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+-- Copyright (c) 1991-2002, The Numerical ALgorithms Group Ltd.
+-- All rights reserved.
+-- Copyright (C) 2007, 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"
+)package "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) = 'fromPoint =>
+ htpLabelInputString(htPage,'from)
+ '"%minusInfinity"
+ upperLimit :=
+ htpButtonValue(htPage,'toButton) = '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 ^= '"") 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 ^= '"") then
+ titlePart := (title = '"" => 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 ^= '"") then
+ titlePart := (title = '"" => 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 NILl))
+ (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()
+
+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)
+
+