path: root/src/interp/bc-misc.boot

-- Copyright (c) 1991-2002, The Numerical ALgorithms Group Ltd.
-- All rights reserved.
-- Copyright (C) 2007-2009, Gabriel Dos Reis.
-- 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.


import bc_-util
namespace BOOT

--Hypertex commands other than solve and matrix

bcDrawIt2(ind,a,b) == strconc('"{}",ind,'"=",a,'"{}..",b,'"{}")

bcIndefiniteIntegrate() ==
  htInitPage("Indefinite Integration Basic Command",nil)
  htMakePage '(
     (domainConditions
       (isDomain EM $EmptyMode)
       (isDomain S (String))
       (isDomain SY (Symbol)))
     (text . "\newline ")
     (text . "\menuitemstyle{}\tab{2}")
     (text . "Enter the {\em function} you would like to integrate:")
     (text . "\newline\tab{2} ")
     (bcStrings (45 "1/(x**2 + 6)" integrand EM))
     (text . "\blankline")
     (text . "\newline ")
     (text . "\menuitemstyle{}\tab{2}")
     (text . "Enter the {\em variable of integration}:")
     (text . "\tab{37}")
     (bcStrings (10 x symbol SY))
     (doneButton "Continue" bcIndefiniteIntegrateGen))
  htShowPage()

bcIndefiniteIntegrateGen htPage ==
  integrand := htpLabelInputString(htPage,'integrand)
  var := htpLabelInputString(htPage,'symbol)
  bcGen strconc('"integrate(",integrand,'",",var,")")


bcDefiniteIntegrate() ==
  htInitPage("Definite Integration Basic Command",nil)
  htMakePage '(
     (domainConditions
       (isDomain EM $EmptyMode)
       (isDomain S (String))
       (isDomain SY (Symbol)))
     (text . "\newline ")
     (text . "\menuitemstyle{}\tab{2}")
     (text . "Enter the {\em function} you would like to integrate:")
     (text . "\newline\tab{2} ")
     (bcStrings (45 "1/(x**2 + 6)" integrand EM))
     (text . "\blankline")
     (text . "\newline ")
     (text . "\menuitemstyle{}\tab{2}")
     (text . "Enter the {\em variable of integration}:")
     (text . "\tab{37}")
     (bcStrings (10 x symbol SY))
     (text . "\blankline")
     (text . "\newline ")
     (text . "\menuitemstyle{}\tab{2}")
     (text . "\newline Enter {\em lower limit}:")
     (radioButtons fromButton
       ("" "Minus infinity" minusInfinity)
       (""  (
         (text . "A finite point:\tab{15}")
         (bcStrings (10 0 from EM . bcOptional))) fromPoint))
     (text . "\blankline")
     (text . "\newline ")
     (text . "\menuitemstyle{}\tab{2}")
     (text . "\indent{2}\newline Enter {\em upper limit}:")
     (radioButtons toButton
       ("" "Plus infinity" plusInfinity)
       ("" (
         (text "A finite point:\tab{15}")
         (bcStrings (10 y to EM . bcOptional))) toPoint))
     (doneButton "Continue" bcDefiniteIntegrateGen))
  htShowPage()

bcDefiniteIntegrateGen htPage ==
  integrand := htpLabelInputString(htPage,'integrand)
  var := htpLabelInputString(htPage,'symbol)
  lowerLimit :=
    htpButtonValue(htPage,'fromButton) is 'fromPoint =>
      htpLabelInputString(htPage,'from)
    '"%minusInfinity"
  upperLimit :=
    htpButtonValue(htPage,'toButton) is 'toPoint =>
      htpLabelInputString(htPage,'to)
    '"%plusInfinity"
  varpart := strconc(var,'" = ",lowerLimit,'"..",upperLimit)
  bcGen
   strconc('"integrate(",integrand,'",",varpart,'")")

bcSum() ==
  htInitPage("Sum Basic Command",nil)
  htMakePage '(
    (domainConditions
       (isDomain EM $EmptyMode)
       (isDomain S (String))
       (isDomain SY (Symbol)))
    (text . "\newline ")
    (text . "\menuitemstyle{}\tab{2}")
    (text . "Enter the {\em function} you would like to sum:")
    (text . "\newline\tab{2} ")
    (bcStrings (44 "i**3" summand EM))
    (text . "\blankline ")
    (text . "\newline ")
    (text . "\menuitemstyle{}\tab{2}")
    (text . "Enter the {\em summation index}:")
    (text . "\tab{36}")
    (bcStrings (10 i index SY))
    (text . "\blankline ")
    (text . "\newline ")
    (text . "\menuitemstyle{}\tab{2}")
    (text . "Enter the limits of the sum:")
    (text . "\newline\tab{10}{\em From:}")
    (bcStrings (10 1 first S))
    (text . "\tab{32}{\em To:}")
    (text . "\tab{36}")
    (bcStrings (10  n  last S))
    (doneButton "Continue" bcSumGen))
  htShowPage()

bcSumGen htPage ==
  mand := htpLabelInputString(htPage,'summand)
  index := htpLabelInputString(htPage,'index)
  first := htpLabelInputString(htPage,'first)
  last := htpLabelInputString(htPage,'last)
  bcGen strconc('"sum(",mand,'",",index,'" = ",first,'"..",last,'")")

