private void fastColoredTextBox1_TextChanged(object sender, FastColoredTextBoxNS.TextChangedEventArgs e)
{
// lasttext = fastColoredTextBox1.Text;
if (MATH2.MasterForm.Clear)
{
Console.Clear();
}
comboBox1.Items.Clear();
try
{
OnTextChanged(fastColoredTextBox1.Text);
}
catch { }
try
{
// url = @"http://www.texrendr.com/cgi-bin/mathtex.cgi?\dpi{" + trackBar1.Value.ToString() + @"}" + LaTeX.Print(Infix.ParseOrThrow(fastColoredTextBox1.Text));
//Console.WriteLine(url);
laTeXDisplay1.LoadLatex(LaTeX.Print(Infix.ParseOrThrow(fastColoredTextBox1.Text)));
}
catch
{
//url = @"http://www.texrendr.com/cgi-bin/mathtex.cgi?\dpi{" + trackBar1.Value.ToString() + @"}" + fastColoredTextBox1.Text;
laTeXDisplay1.LoadLatex(fastColoredTextBox1.Text);
}
}
private int WrongAnswer(int[] numbers)
{
int wrongAnswer = 0;
int solution = (int)((SymbolicExpression)Infix.ParseOrThrow(SolutionInfix)).RealNumberValue;
var rng = new Random();
bool ok = false;
for (int tries = 0; tries < 30 && !ok; tries++)
{
int method = rng.Next(3);
switch (method)
{
case 0:
// multiply with slightly changed numbers
wrongAnswer = numbers[1];
for (int i = 0; i < numbers.Length; i++)
{
if (i == 1)
{
continue;
}
wrongAnswer *= (numbers[i] + (rng.NextBoolean() ? 1 : -1));
}
break;
case 1:
// multiply with slightly changed numbers
wrongAnswer = numbers[0];
for (int i = 1; i < numbers.Length; i++)
{
wrongAnswer *= (numbers[i] + (rng.NextBoolean() ? 1 : -1));
}
break;
default:
// just roll something in the range of the solution
int range = Math.Abs(solution / 4) + 3;
wrongAnswer = solution + rng.Next(solution - range, solution + range + 1);
break;
}
// check if the answer is ok
ok = true;
// check if the answer is identical to another
foreach (string answer in AnswersInfix)
{
// if it is, begin anew
if (answer != null && answer.Equals(wrongAnswer.ToString()))
{
ok = false;
}
}
// check if the answer is actually a solution
if (IsSolution(wrongAnswer.ToString()))
{
ok = false;
tries--;
}
}
return(wrongAnswer);
}
// private void PUpdated(Arg a)
// {
//// a.parent.UpdateArgs(flowLayoutPanel2.Controls);
// }
//private void LoadArgs(MATH2.IMathPlugin plugin)
//{
// List<Arg> args = plugin.GetArgs();
// foreach (Arg arg in args)
// {
// arg.parent = plugin;
// arg.r = new Arg.Return(PUpdated);
// //flowLayoutPanel2.Controls.Add(arg.GetControl());
// Console.WriteLine("added arg " + arg.displayname);
// }
//}
private void OnTextChanged(string raw)//or whatever moooooo
{
List <int> probs = new List <int>();
Expression ex = null;
try
{
ex = Infix.ParseOrThrow(fastColoredTextBox1.Text);
}
catch { }
try
{
foreach (var item in plugins)
{
probs.Add(GetProb(Activator.CreateInstance(item) as MATH2.IMathPlugin, raw, ex));
}
}
catch (Exception e)
{
Console.WriteLine(e);
}
foreach (var plugin in plugins)
{
comboBox1.Items.Add(plugin.Name);
}
comboBox1.SelectedIndex = probs.IndexOf(probs.Max());
comboBox1_SelectedIndexChanged(null, null);
// Console.Clear();
}
public void calculaH_K(double[] coeficientes)
{
double a = coeficientes[0];
double b = coeficientes[1];
double c = coeficientes[2];
double d = coeficientes[3];
double e = coeficientes[4];
double f = coeficientes[5];
var A = Matrix <double> .Build.DenseOfArray(new double[, ]
{
{ Convert.ToInt32(a), Convert.ToInt32(b / 2) },
{ Convert.ToInt32(b / 2), Convert.ToInt32(c) },
});
MessageBox.Show("Matriz para calcular H e K: " + A.ToString());
var B = Vector <double> .Build.Dense(new double[] { -(d / 2), -(e / 2) });
var x = A.Solve(B);
MessageBox.Show("H e K: " + x.ToString());
h = x[0];
k = x[1];
if (!Double.IsInfinity(getH())) // Se o determinante deu diferente de zero foi possível realizar a translação
{
// Achar o novo termo independente da equação: (p.96)
setF((getD() / 2) * getH() + (getE() / 2) * getK() + getF());
var eq = Infix.ParseOrThrow(getA().ToString() + "*u*u+" + getB().ToString() + "*u*v+" + getC().ToString() + "*v*v+" + getF().ToString());
var expanded = Algebraic.Expand(eq);
MessageBox.Show("Translação realizada!\nNova equação da cônica:\n" + Infix.FormatStrict(expanded) + " ", "Translação Concluida", MessageBoxButtons.OK, MessageBoxIcon.Exclamation);
MessageBox.Show("Iniciando Rotação para elimianar o termo quadrático misto", "Iniciando Rotação", MessageBoxButtons.OK, MessageBoxIcon.Exclamation);
}
}
private void trackBar1_ValueChanged(object sender, EventArgs e)
{
string url = "";
laTeXDisplay1.size = trackBar1.Value;
try
{
// url = @"http://www.texrendr.com/cgi-bin/mathtex.cgi?\dpi{" + trackBar1.Value.ToString() + @"}" + LaTeX.Print(Infix.ParseOrThrow(fastColoredTextBox1.Text));
//Console.WriteLine(url);
laTeXDisplay1.LoadLatex(LaTeX.Print(Infix.ParseOrThrow(fastColoredTextBox1.Text)));
}
catch
{
//url = @"http://www.texrendr.com/cgi-bin/mathtex.cgi?\dpi{" + trackBar1.Value.ToString() + @"}" + fastColoredTextBox1.Text;
laTeXDisplay1.LoadLatex(fastColoredTextBox1.Text);
// Console.WriteLine(char.MinValue);
// int no = (int)char.MinValue;
// while (no != char.MaxValue)
//{
// char c = (char)no;
//System.Console.WriteLine("CharID: " + no + " | Bin: "
// + string.Join(" ", System.Text.Encoding.UTF8.GetBytes(c.ToString()).Select(byt =>
// System.Convert.ToString(byt, 2).PadLeft(8, '0')))
//+ " | Display: " + c);
//no++;
//}
}
// laTeXDisplay1.LoadLatex(new Uri(url));
}
public string mostraNovaEquacao()
{
/*var s = Expr.Variable("s");
* var t = Expr.Variable("t");*/
//MessageBox.Show("Equação geral: " + aL + "s² + " + cL + "t² - " + aL * cL + " = 0");
double[] num =
{
getAL(), getBL(), getCL(), getDL(), getEL(), getF()
};
double max = 0;
for (int i = 0; i < 6; i++)
{
if (num[i] > max)
{
max = num[i];
}
}
long[] num2 =
{
(long)max, (long)max, (long)max, (long)max, (long)max, (long)max
};
int j = 0;
for (int i = 0; i < 6; i++)
{
if (num[i] != 0)
{
num2[j] = (long)num[i];
j++;
}
}
double div = (double)Euclid.GreatestCommonDivisor(num2);
MessageBox.Show("MMC: " + div);
if (div != null && div != 0)
{
setAL(getAL() / div);
setBL(getBL() / div);
setCL(getCL() / div);
setDL(getDL() / div);
setEL(getEL() / div);
setF(getF() / div);
} // Simplifica a equação com o maior divisor entre eles
var eq = Infix.ParseOrThrow(getAL().ToString() + "*u*u+" + getBL().ToString() + "*u*v+" + getCL().ToString() + "*v*v+" + getDL().ToString() + "*u+" + getEL().ToString() + "*v+" + getF().ToString());
var expanded = Algebraic.Expand(eq);
MessageBox.Show("Equação Geral: " + Infix.FormatStrict(expanded), "Equação", MessageBoxButtons.OK, MessageBoxIcon.Exclamation);
// Agora falta simplificar a equação
return(Infix.FormatStrict(expanded).ToString());
}
public int[][] ConvertLogicToConditional(string Logic)
{
string NewLogic = Logic.Replace("&&", "*").Replace("||", "+").Replace("&", "*").Replace("|", "+");
Dictionary <string, int> LetterToNum = new Dictionary <string, int>();
foreach (var i in ExtractNumbers(Logic))
{
var Letter = IndexToColumn(i + 1);
LetterToNum.Add(Letter, i);
}
