tab{42}")
    (bcStrings (8 "1.0E21" bu6 F))
    (text . "\newline \tab{2}")
    (bcStrings (8 "-0.01" bl7 F))
    (text . "\tab{27} X7 \tab{42}")
    (bcStrings (8 "1.0E21" bu7 F))
    (text . "\newline \tab{2}")
    (bcStrings (8 "-0.13" bl8 F))
    (text . "\space{1}")
    (bcStrings (26 "X[1]+X[2]+X[3]+X[4]+X[5]+X[6]+X[7]" c8 EM))
    (text . "\tab{42}")
    (bcStrings (8 "-0.13" bu8 F))
    (text . "\newline \tab{2}")
    (bcStrings (8 "-1.0E21" bl9 F))
    (text . "\space{1}")
    (bcStrings (26 "0.15*X[1]+0.04*X[2]+0.02*X[3]+0.04*X[4]+0.02*X[5]+0.01*X[6]+0.03*X[7]" c9 EM))
    (text . "\tab{42}")
    (bcStrings (8 "-0.0049" bu9 F))
    (text . "\newline \tab{2}")
    (bcStrings (8 "-1.0E21" bl10 F))
    (text . "\space{1}")
    (bcStrings (26 "0.03*X[1]+0.05*X[2]+0.08*X[3]+0.02*X[4]+0.06*X[5]+0.01*X[6]" c10 EM))
    (text . "\tab{42}")
    (bcStrings (8 "-0.0064" bu10 F))
    (text . "\newline \tab{2}")
    (bcStrings (8 "-1.0E21" bl11 F))
    (text . "\space{1}")
    (bcStrings (26 "0.02*X[1]+0.04*X[2]+0.01*X[3]+0.02*X[4]+0.02*X[5]" c11 EM))
    (text . "\tab{42}")
    (bcStrings (8 "-0.0037" bu11 F))
    (text . "\newline \tab{2}")
    (bcStrings (8 "-1.0E21" bl12 F))
    (text . "\space{1}")
    (bcStrings (26 "0.02*X[1]+0.03*X[2]+0.01*X[5]" c12 EM))
    (text . "\tab{42}")
    (bcStrings (8 "-0.0012" bu12 F))
    (text . "\newline \tab{2}")
    (bcStrings (8 "-0.0992" bl13 F))
    (text . "\space{1}")
    (bcStrings (26 "0.7*X[1]+0.75*X[2]+0.8*X[3]+0.75*X[4]+0.8*X[5]+0.97*X[6]" c13 EM))
    (text . "\tab{42}")
    (bcStrings (8 "1.0E21" bu13 F))
    (text . "\newline \tab{2}")
    (bcStrings (8 "-0.003" bl14 F))
    (text . "\space{1}")
    (bcStrings (26 "0.02*X[1]+0.06*X[2]+0.08*X[3]+0.12*X[4]+0.02*X[5]+0.01*X[6]+0.97*X[7]" c14 EM))
    (text . "\tab{42}")
    (bcStrings (8 "0.002" bu14 F))
    (text . "\blankline \menuitemstyle{}\tab{2} Enter initial guess of the")
    (text . " solution vector {\it x(n)}: \newline \tab{2} ")
    (bcStrings (8 "-0.01" x1 F))
    (text . "\newline\tab{2}")
    (bcStrings (8 "-0.03" x2 F))
    (text . "\newline\tab{2}")
    (bcStrings (8 "0.0" x3 F))
    (text . "\newline\tab{2}")
    (bcStrings (8 "-0.01" x4 F))
    (text . "\newline\tab{2}")
    (bcStrings (8 "-0.1" x5 F))
    (text . "\newline\tab{2}")
    (bcStrings (8 "0.02" x6 F))
    (text . "\newline\tab{2}")
    (bcStrings (8 "0.01" x7 F))
    (text . "\blankline"))
  htMakeDoneButton('"Continue",'annaOptGen)
  htpSetProperty(page,'constraints,constraints)
  htpSetProperty(page,'cons,cons)
  htpSetProperty(page,'n,n)
  htShowPage()

annaOptDefaultSolve4() ==
  n := '7
  constraints := '"cf"
  cons := '7
  page := htInitPage('"Minimization of a Multivariate Function using AXIOM/NAG Expert System", nil)
  htMakePage '(
    (domainConditions
      (isDomain F (Float))
       (isDomain EM $EmptyMode))
    (text . "\menuitemstyle{}\tab{2} ")
