var variables = new Array("a","b","c","d","e","f","g","h","i","j","k","l","m","n","o","p","q","r","s","t","u","v","w","x","y","z"); var currentVariables = new Array (); var vars = ""; var equations; var coefficients = new Array (); var coef; var constants = new Array (); var inverse = new Array (); var regdec = /[0-9.]/; var browser = navigator.userAgent; if (/opera/.test(browser)) { var broken = true; } if (/MSIE/.test(browser)) { var broken = true; } function solve() { // Clear any global variables from the previous equations. currentVariables = new Array (); vars = ""; equations = new Array(); coefficients = new Array (); coef = new Array (); constants = new Array (); inverse = new Array (); // Get the equations from the user input, and initialize the display of the equations. var textarea = $('equations'); var hidden = $('hidden'); hidden.style.display = "block"; var solution = $('solution'); solution.innerHTML = ""; // Split the block the user has entered into separate equations. equations = textarea.value.split(/\n/); // Spit the equations back at the user as confirmation they have been entered correctly. displaySolution("Confirm the equations have been entered correctly.
"); for (var i = 0; i < equations.length;i++) { equations[i] = equations[i].replace(/ /g,""); equations[i] = equations[i].replace(/\r/,""); if (equations[i]=="") { var temp = equations.pop(); continue; } equations[i] = equations[i].toLowerCase(); displaySolution(equations[i]); } // Confirm that the equations have at least a chance at being solvable. Check here to look for obvious syntax errors. for (i = 0; i < equations.length;i++) { incrementCurrentVariables(equations[i],i,equations); if (invalidSyntax(equations[i])) { displaySolution("
There is an error in your syntax"); return; } } if (vars.length > equations.length) { displaySolution("There are too many variables to determine the solutions exactly."); return; } if (vars.length < equations.length) { displaySolution("
There are more equations than variables. Please simplify your equations."); return; } // Start making the equations easier to parse. This will be expanded eventually to allow many different ways of entering the equations. var tempeq = new Array(); var same = true; for (i = 0; i < equations.length;i++) { tempeq[i] = equations[i]; equations[i] = removeImplicit(equations[i]); var sides = equations[i].split("="); sides[0] = removeImplicit(sides[0]); sides[1] = removeImplicit(sides[1]); equations[i] = sides[0] + "=" + sides[1]; if (tempeq[i]!=equations[i]) { same = false; } } if (!same) { displaySolution("
Remove any implicit multiplication.
"); for (i = 0; i < equations.length;i++) { displaySolution(equations[i]); } } same = true; for (i = 0; i < equations.length;i++) { tempeq[i] = equations[i]; var sides = equations[i].split("="); sides[0] = fixDivision(sides[0]); sides[1] = fixDivision(sides[1]); equations[i] = sides[0] + "=" + sides[1]; if (tempeq[i]!=equations[i]) { same = false; } } if (!same) { displaySolution("
Fix any division present in the equations.
"); for (i = 0; i < equations.length;i++) { displaySolution(equations[i]); } } same = true; for (i = 0; i < equations.length;i++) { tempeq[i] = equations[i]; var sides = equations[i].split("="); sides[0] = foil(sides[0]); sides[1] = foil(sides[1]); equations[i] = sides[0] + "=" + sides[1]; if (tempeq[i]!=equations[i]) { same = false; } } if (!same) { displaySolution("
Multiply out any double brackets in the equations using FOIL.
"); for (i = 0; i < equations.length; i++) { displaySolution(equations[i]); } } same = true; for (i = 0; i < equations.length; i++) { tempeq[i] = equations[i]; var sides = equations[i].split("="); sides[0] = removeParenthesis(sides[0]); sides[1] = removeParenthesis(sides[1]); equations[i] = sides[0] + "=" + sides[1]; if (tempeq[i]!=equations[i]) { same = false; } } if (!same) { displaySolution("
Remove any existing parenthesis.
"); for (i = 0; i < equations.length; i++) { displaySolution(equations[i]); } } same = true; for (i = 0; i < equations.length; i++) { tempeq[i] = equations[i]; var sides = equations[i].split("="); sides[0] = collectLikeTerms(sides[0]); sides[1] = collectLikeTerms(sides[1]); equations[i] = sides[0] + "=" + sides[1]; if (tempeq[i]!=equations[i]) { same = false; } } if (!same) { displaySolution("
Collect like terms.