bcProduct() ==
  htInitPage("Product Basic Command",nil)
  htMakePage '(
    (domainConditions
       (isDomain EM $EmptyMode)
       (isDomain S (String))
       (isDomain SY (Symbol)))
    (text . "Enter the {\em function} you would like to compute the product of:")
    (inputStrings ("" "" 45 "i**2" mand EM))
    (text . "\vspace{1}\newline")
    (inputStrings ("Enter the {\em index of the product}:" "" 5 i index SY))
    (text . "\vspace{1}\newline Enter the limits of the index:")
    (inputStrings
      ("\newline{\em From:}" "" 10 "1" first  EM)
      ("{\em To:}\space{2}" "" 10  "n" last   EM))
    (doneButton "Continue" bcProductGen))
  htShowPage()

bcProductGen htPage ==
  mand := htpLabelInputString(htPage,'mand)
  index := htpLabelInputString(htPage,'index)
  first := htpLabelInputString(htPage,'first)
  last := htpLabelInputString(htPage,'last)
  bcGen strconc('"product(",mand,'",",index,'",",first,'",",last,'")")

bcDifferentiate() ==
  htInitPage("Differentiate Basic Command",nil)
  htMakePage '(
    (domainConditions
       (isDomain EM $EmptyMode)
       (isDomain S (String))
       (isDomain SY (Symbol)))
    (text . "\newline ")
    (text . "\menuitemstyle{}\tab{2}")
    (text . "Enter the {\em function} you want to differentiate:")
    (text . "\newline\tab{2} ")
    (bcStrings (55 "sin(x*y)" diffand EM))
    (text . "\blankline")
    (text . "\newline ")
    (text . "\menuitemstyle{}\tab{2}")
    (text . "\newline List the {\em variables} you want to differentiate with respect to?")
    (text . "\newline\tab{2} ")
    (bcStrings (55 "x y" variables S . quoteString))
    (text . "\blankline")
    (text . "\newline ")
    (text . "\menuitemstyle{}\tab{2}")
    (text . "\newline List the number of {\em times} you want to differentiate with respect to each variable (leave blank if once for each)")
    (text . "\newline\tab{2} ")
    (bcStrings (55 "1 2" times S . quoteString)))
  htMakeDoneButton('"Continue", 'bcDifferentiateGen)
  htShowPage()

bcDifferentiateGen htPage ==
  mand := htpLabelInputString(htPage,'diffand)
  varlist := bcString2WordList htpLabelInputString(htPage,'variables)
  indexList := bcString2WordList htpLabelInputString(htPage,'times)
  varpart :=
    #varlist > 1 => bcwords2liststring varlist
    first varlist
  indexpart :=
    null indexList => nil
    null rest indexList => first indexList
    #indexList = #varlist => bcwords2liststring indexList
    bcError '"You must say how many times you want to differentiate with respect to each variable---or leave that entry blank"
  lastPart :=
    indexpart => strconc('",",indexpart,'")")
    '")"
  bcGen strconc('"differentiate(",mand,'",",varpart,lastPart)

bcDraw() ==
  htInitPage('"Draw Basic Command",nil)
  bcHt '"What would you like to draw?"
  bcHt '"\newline\centerline{{\em Two Dimensional Plots}}\newline"
  bcHt '"\lispdownlink{A function of one variable}{(|bcDraw2Dfun|)}"
  bcHt '"\space{2}y = f(x)\newline"
  bcHt '"\lispdownlink{A parametrically defined curve}{(|bcDraw2Dpar|)}"
  bcHt '"\space{2}(x(t), y(t))\newline"
  bcHt '"\lispdownlink{A solution to a polynomial equation}{(|bcDraw2DSolve|)}"
  bcHt '"\space{2} p(x,y) = 0\newline"
  bcHt '"\vspace{1}\newline "
  bcHt '"\centerline{{\em Three Dimensional Surfaces}}\newline\newline"
  bcHt '"\lispdownlink{A function of two variables}{(|bcDraw3Dfun|)}"
  bcHt '"\space{2} z = f(x,y)\newline"
  bcHt '"\lispdownlink{A parametrically defined tube}{(|bcDraw3Dpar|)}"
  bcHt '"\space{2}(x(t), y(t), z(t))\newline"
  bcHt '"\lispdownlink{A parameterically defined surface}{(|bcDraw3Dpar1|)}"
  bcHt '"\space{2}(x(u,v), y(u,v), z(u,v))\newline"
  htShowPage()


bcDraw2Dfun() ==
  htInitPage('"Draw Basic Command",nil)
  htMakePage '(
    (domainConditions
       (isDomain EM $EmptyMode)
       (isDomain F (Float))
       (isDomain SY (Symbol)))
    (text
      "\centerline{Drawing {\em y = f(x)}}\newline "
      "\centerline{where {\em y} is the dependent variable and}\newline "
      "\centerline{where {\em x} is the independent variable}\vspace{1}\newline "
      "\menuitemstyle{}\tab{2}What {\em function} f would you like to draw?\newline\tab{2}")
    (bcStrings (55 "x*cos(x)" function EM))
    (text . "\vspace{1}\newline\menuitemstyle{}\tab{2}Enter {\em dependent} variable:")
    (bcStrings (6 y dependent SY))
    (text . "\newline\vspace{1}\newline ")
    (text . "\menuitemstyle{}\tab{2}Enter {\em independent} variable and {\em range}:\newline\tab{2} ")
    (text . "{\em Variable:}")
    (bcStrings (6 x ind SY))
    (text . "ranges {\em from:}")
    (bcStrings (9 0 from1 F))
    (text . "{\em to:}")
    (bcStrings (9 30 to1 F))
    (text
      "\indent{0}\vspace{1}\newline\menuitemstyle{}\tab{2} "
      "Optionally enter a {\em title} for your curve:"
      )
    (bcStrings (15 "y = x*cos(x)" title S))
    (text . "\indent{0}")
    (doneButton "Continue" bcDraw2DfunGen)
    (text . "{}"))
  htShowPage()