    (text . "Enter the objective function, {\it F(x)} in terms of X[1]...X[n]: ")
    (text . "\newline \tab{2} ")
    (bcStrings (51 "-0.2*(0.1*X[1]+X[2]+X[3]+X[4]+X[5]-0.2*(X[6]+X[7]))" f EM))
    (text . "\blankline \menuitemstyle{}\tab{2} Enter lower and upper ")
    (text . "boundary conditions {\it bl(n)} and {\it bu(n)}: ")
    (text . "\newline \tab{5} Lower \tab{25} Constraint \tab{45} Upper ")
    (text . "\newline \tab{2}")
    (bcStrings (8 "-0.01" bl1 F))
    (text . "\tab{27} X1 \tab{42}")
    (bcStrings (8 "0.01" bu1 F))
    (text . "\newline \tab{2}")
    (bcStrings (8 "-0.1" bl2 F))
    (text . "\tab{27} X2 \tab{42}")
    (bcStrings (8 "0.15" bu2 F))
    (text . "\newline \tab{2}")
    (bcStrings (8 "-0.01" bl3 F))
    (text . "\tab{27} X3 \tab{42}")
    (bcStrings (8 "0.03" bu3 F))
    (text . "\newline \tab{2}")
    (bcStrings (8 "-0.04" bl4 F))
    (text . "\tab{27} X4 \tab{42}")
    (bcStrings (8 "0.04" bu4 F))
    (text . "\newline \tab{2}")
    (bcStrings (8 "-0.1" bl5 F))
    (text . "\tab{27} X5 \tab{42}")
    (bcStrings (8 "0.05" bu5 F))
    (text . "\newline \tab{2}")
    (bcStrings (8 "-0.01" bl6 F))
    (text . "\tab{27} X6 \tab{42}")
    (bcStrings (8 "1.0E21" bu6 F))
    (text . "\newline \tab{2}")
    (bcStrings (8 "-0.01" bl7 F))
    (text . "\tab{27} X7 \tab{42}")
    (bcStrings (8 "1.0E21" bu7 F))
    (text . "\newline \tab{2}")
    (bcStrings (8 "-0.13" bl8 F))
    (text . "\space{1}")
    (bcStrings (26 "X[1]+X[2]+X[3]+X[4]+X[5]+X[6]+X[7]" c8 EM))
    (text . "\tab{42}")
    (bcStrings (8 "-0.13" bu8 F))
    (text . "\newline \tab{2}")
    (bcStrings (8 "-1.0E21" bl9 F))
    (text . "\space{1}")
    (bcStrings (26 "0.15*X[1]+0.04*X[2]+0.02*X[3]+0.04*X[4]+0.02*X[5]+0.01*X[6]+0.03*X[7]" c9 EM))
    (text . "\tab{42}")
    (bcStrings (8 "-0.0049" bu9 F))
    (text . "\newline \tab{2}")
    (bcStrings (8 "-1.0E21" bl10 F))
    (text . "\space{1}")
    (bcStrings (26 "0.03*X[1]+0.05*X[2]+0.08*X[3]+0.02*X[4]+0.06*X[5]+0.01*X[6]" c10 EM))
    (text . "\tab{42}")
    (bcStrings (8 "-0.0064" bu10 F))
    (text . "\newline \tab{2}")
    (bcStrings (8 "-1.0E21" bl11 F))
    (text . "\space{1}")
    (bcStrings (26 "0.02*X[1]+0.04*X[2]+0.01*X[3]+0.02*X[4]+0.02*X[5]" c11 EM))
    (text . "\tab{42}")
    (bcStrings (8 "-0.0037" bu11 F))
    (text . "\newline \tab{2}")
    (bcStrings (8 "-1.0E21" bl12 F))
    (text . "\space{1}")
    (bcStrings (26 "0.02*X[1]+0.03*X[2]+0.01*X[5]" c12 EM))
    (text . "\tab{42}")
    (bcStrings (8 "-0.0012" bu12 F))
    (text . "\newline \tab{2}")
    (bcStrings (8 "-0.0992" bl13 F))
    (text . "\space{1}")
    (bcStrings (26 "0.7*X[1]+0.75*X[2]+0.8*X[3]+0.75*X[4]+0.8*X[5]+0.97*X[6]" c13 EM))
    (text . "\tab{42}")
    (bcStrings (8 "1.0E21" bu13 F))
    (text . "\newline \tab{2}")
    (bcStrings (8 "-0.003" bl14 F))
    (text . "\space{1}")
    (bcStrings (26 "0.02*X[1]+0.06*X[2]+0.08*X[3]+0.12*X[4]+0.02*X[5]+0.01*X[6]+0.97*X[7]" c14 EM))