"); for (i = 0; i < equations.length; i++) { displaySolution(equations[i]); } } for (i = 0; i < equations.length; i++) { tempeq[i] = equations[i]; var sides = equations[i].split("="); if ((/\^/.test(sides[0]))||(/\^/.test(sides[1]))) { tempeq[0] = sides[0]; tempeq[1] = sides[0]; var left = collectSquared(sides[0],sides[1]); var right = 0; var linear = false; sides[0] = left; sides[1] = right; if ((tempeq[0] != sides[0])||(tempeq[1] != sides[0])) { displaySolution("
Getting every term onto the left side of the equation...
"); displaySolution(sides[0]+"="+sides[1]); } if (sides[0].charAt(0)) { var a = parseFloat(/^[0-9.-]*/.exec(sides[0])); sides[0] = sides[0].replace(/^[0-9.-]*[a-z]\^2(?=[+-])/,""); sides[0] = sides[0].replace(/^\+/,""); var b = parseFloat(/^[0-9.-]*[a-z]/.exec(sides[0])); sides[0] = sides[0].replace(/^[0-9.-]*[a-z](?=[+-])/,""); sides[0] = sides[0].replace(/^\+/,""); var c = parseFloat(sides[0]); var discriminant = Math.pow(b,2)-4*a*c; if (discriminant >= 0 ) { displaySolution("
Find the solutions to the equation using the quadratic formula...
"); displaySolution(vars.charAt(0)+"1 = " + Math.round((-1*b+Math.sqrt(discriminant))/(2*a)*100000)/100000); displaySolution(vars.charAt(0)+"2 = " + Math.round((-1*b-Math.sqrt(discriminant))/(2*a)*100000)/100000 + "
"); } else { displaySolution("
Find the solutions to the equation using the quadratic formula...solutions are complex...
"); var complex = Math.round(Math.sqrt(-1*discriminant)/(2*a)*100000)/100000; var real = Math.round((-1*b)/(2*a)*100000)/100000; displaySolution(vars.charAt(0)+"1 = " + real + "-" + complex + "i
"); displaySolution(vars.charAt(0)+"2 = " + real + "+" + complex + "i
"); } return; } else { var left = collectVars(sides[0],sides[1]); var right = collectNums(sides[0],sides[1]); equations[i] = left + "=" + right; if (tempeq[i]!=equations[i]) { same = false; } } } else { var left = collectVars(sides[0],sides[1]); var right = collectNums(sides[0],sides[1]); equations[i] = left + "=" + right; if (tempeq[i]!=equations[i]) { same = false; } } } // Collect the coefficients of each variable into an array. for (i = 0; i < equations.length; i++) { coefficients[i] = findCoefficients(equations[i],i); } if (!same) { displaySolution("
Move variables to the left of the equal sign, and numbers to the right...
"); for (i = 0; i < equations.length; i++) { displaySolution(equations[i]); } } // Don't go through Gaussian elimination if we have a single variable problem. if (equations.length==1) { var sides = equations[0].split("="); var xnum = parseFloat(sides[0]); var num = parseFloat(sides[1]); sides[0] = vars.charAt(0); if (xnum) { sides[1] = Math.round(num/xnum*100000)/100000; displaySolution("
Solving for " + vars.charAt(0) + "
"); displaySolution(sides[0]+"="+sides[1]); } else { if (num) { displaySolution("
No solution for " + vars.charAt(0) + "
"); } else { displaySolution("
Infinite solutions for " + vars.charAt(0) + "
"); } } return; } // Initialize the identity matrix identityMatrix(); //Find the inverse of the matrix given using Gaussian elimination. displaySolution("
Attempting Gaussian Elimination.
"); if (gaussianElimination()) { displaySolution("Constructed the inverse
"); displaySolution(displayMatrix(inverse)); var inv = product(inverse,coefficients); displaySolution("Checking the inverse and the coefficients matrix are actually inverses.
