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authordos-reis <gdr@axiomatics.org>2007-08-14 05:14:52 +0000
committerdos-reis <gdr@axiomatics.org>2007-08-14 05:14:52 +0000
commitab8cc85adde879fb963c94d15675783f2cf4b183 (patch)
treec202482327f474583b750b2c45dedfc4e4312b1d /src/interp/bc-solve.boot.pamphlet
downloadopen-axiom-ab8cc85adde879fb963c94d15675783f2cf4b183.tar.gz
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+\documentclass{article}
+\usepackage{axiom}
+\begin{document}
+\title{\$SPAD/src/interp bc-solve.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 basic Solve Command
+$systemType := nil
+$numberOfEquations := 0
+$solutionMethod := nil
+
+bcSolve() ==
+ htInitPage('"Solve Basic Command", nil)
+ htMakePage '(
+ (text . "What do you want to solve? ")
+ (text . "\beginmenu")
+ (text . "\item ")
+ (bcLinks ("\menuitemstyle{A System Of Linear Equations}" "" bcLinearSolve linear))
+ (text . "\item ")
+ (bcLinks ("\menuitemstyle{A System of Polynomial Equations}" "" bcSystemSolve polynomial))
+ (text . "\item ")
+ (bcLinks ("\menuitemstyle{A Single Polynomial Equation}" "" bcSolveSingle onePolynomial))
+ (text . "\endmenu"))
+ htShowPage()
+
+bcLinearSolve(p,nn) ==
+ htInitPage('"Basic Solve Command", nil)
+ htMakePage '(
+ (text . "How do you want to enter the equations?")
+ (text . "\beginmenu")
+ (text . "\item ")
+ (text . "\newline ")
+ (bcLinks ("\menuitemstyle{Directly as equations}" "" bcLinearSolveEqns equations))
+ (text . "\item ")
+ (text . "\newline ")
+ (bcLinks ("\menuitemstyle{In matrix form}" "" bcLinearSolveMatrix matrix))
+ (text . "\indentrel{16}\tab{0}")
+ (text . " \spad{AX = B}, where \spad{A} is a matrix of coefficients and \spad{B} is a vector" )
+ (text . "\indentrel{-16}\item ")
+ (text . "\endmenu"))
+ htShowPage()
+
+bcLinearSolveEqns(htPage, p) ==
+ htInitPage('"Basic Solve Command", nil)
+ htMakePage '(
+ (domainConditions (isDomain PI (PositiveInteger)))
+ (inputStrings
+ ("Enter the {\em number} of equations:" "" 5 2 numberOfEquations PI)))
+ htMakeDoneButton('"Continue", 'bcLinearSolveEqns1)
+ htShowPage()
+
+bcSystemSolve(htPage, p) ==
+ htInitPage('"Basic Solve Command", nil)
+ htMakePage '(
+ (domainConditions (isDomain PI (PositiveInteger)))
+ (inputStrings
+ ("Enter the {\em number} of equations:" "" 5 2 numberOfEquations PI)))
+ htMakeDoneButton('"Continue", 'bcSystemSolveEqns1)
+ htShowPage()
+
+bcSolveSingle(htPage,p) ==
+ htpSetProperty(htPage,'systemType, 'onePolynomial)
+ htpSetProperty(htPage,'exitFunction,'bcInputSolveInfo)
+ bcInputEquations(htPage,'exact)
+
+bcSystemSolveEqns1 htPage ==
+ htpSetProperty(htPage,'systemType,'polynomial)
+ htpSetProperty(htPage,'exitFunction,'bcInputSolveInfo)
+ bcInputEquations(htPage,'exact)
+
+bcLinearSolveEqns1 htPage ==
+ htpSetProperty(htPage,'systemType,'linear)
+ htpSetProperty(htPage,'exitFunction,'bcLinearSolveEqnsGen)
+ bcInputEquations(htPage,'exact)
+
+bcInputSolveInfo htPage ==
+ page := htInitPage('"Solve Basic Command", htpPropertyList htPage)
+ htpSetProperty(page,'numberOfEquations,htpProperty(htPage,'numberOfEquations))
+ htpSetProperty(page,'inputArea,htpInputAreaAlist htPage)
+ htMakePage '(
+ (domainConditions (isDomain PI (PositiveInteger)))
+ (text . "What would you like?")