    (text . "\tab{42}")
    (bcStrings (8 "0.002" bu14 F))
    (text . "\blankline \menuitemstyle{}\tab{2} Enter initial guess of the")
    (text . " solution vector {\it x(n)}: \newline \tab{2} ")
    (bcStrings (8 "-0.01" x1 F))
    (text . "\newline\tab{2}")
    (bcStrings (8 "-0.03" x2 F))
    (text . "\newline\tab{2}")
    (bcStrings (8 "0.0" x3 F))
    (text . "\newline\tab{2}")
    (bcStrings (8 "-0.01" x4 F))
    (text . "\newline\tab{2}")
    (bcStrings (8 "-0.1" x5 F))
    (text . "\newline\tab{2}")
    (bcStrings (8 "0.02" x6 F))
    (text . "\newline\tab{2}")
    (bcStrings (8 "0.01" x7 F))
    (text . "\blankline"))
  htMakeDoneButton('"Continue",'annaOptGen)
  htpSetProperty(page,'constraints,constraints)
  htpSetProperty(page,'cons,cons)
  htpSetProperty(page,'n,n)
  htShowPage()

annaOptDefaultSolve3() ==
  n := '4
  constraints := '"cf"
  cons := '3
  page := htInitPage('"Minimization of a Multivariate Function using AXIOM/NAG Expert System", nil)
  htMakePage '(
    (domainConditions
      (isDomain F (Float))
       (isDomain EM $EmptyMode))
    (text . "\menuitemstyle{}\tab{2} ")
    (text . "Enter the objective function, {\it F(x)} in terms of X[1]...X[n]: ")
    (text . "\newline \tab{2} ")
    (bcStrings (48 "X[1]*X[4]*(X[1]+X[2]+X[3])+X[3]" f EM))
    (text . "\blankline \menuitemstyle{}\tab{2} Enter lower and upper ")
    (text . "boundary conditions {\it bl(n)} and {\it bu(n)}: ")
    (text . "\newline \tab{5} Lower \tab{25} Constraint \tab{45} Upper ")
    (text . "\newline \tab{2}")
    (bcStrings (8 "1.0" bl1 F))
    (text . "\tab{27} X1 \tab{42}")
    (bcStrings (8 "5.0" bu1 F))
    (text . "\newline \tab{2}")
    (bcStrings (8 "1.0" bl2 F))
    (text . "\tab{27} X2 \tab{42}")
    (bcStrings (8 "5.0" bu2 F))
    (text . "\newline \tab{2}")
    (bcStrings (8 "1.0" bl3 F))
    (text . "\tab{27} X3 \tab{42}")
    (bcStrings (8 "5.0" bu3 F))
    (text . "\newline \tab{2}")
    (bcStrings (8 "1.0" bl4 F))
    (text . "\tab{27} X4 \tab{42}")
    (bcStrings (8 "5.0" bu4 F))
    (text . "\newline \tab{2}")
    (bcStrings (8 "-1.E25" bl5 F))
    (text . "\space{1}")
    (bcStrings (26 "X[1]+X[2]+X[3]+X[4]" c5 EM))
    (text . "\tab{42}")
    (bcStrings (8 "20.0" bu5 F))
    (text . "\newline \tab{2}")
    (bcStrings (8 "-1.E25" bl6 F))
    (text . "\space{1}")
    (bcStrings (26 "X[1]**2+X[2]**2+X[3]**2+X[4]**2" c6 EM))
    (text . "\tab{42}")
    (bcStrings (8 "40.0" bu6 F))
    (text . "\newline \tab{2}")
    (bcStrings (8 "25.0" bl7 F))
    (text . "\space{1}")
    (bcStrings (26 "X[1]*X[2]*X[3]*X[4]" c7 EM))
    (text . "\tab{42}")
    (bcStrings (8 "1.E25" bu7 F))
    (text . "\blankline \menuitemstyle{}\tab{2} Enter initial guess of the")
    (text . " solution vector {\it x(n)}: \newline \tab{2} ")
    (bcStrings (8 "1.0" x1 F))
    (text . "\newline\tab{2}")