bcDraw2DfunGen htPage ==
  fun := htpLabelInputString(htPage,'function)
  dep := htpLabelInputString(htPage,'dependent)
  ind := htpLabelInputString(htPage,'ind)
  from1 := htpLabelInputString(htPage,'from1)
  to1 := htpLabelInputString(htPage,'to1)
  title := htpLabelInputString(htPage,'title)
  if (title isnt '"") then
    titlePart := strconc('"{}",'"title ==_"",title,'"_"")
    bcFinish('"draw",fun,bcDrawIt2(ind,from1,to1),titlePart)
  else
    bcFinish('"draw",fun,bcDrawIt2(ind,from1,to1))


bcDraw2Dpar() ==
  htInitPage('"Draw Basic Command",nil)
  htMakePage '(
    (domainConditions
       (isDomain EM $EmptyMode)
       (isDomain F (Float))
       (isDomain SY (Symbol)))
    (text
      "\centerline{Drawing a parametrically defined curve:}\newline "
      "\centerline{{\em ( f1(t), f2(t) )}}\newline "
      "\centerline{in terms of two functions {\em f1} and {\em f2}}"
      "\centerline{and an independent variable {\em t}}\vspace{1}\newline"
      "\menuitemstyle{}\tab{2}Enter the two {\em functions:}")
    (text . "\newline\tab{2}{\em Function 1:}")
    (bcStrings (44 "-9*sin(4*t/5)" function1 EM))
    (text . "\newline\tab{2}{\em Function 2:}")
    (bcStrings (44 "8*sin(t)" function2 EM))
    (text ."\vspace{1}\newline\menuitemstyle{}\tab{2}Enter {\em independent} variable and range:\newline\tab{2} ")
    (text . "{\em Variable:}")
    (bcStrings (6 t ind SY))
    (text . "ranges {\em from:}")
    (bcStrings (9 "-5*\%pi" from1 F))
    (text . "{\em to:}")
    (bcStrings (9 "5*\%pi" to1 F))
    (text
      "\vspace{1}\newline\menuitemstyle{}\tab{2}"
      "Optionally enter a {\em title} for your curve:")
    (bcStrings (15 "Lissajous" title S))
    (text . "\indent{0}")
    (doneButton "Continue" bcDraw2DparGen))
  htShowPage()

bcDraw2DparGen htPage ==
  fun1 := htpLabelInputString(htPage,'function1)
  fun2 := htpLabelInputString(htPage,'function2)
  ind := htpLabelInputString(htPage,'ind)
  from1 := htpLabelInputString(htPage,'from1)
  to1 := htpLabelInputString(htPage,'to1)
  title := htpLabelInputString(htPage,'title)
  curvePart := strconc('"curve(",'"{}",fun1,'",{}",fun2,'")")
  if (title isnt '"") then
    titlePart := (title is '"" => nil; strconc('"{}",'"title ==_"",title,'"_""))
    bcFinish('"draw",curvePart,bcDrawIt2(ind,from1,to1),titlePart)
  else
    bcFinish('"draw",curvePart,bcDrawIt2(ind,from1,to1))

bcDraw2DSolve() ==
  htInitPage('"Draw Basic Command",nil)
  htMakePage '(
    (domainConditions
       (isDomain EM $EmptyMode)
       (isDomain F (Float))
       (isDomain SY (Symbol)))
    (text
      "\centerline{Plotting the solution to {\em p(x,y) = 0}, where} "
      "\centerline{{\em p} is a polynomial in two variables {\em x} and {\em y}}"
      "\vspace{1}\newline\menuitemstyle{}\tab{2}Enter the {\em polynomial} p:"
      "\newline\tab{2}")
    (bcStrings (40 "y**2+7*x*y-(x**3+16*x)" function EM))
    (text . "\vspace{1}\newline\menuitemstyle{}\tab{2}Enter the {\em variables}:")
    (text . "\newline\tab{2}{\em Variable 1:} ")
    (bcStrings (4 x independent1 SY))
    (text . "ranges {\em from:}")
    (bcStrings (9 -15 from1 F))
    (text . "{\em to:}")
    (bcStrings (9 10 to1 F))
    (text . "\newline\tab{2}{\em Variable 2:} ")
    (bcStrings (4 y independent2 SY))
    (text . "ranges {\em from:}")
    (bcStrings (9 -10 from2 F))
    (text . "{\em to:}")
    (bcStrings (9 50 to2 F))
    (text
      "\indent{0}\vspace{1}\newline\menuitemstyle{}\tab{2} "
      "Optionally enter a {\em title} for your curve:")
    (bcStrings (15 "" title S))
    (text . "\indent{0}"))
  htMakeDoneButton('"Continue",'bcDraw2DSolveGen)
  htShowPage()