+ (text . "\beginmenu")
+ (text . "\item ")
+ (bcLinks ("\menuitemstyle{Exact Solutions}" "" bcSolveEquations exact))
+ (text . "\indentrel{18}\tab{0} ")
+ (text . "Solutions expressed in terms of {\em roots} of irreducible polynomials")
+ (text . "\indentrel{-18}")
+ (text . "\item ")
+ (bcLinks ("\menuitemstyle{Numeric Solutions}" "" bcSolveEquationsNumerically numeric))
+ (text . "\indentrel{18}\tab{0} ")
+ (text . "Solutions expressed in terms of approximate real or complex {\em numbers}")
+ (text . "\indentrel{-18}")
+ (text . "\item ")
+ (bcLinks ("\menuitemstyle{Radical Solutions}" "" bcSolveEquations radical))
+ (text . "\indentrel{18}\tab{0} ")
+ (text . "Solutions expressed in terms of {\em radicals} if it is possible")
+ (text . "\indentrel{-18}")
+ (text . "\endmenu"))
+ htShowPage()
+
+bcInputEquations(htPage,solutionMethod) ==
+ numEqs :=
+ htpProperty(htPage, 'systemType) = 'onePolynomial => 1
+ $bcParseOnly => PARSE_-INTEGER htpLabelInputString(htPage,'numberOfEquations)
+ objValUnwrap htpLabelSpadValue(htPage, 'numberOfEquations)
+ linearPred := htpProperty(htPage,'systemType) = 'linear
+ labelList :=
+ numEqs = 1 => '(
+ (bcStrings (42 "x^2+1" l1 P))
+ (text . " = ")
+ (bcStrings (6 0 r1 P)))
+ "append"/[f(i,numEqs,linearPred) for i in 1..numEqs] where f(i,n,linearp) ==
+ spacer := (i > 99 => 0; i > 9 => 1; 2)
+ prefix := STRCONC('"\newline\tab{2}{\em Equation ",STRINGIMAGE i,'":}")
+ prefix := STRCONC(prefix,'"\space{",STRINGIMAGE spacer,'"}")
+ lnam := INTERN STRCONC('"l",STRINGIMAGE i)
+ rnam := INTERN STRCONC('"r",STRINGIMAGE i)
+ var:=
+ linearp => bcMakeLinearEquations(i,n)
+ bcMakeEquations(i,n)
+ [['text,:prefix],['bcStrings,[30,var,lnam,'P]],'(text . " = "),['bcStrings,[5,"0",rnam,'P]]]
+ equationPart := [
+ '(domainConditions
+ (isDomain P (Polynomial $EmptyMode))
+ (isDomain S (String))
+ (isDomain PI (PositiveInteger))),
+ :labelList]
+ page := htInitPage('"Solve Basic Command", htpPropertyList htPage)
+ htpSetProperty(page, 'numberOfEquations, numEqs)
+ htpSetProperty(page, 'solutionMethod,solutionMethod)
+ htSay '"\newline\menuitemstyle{}\tab{2}"
+ htSay
+ numEqs = 1 => '"Enter the {\em Equation}:"
+ '"Enter the {\em Equations}:"
+ htSay '"\newline\tab{2}"
+ htMakePage equationPart
+ bcHt '"\blankline "
+ htSay '"\newline\menuitemstyle{}\tab{2}"
+ htMakePage
+ numEqs = 1 => '(
+ (text ."Enter the {\em unknown} (leave blank if implied): ")
+ (text . "\tab{48}")
+ (bcStrings (6 "x" unknowns S . quoteString)))
+ ['(text . "Enter the unknowns (leave blank if implied):"),
+ '(text . "\tab{44}"),
+ ['bcStrings, [10,bcMakeUnknowns(numEqs),'unknowns,'P]]]
+ htMakeDoneButton('"Continue", 'bcInputEquationsEnd)
+ htShowPage()
+
+bcCreateVariableString(i) ==
+ STRCONC('"x",STRINGIMAGE i)
+
+bcMakeUnknowns(number)==
+ APPLY('CONCAT,[STRCONC(bcCreateVariableString(i)," ") for i in 1..number])
+
+bcMakeEquations(i,number)==
+ number =1 => STRCONC(bcCreateVariableString(1),"^2+1")
+ bcCreateVariableString(i)
+ STRCONC(