    (bcStrings (8 "5.0" x2 F))
    (text . "\newline\tab{2}")
    (bcStrings (8 "5.0" x3 F))
    (text . "\newline\tab{2}")
    (bcStrings (8 "1.0" x4 F))
    (text . "\blankline"))
  htMakeDoneButton('"Continue",'annaOptGen)
  htpSetProperty(page,'constraints,constraints)
  htpSetProperty(page,'cons,cons)
  htpSetProperty(page,'n,n)
  htShowPage()

annaOptDefaultSolve2() ==
  n := '4
  constraints := '"cf"
  cons := '0
  page := htInitPage('"Minimization of a Multivariate Function using AXIOM/NAG Expert System", nil)
  htMakePage '(
    (domainConditions
      (isDomain F (Float))
       (isDomain EM $EmptyMode))
    (text . "\menuitemstyle{}\tab{2} ")
    (text . "Enter the objective function, {\it F(x)} in terms of X[1]...X[n]: ")
    (text . "\newline \tab{2} ")
    (bcStrings (70 "(X[1]+10*X[2])**2+5*(X[3]-X[4])**2+(X[2]-2*X[3])**4+10*(X[1]-X[4])**4" f EM))
    (text . "\blankline \menuitemstyle{}\tab{2} Enter lower and upper ")
    (text . "boundary conditions {\it bl(n)} and {\it bu(n)}: ")
    (text . "\newline \tab{5} Lower \tab{25} Constraint \tab{45} Upper ")
    (text . "\newline \tab{2}")
    (bcStrings (8 "1" bl1 F))
    (text . "\tab{27} X1 \tab{42}")
    (bcStrings (8 "3" bu1 F))
    (text . "\newline \tab{2}")
    (bcStrings (8 "-2" bl2 F))
    (text . "\tab{27} X2 \tab{42}")
    (bcStrings (8 "0" bu2 F))
    (text . "\newline \tab{2}")
    (bcStrings (8 "-1.0E-6" bl3 F))
    (text . "\tab{27} X3 \tab{42}")
    (bcStrings (8 "1.0E6" bu3 F))
    (text . "\newline \tab{2}")
    (bcStrings (8 "1" bl4 F))
    (text . "\tab{27} X4 \tab{42}")
    (bcStrings (8 "3" bu4 F))
    (text . "\blankline \menuitemstyle{}\tab{2} Enter initial guess of the")
    (text . " solution vector {\it x(n)}: \newline \tab{2} ")
    (bcStrings (8 "3" x1 F))
    (text . "\newline\tab{2}")
    (bcStrings (8 "-1" x2 F))
    (text . "\newline\tab{2}")
    (bcStrings (8 "0" x3 F))
    (text . "\newline\tab{2}")
    (bcStrings (8 "1" x4 F))
    (text . "\blankline"))
  htMakeDoneButton('"Continue",'annaOptGen)
  htpSetProperty(page,'constraints,constraints)
  htpSetProperty(page,'cons,cons)
  htpSetProperty(page,'n,n)
  htShowPage()

annaOptDefaultSolve1() ==

  n := '2
  constraints := '"none"
  cons := '0
  page := htInitPage('"Minimization of a Multivariate Function using AXIOM/NAG Expert System", nil)
  htMakePage '(
    (domainConditions
      (isDomain F (Float))
       (isDomain EM $EmptyMode))
    (text . "\menuitemstyle{} \tab{2} Enter the objective function,")
    (text . " {\it F(x)} in terms of X[1]...X[n]: \newline \tab{2} ")
    (bcStrings (52 "exp(X[1])*(4*X[1]**2+2*X[2]**2+4*X[1]*X[2]+2*X[2]+1)" f EM))
    (text . "\blankline \menuitemstyle{} \tab{2} Enter initial guess of the ")
    (text . "solution vector {\it x(n)}: \newline\tab{2}") 
    (bcStrings (8 "-1.0" x1 F))
    (text . "\newline\tab{2}")
    (bcStrings (8 "1.0" x2 F))
    (text . "\blankline"))