bcDraw2DSolveGen htPage ==
  fun := htpLabelInputString(htPage,'function)
  ind1 := htpLabelInputString(htPage,'independent1)
  from1 := htpLabelInputString(htPage,'from1)
  to1 := htpLabelInputString(htPage,'to1)
  ind2 := htpLabelInputString(htPage,'independent2)
  from2 := htpLabelInputString(htPage,'from2)
  to2 := htpLabelInputString(htPage,'to2)
  title := htpLabelInputString(htPage,'title)
  clipPart := strconc('"{}",'"range==[{}",from1,'"..",to1,",{}",from2,'"..",to2,'"]")
  if (title isnt '"") then
    titlePart := (title is '"" => nil; strconc('"{}",'"title ==_"",title,'"_""))
    bcFinish('"draw",strconc(fun,'" = 0 "),ind1,ind2,clipPart,titlePart)
  else
    bcFinish('"draw",strconc(fun,'" = 0 "),ind1,ind2,clipPart)

bcDraw3Dfun() ==
  htInitPage('"Three Dimensional Draw Basic Command",nil)
  htMakePage '(
    (domainConditions
       (isDomain EM $EmptyMode)
       (isDomain F (Float))
       (isDomain SY (Symbol)))
    (text
      "\centerline{Drawing {\em z = f(x,y)}}\newline "
      "\centerline{where {\em z} is the dependent variable and}\newline "
      "\centerline{where {\em x, y} are the independent variables}\vspace{1}\newline\menuitemstyle{}\tab{2} "
      "What {\em function} f which you like to draw?\newline\tab{2}")
    (bcStrings (55 "exp(cos(x-y)-sin(x*y))-2" function EM))
    (text . "\newline\menuitemstyle{}\tab{2}Enter {\em dependent} variable:")
    (bcStrings (6 z dependent SY))
    (text
      "\vspace{1}\newline\menuitemstyle{}\tab{2}"
      "Enter {\em independent} variables and ranges:\newline\tab{2} "
      "{\em Variable:}")
    (bcStrings (6 x independent1 SY))
    (text . "ranges {\em from:}")
    (bcStrings (9 -5 from1 F))
    (text . "{\em to:}")
    (bcStrings (9 5 to1 F))
    (text . "\newline\tab{2}{\em Variable:}")
    (bcStrings (6 y independent2 SY))
    (text . "ranges {\em from:}")
    (bcStrings (9 -5 from2 F))
    (text . "{\em to:}")
    (bcStrings (9 5 to2 F))
    (text
      "\indent{0}\vspace{1}\newline\menuitemstyle{}\tab{2} "
      "Optionally enter a {\em title} for your surface:")
    (bcStrings (15 "" title S))
    (text . "\indent{0}")
    (doneButton "Continue" bcDraw3DfunGen))
  htShowPage()

bcDraw3DfunGen htPage ==
  fun := htpLabelInputString(htPage,'function)
  dep := htpLabelInputString(htPage,'dependent)
  ind1 := htpLabelInputString(htPage,'independent1)
  from1 := htpLabelInputString(htPage,'from1)
  to1 := htpLabelInputString(htPage,'to1)
  ind2 := htpLabelInputString(htPage,'independent2)
  from2 := htpLabelInputString(htPage,'from2)
  to2 := htpLabelInputString(htPage,'to2)
  title := htpLabelInputString(htPage,'title)
  if (title ~= '"") then
    titlePart := (title = '"" => nil;strconc('"{}",'"title ==_"",title,'"_""))
    bcFinish('"draw",fun,bcDrawIt2(ind1,from1,to1),bcDrawIt2(ind2,from2,to2),titlePart)
  else
    bcFinish('"draw",fun,bcDrawIt2(ind1,from1,to1),bcDrawIt2(ind2,from2,to2))

bcDraw3Dpar() ==
  htInitPage('"Draw Basic Command",nil)
  htMakePage '(
    (domainConditions
       (isDomain EM $EmptyMode)
       (isDomain F (Float))
       (isDomain SY (Symbol)))
    (text
      "\centerline{Drawing a parametrically defined curve:"
      "{\em ( f1(t), f2(t), f3(t) )}}\newline "
      "\centerline{in terms of three functions {\em f1}, {\em f2}, and {\em f3}}\newline "
      "\centerline{and an independent variable {\em t}}\vspace{1}\newline\menuitemstyle{}\tab{2} "
      "Enter the three {\em functions} of the independent variable:")
    (text . "\newline\tab{2}{\em Function f1:}")
    (bcStrings (42 "1.3*cos(2*t)*cos(4*t) + sin(4*t)*cos(t)" function1 EM))
    (text . "\newline\tab{2}{\em Function f2:}")
    (bcStrings  (42 "1.3*sin(2*t)*cos(4*t) - sin(4*t)*sin(t)" function2 EM))
    (text . "\newline\tab{2}{\em Function f3:}")
    (bcStrings  (42 "2.5*cos(4*t)" function3 EM))
    (text ."\vspace{1}\newline\menuitemstyle{}\tab{2}Enter {\em independent} variable and range:\newline\tab{2} ")
    (text ."{\em Variable:}")
    (bcStrings (6 t ind SY))
    (text . "ranges {\em from:}")
    (bcStrings (9 0 from1 F))
    (text "{\em to:}")
    (bcStrings (9 "4*\%pi" to1 F))
    (text
      "\indent{0}\vspace{1}\newline\menuitemstyle{}\tab{2} "
      "Optionally enter a {\em title} for your surface:")
    (bcStrings (15 "knot" title S))
    (text . "\indent{0}")
    (doneButton "Continue" bcDraw3DparGen))
  htShowPage()