"); displaySolution(displayMatrix(inv)); // Find the solution of the equations var solution = findSolution(); var variableVector = new Array(); for (var j = 0; j < vars.length; j++) { variableVector[j] = new Array (); variableVector[j][0] = vars.charAt(j); } displaySolution("The solution vector
"); displaySolution("
" + displayMatrix(variableVector) + "
=
" + displayMatrix(solution) + "
"); } return; } // Check for obvious syntax errors. function invalidSyntax(equation) { var sides = equation.split("="); for (var j=0;j < 2; j++) { if (/\$|\*|\!|"|'|£|%|&|{|}|@|\:|;|'|#|~|¬|`|,|<|>|\?|\\/.test(sides[j])) { return true; } if (/[a-z][a-z]/.test(sides[j])) { return true; } if (/\(|\)/.test(sides[j])) { if (/\((.*?)\)/.test(sides[j])) { return false; } else { return true; } } if (/[0-9](?=\^)/.test(sides[j])) { return true; } if (/[a-z](?=\^[^2])/.test(sides[j])) { return true; } } return false; } // Collect like terms on each side of the equation. function collectLikeTerms(side) { var regsign = /[+-]/; var pos; var matches = new Array(); var chars; var terms = side.split(regsign); var term = 0; if (terms[0] == side) { return side; } var signs = side.split(/[^+-]*/g); if (terms[0]=="") { for (var i=0; i < terms.length-1; i++) { terms[i] = terms[i+1] } terms.pop(); } if (signs.length < terms.length) { for (var j = terms.length-1; j >-1 ; j--) { signs[j+1] = signs[j]; } signs[0] = ""; } for (var j=0; j < signs.length; j++) { if (signs[j]=="+") { signs[j]=""; } } side = ""; var num = 0; for (var i = 0; i < terms.length; i++) { if (matches = /[a-z]/.exec(terms[i])) { continue; } if (terms[i]=="") { continue; } else { num += parseFloat(signs[i] + parseFloat(terms[i].replace(/[a-z]/,""))); } } for (var j = 0; j < vars.length; j++) { var xnum = 0; var regvar = new RegExp (vars.charAt(j)); for (var i = 0; i < terms.length; i++) { if (terms[i]=="") { continue; } if (/\^/.test(terms[i])) { term += parseFloat(signs[i] + parseFloat(terms[i])); terms[i] = ""; continue; } if (matches = regvar.exec(terms[i])) { chars = matches[0]; xnum += parseFloat(signs[i] + parseFloat(terms[i].replace(regvar,""))); } } if (xnum > 0) { if (j!=0) { side += "+" + xnum + chars; } else { side += xnum + chars; } } if (xnum < 0) { side += xnum + chars; } } if (num < 0) { side = side + num; } if (num > 0) { side = side + "+" + num; } if (parseFloat(term)) { if (xnum > 0) { side = term + vars.charAt(0)+ "^2" + "+" + side; } else { side = term + vars.charAt(0)+ "^2" + side; } } return side; } // Converts all instances of division to multiplication. function fixDivision(side) { var reg = /\//; var regdec = /[0-9.]/; var matches; var matches2; var pos; var rightpos; var leftpos; var right = ""; var left = ""; var leftnum = ""; var j = 0; while ((matches = reg.exec(side))&&(j < 5)) { for (var i = 0; i < matches.length; i++) { pos = side.indexOf(matches[0]); rightpos = ++pos; leftpos = --pos-1; while (matches2 = regdec.exec(side.charAt(rightpos))) { right = right + matches2[0]; rightpos++; } // Here I need to break the logic up into 3 possible characters left of the division sign. // The character is a number. if (matches2 = /[0-9]/.exec(side.charAt(leftpos))) { while (matches2 = regdec.exec(side.charAt(leftpos))) { leftnum = matches2[0] + leftnum; leftpos--; } } // The character is an x. This has 2 subpossibilities. Either it will be preceded again by a number, or it will // be a solitary x (with an implicit 1 - which we might as well insert now). if (matches2 = /[a-z]/.exec(side.charAt(pos-1))) { var chars = side.charAt(pos-1); if (matches2 = regdec.exec(side.charAt(pos-2))) { leftpos--; while (matches2 = regdec.exec(side.charAt(leftpos))) { leftnum = matches2[0] + leftnum; leftpos--; } left = chars; } else { // This should work... leftpos--; leftnum = 1; left = chars; } } // The character is a ). This also has 3 subpossibilities. The parenthesis will