+ STRCONC(
+ APPLY('CONCAT,[STRCONC(bcCreateVariableString(j),"+") for j in 1..number]),"1"),
+ STRCONC("-2*",STRCONC(bcCreateVariableString(i),"^2")))
+
+
+bcMakeLinearEquations(i,number)==
+ number = 1 => bcCreateVariableString(1)
+ number = 2 =>
+ i=1 => STRCONC(bcCreateVariableString(1),STRCONC("+",bcCreateVariableString(2)))
+ STRCONC(bcCreateVariableString(1),STRCONC("-",bcCreateVariableString(2)))
+ STRCONC(
+ STRCONC(
+ APPLY('CONCAT,[STRCONC(bcCreateVariableString(j),"+") for j in 1..number]),"1"),
+ STRCONC("-2*",bcCreateVariableString(i)))
+
+
+bcInputEquationsEnd htPage ==
+ fun := htpProperty(htPage, 'exitFunction) => FUNCALL(fun,htPage)
+ systemError nil
+
+bcSolveEquationsNumerically(htPage,p) ==
+ page := htInitPage('"Solve Basic Command", htpPropertyList htPage)
+ htMakePage '(
+ (text . "What would you like?")
+ (radioButtons choice
+ ("Real roots expressed as rational numbers" "" rr)
+ ("Real roots expressed as floats" "" rf)
+ ("Complex roots expressed as rational numbers" "" cr)
+ ("Complex roots expressed as floats" "" cf))
+ (text . "\vspace{1}\newline")
+ (inputStrings
+ ("Enter the number of desired {\em digits} of accuracy" "" 5 20 acc PI)))
+ htMakeDoneButton('"Continue", 'bcSolveNumerically1)
+ htShowPage()
+
+bcSolveNumerically1(htPage) ==
+ bcSolveEquations(htPage,'numeric)
+
+--bcSolveNumerically1(htPage,kind) ==
+-- htpSetProperty(htPage,'kind,kind)
+-- bcSolveEquations(htPage,'numeric)
+
+bcSolveEquations(htPage,solutionMethod) ==
+ if solutionMethod = 'numeric then
+ digits := htpLabelInputString(htPage,'acc)
+ kind := htpButtonValue(htPage,'choice)
+ accString :=
+ kind in '(rf cf) => STRCONC('"1.e-",digits)
+ STRCONC('"1/10**",digits)
+ alist := htpProperty(htPage,'inputArea)
+ [[.,varpart,:.],:r] := alist
+ varlist := bcString2WordList varpart
+ varString := (rest varlist => bcwords2liststring varlist; first varlist)
+ eqnString := bcGenEquations r
+ solutionMethod = 'numeric =>
+ name :=
+ kind in '(rf rr) => '"solve"
+ '"complexSolve"
+ bcFinish(name,eqnString,accString)
+ name :=
+ solutionMethod = 'radical => '"radicalSolve"
+ '"solve"
+ bcFinish(name,eqnString,varString,accString)
+
+bcLinearSolveMatrix(htPage,junk) ==
+ bcReadMatrix 'bcLinearSolveMatrix1
+
+bcLinearSolveMatrix1 htPage ==
+ page := htInitPage('"Linear Solve Basic Command",htpPropertyList htPage)
+ htpSetProperty(page,'matrix,bcLinearExtractMatrix htPage)
+ htMakePage '(
+ (text . "The right side vector B is:")
+ (lispLinks
+ ("Zero:" "the system is homogeneous" bcLinearSolveMatrixHomo homo)
+ ("Not zero:" "the system is not homogeneous" bcLinearSolveMatrixInhomo nothomo)))
+ htShowPage()
+
+bcLinearExtractMatrix htPage == REVERSE htpInputAreaAlist htPage
+
+bcLinearSolveMatrixInhomo(htPage,junk) ==
+ nrows := htpProperty(htPage,'nrows)
+ ncols := htpProperty(htPage,'ncols)
+ labelList :=
+ [f(i) for i in 1..ncols] where f(i) ==
+ spacer := (i > 99 => 0; i > 9 => 1; 2)
+ prefix := STRCONC('"{\em Coefficient ",STRINGIMAGE i,'":}")