bcDraw3DparGen htPage ==
  fun1 := htpLabelInputString(htPage,'function1)
  fun2 := htpLabelInputString(htPage,'function2)
  fun3 := htpLabelInputString(htPage,'function3)
  ind := htpLabelInputString(htPage,'ind)
  from1 := htpLabelInputString(htPage,'from1)
  to1 := htpLabelInputString(htPage,'to1)
  title := htpLabelInputString(htPage,'title)
  curvePart := strconc('"curve(",'"{}",fun1,'",{}",fun2,'",{}",fun3,'")")
  tubePart := '"{}tubeRadius==.25,{}tubePoints==16"
  if (title ~= '"") then
    titlePart := (title = '"" => nil; strconc('"{}",'"title ==_"",title,'"_""))
    bcFinish('"draw",curvePart,bcDrawIt2(ind,from1,to1),tubePart,titlePart)
  else
    bcFinish('"draw",curvePart,bcDrawIt2(ind,from1,to1),tubePart)

bcDraw3Dpar1() ==
  htInitPage('"Draw Basic Command",nil)
  htMakePage '(
    (domainConditions
       (isDomain EM $EmptyMode)
       (isDomain F (Float))
       (isDomain SY (Symbol)))
    (text
      "\centerline{Drawing a parametrically defined surface:}\newline "
      "\centerline{{\em ( f1(u,v), f2(u,v), f3(u,v) )}}\newline "
      "\centerline{in terms of three functions {\em f1}, {\em f2}, and {\em f3}}\newline "
      "\centerline{and two independent variables {\em u} and {\em v}}\vspace{1}\newline\menuitemstyle{}\tab{2}"
      "Enter the three {\em functions} of the independent variables:")
    (text . "\newline\tab{2}")
    (text . "{\em Function f1:}")
    (bcStrings (43 "u*sin(v)" function1 EM))
    (text . "\newline\tab{2}")
    (text . "{\em Function f2:}")
    (bcStrings (43 "v*cos(u)" function2 EM))
    (text . "\newline\tab{2}")
    (text . "{\em Function f3:}")
    (bcStrings (43 "u*cos(v)" function3 EM))
    (text . "\newline\menuitemstyle{}\tab{2}Enter independent {\em variables} and ranges:")
    (text . "\newline\tab{2}")
    (text . "{\em Variable 1:}")
    (bcStrings (5 u ind1 SY))
    (text . "ranges {\em from:}")
    (bcStrings (9 "-\%pi" from1 F))
    (text . "{\em to:}")
    (bcStrings (9 "\%pi" to1 F))
    (text . "\newline\tab{2}")
    (text . "{\em Variable 2:}")
    (bcStrings (5 v ind2 SY))
    (text . "ranges {\em from:}")
    (bcStrings (9 "-\%pi/2" from2 F))
    (text . "{\em to:}")
    (bcStrings (9 "\%pi/2" to2 F))
    (text
      "\indent{0}\newline\menuitemstyle{}\tab{2} "
      "Optionally enter a {\em title} for your surface:")
    (bcStrings (15 "surface" title S))
    (text . "\indent{0}"))
  htMakeDoneButton ('"Continue",'bcDraw3Dpar1Gen)
  htShowPage()

bcDraw3Dpar1Gen htPage ==
  fun1 := htpLabelInputString(htPage,'function1)
  fun2 := htpLabelInputString(htPage,'function2)
  fun3 := htpLabelInputString(htPage,'function3)
  ind1 := htpLabelInputString(htPage,'ind1)
  from1 := htpLabelInputString(htPage,'from1)
  to1 := htpLabelInputString(htPage,'to1)
  ind2 := htpLabelInputString(htPage,'ind2)
  from2 := htpLabelInputString(htPage,'from2)
  to2 := htpLabelInputString(htPage,'to2)
  title := htpLabelInputString(htPage,'title)
  r1 := bcDrawIt2(ind1,from1,to1)
  r2 := bcDrawIt2(ind2,from2,to2)
  surfacePart := strconc('"surface(",'"{}",fun1,'",{}",fun2,'",{}",fun3,'")")
  if (title ~= '"") then
    titlePart := (title = '"" => nil; strconc('"{}",'"title ==_"",title,'"_""))
    bcFinish('"draw",surfacePart,r1,r2,titlePart)
  else
    bcFinish('"draw",surfacePart,r1,r2)