  htMakeDoneButton('"Continue",'annaOptGen)
  htpSetProperty(page,'constraints,constraints)
  htpSetProperty(page,'cons,cons)
  htpSetProperty(page,'n,n)
  htShowPage()

annaOptGen htPage ==
  n := htpProperty(htPage,'n)
  cons := htpProperty(htPage,'cons)
  constraints := htpProperty(htPage,'constraints)
  alist := htpInputAreaAlist htPage
  y := alist
  for i in 1..n repeat
    init := STRCONC((first y).1,'"")
    initList := [init,:initList]
    y := rest y
  initString := bcwords2liststring initList
  if constraints = '"cf" then
    for i in 1..cons repeat 
      upper := STRCONC((first y).1,'"") 
      uList := [upper,:uList]
      y := rest y
      con := STRCONC((first y).1," ")
      cList := [con,:cList]
      y := rest y
      lower := STRCONC((first y).1,'"")
      lList := [lower,:lList]
      y := rest y
    for i in 1..n repeat
      upper := STRCONC((first y).1,'"")
      uList := [upper,:uList]
      y := rest y
      lower := STRCONC((first y).1,'"")
      lList := [lower,:lList]
      y := rest y
  uString := bcwords2liststring uList
  cString := bcwords2liststring cList
  lString := bcwords2liststring lList
  f := STRCONC((first y).1,'"")
  prefix := STRCONC('"optimize(",f,", ")
  if constraints = '"none" then
    midfix := initString
  else
    if cons = '0 then
      midfix := STRCONC(initString,", ",lString,", ",uString)
    else
      midfix := STRCONC(initString,", ",lString,", ",cString,", ",uString)
  suffix := STRCONC(prefix, midfix,")")
  annaGen suffix

annaOpt2() ==
  htInitPage('"Minimization of a Sum of Squares using AXIOM/NAG Expert System",nil)
  htMakePage '(
    (domainConditions
     (isDomain PI (PositiveInteger)))
    (text . "Analyses the functions for various attributes, chooses and ")
    (text . "then uses a suitable optimization routine for finding the ")
    (text . "minimum of a sum of squares of {\it m} nonlinear functions in ")
    (text . "{\it n} variables ({\it m} \htbitmap{great=} {\it n}), i.e., it ")
    (text . "is applicable to problems of the form ")
    (text . "\center{\htbitmap{e04fdf}} where \center{\htbitmap{e04fdf1}}")
    (text . "The routines are intended for ")
    (text . "functions which have continous first and second derivatives, ")
    (text . "though they will usually work if the derivatives have occasional ")
    (text . "discontinuities. ")
    (text . "\blankline ")
    (text . "\menuitemstyle{}\tab{2}")
    (text . "Number of functions {\it \htbitmap{fi}(x)}, {\it m}:")
    (text . "\newline\tab{2} ")
    (bcStrings (5 15 m PI))
    (text . "\blankline ")
    (text . "\menuitemstyle{}\tab{2}")
    (text . "Number of variables \htbitmap{xj}, {\it n}:")
    (text . "\newline\tab{2} ")
    (bcStrings (5 3 n PI))
    (text . "\blankline ")
    (text . "\newline \menuitemstyle{} \tab{2} Do you wish for a check for ")
    (text . "goodness of fit of the least squares model?")