LetterToNum = LetterToNum.OrderBy(x => x.Value).Reverse().ToDictionary(kvp => kvp.Key, kvp => kvp.Value);
foreach (var i in LetterToNum)
{
//Debugging.Log(i.ToString());
NewLogic = NewLogic.Replace(i.Value.ToString(), i.Key);
}
//Debugging.Log(NewLogic);
Expression LogicSet = Infix.ParseOrThrow(NewLogic);
var Output = Algebraic.Expand(LogicSet);
string ExpandedLogic = Infix.Format(Output).Replace(" ", "");
//Debugging.Log(ExpandedLogic);
foreach (var i in LetterToNum)
{
ExpandedLogic = ExpandedLogic.Replace(i.Key, i.Value.ToString());
}
ExpandedLogic = HandlePowers(ExpandedLogic.Replace(" ", ""));
return(ExpandedLogic.Split('+').Select(x => x.Split('*').Select(y => int.Parse(y)).ToArray()).ToArray());
}
static void Main(string[] args)
{
Console.Write("Expression: ");
var expr = Console.ReadLine();
var parsed = Infix.ParseOrThrow(expr);
var res = Evaluate.Evaluate(new Dictionary <String, FloatingPoint>(), parsed);
Console.WriteLine(res);
}
public Surface(string expression)
{
if (expression == null)
{
throw new NullReferenceException();
}
_expression = Compile.compileExpression2(Infix.ParseOrThrow(expression), Symbol.NewSymbol("x"), Symbol.NewSymbol("y")).Value;
}
//mostraNovaEquacao2 retorna a equação após fazer a rotação e a translação conforme o caso na pag 99 das notas de aula
public string mostraNovaEquacao2()
{
// O termo independente continua o mesmo pois não foi realizada a translação
double[] num =
{
getAL(), getBL(), getCL(), getDL(), getEL(), getF()
};
double max = 0;
for (int i = 0; i < 6; i++)
{
if (num[i] > max)
{
max = num[i];
}
}
long[] num2 =
{
(long)max, (long)max, (long)max, (long)max, (long)max, (long)max
};
int j = 0;
for (int i = 0; i < 6; i++)
{
if (num[i] != 0)
{
num2[j] = (long)num[i];
j++;
}
}
double div = (double)Euclid.GreatestCommonDivisor(num2);
MessageBox.Show("MMC: " + div);
if (div != null && div != 0)
{
setAL(getAL() / div);
setBL(getBL() / div);
setCL(getCL() / div);
setDL(getDL() / div);
setEL(getEL() / div);
setF(getF() / div);
} // Simplifica a equação com o maior divisor entre eles
var eq = Infix.ParseOrThrow(getAL().ToString() + "*u*u+" + getBL().ToString() + "*u*v+" + getCL().ToString() + "*v*v+" + getDL().ToString() + "*u+" + getEL().ToString() + "*v+" + getF().ToString());
var expanded = Algebraic.Expand(eq);
MessageBox.Show("Equação Geral: " + Infix.FormatStrict(expanded), "Equação", MessageBoxButtons.OK, MessageBoxIcon.Exclamation);
return(Infix.FormatStrict(expanded).ToString());
// B = 0
// Agora simplificar a equação
}
public static string GetFullFormulaOptions([ExcelArgument(AllowReference = true)] object arg, bool replaceRef = false, bool resolveName = false, int decimalPlaces = 5)
{
try
{
//this removes the volatile flag
XlCall.Excel(XlCall.xlfVolatile, false);
ExcelReference theRef = (ExcelReference)arg;
Excel.Range rng = ReferenceToRange(theRef);
Debug.Print("Get formula for {0}", rng.Address);
ws = rng.Parent as Excel.Worksheet;
var parser = GetParser(rng);
var root = parser.Root;
var newFormula = GetFormulaForFunc(root, replaceRef, resolveName, -1);
Debug.Print(newFormula);
//remove the SUMs
var noSumVersion = GetFormulaWithoutSum(new XLParser.FormulaAnalyzer(newFormula).Root);
var cleanFormula = Infix.Format(Infix.ParseOrThrow(noSumVersion));
Debug.Print(cleanFormula);
var finalFormula = cleanFormula;
if (decimalPlaces > -1)
{
Debug.Print("Going back through a 2nd time");
cleanFormula = CleanUpSqrtAbs(cleanFormula);
parser = GetParser(cleanFormula);
var secondParserResult = GetFormulaForFunc(parser.Root, replaceRef, resolveName, decimalPlaces);
finalFormula = Infix.Format(Infix.ParseOrThrow(secondParserResult));
}
//see if a short version of the formula is available
var algFormula = Infix.Format(Algebraic.Expand(Infix.ParseOrThrow(finalFormula)));
var ratFormula = Infix.Format(Rational.Expand(Infix.ParseOrThrow(finalFormula)));
var shortFormula = new[] { algFormula, ratFormula, finalFormula }.OrderBy(c => c.Length).First();
//go through formula and search for |..| to replace with ABS(..)
shortFormula = CleanUpSqrtAbs(shortFormula);
return(shortFormula);
}
catch (Exception e)
{
Debug.Print(e.ToString());
return(e.ToString());
}
}
private List <MathNet.Symbolics.Expression> GetListEquations(string[] strEquations)
{
List <MathNet.Symbolics.Expression> equations = new List <MathNet.Symbolics.Expression>();
for (int i = 0; i < strEquations.Length; i++)
{
equations.Add(Infix.ParseOrThrow(strEquations[i].Replace('=', '-').Replace(",", ".")));
}
return(equations);
}
public static double Evaluate(double x, string expr)
{
var parsed = Infix.ParseOrThrow(expr);
var values = new Dictionary <String, FloatingPoint>();
values.Add("x", x);
var res = MathNet.Symbolics.Evaluate.Evaluate(values, parsed);
return(res.RealValue);
}
internal bool IsSolution(string answerInfix)
{
var answerExpr = Infix.ParseOrUndefined(answerInfix);
if (answerExpr.IsUndefined)
{
return(false);
}
else
{
return(answerExpr.Equals(Infix.ParseOrThrow(SolutionInfix)));
}
}
public async Task <SearchResultCollection> SearchAsync(SearchQuery query, CancellationToken ct)
{
string latex;
string infix;
double?evaluated;
try
{
// simplify
var expression = Infix.ParseOrThrow(query.QueryString);
latex = LaTeX.Format(expression);
infix = Infix.Format(expression);
// try to calculate
var symbols = new Dictionary <string, FloatingPoint>();
try
{
evaluated = Evaluate.Evaluate(symbols, expression).RealValue;
}
catch (Exception ex)
{
// expression valid, but can't be calculated
return(null);
}
}
catch (Exception ex)
{
// expression error
return(null);
}
var results = new SearchResultCollection
{
Title = "Math evaluation",
Relevance = evaluated != null ? SearchResultRelevance.ONTOP : SearchResultRelevance.DEFAULT,
FontAwesomeIcon = "Calculator"
};
results.Results = new ObservableCollection <SearchResult>
{
new MathSearchResult
{
Title = infix,
LaTeXExpression = latex,
LaTeXEvaluated = evaluated != null ? "= " + evaluated : "",
ParentCollection = results
}
};
return(results);
}
private int WrongAnswer(Random rng, int[] summands)
{
int wrongAnswer = 0;
int solution = (int)((SymbolicExpression)Infix.ParseOrThrow(SolutionInfix)).RealNumberValue;
int tries = 0;
start:
tries++;
int algorithm = rng.Next(0, 3);
switch (algorithm)
{
case 0:
// take the solution and add or substract 1 or 2
wrongAnswer = solution + rng.Next(-2, 3);
break;
case 1:
// take the solution and add or substract 10 or 20
wrongAnswer = solution + rng.Next(-2, 3) * 10;
break;
default:
// just roll something in the range of the solution
wrongAnswer = solution + rng.Next(solution - (solution / 4) - 3, solution + (solution / 4) + 4);
break;
}
// check if the answer is identical to another
foreach (string answer in AnswersInfix)
{
// if it is, begin anew
if (answer != null && answer.Equals(wrongAnswer.ToString()) && tries < 20)
{
goto start;
}
}
// check if the answer is actually a solution
if (IsSolution(wrongAnswer.ToString()))
{
goto start;
}