bcSeries() ==
  htInitPage('"Series Basic Command",nil)
  htMakePage '(
    (domainConditions
       (isDomain EM $EmptyMode)
       (isDomain S (String))
       (isDomain SY (Symbol)))
   (text .  "Create a series by: ")
   (text . "\beginmenu")
   (text . "\item ")
   (bcLinks ("\menuitemstyle{Expansion}" "" bcSeriesExpansion NIL))
   (text . "\tab{11}Expand a function in a series around a point")
   (text . "\item ")
   (bcLinks ("\menuitemstyle{Formula}"  "" bcSeriesByFormula NIL))
   (text . "\tab{11}Give a formula for the {\em i}'th coefficient")
   (text . "\endmenu"))
  htShowPage()

bcSeriesExpansion(a,b) ==
  htInitPage('"Series Expansion Basic Command",nil)
  htMakePage '(
    (domainConditions
       (isDomain EM $EmptyMode)
       (isDomain EEM (Expression $EmptyMode))
       (isDomain S (String))
       (isDomain SY (Symbol)))
    (text . "\newline ")
    (text . "\menuitemstyle{}\tab{2}")
    (text . "Enter the {\em function} you want to expand in a power series")
    (text . "\newline\tab{2} ")
    (bcStrings (55 "log(cot(x))" function EM))
    (text . "\blankline ")
    (text . "\newline ")
    (text . "\menuitemstyle{}\tab{2}")
    (text . "Enter the {\em power series variable}")
    (text . "\tab{49}")
    (bcStrings (8 x variable SY))
    (text . "\blankline ")
    (text . "\newline ")
    (text . "\menuitemstyle{}\tab{2}")
    (text . "Enter the {\em point} about which you want to expand")
    (text . "\tab{49}")
    (bcStrings (8 "\%pi/2" point EM)))
  htMakeDoneButton('"Continue",'bcSeriesExpansionGen)
  htShowPage()

bcSeriesExpansionGen htPage ==
  fun := htpLabelInputString(htPage,'function)
  var := htpLabelInputString(htPage,'variable)
  point := htpLabelInputString(htPage,'point)
  terms := htpLabelInputString(htPage,'numberOfTerms)
  bcFinish("series",fun,strconc(var,'" = ",point))

bcSeriesByFormula(a,b) ==
  htInitPage('"Power Series Basic Command",nil)
  htMakePage '(
    (text . "Select the kind of power series you want to create:")
    (text . "\beginmenu")
    (text . "\item ")
    (bcLinks ("\menuitemstyle{Taylor Series}" "" bcTaylorSeries taylor))
    (text . "\newline Series where the exponent ranges over the integers from a {\em non-negative integer} value to plus infinity by an arbitrary {\em positive integer} step size")
    (text . "\item ")
    (bcLinks ("\menuitemstyle{Laurent Series}" "" bcLaurentSeries laurent))
    (text . "\newline Series where the exponent ranges from an arbitrary {\em integer} value to plus infinity by an arbitrary {\em positive integer} step size")
    (text . "\item ")
    (bcLinks ("\menuitemstyle{Puiseux Series}" "" bcPuiseuxSeries puiseux))
    (text . "\newline Series where the exponent ranges from an arbitrary {\em rational value} to plus infinity by an arbitrary {\em positive rational number} step size")
    (text . "\endmenu"))
  htShowPage()

bcTaylorSeries(a,b) ==
  htInitPage('"Taylor Series Basic Command",nil)
  htMakePage '(
    (domainConditions
       (isDomain EM $EmptyMode)
       (isDomain EEM (Expression $EmptyMode))
       (isDomain S (String))
       (isDomain SY (Symbol)))
    (text . "\menuitemstyle{}\tab{2}")
    (text . "Enter the formula for the general coefficient of the series")
    (text . "\newline\tab{2} ")
    (bcStrings (55 "1/factorial(i)" formula EM))
    (text . "\blankline ")
    (text . "\menuitemstyle{}\tab{2}")
    (text . "Enter the {\em index variable} for your formula")
    (text . "\tab{49}")
    (bcStrings (8 i index SY))
    (text . "\newline ")
    (text . "\menuitemstyle{}\tab{2}")
    (text . "Enter the {\em power series variable}")
    (text . "\tab{49}")
    (bcStrings (8 x variable SY))
    (text . "\newline ")
    (text . "\menuitemstyle{}\tab{2}")
    (text . "Enter the {\em point} about which you want to expand")
    (text . "\tab{49}")
    (bcStrings (8 0 point EM))
    (text . "\blankline ")
    (text ."For Taylor Series, the exponent of the power series variable ranges  from an {\em initial value}, an arbitrary non-negative integer, to plus infinity; the {\em step size} is any positive integer.")
    (text . "\blankline ")
    (text . "\newline ")
    (text . "\menuitemstyle{}\tab{2}")
    (text . "Enter the {\em initial value} of the index (an integer)")
    (text . "\tab{49}")
    (bcStrings (8 "0" min I))
    (text . "\newline ")
    (text . "\menuitemstyle{}\tab{2}")
    (text . "Enter the {\em step size} (a positive integer)")
    (text . "\tab{49}")
    (bcStrings (8 "1" step PI))
    (doneButton "Continue" bcTaylorSeriesGen))
  htShowPage()