either be preceeded by a number, a ) or a sign. // This case is slightly tricky because I cannot make any assumptions about what is inside the parenthesis. if (matches2 = /[\)]/.exec(side.charAt(pos-1))) { // First find the other set of parenthesis, while keeping track of the characters in between. leftpos--; matches2 = /\(/.exec(side.charAt(leftpos)); while (!matches2) { left = side.charAt(leftpos) + left; leftpos--; matches2 = /\(/.exec(side.charAt(leftpos)); } left = "(" + left + ")"; leftpos--; // If there is another set of parenthesis, find the end of it as well. if (side.charAt(leftpos)==")") { matches2 = /\(/.exec(side.charAt(leftpos)); while (!matches2) { left = side.charAt(leftpos) + left; leftpos--; matches2 = /\(/.exec(side.charAt(leftpos)); } left = "(" + left; leftpos--; } if (matches2 = /[0-9]/.exec(side.charAt(leftpos))) { while (matches2 = regdec.exec(side.charAt(leftpos))) { leftnum = matches2[0] + leftnum; leftpos--; } } else { leftnum = 1; } } // Now update the main string. leftnum = parseFloat(leftnum)/parseFloat(right); matches2 = side.substring(leftpos+1, rightpos); side = side.replace(matches2, leftnum + left); } j++; // Reset the temporary storage variables. leftnum = ""; rightnum = ""; right = ""; left = ""; } return side; } // Collect all of the variables on the left hand side of the equals sign. function collectVars(leftside, rightside) { var rightnum; var leftnum; var templeft = ""; var tempright = ""; var matches; for (var j = 0; j < vars.length; j++) { var regvar = new RegExp (vars.charAt(j)); leftnum = matchNum(regvar,leftside); rightnum = matchNum(regvar,rightside); if ((rightnum)||(leftnum)) { leftnum = leftnum - rightnum; } if (j != 0) { if (leftnum >= 0) { sign = "+"; } else { sign = ""; } templeft += sign + leftnum + vars.charAt(j); } else { templeft = leftnum + vars.charAt(j); } } return templeft; } // Regular expressions function to find the value of the numbers before a variable. function matchNum(regvar,side) { var num = ""; var sign; if (matches = regvar.exec(side)) { var pos = side.indexOf(matches[0])-1; sign = false; if (side.charAt(pos)=="+") { num = 1; } if (side.charAt(pos)=="-") { num = 1; sign = true; } while (matches2 = regdec.exec(side.charAt(pos))) { num = matches2[0] + num; pos--; } if (side.charAt(pos)=="-") { sign = true; } if (sign) { num = "-" + num; } } if (num == "") { num = 0; } return num; } // Regular expressions tester to find the value of the number at the end of the expression. function findNum(side) { var pos = side.length-1; var num = ""; var sign = false; var matches; if (matches = /[a-z]/.exec(side.charAt(pos))) { return 0; } while (matches = regdec.exec(side.charAt(pos))) { num = matches[0] + num; pos--; } if (side.charAt(pos)=="-") { sign = true; } if (sign) { num = "-" + num; } return num; } // Collect all of the numbers on the right hand side of the equals sign. function collectNums(leftside,rightside) { rightside = findNum(rightside)- findNum(leftside); return rightside; } // Remove the implicit multiplication from the algebra. function removeImplicit(equation) { var reg = /(\+|-|\()(\(|[a-z])/; var reg2 = /\(|[a-z]/; var pos; var matches; // Handle the cases when x appears elsewhere in the expression. while (matches = reg.exec(equation)) { pos = equation.indexOf(matches[0])+1; equation = equation.replace(matches[0],matches[0].charAt(0) + "1" + matches[0].charAt(1)); } // Handle the leading variable case or leading parenthesis case. if (matches = reg2.exec(equation.charAt(0))) { return "1" + equation; } return equation; } // Multiply out parenthesis. function foil(side) { var regfoil = /\(([a-z0-9.+-]*)\)\(([a-z0-9.