// check if the answer is larger than each summand (it would be too simple if else)
for (int i = 0; i < summands.Length; i++)
{
if (wrongAnswer <= summands[i] && tries < 20)
{
goto start;
}
}
return(wrongAnswer);
}
private void Button_EvaluateExpression_Click(object sender, RoutedEventArgs e)
{
try {
Expr expression = Infix.ParseOrThrow(TextBox_ExpressionInput.Text);
string symbolstr = TextBox_InputSymbol.Text;
string x1 = TextBox_InputX1.Text;
string x2 = TextBox_InputX2.Text;
string ep = TextBox_InputEpsilon.Text;
var result = new SecantMethodDecimal()
{
Function = expression,
SymbolStr = symbolstr,
Epsillon = Decimal.Parse(ep)
};
result.ComputeSecantMethod(Decimal.Parse(x1), Decimal.Parse(x2));
this.ListView_Solution.ItemsSource = result.Results;
UIHelper.ResizeListViewColumnsToContent(this.ListView_Solution, null);
var lastResult = result.Results.Last();
int decimalPlaces = UIHelper.CountDigitsAfterDecimal(TextBox_InputEpsilon.Text);
this.FC_Aproximation.Formula = result.GetAprox.ToString();
this.FC_AproximationRounded.Formula = result.GetRoundedOff.ToString();
this.FC_AproximationChopped.Formula = result.GetChoppedOff.ToString();
SnackBarNotif.MessageQueue.Enqueue(
UIHelper.NewSnackbarMessage(
PackIconKind.CheckAll,
"Success! Check solution and results!",
Colors.DarkGreen,
0.5
)
);
} catch {
//show error message
SnackBarNotif.MessageQueue.Enqueue(
UIHelper.NewSnackbarMessage(
PackIconKind.SignCaution,
"Error! Unable to compute aproximation!",
Colors.HotPink,
0.5
)
);
}
}
private int WrongAnswer(int[] numbers)
{
int wrongAnswer = 0;
int solution = (int)((SymbolicExpression)Infix.ParseOrThrow(SolutionInfix)).RealNumberValue;
var rng = new Random();
int tries = 0;
start:
int method = rng.Next(3);
switch (method)
{
case 0:
// take the solution and add or substract 1 or 2
wrongAnswer = solution + rng.Next(-3, 4);
break;
case 1:
// take the solution and add or substract 10 or 20
wrongAnswer = solution + rng.Next(-2, 3) * 10;
break;
default:
// just roll something in the range of the solution
int range = Math.Abs(solution / 4) + 3;
wrongAnswer = solution + rng.Next(solution - range, solution + range + 1);
break;
}
tries++;
// check if the answer is identical to another
foreach (string answer in AnswersInfix)
{
// if it is, begin anew
if (answer != null && answer.Equals(wrongAnswer.ToString()) && tries < 20)
{
goto start;
}
}
// check if the answer is actually a solution
if (IsSolution(wrongAnswer.ToString()))
{
goto start;
}
// check if the answer is smaller than the first number
if (wrongAnswer > numbers[0] && tries < 20)
{
goto start;
}
return(wrongAnswer);
}
private static void OnTextChanged(string raw)//or whatever moooooo
{
List <int> probs = new List <int>();
Expression e = null;
try
{
e = Infix.ParseOrThrow(raw);
}
catch { }
foreach (var item in plugins)
{
probs.Add(GetProb(Activator.CreateInstance(item) as MATH2.IMathPlugin, raw, e));
}
MATH2.IMathPlugin pl = Activator.CreateInstance(plugins[probs.IndexOf(probs.Max())]) as MATH2.IMathPlugin;
Console.WriteLine("Using the " + plugins[probs.IndexOf(probs.Max())].Name + " solver to solve your question:");
List <Step> steps = null;
try
{
steps = pl.Solve(raw, e);
Console.WriteLine("Answer: " + steps.Last());
}
catch (Exception exc)
{
if (MATH2.MasterForm.Clear)
{
Console.Clear();
}
Console.WriteLine("A " + exc.GetType().Name + " error occured whilst the solver was calculating the answer.");
System.Threading.Thread.Sleep(2000); if (MATH2.MasterForm.Clear)
{
Console.Clear();
}
Main();
}
if (steps != null)
{
// Console.ReadKey();
Console.WriteLine("Steps");
foreach (var step in steps)
{
Console.WriteLine(step);
}
}
// Console.Clear();
}
private void Button_EvaluateExpression_Click(object sender, RoutedEventArgs e)
{
try {
Expr expression = Infix.ParseOrThrow(TextBox_ExpressionInput.Text);
Symbol symbol = Symbol.NewSymbol(TextBox_InputSymbol.Text);
var result = new BisectionResultRow(symbol, expression)
{
A = Double.Parse(TextBox_InputA.Text),
B = Double.Parse(TextBox_InputB.Text),
Epsillon = Double.Parse(TextBox_InputEpsilon.Text)
};
var results = BisectionResultRow.ComputeList(result);
this.ListView_Solution.ItemsSource = results;
UIHelper.ResizeListViewColumnsToContent(this.ListView_Solution, null);
var lastResult = results.Last();
int decimalPlaces = UIHelper.CountDigitsAfterDecimal(TextBox_InputEpsilon.Text);
this.FC_Aproximation.Formula = lastResult.B.ToString();
this.FC_AproximationRounded.Formula = Math.Round(lastResult.B, decimalPlaces).ToString();
this.FC_AproximationChopped.Formula = UIHelper.TruncateDecimal((decimal)lastResult.B, decimalPlaces).ToString();
SnackBarNotif.MessageQueue.Enqueue(
UIHelper.NewSnackbarMessage(
PackIconKind.KeyboardVariant,
"Success! Check solution and results!",
Colors.DarkGreen,
0.5
)
);
}
catch {
//show error message
SnackBarNotif.MessageQueue.Enqueue(
UIHelper.NewSnackbarMessage(
PackIconKind.KeyboardVariant,
"Invalid Input! Function Input (Value to Aprox.) syntax is invalid!",
Colors.HotPink,
0.5
)
);
}
}
private int WrongAnswer(int[] numbers)
{
int wrongAnswer = 0;
int solution = (int)((SymbolicExpression)Infix.ParseOrThrow(SolutionInfix)).RealNumberValue;
var rng = new Random();
bool ok = false;
for (int tries = 0; tries < 30 && !ok; tries++)
{
int method = rng.Next(2);
switch (method)
{
case 0:
// take the solution and add or substract 1 or 2
wrongAnswer = solution + new Random().Next(-3, 4);
break;
default:
// just roll something in the range of the solution
int range = Math.Abs(solution / 2) + 5;
wrongAnswer = solution + rng.Next(solution - range, solution + range + 1);
break;
}
// check if the answer is ok
ok = true;
// check if the answer is identical to another
foreach (string answer in AnswersInfix)
{
// if it is, begin anew
if (answer != null && answer.Equals(wrongAnswer.ToString()))
{
ok = false;
}
}
// check if the answer is actually a solution
if (IsSolution(wrongAnswer.ToString()))
{
ok = false;
tries--;
}
}
return(wrongAnswer);
}
public static List <Expression> ParseSequence(string raw)
{
try
{
List <Expression> ret = new List <Expression>();
StringBuilder sb = new StringBuilder();
foreach (var item in raw.Split(',').ToList())
{
ret.Add(Infix.ParseOrThrow(item.Replace(",", "")));
sb.Append(LaTeX.Print(Infix.ParseOrThrow(item.Replace(",", ""))) + ",");
}
System.Windows.Forms.Clipboard.SetText(sb.ToString());
// Console.WriteLine("Successfully parsed sequence: " + sb.ToString());
return(ret);
}
catch
{
Console.WriteLine("Sequence was in the incorrect format, remember to seperate items by a comma!");
return(null);
}
}
public static List <double> Coeficients(
string strT,
string strS,
string strF,
double q,
int n)
{
Expression T, s, f;
try
{
T = Infix.ParseOrThrow(strT);
s = Infix.ParseOrThrow(strS);
f = Infix.ParseOrThrow(strF);
}
catch (Exception ex)
{
throw new FunctionParseException("Failed to parse function", ex);
}
double h = 1 / (double)n;
var mainDiagonal = MainDiagonal(T, s, n);
