-- Copyright (c) 1991-2002, The Numerical ALgorithms Group Ltd. -- All rights reserved. -- Copyright (C) 2007-2011, 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_-matrix import bc_-misc namespace BOOT -- 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 => readInteger 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 ",toString i,'":}") prefix := strconc(prefix,'"\space{",toString spacer,'"}") lnam := makeSymbol strconc('"l",toString i) rnam := makeSymbol strconc('"r",toString 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",toString i) bcMakeUnknowns(number)== apply(function strconc,[strconc(bcCreateVariableString(i),'" ") for i in 1..number]) bcMakeEquations(i,number)== number =1 => strconc(bcCreateVariableString(1),'"^2+1") bcCreateVariableString(i) strconc( strconc( apply(function strconc,[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(function strconc,[strconc(bcCreateVariableString(j),'"+") for j in 1..number]),'"1"), strconc('"-2*",bcCreateVariableString(i))) bcInputEquationsEnd htPage == fun := htpProperty(htPage, 'exitFunction) => apply(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 ",toString i,'":}") if spacer ~= 0 then prefix := strconc(prefix,'"\space{",toString spacer,'"}") name := makeSymbol strconc('"c",toString 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