bcSeriesByFormulaGen htPage == 
  bcNotReady htPage

bcLaurentSeries(a,b) ==
  htInitPage('"Laurent Series Basic Command",nil)
  htMakePage '(
    (domainConditions
       (isDomain EM $EmptyMode)
       (isDomain EEM (Expression $EmptyMode))
       (isDomain S (String))
       (isDomain I (Integer))
       (isDomain PI (PositiveInteger))
       (isDomain SY (Symbol)))
    (text . "\newline ")
    (text . "\menuitemstyle{}\tab{2}")
    (text . "Enter the formula for the general coefficient of the series")
    (text . "\newline\tab{2} ")
    (bcStrings (55 "(-1)**(n - 1)/(n + 2)" formula EM))
    (text . "\vspace{1}\newline ")
    (text . "\menuitemstyle{}\tab{2}")
    (text . "Enter the {\em index variable} for your formula")
    (text . "\tab{49}")
    (bcStrings (8 n index SY))
    (text . "\newline ")
    (text . "\menuitemstyle{}\tab{2}")
    (text . "Enter the {\em power series variable}")
    (text . "\tab{49}")
    (bcStrings (8 x variable SY))
    (text . "\newline ")
    (text . "\menuitemstyle{}\tab{2}")
    (text . "Enter the {\em point} about which you want to expand")
    (text . "\tab{49}")
    (bcStrings (8 0 point F))
    (text . "\blankline")
    (text . "\newline For Laurent Series, the exponent of the power series variable ranges from an {\em initial value}, an arbitrary integer value, to plus infinity; the {\em step size} is any positive integer.")
    (text . "\blankline")
    (text . "\menuitemstyle{}\tab{2}")
    (text . "Enter the {\em initial value} of the index (an integer)")
    (text . "\tab{49}")
    (bcStrings (8 "-1" min I))
    (text . "\newline ")
    (text . "\menuitemstyle{}\tab{2}")
    (text . "Enter the {\em step size} (a positive integer)")
    (text . "\tab{49}")
    (bcStrings (8 "1" step PI))
    (doneButton "Continue" bcLaurentSeriesGen))
  htShowPage()

bcPuiseuxSeries(a,b) ==
  htInitPage('"Puiseux Series Basic Command",nil)
  htMakePage '(
    (domainConditions
       (isDomain EM $EmptyMode)
       (isDomain EEM (Expression $EmptyMode))
       (isDomain S (String))
       (isDomain I (Integer))
       (isDomain PI (PositiveInteger))
       (isDOmain RN (Fraction (Integer)))
       (isDomain SY (Symbol)))
    (text . "\newline ")
    (text . "\menuitemstyle{}\tab{2}")
    (text ."Enter the {\em formula} for the general coefficient of the series")
    (text . "\newline\tab{2} ")
    (bcStrings(55 "(-1)**((3*n - 4)/6)/factorial(n - 1/3)" formula EM))
    (text . "\vspace{1}\newline ")
    (text . "\menuitemstyle{}\tab{2}")
    (text . "Enter the {\em index variable} for your formula")
    (text . "\tab{49}")
    (bcStrings (8 n index SY))
    (text . "\newline ")
    (text . "\menuitemstyle{}\tab{2}")
    (text . "Enter the {\em power series variable}")
    (text . "\tab{49}")
    (bcStrings (8 x variable SY))
    (text . "\newline ")
    (text . "\menuitemstyle{}\tab{2}")
    (text . "Enter the {\em point} about which you want to expand")
    (text . "\tab{49}")
    (bcStrings (8 0 point F))
    (text . "\blankline ")
    (text . "For Puiseux Series, the exponent of the power series variable ranges from an {\em initial value}, an arbitary rational number, to plus infinity; the {\em step size} is an any positive rational number.")
    (text . "\blankline ")
    (text . "\newline ")
    (text . "\menuitemstyle{}\tab{2}")
    (text . "Enter the {\em initial value} of index (a rational number)")
    (text . "\tab{51}")
    (bcStrings (6 "4/3" min RN))
    (text . "\newline ")
    (text . "\menuitemstyle{}\tab{2}")
    (text . "Enter the {\em step size} (a positive rational number)")
    (text . "\tab{51}")
    (bcStrings (6 "2" step RN))
    (doneButton "Continue" bcPuiseuxSeriesGen))
  htShowPage()

bcTaylorSeriesGen htPage == bcSeriesGen(htPage)

bcLaurentSeriesGen htPage ==
  bcSeriesGen(htPage)

bcPuiseuxSeriesGen htPage ==
  bcSeriesGen(htPage)

bcSeriesGen(htPage) ==
  step:= htpLabelInputString(htPage,'step)
  min := htpLabelInputString(htPage,'min)
  formula := htpLabelInputString(htPage,'formula)
  index   := htpLabelInputString(htPage,'index)
  var := htpLabelInputString(htPage,'variable)
  point := htpLabelInputString(htPage,'point)
  varPart := strconc(var,'" = ",point)
  minPart := strconc(min,'"..")
  bcFinish('"series",strconc(index,'" +-> ",formula),varPart,minPart,step)