var subDiagonal = SubDiagonal(T, s, n);
var superDiagonal = new List <double>(subDiagonal);
subDiagonal.Insert(0, 0);
superDiagonal.Add(0);
var constantTerms = ConstantTerms(f, q, n);
var coefs = TridiagonalMatrixAlgorithm(
subDiagonal,
mainDiagonal,
superDiagonal,
constantTerms);
coefs.Add(0);
return(coefs);
}
public static double EvaluateFunction(double t, double y, string function)
{
SymbolicExpression expression = Infix.ParseOrThrow(function);
Dictionary <string, FloatingPoint> variables = new Dictionary <string, FloatingPoint>
{
{ "t", t },
{ "y", y }
};
double result;
try
{
result = expression.Evaluate(variables).RealValue;
}
catch (Exception)
{
result = 0;
}
return(result);
}
public static void ParseFormula()
{
var _app = ExcelDnaUtil.Application;
app = (Excel.Application)_app;
ws = (Excel.Worksheet)app.ActiveSheet;
Excel.Range rng = (Excel.Range)app.ActiveCell;
Debug.Print(rng.Formula.ToString());
var parser = GetParser(rng);
var root = parser.Root;
var newFormula = GetFormulaForFunc(root, true, true, -1);
Debug.Print("processed formula: " + newFormula);
MessageBox.Show(newFormula);
var newParser = new XLParser.FormulaAnalyzer(newFormula);
var noSumVersion = GetFormulaWithoutSum(newParser.Root);
Debug.Print("no sum version: " + noSumVersion);
useSympyToCleanUpFormula(noSumVersion);
//take that formula and process as math
var exp = Infix.ParseOrThrow(noSumVersion);
Debug.Print("mathdotnet verison: " + Infix.Format(exp));
Debug.Print("expanded verison: " + Infix.Format(Algebraic.Expand(exp)));
Debug.Print("variables: " + string.Join(",", Structure.CollectIdentifierSymbols(exp).Select(c => c.Item)));
//GenerateFullTreeWithReferences(root);
}
public static void initFunctions(string a, string b, string f1In, string f2In)
{
try
{
x0 = double.Parse(a);
y0 = double.Parse(b);
x = Expr.Symbol("x");
y = Expr.Symbol("y");
//Functions should be declared before compilation
var parsedF1 = Infix.ParseOrThrow(f1In);
var parsedF2 = Infix.ParseOrThrow(f2In);
f1 = parsedF1;
f2 = parsedF2;
}
catch (Exception ex)
{
Console.ForegroundColor = ConsoleColor.Red;
Console.Error.WriteLine(ex.Message);
Console.ReadKey();
Environment.Exit(-1);
}
//But can be given from input
}
internal SolveChallenge(int answerCount = 4, int minNum = STD_MIN_NUM, int maxNum = STD_MAX_NUM, bool dummy = false)
{
QuestionNodeHeight = 340f;
NodeHeight = 320f;
CreateAnswerArrays(answerCount);
if (dummy)
{
return;
}
// prepare the RNG
var rng = new Random();
// choose the variables
string[] signs = new string[3];
string[] variables = new string[3];
for (int i = 0; i < variables.Length; i++)
{
if (rng.NextBoolean())
{
// choose a letter
switch (rng.Next(9))
{
case 0: variables[i] = "a"; break;
case 1: variables[i] = "b"; break;
case 2: variables[i] = "c"; break;
case 3: variables[i] = "y"; break;
case 4: variables[i] = "t"; break;
case 5: variables[i] = "k"; break;
case 6: variables[i] = "i"; break;
case 7: variables[i] = "s"; break;
case 8: variables[i] = "p"; break;
case 9: variables[i] = "r"; break;
}
}
else
{
// choose a number
if (rng.NextBoolean())
{
variables[i] = rng.Next(minNum, maxNum).ToString();
}
else
{
variables[i] = 1.ToString();
}
}
if (rng.Next(4) == 0)
{
signs[i] = "-";
}
else
{
signs[i] = "";
}
}
// create the challenge
const string LA_MUL = @"\cdot";
var challengeType = rng.Next(5);
string side1Infix = "";
string side1LaTeX = "";
string side2Infix = "";
string side2LaTeX = "";
bool NegStr(string str)
{
return(str.StartsWith("-"));
}
string SignedVar(int i)
{
return(signs[i] + variables[i]);
}
string MulFromLeft(int i)
{
return(variables[i].Equals("1") ? signs[i] : SignedVar(i) + " " + LA_MUL + " ");
}
string MulStrFromLeft(string str)
{
return(str.Equals("1") ? "" : (str.Equals("-1") ? "-" : str + " " + LA_MUL + " "));
}
string AddFromRight(string str)
{
return((NegStr(str) ? "" : " + ") + str);
}
string SubFromRight(string str)
{
return(NegStr(str) ? " + " + str.Substring(1) : str);
}
switch (challengeType)
{
case 0:
{
side1Infix = SignedVar(0);
side1LaTeX = SignedVar(0);
side2Infix = "x * " + SignedVar(1) + " + x * " + SignedVar(2);
side2LaTeX = MulFromLeft(1) + "x" + AddFromRight(MulFromLeft(2) + "x");
}
break;
case 1:
{
side1Infix = SignedVar(0) + " * x";
side1LaTeX = MulFromLeft(0) + "x";
side2Infix = SignedVar(1) + " + " + SignedVar(2) + " * x";
side2LaTeX = SignedVar(1) + AddFromRight(MulFromLeft(2) + "x");
}
break;
case 2:
{
side1Infix = "(" + SignedVar(0) + " + " + SignedVar(1) + ") / x";
side1LaTeX = @"\frac{" + SignedVar(0) + AddFromRight(SignedVar(1)) + "}{ x }";
side2Infix = SignedVar(2);
side2LaTeX = SignedVar(2);
}
break;
case 3:
{
side1Infix = SignedVar(0) + " + " + SignedVar(1);
side1LaTeX = SignedVar(0) + AddFromRight(SignedVar(1));
side2Infix = "x / " + SignedVar(2);
side2LaTeX = @"\frac{ x }{" + SignedVar(2) + "}";
}
break;
case 4:
{
side1Infix = SignedVar(0) + " / " + SignedVar(1);
side1LaTeX = @"\frac{" + SignedVar(0) + "}{" + SignedVar(1) + "}";
side2Infix = SignedVar(2) + " / x";
side2LaTeX = @"\frac{" + SignedVar(2) + "}{ x }";
}
break;
}
// shuffle the sides
if (rng.NextBoolean())
{
ChallengeInfix = side1Infix + " = " + side2Infix;
ChallengeLaTeX = side1LaTeX + " = " + side2LaTeX;
}
else
{
ChallengeInfix = side2Infix + " = " + side1Infix;
ChallengeLaTeX = side2LaTeX + " = " + side1LaTeX;
}
// create the solution
switch (challengeType)
{
case 0:
{
SolutionInfix = SignedVar(0) + " / (" + SignedVar(1) + " + " + SignedVar(2) + ")";
// the following SolutionLaTeX-commands are commented out, because it's simply better (more beautiful/ easier to read) to use Latex.Format
//SolutionLaTeX = @"x = \frac{" + SignedVar(0) + "}{" + SignedVar(1) + AddFromRight(SignedVar(2)) + "}";
}
break;
case 1:
{
SolutionInfix = SignedVar(1) + " / (" + SignedVar(0) + " - " + SignedVar(2) + ")";
//SolutionLaTeX = @"x = \frac{" + SignedVar(1) + "}{" + SignedVar(0) + SubFromRight(SignedVar(2)) + "}";
}
break;
case 2:
{
SolutionInfix = "(" + SignedVar(0) + " + " + SignedVar(1) + ") / " + SignedVar(2);
//SolutionLaTeX = @"x = \frac{" + SignedVar(0) + AddFromRight(SignedVar(1)) + "}{" + SignedVar(2) + "}";
}
break;
case 3:
{
SolutionInfix = "(" + SignedVar(0) + " + " + SignedVar(1) + ") * " + SignedVar(2);
//SolutionLaTeX = "x = " + MulStrFromLeft("(" + SignedVar(0) + AddFromRight(SignedVar(1)) + ")") + SignedVar(2);
}
break;
case 4:
{
SolutionInfix = "(" + SignedVar(2) + " * " + SignedVar(1) + ") / " + SignedVar(0);
//SolutionLaTeX = @"x = \frac{" + MulFromLeft(2) + SignedVar(1) + "}{" + SignedVar(0) + "}";
}
break;
}
SolutionLaTeX = "x = " + LaTeX.Format(Infix.ParseOrThrow(SolutionInfix));
// map it to a random answer
int solutionIndex = rng.Next(answerCount);
AnswersInfix[solutionIndex] = SolutionInfix;
AnswersLaTeX[solutionIndex] = SolutionLaTeX;
// generate the false answers
for (int i = 0; i < answerCount; i++)
{
// don't overwrite the solution
if (i == solutionIndex)
{
continue;
}