+ if spacer ^= 0 then
+ prefix := STRCONC(prefix,'"\space{",STRINGIMAGE spacer,'"}")
+ name := INTERN STRCONC('"c",STRINGIMAGE i)
+ [prefix,"",30, 0,name, 'P]
+ page := htInitPage('"Linear Solve Basic Command",htpPropertyList htPage)
+ htpSetProperty(page,'matrix,htpProperty(htPage,'matrix))
+ htpSetProperty(page,'nrows,nrows)
+ htpSetProperty(page,'ncols,ncols)
+ htMakePage [
+ '(domainConditions (isDomain P (Polynomial $EmptyMode))),
+ '(text . "Enter the right side vector B:"),
+ ['inputStrings, :labelList],
+ '(text . "\vspace{1}\newline Do you want:" ),
+ '(lispLinks
+ ("All the solutions?" "" bcLinearSolveMatrixInhomoGen all)
+ ("A particular solution?" "" bcLinearSolveMatrixInhomoGen particular))]
+ htShowPage()
+
+bcLinearSolveMatrixInhomoGen(htPage,key) == bcLinearMatrixGen(htPage,key)
+
+bcLinearSolveMatrixHomo(htPage,key) == bcLinearMatrixGen(htPage,'homo)
+
+bcLinearMatrixGen(htPage,key) ==
+ matform := bcMatrixGen htPage
+ key = 'homo => bcFinish('"nullSpace",matform)
+ vector := [x.1 for x in REVERSE htpInputAreaAlist htPage]
+ vecform := bcVectorGen vector
+ form := bcMkFunction('"solve",matform,[vecform])
+ bcGen
+ key = 'particular => STRCONC(form,'".particular")
+ form
+
+linearFinalRequest(nhh,mat,vect) ==
+ sayBrightly '"Do you want more information on the meaning of the output"
+ sayBrightly '" (1) no "
+ sayBrightly '" (2) yes "
+ tt := bcQueryInteger(1,2,true)
+ tt=1 => sayBrightly '"Bye Bye"
+ tt=2 => explainLinear(nhh)
+
+explainLinear(flag) ==
+ flag="notHomogeneous" =>
+ '("solve returns a particular solution and a basis for"
+ "the vector space of solutions for the homogeneous part."
+ "The particular solution is _"failed_" if one cannot be found.")
+ flag= "homogeneous" =>
+ '("solve returns a basis for"
+ "the vector space of solutions for the homogeneous part")
+ systemError nil
+
+finalExactRequest(equations,unknowns) ==
+ sayBrightly '"Do you like:"
+ sayBrightly '" (1) the solutions how they are displayed"
+ sayBrightly '" (2) to get ????"
+ sayBrightly '" (3) more information on the meaning of the output"
+ tt := bcQueryInteger(1,3,true)
+ tt=1 => sayBrightly '"Bye Bye"
+ tt=2 => moreExactSolution(equations,unknowns,flag)
+ tt=3 => explainExact(equations,unknowns)
+
+bcLinearSolveEqnsGen htPage ==
+ alist := htpInputAreaAlist htPage
+ if vars := htpLabelInputString(htPage,'unknowns) then
+ varlist := bcString2WordList vars
+ varString := (rest varlist => bcwords2liststring varlist; first varlist)
+ alist := rest alist --know these are first on the list
+ eqnString := bcGenEquations alist
+ bcFinish('"solve",eqnString,varString)
+
+bcGenEquations alist ==
+ y := alist
+ while y repeat
+ right := (first y).1
+ y := rest y
+ left := (first y).1
+ y := rest y
+ eqnlist := [STRCONC(left,'" = ",right),:eqnlist]
+ rest eqnlist => bcwords2liststring eqnlist
+ first eqnlist
+
+
+
+
+
+
+
+
+
+
+
+@
+\eject
+\begin{thebibliography}{99}
+\bibitem{1} nothing
+\end{thebibliography}
+\end{document}