open-axiom repository from github
-- 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)