// choose a random algorithm to create the next answer
bool[] alreadyTried = new bool[7];
string infix = Infix.ParseOrThrow(SolutionInfix).Equals(0) ? "1" : "0";
int method = -1;
bool ok = false;
for (int tries = 0; tries < 30 && !ok; tries++)
{
var whileTries = 0;
switch (challengeType)
{
case 0:
{
do
{
whileTries++;
if (method != -1)
{
alreadyTried[method] = true;
}
method = rng.Next(7);
switch (method)
{
case 0:
{
infix = "(" + SignedVar(0) + " - " + SignedVar(2) + ") / " + SignedVar(1);
}
break;
case 1:
{
infix = SignedVar(0) + " - " + SignedVar(1) + " - " + SignedVar(2);
}
break;
case 2:
{
infix = SignedVar(0) + " - (" + SignedVar(1) + " + " + SignedVar(2) + ")";
}
break;
case 3:
{
infix = SignedVar(0) + " / (" + SignedVar(1) + " * " + SignedVar(2) + ")";
}
break;
case 4:
{
infix = SignedVar(1) + " + " + SignedVar(2);
}
break;
case 5:
{
infix = SignedVar(1) + " / (" + SignedVar(0) + " + " + SignedVar(2) + ")";
}
break;
case 6:
{
infix = SignedVar(2) + " / (" + SignedVar(0) + " + " + SignedVar(1) + ")";
}
break;
}
}while (alreadyTried[method] && whileTries < 14);
}
break;
case 1:
{
do
{
whileTries++;
if (method != -1)
{
alreadyTried[method] = true;
}
method = rng.Next(6);
switch (method)
{
case 0:
{
infix = SignedVar(1) + " / (" + SignedVar(2) + " - " + SignedVar(0) + ")";
}
break;
case 1:
{
infix = SignedVar(0) + " / (" + SignedVar(1) + " + " + SignedVar(2) + ")";
}
break;
case 2:
{
infix = "(" + SignedVar(0) + " + " + SignedVar(1) + ") / " + SignedVar(2);
}
break;
case 3:
{
infix = "(" + SignedVar(2) + " * " + SignedVar(1) + ") /" + SignedVar(0);
}
break;
case 4:
{
infix = "(" + SignedVar(0) + " + " + SignedVar(1) + ") *" + SignedVar(2);
}
break;
case 5:
{
infix = "(" + SignedVar(0) + " + " + SignedVar(2) + ") /" + SignedVar(1);
}
break;
}
}while (alreadyTried[method] && whileTries < 14);
}
break;
case 2:
{
do
{
whileTries++;
if (method != -1)
{
alreadyTried[method] = true;
}
method = rng.Next(6);
switch (method)
{
case 0:
{
infix = SignedVar(0) + " / (" + SignedVar(1) + " + " + SignedVar(2) + ")";
}
break;
case 1:
{
infix = SignedVar(1) + " / (" + SignedVar(0) + " - " + SignedVar(2) + ")";
}
break;
case 2:
{
infix = "1 / (" + SignedVar(2) + " - " + SignedVar(0) + " - " + SignedVar(1) + ")";
}
break;
case 3:
{
infix = "(" + SignedVar(0) + " + " + SignedVar(2) + ") /" + SignedVar(1);
}
break;
case 4:
{
infix = "(" + SignedVar(1) + " + " + SignedVar(2) + ") /" + SignedVar(0);
}
break;
case 5:
{
infix = "(" + SignedVar(1) + " - " + SignedVar(0) + ") /" + SignedVar(2);
}
break;
}
}while (alreadyTried[method] && whileTries < 14);
}
break;
case 3:
{
do
{
whileTries++;
if (method != -1)
{
alreadyTried[method] = true;
}
method = rng.Next(6);
switch (method)
{
case 0:
{
infix = "(" + SignedVar(0) + " + " + SignedVar(1) + ") /" + SignedVar(2);
}
break;
case 1:
{
infix = SignedVar(0) + " / (" + SignedVar(1) + " + " + SignedVar(2) + ")";
}
break;
case 2:
{
infix = SignedVar(1) + " / (" + SignedVar(0) + " - " + SignedVar(2) + ")";
}
break;
case 3:
{
infix = "(" + SignedVar(0) + " + " + SignedVar(2) + ") *" + SignedVar(1);
}
break;
case 4:
{
infix = "(" + SignedVar(1) + " + " + SignedVar(2) + ") *" + SignedVar(0);
}
break;
case 5:
{
infix = "(" + SignedVar(2) + " - " + SignedVar(1) + ") *" + SignedVar(0);
}
break;
}
}while (alreadyTried[method] && whileTries < 14);
}
break;
case 4:
{
do
{
whileTries++;
if (method != -1)
{
alreadyTried[method] = true;
}
method = rng.Next(6);
switch (method)
{
case 0:
{
infix = SignedVar(0) + " / (" + SignedVar(1) + " + " + SignedVar(2) + ")";
}
break;
case 1:
{
infix = SignedVar(1) + " / (" + SignedVar(0) + " - " + SignedVar(2) + ")";
}
break;
case 2:
{
infix = "(" + SignedVar(0) + " * " + SignedVar(1) + ") /" + SignedVar(2);
}
break;
case 3:
{
infix = "(" + SignedVar(0) + " * " + SignedVar(2) + ") /" + SignedVar(1);
}
break;
case 4:
{
infix = SignedVar(2) + " / (" + SignedVar(0) + " * " + SignedVar(1) + ")";
}
break;
case 5:
{
infix = SignedVar(0) + " / (" + SignedVar(2) + " * " + SignedVar(1) + ")";
}
break;
}
}while (alreadyTried[method] && whileTries < 14);
}
break;
}
// check if the answer is ok
ok = true;
// check if the answer is identical to another
foreach (string answer in AnswersInfix)
{
// if it is, begin anew
if (answer != null && answer.Equals(infix))
{
ok = false;
}
}
// check if the answer is actually a solution
if (IsSolution(infix))
{
ok = false;
tries--;
}
}
AnswersInfix[i] = infix;
AnswersLaTeX[i] = "x = " + LaTeX.Format(Infix.ParseOrThrow(AnswersInfix[i]));
}
}
private void Algorithm()
{
_main.Header();
var result = "U(";
var p_values = "";
var xi = "";
for (int i = 1; i <= _main.CountParams; i++)
{
if (i == _main.CountParams)
{
xi += "x_" + i;
_alpha_ln_xi += _main.ConvertCommaToDot(_alpha[i - 1].ToString()) + "*\\ln(x_" + i + ")";
}
else
{
xi += "x_" + i + ",";
_alpha_ln_xi += _main.ConvertCommaToDot(_alpha[i - 1].ToString()) + "*\\ln(x_" + i + ") + ";
}
p_values += "p_" + i + " = " + _main.ConvertCommaToDot(_main.PValuesParams[i - 1]);
_pi += "p_" + i;
if (i < _main.CountParams)
{
_pi += "," + _main.SetText(" ");
p_values += ",";
}
}
_main.ResultCollection.Add(_main.RedLine);
_main.ResultCollection.Add(new Result() { ItemResult = _main.RenderFormula(result + xi + ")=" + _alpha_ln_xi), Align = HorizontalAlignment.Center });
_main.ResultCollection.Add(new Result() { ItemResult = _main.RenderFormula(p_values), Align = HorizontalAlignment.Center });
_main.ResultCollection.Add(new Result() { ItemResult = _main.RenderFormula(_main.SetText("Решение:", true)) });
_main.ResultCollection.Add(new Result() { ItemResult = _main.RenderFormula(_main.SetText("1. Решим задачу оптимального поведения потребителя, если цены благ соответственно равны ", true)) });
_main.ResultCollection.Add(new Result() { ItemResult = _main.RenderFormula(p_values + _main.SetText(" и доход равен ") + "M = " + _main.MParam + ".") });
_main.ResultCollection.Add(new Result() { ItemResult = _main.RenderFormula(_main.SetText("Найдем функции спроса потребителя:", true)) });
for (int i = 1; i <= _main.CountParams; i++)
{
_main.ResultCollection.Add(new Result() { ItemResult = _main.RenderFormula("x_" + i + " = f_" + i + "(" + _pi + ",M);"), Align = HorizontalAlignment.Center });
}
result = _main.SetText("где ");
var blag = "";
for (int i = 1; i <= _main.CountParams; i++)
{
_xi += "x_" + i;
blag += i + "-го";
if (i < _main.CountParams)
{
_xi += ", ";
}
if (i < _main.CountParams - 1)
{
blag += ", ";
}
else if (i == _main.CountParams - 1)
{
blag += " и ";
}
}
_main.ResultCollection.Add(new Result() { ItemResult = _main.RenderFormula(result + _xi + _main.SetText(" - количество приобретаемого блага " + blag + " вида.")) });
_main.ResultCollection.Add(new Result() { ItemResult = _main.RenderFormula(_main.SetText("Для этого решим следующую задачу оптимального поведения потребителя.", true)) });
_main.ResultCollection.Add(new Result() { ItemResult = _main.RenderFormula(_main.SetText("Математическая модель задачи имеет вид:")) });