    (radioButtons goodness
        (" " "  No" nogood)
        (" " "  Yes" good))
    (text . "\blankline "))
  htMakeDoneButton('"Continue", 'annaOpt2Solve)
  htShowPage()

annaOpt2Solve htPage ==
  g := htpButtonValue(htPage,'goodness)
  goodness := 
    g = 'nogood => '"nogood"
    '"good"
  n :=
    $bcParseOnly => PARSE_-INTEGER htpLabelInputString(htPage, 'n)
    objValUnwrap htpLabelSpadValue(htPage, 'n)
  m :=
    $bcParseOnly => PARSE_-INTEGER htpLabelInputString(htPage, 'm)
    objValUnwrap htpLabelSpadValue(htPage, 'm)
  m = '15 and n = '3 and goodness = '"nogood" => annaOpt2DefaultSolve()
  m = '15 and n = '3  => annaOpt2DefaultSolve2()
  fList := 
    "append"/[f(i) for i in 1..m] where f(i) ==
      lineEnd := ('"\newline\tab{2}")
      fnam := INTERN STRCONC ('"f",STRINGIMAGE i)
      [['text,:lineEnd], ['bcStrings,[42, '"X[1]", fnam, 'EM]]]
  xmiddle := ('"\blankline \menuitemstyle{}\tab{2} Enter initial guess of the")
  xmiddle := STRCONC(xmiddle,'" solution vector {\it x(n)}: ")
  xList := 
    "append"/[fg(i) for i in 1..n] where fg(i) ==
      xnam := INTERN STRCONC ('"x",STRINGIMAGE i)
      [['text,'"\newline\tab{2}"],['bcStrings,[8, '"0.0", xnam, 'F]]]
  xList := [['text,:xmiddle],:xList]
  equationPart := [
     '(domainConditions 
        (isDomain EM $EmptyMode)
          (isDomain F (Float))),
              :fList,:xList]
  page := htInitPage('"Minimization of a Sum of Squares using AXIOM/NAG Expert System",nil)
  htSay '"\menuitemstyle{}\tab{2} "
  htSay '"Enter the objective functions, {\it F(x)} in terms of X[1]...X[n]: "
  htSay '"\newline \tab{2} "
  htMakePage equationPart
  htMakeDoneButton('"Continue",'annaOpt2Gen)
  htpSetProperty(page,'n,n)
  htpSetProperty(page,'m,m)
  htpSetProperty(page,'goodness,goodness)
  htShowPage()

annaOpt2DefaultSolve() ==
  goodness := '"nogood"
  n := '3
  m := '15
  page := htInitPage('"Minimization of a Sum of Squares using AXIOM/NAG Expert System",nil)
  htMakePage '(
    (domainConditions 
       (isDomain EM $EmptyMode)
       (isDomain F (Float))
       (isDomain I (Integer)))
    (text . "\newline ")
    (text . "\menuitemstyle{}\tab{2}")
    (text . "Enter the functions \htbitmap{fi} below ")
    (text . "in terms of X[1]...X[n]: ")
    (text . "\newline ")
    (text . "\newline {\em Function 1:} \space{1}")
    (bcStrings (42 "(X[3]+15*X[2])**(-1)+X[1]-0.14" f1 EM))
    (text . "\newline {\em Function 2:} \space{1}")
    (bcStrings (42 "2*(2*X[3]+14*X[2])**(-1)+X[1]-0.18" f2 EM))
    (text . "\newline {\em Function 3:} \space{1}")
    (bcStrings (42 "3*(3*X[3]+13*X[2])**(-1)+X[1]-0.22" f3 EM))