+-]*)\)/; var matches; var matches2; var factor1; var factor2; var sign1; var sign2; var num; var tmp = 0; var tmp2; while (matches = regfoil.exec(side)) { factor1 = matches[1].split(/[+-]/); factor2 = matches[2].split(/[+-]/); sign1 = matches[1].split(/[^+-]*/g); sign2 = matches[2].split(/[^+-]*/g); if (factor1[0]=="") { for (var i=0; i < factor1.length-1; i++) { factor1[i] = factor1[i+1] } factor1.pop(); } if (factor2[0]=="") { for (i=0; i < factor2.length-1; i++) { factor2[i] = factor2[i+1] } factor2.pop(); } if (sign1.length < factor1.length) { for (var j=0; j < factor1.length; j++) { sign1[j+1] = sign1[j]; } sign1[0] = ""; } if (sign2.length < factor2.length) { for (var j=0; j < factor2.length; j++) { sign2[j+1] = sign2[j]; } sign2[0] = ""; } for (var j=0; j < sign1.length; j++) { if (sign1[j]=="+") { sign1[j]=""; } } for (j=0; j < sign2.length; j++) { if (sign2[j]=="+") { sign2[j]=""; } } var terms = new Array(factor1.length*factor2.length); for (i=0; i < factor1.length; i++) { for (var j=0; j < factor2.length; j++) { if (/[a-z]/.test(factor1[i])) { if (/[a-z]/.test(factor2[j])) { terms[tmp] = (sign1[i] + parseFloat(factor1[i]))*(sign2[j] + parseFloat(factor2[j])) + vars.charAt(0) + "^2"; } else { terms[tmp] = (sign1[i] + parseFloat(factor1[i]))*(sign2[j] + parseFloat(factor2[j])) + vars.charAt(0); } } else { if (/[a-z]/.test(factor2[j])) { terms[tmp] = (sign1[i] + parseFloat(factor1[i]))*(sign2[j] + parseFloat(factor2[j])) + vars.charAt(0); } else { terms[tmp] = (sign1[i] + parseFloat(factor1[i]))*(sign2[j] + parseFloat(factor2[j])); } } tmp++; } } var term = new Array(0,0,0); var num = ""; var pos = side.indexOf(matches[0])-1; if (side.charAt(pos)=="+") { num = 1; } if (side.charAt(pos)=="-") { num = 1; sign = true; } while (matches2 = regdec.exec(side.charAt(pos))) { num = matches2[0] + num; pos--; } for (j=0; j < terms.length; j++) { if (/\^/.test(terms[j])) { term[0] = Math.round(num*parseFloat(terms[j])*100000)/100000 + vars.charAt(0) + "^2"; terms[j] = ""; } if (/[a-z]/.test(terms[j])) { term[1] += Math.round(num*parseFloat(terms[j])*100000)/100000; terms[j] = ""; } if (/[0-9]/.test(terms[j])) { term[2] += Math.round(num*terms[j]*100000)/100000; } } if (term[1] > 0) { term[1] = "+" + Math.round(term[1]*100000)/100000 + vars.charAt(0); } if (term[1] < 0 ) { term[1] = Math.round(term[1]*100000)/100000 + vars.charAt(0); } if (!term[1]) { term[1] = ""; } if (term[2] > 0) { term[2] = "+" + term[2]; } if (term[2] == 0) { term[2] = ""; } term = term.join(""); side = side.replace(num+matches[0],term); } return side; } // Remove the parenthesis from an equation. function removeParenthesis(side) { var regpar = /\((.*?)\)/; var regsign = /[+-]/; var matches; var matches2; var string; var string2; var sign = null; var pos; var num = ""; var text; while (((matches = regpar.exec(side)) != undefined)) { num = ""; pos = side.indexOf(matches[0])-1; if (side.charAt(pos)=="+") { num = 1; } if (side.charAt(pos)=="-") { num = 1; sign = true; } while (matches2 = regdec.exec(side.charAt(pos))) { num = matches2[0] + num; pos--; } if (side.charAt(pos)=="-") { sign = true; } side = side.substr(0,pos+1) + side.substr(pos+num.length+1); string = matches[1].split(regsign); for (var j=0; j < string.length;j++) { if ((0+string[j]) == parseFloat(string[j])) { string[j] = string[j]*num; } else { if (/\^/.test(string[j])) { matches2 = /[a-z]/.exec(string[j]); string[j] = num*parseFloat(string[j]) + string[j].substr(string[j].indexOf(matches2[0])); } else { string[j] = num*parseFloat(string[j]) + string[j].charAt(string[j].length-1); } } } text = new Array (); pos = matches[1].split(/[^+-]/); var temp = 0; for (j = 0; j < pos.length; j++) { if (pos[j]!="") { text[temp] = pos[j]; temp++; } } pos = text; text = string[0]; for (j = 1; j < string.length; j++) { if (sign!