_main.ResultCollection.Add(new Result() { ItemResult = _main.RenderFormula(@"\alpha_j > 0, x_j > 0, j = \overline{1, " + _main.CountParams +"}" + _main.SetText(" (1)")), Align = HorizontalAlignment.Center });
for (int i = 1; i <= _main.CountParams; i++)
{
_pi_xi += "x_" + i + "*p_" + i;
_minus_pi_xi += "- x_" + i + "*p_" + i;
if (i < _main.CountParams)
{
_pi_xi += " + ";
_minus_pi_xi += " ";
}
}
_main.ResultCollection.Add(new Result() { ItemResult = _main.RenderFormula(_pi_xi + " = M" + _main.SetText(" (2)")), Align = HorizontalAlignment.Center });
_main.ResultCollection.Add(new Result() { ItemResult = _main.RenderFormula("U = " + _alpha_ln_xi + " \\rightarrow max" + _main.SetText(" (3)")), Align = HorizontalAlignment.Center });
_main.ResultCollection.Add(new Result() { ItemResult = _main.RenderFormula(_main.SetText("Левая часть условия (2) – стоимость приобретаемых благ, а условие (3) означает, что полезность этих", true)) });
_main.ResultCollection.Add(new Result() { ItemResult = _main.RenderFormula(_main.SetText("благ должна быть максимальной.")) });
_main.ResultCollection.Add(new Result() { ItemResult = _main.RenderFormula(_main.SetText("Решим задачу методом множителей Лагранжа. Функция Лагранжа:", true)) });
result = "L(" + _xi + ",\\lambda) = U(" + _xi + ") + \\lambda(M " + _minus_pi_xi + ").";
_main.ResultCollection.Add(new Result() { ItemResult = _main.RenderFormula(_main.SetText("", true) + result) });
result = "L(" + _xi + ",\\lambda) = " + _alpha_ln_xi + " + \\lambda(M " + _minus_pi_xi + ").";
_L = _alpha_ln_xi + "+" + _lambda + "*(" + _M + _minus_pi_xi + ")";
_main.ResultCollection.Add(new Result() { ItemResult = _main.RenderFormula(_main.SetText("", true) + result) });
_main.ResultCollection.Add(new Result() { ItemResult = _main.RenderFormula(_main.SetText("Найдем частные производные функции Лагранжа и приравняем их к нулю:", true)) });
for (int i = 0; i < _main.CountParams; i++)
{
_lst.Add(_main.Diff(_L.Replace("\\", ""), _variables[i]));
_main.ResultCollection.Add(new Result() { ItemResult = _main.RenderFormula(_main.SetText("", true) + @"\frac{\partial L}{\partial x_" + (i + 1) + "} = " + (_lst[i] as Expr).ToLaTeX().Replace(_lambda, @"\lambda") + " = 0") });
}
_main.ResultCollection.Add(new Result() { ItemResult = _main.RenderFormula(_main.SetText("", true) + @"\frac{\partial L}{\partial \lambda } = " + _M + _minus_pi_xi + " = 0") });
_main.ResultCollection.Add(_main.RedLine);
for (int i = 0; i < _lst.Count; i++)
{
_main.ResultCollection.Add(new Result() { ItemResult = _main.RenderFormula(_main.SetText("", true) + (_lst[i] as Expr).Substitute(Expr.Parse("p_" + (i + 1)), Expr.Parse("0")).ToLaTeX() + " = " + @"\lambda*p_" + (i + 1)) });
}
_main.ResultCollection.Add(_main.RedLine);
for (int i = 0; i < _lst.Count; i++)
{
var root = _main.FindRoot(ExprLast.Symbol("x_" + (i + 1)), Infix.ParseOrThrow((_lst[i] as Expr).ToString()));
_lst.RemoveAt(i);
_lst.Insert(i, root);
_main.ResultCollection.Add(new Result() { ItemResult = _main.RenderFormula(_main.SetText("", true) + "x_" + (i + 1) + " = " + (_lst[i] as Expr).ToLaTeX().Replace(_lambda, @"\" + _lambda)) });
}
_main.ResultCollection.Add(_main.RedLine);
_main.ResultCollection.Add(new Result() { ItemResult = _main.RenderFormula(_main.SetText("", true) + _pi_xi + " = " + _M + _main.SetText(" (4)")) });
_main.ResultCollection.Add(new Result() { ItemResult = _main.RenderFormula(_main.SetText("Подставим найденные значения ", true) + _xi + _main.SetText(" в (4) и выразим ") + @"\" + _lambda) });
result = _pi_xi;
for (int i = 0; i < _lst.Count; i++)
{
var expr = Expr.Parse(result).Substitute(Expr.Parse("x_" + (i + 1)), _lst[i] as Expr);
result = _main.ConvertExprLastToExpr(Rational.Simplify(ExprLast.Symbol("x_" + (i + 1)), _main.ConvertExprToExprLast(expr))).ToString();
}
_main.ResultCollection.Add(new Result() { ItemResult = _main.RenderFormula(_main.SetText("", true) + Expr.Parse(result).ToLaTeX().Replace(_lambda, @"\" + _lambda) + " = " + _M) });
result += "-" + _M;
var lam_star = _main.FindRoot(ExprLast.Symbol(_lambda), Infix.ParseOrThrow(result));
_main.ResultCollection.Add(new Result() { ItemResult = _main.RenderFormula(_main.SetText("", true) + @"\lambda^* = " + lam_star.ToLaTeX() + " = " + lam_star.Substitute("M", _main.MParam).ToLaTeX()) });
_main.ResultCollection.Add(new Result() { ItemResult = _main.RenderFormula(_main.SetText("", true) + _main.SetText(@"Найдем оптимальный набор благ потребителя.")) });
result = @"X^* = (";
for (int i = 0; i < _main.CountParams; i++)
{
result += "x_" + (i + 1) + "^*";
if (i < _main.CountParams - 1)
{
result += ",";
}
}
_main.ResultCollection.Add(new Result() { ItemResult = _main.RenderFormula(_main.SetText("", true) + result + ")" + _main.SetText(@" при заданных ценах на блага и доходе:")) });
_main.ResultCollection.Add(_main.RedLine);
for (int i = 0; i < _main.CountParams; i++)
{
var res = (_lst[i] as Expr).Substitute(Expr.Parse(_lambda), lam_star);
_main.ResultCollection.Add(new Result() { ItemResult = _main.RenderFormula(_main.SetText("", true) + "x_" + (i + 1) + "^* = " + res.ToLaTeX()) });
_lst[i] = res;
}
_main.ResultCollection.Add(_main.RedLine);
_main.ResultCollection.Add(new Result() { ItemResult = _main.RenderFormula(_main.SetText("", true) + p_values + ", M = " + _main.ConvertCommaToDot(_main.MParam)) });
_main.ResultCollection.Add(_main.RedLine);
for (int i = 0; i < _main.CountParams; i++)
{
var res = (_lst[i] as Expr).Substitute(Expr.Parse(_M), Expr.Parse(_main.ConvertCommaToDot(_main.MParam))).Substitute(Expr.Parse("p_" + (i + 1)), Expr.Parse(_main.ConvertCommaToDot(_main.PValuesParams[i])));
_main.ResultCollection.Add(new Result() { ItemResult = _main.RenderFormula(_main.SetText("", true) + "x_" + (i + 1) + "^* = " + res.ToLaTeX()) });
_x_star[i] = double.Parse(_main.ConvertDotToComma(res.RealNumberValue.ToString()));
}
result = @"X^* = (";
for (int i = 0; i < _main.CountParams; i++)
{
result += "x_" + (i + 1) + "^*";
if (i < _main.CountParams - 1)
{
result += ",";
}
}
_main.ResultCollection.Add(new Result() { ItemResult = _main.RenderFormula(_main.SetText("Проверим, выполняется ли для найденного оптимального решения ", true) + result + _main.SetText(") бюджетное ограничение:")) });
_main.ResultCollection.Add(new Result() { ItemResult = _main.RenderFormula(_pi_xi + " = M"), Align = HorizontalAlignment.Center });
result = "";
for (int i = 0; i < _main.CountParams; i++)
{
result += _main.ConvertCommaToDot(_main.PValuesParams[i]) + "*" + _main.ConvertCommaToDot(_x_star[i]);
if (i < _main.CountParams - 1)
{
result += "+";
}
}
_main.ResultCollection.Add(_main.RedLine);
_main.ResultCollection.Add(new Result() { ItemResult = _main.RenderFormula(result + " = " + _main.ConvertCommaToDot(_main.MParam)), Align = HorizontalAlignment.Center });
_main.ResultCollection.Add(_main.RedLine);