    (text . "\newline {\em Function 4:} \space{1}")
    (bcStrings (42 "4*(4*X[3]+12*X[2])**(-1)+X[1]-0.25" f4 EM))
    (text . "\newline {\em Function 5:} \space{1}")
    (bcStrings (42 "5*(5*X[3]+11*X[2])**(-1)+X[1]-0.29" f5 EM))
    (text . "\newline {\em Function 6:} \space{1}")
    (bcStrings (42 "6*(6*X[3]+10*X[2])**(-1)+X[1]-0.32" f6 EM))
    (text . "\newline {\em Function 7:} \space{1}")
    (bcStrings (42 "7*(7*X[3]+9*X[2])**(-1)+X[1]-0.35" f7 EM))
    (text . "\newline {\em Function 8:} \space{1}")
    (bcStrings (42 "8*(8*X[3]+8*X[2])**(-1)+X[1]-0.39" f8 EM))
    (text . "\newline {\em Function 9:} \space{1}")
    (bcStrings (42 "9*(7*X[3]+7*X[2])**(-1)+X[1]-0.37" f9 EM))
    (text . "\newline {\em Function 10:} \space{1}")
    (bcStrings (42 "10*(6*X[3]+6*X[2])**(-1)+X[1]-0.58" f10 EM))
    (text . "\newline {\em Function 11:} \space{1}")
    (bcStrings (42 "11*(5*X[3]+5*X[2])**(-1)+X[1]-0.73" f11 EM))
    (text . "\newline {\em Function 12:} \space{1}")
    (bcStrings (42 "12*(4*X[3]+4*X[2])**(-1)+X[1]-0.96" f12 EM))
    (text . "\newline {\em Function 13:} \space{1}")
    (bcStrings (42 "13*(3*X[3]+3*X[2])**(-1)+X[1]-1.34" f13 EM))
    (text . "\newline {\em Function 14:} \space{1}")
    (bcStrings (42 "14*(2*X[3]+2*X[2])**(-1)+X[1]-2.1" f14 EM))
    (text . "\newline {\em Function 15:} \space{1}")
    (bcStrings (42 "15*(X[3]+X[2])**(-1)+X[1]-4.39" f15 EM))
    (text . "\blankline ")
    (text . "\menuitemstyle{}\tab{2}")
    (text . "Enter initial guess of the solution vector {\it x(n)}: \newline \tab{2}")
    (bcStrings (8 "0.5" x1 F))
    (text . "\newline \tab{2}")
    (bcStrings (8 "1.0" x2 F))
    (text . "\newline \tab{2}")
    (bcStrings (8 "1.5" x3 F)))
  htMakeDoneButton('"Continue",'annaOpt2Gen)
  htpSetProperty(page,'n,n)
  htpSetProperty(page,'m,m)
  htpSetProperty(page,'goodness,goodness)
  htShowPage()

annaOpt2DefaultSolve2() ==
  goodness := '"good"
  n := '3
  m := '15
  page := htInitPage('"Minimization of a Sum of Squares using AXIOM/NAG Expert System",nil)
  htMakePage '(
    (domainConditions 
       (isDomain EM $EmptyMode)
       (isDomain F (Float))
       (isDomain I (Integer)))
    (text . "\newline ")
    (text . "\menuitemstyle{}\tab{2}")
    (text . "Enter the functions \htbitmap{fi} below ")
    (text . "in terms of X[1]...X[n]: ")
    (text . "\newline ")
    (text . "\newline {\em Function 1:} \space{1}")
    (bcStrings (42 "(X[3]+15*X[2])**(-1)+X[1]-0.14" f1 EM))
    (text . "\newline {\em Function 2:} \space{1}")
    (bcStrings (42 "2*(2*X[3]+14*X[2])**(-1)+X[1]-0.18" f2 EM))