bcLimit() ==
  htInitPage('"Limit Basic Command",nil)
  htMakePage '(
   (domainConditions
       (isDomain EM $EmptyMode)
       (isDomain S (String))
       (isDomain SY (Symbol)))
   (text . "What kind of limit do you want to compute? ")
   (text . "\blankline ")
   (text . "\beginmenu")
   (text . "\item ")
   (bcLinks ("\menuitemstyle{A real limit?}" "" bcRealLimit real))
   (text . "\indentrel{17}\tab{0}")
   (text . "The limit as the variable approaches a {\em real} value along the real axis")
   (text . "\indentrel{-17}")
   (text . "\item ")
   (text . "\blankline ")
   (bcLinks ("\menuitemstyle{A complex limit?}" "" bcComplexLimit complex))
   (text . "\indentrel{17}\tab{0}")
   (text . "The limit as the variable approaches a {\em complex} value along any path in the complex plane")
   (text . "\indentrel{-17}")
   (text . "\endmenu")
    )
  htShowPage()

bcRealLimit(a,b) ==
  htInitPage('"Real Limit Basic Command",nil)
  htMakePage '(
    (domainConditions
       (isDomain EM $EmptyMode)
       (isDomain S (String))
       (isDomain F (Float))
       (isDomain SY (Symbol)))
    (text . "\newline ")
    (text . "\menuitemstyle{}\tab{2}")
    (text . "Enter the {\em function} you want to compute the limit of:")
    (text . "\newline\tab{2} ")
    (bcStrings (45 "x*sin(1/x)" expression EM))
    (text . "\blankline")
    (text . "\newline ")
    (text . "\menuitemstyle{}\tab{2}")
    (text . "Enter the name of the {\em variable}: ")
    (text . "\tab{41}")
    (bcStrings (6 x variable SY))
    (text . "\blankline")
    (text . "\newline ")
    (text . "\menuitemstyle{}\tab{2}")
    (text . "Compute the limit at")
    (radioButtons location
      ("A finite point:" (
        (text . "\tab{33}")
        (bcStrings (6 0 point F))) finitePoint)
      ("Plus infinity" "" plusInfinity)
      ("Minus infinity" "" minusInfinity))
    (doneButton "Continue" bcRealLimitGen))
  htShowPage()

bcRealLimitGen htPage ==
  (p := htpButtonValue(htPage,'location)) ~= 'finitePoint =>
    fun := htpLabelInputString(htPage,'expression)
    var := htpLabelInputString(htPage,'variable)
    loc :=
      p = 'plusInfinity => '"%plusInfinity"
      '"%minusInfinity"
    bcFinish('"limit",fun,strconc(var,'" = ",loc))
  page := htInitPage('"Real Limit Basic Command",nil)
  htMakePage '(
    (text . "Compute the limit")
    (lispLinks
       ("\menuitemstyle{From both directions}" "" bcRealLimitGen1 both)
       ("\menuitemstyle{From the right}" "" bcRealLimitGen1 right)
       ("\menuitemstyle{From the left}" "" bcRealLimitGen1 left)))
  htpSetProperty(page,'fun,htpLabelInputString(htPage,'expression))
  htpSetProperty(page,'var,htpLabelInputString(htPage,'variable))
  htpSetProperty(page,'loc,htpLabelInputString(htPage,'point))
  htShowPage()

bcRealLimitGen1(htPage,key) ==
  direction :=
    key = 'right => '"_"right_""
    key = 'left => '"_"left_""
    nil
  fun := htpProperty(htPage,'fun)
  var := htpProperty(htPage,'var)
  loc := htpProperty(htPage,'loc)
  varPart := strconc(var,'" = ",loc)
  bcFinish('"limit",fun,varPart,direction)

bcComplexLimit(a,b) ==
  htInitPage('"Complex Limit Basic Command",nil)
  htMakePage '(
    (domainConditions
        (isDomain EM $EmptyMode)
       (isDomain S (String))
       (isDomain F (Float))
       (isDomain SY (Symbol)))
    (text . "\newline ")
    (text . "\menuitemstyle{}\tab{2}")
    (text . "Enter the {\em function} you want to compute the limit of:")
    (text . "\newline\tab{2} ")
    (bcStrings (40 "sin(a*x)/tan(b*x)" expression EM))
    (text . "\blankline ")
    (text . "\newline ")
    (text . "\menuitemstyle{}\tab{2}")
    (text . "Enter the name of the {\em variable}: ")
    (text . "\tab{37}")
    (bcStrings (5 x variable SY))
    (text . "\blankline ")
    (text . "\newline ")
    (text . "\menuitemstyle{}\tab{2}")
    (text . "Compute the limit at")
    (radioButtons location
      ("A finite point:" (
       (text . "\newline\space{0}Real part:\space{3}")
       (bcStrings (20 0 real F))
       (text . "\newline Complex part:")
       (bcStrings (20 0 complex F))) finitePoint)
      ("Complex infinity" "" complexInfinity))
     (doneButton "Continue" bcComplexLimitGen))
  htShowPage()

bcComplexLimitGen htPage ==
  fun := htpLabelInputString(htPage,'expression)
  var := htpLabelInputString(htPage,'variable)
  loc :=
    (p := htpButtonValue(htPage,'location)) = 'finitePoint =>
      real := htpLabelInputString(htPage,'real)
      comp := htpLabelInputString(htPage,'complex)
      complexPart :=
        comp = '"0" => '""
        comp = '"1" => '"%i"
        strconc(comp,'"*%i")
      real = '"0" =>
        complexPart = '"" => '"0"
        complexPart
      complexPart = '"" => real
      strconc(real,'" + ",complexPart)
    '"%infinity"
  varPart := strconc(var,'" = ",loc)
  bcFinish('"complexLimit",fun,varPart)