_main.ResultCollection.Add(new Result() { ItemResult = _main.RenderFormula(Expr.Parse(result).ToLaTeX() + " = " + _main.ConvertCommaToDot(_main.MParam)), Align = HorizontalAlignment.Center });
result = @"\overline{ X}^ * = (" + _x_star.Aggregate("", (b, n) => b + (!string.IsNullOrEmpty(b) ? ";" : "") + Math.Truncate(n).ToString()) + ")";
_main.ResultCollection.Add(new Result() { ItemResult = _main.RenderFormula(_main.SetText("Если речь идет о неделимых благах, то оптимальный выбор потребителя составит ", true) + result + ",") });
result = _main.SetText(" т.е. ему необходимо приобрести ");
for (int i = 0; i < _main.CountParams; i++)
{
result += (i + 1) + _main.SetText("-го блага - ") + _main.ConvertCommaToDot(Math.Truncate(_x_star[i]));
if (i < _main.CountParams - 2)
{
result += ", ";
}
if (i < _main.CountParams - 1)
{
result += _main.SetText(" и ");
}
}
_main.ResultCollection.Add(new Result() { ItemResult = _main.RenderFormula(result + ".") });
_main.ResultCollection.Add(new Result() { ItemResult = _main.RenderFormula(_main.SetText("Но т.к. мы условились, что речь будет идти о делимых благах, то оптимальный выбор потребителя будет:", true)) });
result = @"\overline{ X}^ * = (" + _x_star.Aggregate("", (b, n) => b + (!string.IsNullOrEmpty(b) ? ";" : "") + _main.ConvertCommaToDot(n.ToString())) + ")";
_main.ResultCollection.Add(new Result() { ItemResult = _main.RenderFormula(_main.SetText("", true) + result + _main.SetText(", т.е. следует приобрести: ")) });
for (int i = 0; i < _main.CountParams; i++)
{
result = _main.SetText("блага ", true) + (i + 1) + _main.SetText("-го вида - ") + _main.ConvertCommaToDot(_x_star[i]);
if (i < _main.CountParams - 1)
{
result += ", ";
}
if (i == _main.CountParams - 1)
{
result += ".";
}
_main.ResultCollection.Add(new Result() { ItemResult = _main.RenderFormula(result) });
}
_main.ResultCollection.Add(_main.RedLine);
_main.ResultCollection.Add(new Result() { ItemResult = _main.RenderFormula(_main.SetText("Решение 2:", true)) });
_main.ResultCollection.Add(new Result() { ItemResult = _main.RenderFormula(_main.SetText("Функции спроса потребителя найдены в пункте 1.", true)) });
_main.ResultCollection.Add(new Result() { ItemResult = _main.RenderFormula(_main.SetText("Вычислим реакции потребителя при изменении дохода М и цен ", true) + _pi + _main.SetText(" в точке оптимума ") + @"\overline{ X}^ *.") });
_main.ResultCollection.Add(new Result() { ItemResult = _main.RenderFormula(_main.SetText("Реакции потребителя при изменении дохода М:", true)) });
var minBlag = -1.0;
var maxBlag = -1.0;
var indMinBlag = -1;
var indMaxBlag = -1;
for (int i = 0; i < _main.CountParams; i++)
{
var res = _main.Diff((_lst[i] as Expr).ToString(), "M");
var p = Expr.Parse(_main.ConvertCommaToDot(_main.PValuesParams[i].ToString()));
var val = double.Parse(_main.ConvertDotToComma(res.Substitute(Expr.Parse("p_" + (i + 1)), p).RealNumberValue.ToString()));
if (i == 0)
{
minBlag = maxBlag = val;
indMinBlag = indMaxBlag = i;
}
if (val < minBlag)
{
minBlag = val;
indMinBlag = i;
}
if (val > maxBlag)
{
maxBlag = val;
indMaxBlag = i;
}
_main.ResultCollection.Add(new Result() { ItemResult = _main.RenderFormula(_main.SetText("", true) + @"\frac{\partial x_" + (i + 1) + @"}{\partial M } = " + res.ToLaTeX() + @"\approx" + _main.ConvertCommaToDot(val.ToString())) });
if (i == 0)
{
_main.ResultCollection.Add(_main.RedLine);
_main.ResultCollection.Add(new Result() { ItemResult = _main.RenderFormula(_main.SetText("Поскольку при увеличении дохода спрос на 1-благо возрастает, то это благо ценное.", true)) });
_main.ResultCollection.Add(_main.RedLine);
}
}
if (_main.CountParams == 2)
{
_main.ResultCollection.Add(new Result() { ItemResult = _main.RenderFormula(_main.SetText("Оставшееся благо также является ценным для потребителя. При этом наиболее ценным является " + (indMaxBlag + 1) + "-е благо, а наименее ценным – " + (indMinBlag + 1) + "-е.", true)) });
}
else
{
_main.ResultCollection.Add(new Result() { ItemResult = _main.RenderFormula(_main.SetText("Остальные блага также являются ценными для потребителя. При этом наиболее ценным является " + (indMaxBlag + 1) + "-е благо, а наименее ценным – " + (indMinBlag + 1) + "-е.", true)) });
}
for (int i = 0; i < _main.CountParams; i++)
{
_main.ResultCollection.Add(_main.RedLine);
_main.ResultCollection.Add(new Result() { ItemResult = _main.RenderFormula(_main.SetText("Определим реакции потребителя при изменении цены на " + (i + 1) + "-е благо:", true)) });
for (int j = 0; j < _main.CountParams; j++)
{
_main.ResultCollection.Add(_main.RedLine);
var res = _main.Diff((_lst[i] as Expr).ToString(), "p_" + (i + 1));
var m = Expr.Parse(_main.ConvertCommaToDot(_main.MParam.ToString()));
var p = Expr.Parse(_main.ConvertCommaToDot(_main.PValuesParams[j].ToString()));
var val = double.Parse(_main.ConvertDotToComma(res.Substitute(Expr.Parse("M"), m).Substitute(Expr.Parse("p_" + (i + 1)), p).RealNumberValue.ToString()));
_main.ResultCollection.Add(new Result() { ItemResult = _main.RenderFormula(_main.SetText("", true) + @"\frac{\partial x_" + (j + 1) + @"}{\partial p_" + (i + 1) + " } = " + res.ToLaTeX() + (val == 0 ? "=" : @"\approx") + _main.ConvertCommaToDot(val.ToString()) + (val != 0 ? " (" + (val >= 0 ? ">" : "<") + "0)" : "")) });
if (i == j && val < 0)
{
_main.ResultCollection.Add(new Result() { ItemResult = _main.RenderFormula(_main.SetText("С увеличением цены на " + (i + 1) + "-е благо спрос на него уменьшается, значит, "+ (j+1)+"-е благо нормальное.", true)) });
}
else if (i == j && val > 0)
{
_main.ResultCollection.Add(new Result() { ItemResult = _main.RenderFormula(_main.SetText("С увеличением цены на " + (i + 1) + "-е благо спрос на него уменьшается, значит, " + (j + 1) + "-е благо ненормальное.", true)) });
}
else if (val < 0)
{
_main.ResultCollection.Add(new Result() { ItemResult = _main.RenderFormula(_main.SetText("С увеличением цены на " + (i + 1) + "-е благо спрос на " + (j + 1) + "-е благо увеличивается, эти блага взаимодополняемые.", true)) });
}
else if (val > 0)
{
_main.ResultCollection.Add(new Result() { ItemResult = _main.RenderFormula(_main.SetText("С увеличением цены на " + (i + 1) + "-е благо спрос на " + (j + 1) + "-е благо увеличивается, эти блага взаимозаменяемые.", true)) });
}
}
}
result = @"\overline{ X}^ * = (";
for (int i = 0; i < _main.CountParams; i++)
{
result += "x_" + (i + 1) + "^*";
if (i < _main.CountParams - 1)
{
result += ",";
}
}
_main.ResultCollection.Add(_main.RedLine);
_main.ResultCollection.Add(new Result() { ItemResult = _main.RenderFormula(_main.SetText("Решение3:", true)) });
_main.ResultCollection.Add(new Result()
{
ItemResult = _main.RenderFormula(_main.SetText("Вычислим предельные полезности благ в точке экстремума ", true) + result + ")" +
_main.SetText(". Это значения частных производных "))
});
_main.ResultCollection.Add(new Result() { ItemResult = _main.RenderFormula(_main.SetText("функции полезности ") + "U = (" + _xi + ")" + _main.SetText(" по соответствующим аргументам в точке ") + @"\overline{ X}^*.") });