    (text . "\newline {\em Function 3:} \space{1}")
    (bcStrings (42 "3*(3*X[3]+13*X[2])**(-1)+X[1]-0.22" f3 EM))
    (text . "\newline {\em Function 4:} \space{1}")
    (bcStrings (42 "4*(4*X[3]+12*X[2])**(-1)+X[1]-0.25" f4 EM))
    (text . "\newline {\em Function 5:} \space{1}")
    (bcStrings (42 "5*(5*X[3]+11*X[2])**(-1)+X[1]-0.29" f5 EM))
    (text . "\newline {\em Function 6:} \space{1}")
    (bcStrings (42 "6*(6*X[3]+10*X[2])**(-1)+X[1]-0.32" f6 EM))
    (text . "\newline {\em Function 7:} \space{1}")
    (bcStrings (42 "7*(7*X[3]+9*X[2])**(-1)+X[1]-0.35" f7 EM))
    (text . "\newline {\em Function 8:} \space{1}")
    (bcStrings (42 "8*(8*X[3]+8*X[2])**(-1)+X[1]-0.39" f8 EM))
    (text . "\newline {\em Function 9:} \space{1}")
    (bcStrings (42 "9*(7*X[3]+7*X[2])**(-1)+X[1]-0.37" f9 EM))
    (text . "\newline {\em Function 10:} \space{1}")
    (bcStrings (42 "10*(6*X[3]+6*X[2])**(-1)+X[1]-0.58" f10 EM))
    (text . "\newline {\em Function 11:} \space{1}")
    (bcStrings (42 "11*(5*X[3]+5*X[2])**(-1)+X[1]-0.73" f11 EM))
    (text . "\newline {\em Function 12:} \space{1}")
    (bcStrings (42 "12*(4*X[3]+4*X[2])**(-1)+X[1]-0.96" f12 EM))
    (text . "\newline {\em Function 13:} \space{1}")
    (bcStrings (42 "13*(3*X[3]+3*X[2])**(-1)+X[1]-1.34" f13 EM))
    (text . "\newline {\em Function 14:} \space{1}")
    (bcStrings (42 "14*(2*X[3]+2*X[2])**(-1)+X[1]-2.1" f14 EM))
    (text . "\newline {\em Function 15:} \space{1}")
    (bcStrings (42 "15*(X[3]+X[2])**(-1)+X[1]-4.39" f15 EM))
    (text . "\blankline ")
    (text . "\menuitemstyle{}\tab{2}")
    (text . "Enter initial guess of the solution vector {\it x(n)}: \newline \tab{2}")
    (bcStrings (8 "0.5" x1 F))
    (text . "\newline \tab{2}")
    (bcStrings (8 "1.0" x2 F))
    (text . "\newline \tab{2}")
    (bcStrings (8 "1.5" x3 F)))
  htMakeDoneButton('"Continue",'annaOpt2Gen)
  htpSetProperty(page,'n,n)
  htpSetProperty(page,'m,m)
  htpSetProperty(page,'goodness,goodness)
  htShowPage()

annaOpt2Gen htPage ==

  goodness := htpProperty(htPage,'goodness)
  n := htpProperty(htPage,'n)
  m := htpProperty(htPage,'m)
  alist := htpInputAreaAlist htPage
  y := alist
  for i in 1..n repeat
    init := STRCONC((first y).1,'"")
    initList := [init,:initList]
    y := rest y
  initString := bcwords2liststring initList
  for i in 1..m repeat
    f := STRCONC((first y).1," ")
    fList := [f,:fList]
    y := rest y
  fString := bcwords2liststring fList
  prefix :=
    goodness = '"good" => '"goodnessOfFit( "
    '"optimize( "
  midfix := STRCONC(fString,", ",initString)
  suffix := STRCONC(prefix, midfix,")")
  annaGen suffix