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authordos-reis <gdr@axiomatics.org>2007-09-20 03:58:10 +0000
committerdos-reis <gdr@axiomatics.org>2007-09-20 03:58:10 +0000
commit32d516cbb18276e5060749f85368c5a90346a0f4 (patch)
treeef3d9881bbdb62a623abc7af74384fd2aaa103f4 /src/interp/bc-misc.boot.pamphlet
parent9b71e0a1f285fc207709cf8e90721160af299127 (diff)
downloadopen-axiom-32d516cbb18276e5060749f85368c5a90346a0f4.tar.gz
remove pamphlets - part 4
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-rw-r--r--src/interp/bc-misc.boot.pamphlet946
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diff --git a/src/interp/bc-misc.boot.pamphlet b/src/interp/bc-misc.boot.pamphlet
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--- a/src/interp/bc-misc.boot.pamphlet
+++ /dev/null
@@ -1,946 +0,0 @@
-\documentclass{article}
-\usepackage{axiom}
-\begin{document}
-\title{\$SPAD/src/interp bc-misc.boot}
-\author{The Axiom Team}
-\maketitle
-\begin{abstract}
-\end{abstract}
-\eject
-\tableofcontents
-\eject
-\section{License}
-<<license>>=
--- Copyright (c) 1991-2002, The Numerical ALgorithms Group Ltd.
--- All rights reserved.
---
--- Redistribution and use in source and binary forms, with or without
--- modification, are permitted provided that the following conditions are
--- met:
---
--- - Redistributions of source code must retain the above copyright
--- notice, this list of conditions and the following disclaimer.
---
--- - Redistributions in binary form must reproduce the above copyright
--- notice, this list of conditions and the following disclaimer in
--- the documentation and/or other materials provided with the
--- distribution.
---
--- - Neither the name of The Numerical ALgorithms Group Ltd. nor the
--- names of its contributors may be used to endorse or promote products
--- derived from this software without specific prior written permission.
---
--- THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS
--- IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED
--- TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A
--- PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER
--- OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
--- EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
--- PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
--- PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
--- LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
--- NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
--- SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
-
-@
-<<*>>=
-<<license>>
-
---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)
-
-
-@
-\eject
-\begin{thebibliography}{99}
-\bibitem{1} nothing
-\end{thebibliography}
-\end{document}