_main.ResultCollection.Add(_main.RedLine);
_main.ResultCollection.Add(new Result() { ItemResult = _main.RenderFormula(@"\overline{ X}^ * = (" + _x_star.Aggregate("", (b, n) => b + (!string.IsNullOrEmpty(b) ? ";" : "") + _main.ConvertCommaToDot(n.ToString())) + ")") });
var dU_x_star = new double[_main.CountParams];
for (int i = 0; i < _main.CountParams; i++)
{
_main.ResultCollection.Add(_main.RedLine);
var res = _main.Diff(_alpha_ln_xi.Replace("\\", ""), "x_" + (i + 1));
var x = Expr.Parse(_main.ConvertCommaToDot(_x_star[i].ToString()));
var val = double.Parse(_main.ConvertDotToComma(res.Substitute(Expr.Parse("x_" + (i + 1)), x).RealNumberValue.ToString()));
dU_x_star[i] = val;
_main.ResultCollection.Add(new Result()
{
ItemResult = _main.RenderFormula(_main.SetText("", true) + @"\frac{\partial U}{\partial x_" + (i + 1) + " } = " + res.ToLaTeX() + _main.SetText("; ") +
@"\frac{\partial U}{\partial x_" + (i + 1) + " }(\\overline{ X})^* = " + res.ToLaTeX() + _main.SetText(" = ") + _main.ConvertCommaToDot(val.ToString()))
});
}
_main.ResultCollection.Add(_main.RedLine);
for (int i = 0; i < _main.CountParams; i++)
{
_main.ResultCollection.Add(new Result() { ItemResult = _main.RenderFormula(_main.SetText("На 1 дополнительную единицу " + (i + 1) + "-го блага приходится ", true) + dU_x_star[i] + _main.SetText(" единиц дополнительной полезности.")) });
}
_main.ResultCollection.Add(_main.RedLine);
_main.ResultCollection.Add(new Result() { ItemResult = _main.RenderFormula(_main.SetText("Решение4:", true)) });
_main.ResultCollection.Add(new Result() { ItemResult = _main.RenderFormula(_main.SetText("Вычислим нормы замещения благ в точке оптимума ", true) + "\\overline{X}^*.") });
for (int i = 0; i < _main.CountParams; i++)
{
for (int j = 0; j < _main.CountParams; j++)
{
if (i == j)
continue;
var dudx = dU_x_star[i] / dU_x_star[j];
_main.ResultCollection.Add(_main.RedLine);
_main.ResultCollection.Add(new Result() { ItemResult = _main.RenderFormula(_main.SetText("Норма замены " + (i + 1) + "-го блага " + (j + 1) + "-м:", true)) });
_main.ResultCollection.Add(new Result() { ItemResult = _main.RenderFormula(_main.SetText("", true) + @"n_{" + (j + 1) + "," + (i + 1) + @"} = -\frac{\partial U}{\partial x_" + (i + 1) + @"} : \frac{\partial U}{\partial x_" + (j + 1) + "} = " + _main.ConvertCommaToDot((-dudx).ToString())) });
_main.ResultCollection.Add(new Result() { ItemResult = _main.RenderFormula(_main.SetText("Для замещения 1 единицы " + (i + 1) + "-го блага необходимо дополнительно приобрести ", true) + _main.ConvertCommaToDot((dudx).ToString())) });
_main.ResultCollection.Add(new Result() { ItemResult = _main.RenderFormula(_main.SetText(" единиц " + (j + 1) + "-го блага, чтобы удовлетворенность осталась на прежнем уровне.")) });
}
}
_main.ResultCollection.Add(_main.RedLine);
_main.ResultCollection.Add(new Result() { ItemResult = _main.RenderFormula(_main.SetText("Решение5:", true)) });
_main.ResultCollection.Add(new Result() { ItemResult = _main.RenderFormula(_main.SetText("Вычислим коэффициенты эластичности по доходу и ценам при заданных ценах и доходе: ", true)) });
_main.ResultCollection.Add(new Result() { ItemResult = _main.RenderFormula(p_values + ", M = " + _main.ConvertCommaToDot(_main.MParam.ToString()) + ".") });
var empSum = 0.0;
for (int i = 0; i < _main.CountParams; i++)
{
_main.ResultCollection.Add(_main.RedLine);
_main.ResultCollection.Add(new Result() { ItemResult = _main.RenderFormula(_main.SetText("Для блага " + (i + 1) + ":", true)) });
var res = _main.Diff((_lst[i] as Expr).ToString(), "M").Divide("x_" + (i + 1) + "/M");
var resReplace = res.Substitute("M", _main.ConvertCommaToDot(_main.MParam.ToString())).Substitute("x_" + (i + 1), _main.ConvertCommaToDot(_x_star[i].ToString())).Substitute("p_" + (i + 1), _main.ConvertCommaToDot(_main.PValuesParams[i].ToString())).ToString();
empSum = double.Parse(_main.ConvertDotToComma(resReplace));
var resRound = Math.Round(empSum);
_main.ResultCollection.Add(new Result() { ItemResult = _main.RenderFormula(_main.SetText("", true) + @"E_" + (i + 1) + @"^M = \frac{\partial x_" + (i + 1) + @"}{\partial M } : " + @"\frac{ x_" + (i + 1) + "}{ M } = " + res.ToLaTeX() + " = " + resRound) });
_main.ResultCollection.Add(new Result() { ItemResult = _main.RenderFormula(_main.SetText("При увеличении дохода на 1 % спрос на " + (i + 1) + "-e благо возрастает на 1 %.", true)) });
_main.ResultCollection.Add(new Result() { ItemResult = _main.RenderFormula(_main.SetText("Коэффициенты эластичности по ценам:", true)) });
result = "E_" + (i + 1) + "^M + ";
for (int j = 0; j < _main.CountParams; j++)
{
result += "E_{ " + (i + 1) + "" + (j + 1) + "}^p";
if (j < _main.CountParams - 1)
{
result += " + ";
}
res = _main.Diff((_lst[i] as Expr).ToString(), "p_" + (j + 1)).Divide("x_" + (i + 1) + "/p_" + (j + 1));
resReplace = res.Substitute("M", _main.ConvertCommaToDot(_main.MParam.ToString())).Substitute("x_" + (i + 1), _main.ConvertCommaToDot(_x_star[i].ToString())).Substitute("p_" + (j + 1), _main.ConvertCommaToDot(_main.PValuesParams[i].ToString())).ToString();
var epi = double.Parse(_main.ConvertDotToComma(resReplace));
empSum += epi;
_main.ResultCollection.Add(new Result() { ItemResult = _main.RenderFormula(_main.SetText("", true) + @"E_{" + (i + 1) + "" + (j + 1) + @"}^p = \frac{\partial x_" + (i + 1) + @"}{\partial p_" + (j + 1) + " } : " + @"\frac{ x_" + (i + 1) + "}{ p_" + (j + 1) + " } = " + resReplace) });
var output = "При росте цены на " + (j + 1) + "-е благо на 1 %";
if (epi != 0)
{
if (epi < 0)
{
output += " спрос на него уменьшается на ";
}
else
{
output += "спрос на него увеличивается на ";
}
_main.ResultCollection.Add(new Result() { ItemResult = _main.RenderFormula(_main.SetText(output, true) + _main.ConvertCommaToDot(Math.Abs(epi).ToString()) + _main.SetText("%.")) });
}
else
{
output += " оно является независимым.";
_main.ResultCollection.Add(new Result() { ItemResult = _main.RenderFormula(_main.SetText(output, true)) });
}
_main.ResultCollection.Add(_main.RedLine);
}
_main.ResultCollection.Add(new Result() { ItemResult = _main.RenderFormula(_main.SetText("Проверка:", true)) });
_main.ResultCollection.Add(new Result() { ItemResult = _main.RenderFormula(_main.SetText("", true) + result + " = " + _main.ConvertCommaToDot(empSum.ToString())) });
}
_main.ResultCollection.Add(_main.RedLine);
_main.ResultCollection.Add(new Result() { ItemResult = _main.RenderFormula(_main.SetText("Все расчеты произведены достаточно точно и правильно.", true)) });
}
/// <summary>
///
/// </summary>
/// <param name="expr"></param>
public ExpressionC(string expr)
{
expressions.Add(this);
infix = Infix.ParseOrThrow(expr);
}
/// <summary>
/// Allows you to change this expression without creating a new one
/// </summary>
/// <param name="infix"></param>
public void SetInfix(string infix)
{
this.infix = Infix.ParseOrThrow(infix);
}