=null) { if (pos[j-1] == "-") { var temppos = "+"; } if (pos[j-1] == "+") { var temppos = "-"; } pos[j-1] = temppos; } text = text + pos[j-1] + string[j]; } text = text.replace("NaN",""); side = side.replace(matches[0],text); sign = null; } return side; } // This counts the number of times a string is matched in another string function CountValue( strText, reTargetString ){ var intCount = 0; strText.replace(reTargetString, function(){ intCount++;}); // Return the updated count variable. return (intCount); } // Count the variables in the given string and update the currentVariables array function incrementCurrentVariables (element, index, array) { var matches; currentVariables[index] = new Array(); for (var j = 0; j< variables.length; j++) { if (matches = CountValue (element, new RegExp(variables[j], "g" ))) { currentVariables[index].push(variables[j]); currentVariables[index].push(matches); if (!vars.match(variables[j])) { vars += variables[j]; } } } return; } // Collect the like terms when the equation includes an x^2 function collectSquared(leftside,rightside) { var x2num = Math.round((matchNum(/[a-z]\^2/,leftside)-matchNum(/[a-z]\^2/,rightside))*100000)/100000; leftside = leftside.replace(/[0-9.]*[a-z]\^2/,""); rightside = rightside.replace(/[0-9.]*[a-z]\^2/,""); var xnum = Math.round((matchNum(/[a-z](?!\^)/,leftside)-matchNum(/[a-z](?!\^)/,rightside))*100000)/100000; var num = Math.round((findNum(leftside) - findNum(rightside))*100000)/100000; var pos = 0; if (x2num) { if (xnum >= 0) { if (num >= 0) { leftside = x2num + vars.charAt(0) + "^2+" + xnum + vars.charAt(0) + "+" + num; } else { leftside = x2num + vars.charAt(0) + "^2+" + xnum + vars.charAt(0) + num; } } else { if (num >= 0) { leftside = x2num + vars.charAt(0) + "^2" + xnum + vars.charAt(0) + "+" + num; } else { leftside = x2num + vars.charAt(0) + "^2" + xnum + vars.charAt(0) + num; } } } else { if (num >= 0) { leftside = xnum + vars.charAt(0) + "+" + num; } else { leftside = xnum + vars.charAt(0) + num; } } return leftside; } // Find the constants, this function assumes they are on the right hand side of the equation. function findConstants(equation) { var num = ""; var regdec = /[0-9.]/; pos = equation.length-1; while (matches2 = regdec.exec(equation.charAt(pos))) { num = matches2[0] + num; pos--; } if (equation.charAt(pos)=="-") { num = "-" + num; } return num; } // Find the number of each variable in the array. function findCoefficients(equation,i) { var matches; var reg; var regdec = /[0-9.]/; var pos; var num =""; var matches2; var row = new Array (); constants[i] = findConstants(equations[i]); equations[i] = ""; for (var j = 0; j < vars.length; j++) { reg = new RegExp(vars.charAt(j)); if (matches = reg.exec(equation)) { pos = equation.indexOf(matches[0])-1; while (matches2 = regdec.exec(equation.charAt(pos))) { num = matches2[0] + num; pos--; if (equation.charAt(pos)=="-") { num = "-" + num; } } } if (num=="") { row[j] = 0; num = "0"; } else { row[j] = num; } if (parseFloat(num) < 0) { equations[i] += num + vars.charAt(j); } else { if (j==0) { equations[i] += num + vars.charAt(j); } else { equations[i] += "+" + num + vars.charAt(j); } } num = ""; } equations[i] = equations[i] + "=" + constants[i]; return row; } // Create an appropriate identity matrix to hold our Gaussian elimination. Note that we call it the inverse, since it will eventually be the inverse matrix. function identityMatrix() { for (var i = 0; i < equations.length; i++){ inverse[i] = new Array(); for (var j = 0; j < equations.length; j++) { if (i==j) { inverse[i].push(1); } else { inverse[i].push(0); } } } return; } // Multiply two matrices. function product(left,right) { var answer = new Array(); var sum = 0; for (var i = 0; i < equations.length; i++) { answer[i] = new Array(); for (var j = 0; j < equations.length; j++) { for (var k =0; k < equations.length; k++) { sum += left[i][k]*right[k][j]; } //if (sum==parseFloat(sum)) { answer[i][j] = sum; //} sum = 0; } } return answer; } // Construct a row multiplication matrix function multRow (row, num) { var answer = new Array (); for (var m = 0; m < equations.length; m++) { answer[m] = new Array (); for (var n = 0; n < equations.length; n++) { if (m == n) { if (m == row) { answer[m][n]=num; } else { answer[m][n]=1; } } else { answer[m][n]=0; } } } return answer; } // Construct a row addition (or subtraction) matrix function addRow (row, col, num) { var answer = new Array (); for (var m = 0; m < equations.length; m++) { answer[m] = new Array (); for (var n = 0; n < equations.length; n++) { if (m == n) { answer[m][n] = 1; } else { answer[m][n] = 0; } if ((m==row)&&(n==col)) { answer[m][n] = num; } } } return answer; } // Creates a matrix to swap two rows. You can also to swap to columns by multiplying on the other side. function swapRows(row1,row2) { var answer = new Array(); for (var m = 0; m < equations.length; m++) { answer[m] = new Array (); for (var n = 0; n < equations.length; n++) { if (m==row1) { if (n==row2) { answer[m][n] = 1; continue; } else { answer[m][n] = 0; continue; } } if (m==row2) { if (n==row1) { answer[m][n] = 1; } else { answer[m][n] = 0; } } else { if(n==m) { answer[m][n] = 1; } else { answer[m][n] = 0; } } } } return answer; } // This is the crux of the solving of the equations. We use Gaussian elimination (done in a rigid format) to find // the inverse of the matrix. This inverse will then be multiplied by the constants vector to product the solution. function gaussianElimination() { coef = coefficients; var num = 0; var tmp = 0; var mult; var add; var swp; var step = 1; for (var i = 0; i < equations.length; i++) { num = coef[i][i]; if (num!=0) { mult = multRow(i,1/num); inverse = product(mult,inverse); coef = product(mult,coef); displaySolution("Step " + step+ "
"); step++; displaySolution(displayMatrix(coef)); } else { for (var j = 0; j < equations.length; j++) { tmp += coef[i][j]; } if (tmp == 0) { displaySolution("Indeterminant Solution."); return false; } var mx = maxValue(coef,i); swp = swapRows(i,mx); inverse = product(swp,inverse); coef = product(swp,coef); displaySolution("Step " + step+ "
"); step++; displaySolution(displayMatrix(coef)); num = coef[i][i]; if (num!=0) { mult = multRow(i,1/num); inverse = product(mult,inverse); coef = product(mult,coef); displaySolution("Step " + step+ "
"); step++; displaySolution(displayMatrix(coef)); } else { displaySolution("Indeterminant Solution."); return false; } } for (var j = 0; j < equations.length; j++) { if (i!=j) { num = coef[j][i]; add = addRow (j, i, -1*num); inverse = product(add,inverse); coef = product(add,coef); displaySolution("Step " + step+ "
"); step++; displaySolution(displayMatrix(coef)); } } num = 0; } return true; } // Need special multiplication for finding the answer. function findSolution() { var ans = new Array(); var sum = 0; for (var i = 0; i < equations.length; i++) { ans[i] = new Array(); for (var k = 0; k < equations.length; k++) { sum += inverse[i][k]*constants[k]; } ans[i][0] = sum; sum = 0; } return ans; } // Find the row with the maximum value. function maxValue(arr,col) { var mxm = arr[0][col]; var k; for (var l=0; l < arr.length; l++) { if (arr[l][col]>mxm) { mxm = arr[l][col]; k = l; } } return k; }; // Display a matrix as a table function displayMatrix (matrix) { if (matrix[matrix.length-1][matrix.length-1]==undefined) { var text = "\n"; } else { var text = "
\n"; } for (var i = 0; i < matrix.length; i++) { text += "\n"; for (var j = 0; j < matrix.length; j++) { if (matrix[i][j]==parseFloat(matrix[i][j])) { text += "\n"; continue; } if (matrix[i][j]==vars.charAt(i)) { text += "\n"; } } text += "\n"; } text += "
" + Math.round(matrix[i][j]*100000)/100000 + "" + matrix[i][j] + "
\n"; return text; } // helper function for DOM function $(el) { return document.getElementById(el); } // Display the solution, which currently only includes the rhs and the lhs. function displaySolution(input) { var solution = $('solution'); solution.innerHTML += input + "
\n"; return; }




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