public static Entity ParseExpression(string latexIn)
{
return(MathS.FromString(ConvertToMathString(latexIn)).Simplify());
}
public void Test2() => Assert.IsTrue(Measure(() => MathS.FromString("x + log(2, 4)^2 * sin(cos(sin(cos(5)))) + x^3")) < 10);
public void Test4() => MathS.FromString((MathS.Sin(x) / MathS.Cos(x)).Differentiate(x).Stringize() ?? "");
public void TestMi()
{
Assert.IsTrue(MathS.FromString("-i^2").Eval() == 1);
}
public void TestString(string expr) => Assert.Equal(True, MathS.FromString(expr).EvalBoolean());
public CalcResult Compute()
{
CalcResult res = new CalcResult();
try
{
// INITIALIZATION OF STUFF
Lexer lexer = new Lexer(rawExpression);
TokenList tokenList = lexer.GenerateTokens();
Parser parser = new Parser(tokenList);
PostTokenList postTokenList = parser.Parse();
postTokenList.Freeze();
MathPreprocessor mathPreprocessor = new MathPreprocessor(postTokenList);
mathPreprocessor.Process();
MajorSegmentList majorSegmentList = mathPreprocessor.GetSegments();
List <ExpressionSegment> expressionSegments = new List <ExpressionSegment>();
expressionSegments.Add(
(ExpressionSegment)majorSegmentList.Select("expression").Item()
);
// PROCESSING SOME `WHERE` AND `FOR` TOKENS
for (int i = majorSegmentList.Count - 1; i >= 0; i--)
{
if (majorSegmentList[i] is ExpressionSegment)
{
break;
}
if (majorSegmentList[i] is EqKeyword
&&
(((EqKeyword)majorSegmentList[i]).Type == Keyword.Type.WHERE ||
((EqKeyword)majorSegmentList[i]).Type == Keyword.Type.FOR)
&&
FixedKeyword.IsVariable(((EqKeyword)majorSegmentList[i]).GetBeforeEq())
&&
(CustomData.GetType(((EqKeyword)majorSegmentList[i]).GetAfterEq()) == CustomData.Type.FIXED))
{
string v = ((EqKeyword)majorSegmentList[i]).GetBeforeEq();
string expr = ((EqKeyword)majorSegmentList[i]).GetAfterEq();
expressionSegments[0].Substitute(v, expr);
}
else
{
majorSegmentList[i].Ignored = true;
}
}
MajorSegmentList newExpression = majorSegmentList.CutTill(expressionSegments[0]);
res.InterpretedAs.Add(expressionSegments[0].Build());
List <MajorSegmentList> list = DivideByField(newExpression);
var simplOpt = new MajorSegmentList();
simplOpt.Add(new FieldSegment("simplify", "", Field.Type.SIMPLIFICATION));
list.Insert(0, simplOpt);
// SEQUENTIAL PROCESSING
list.Reverse();
foreach (var fieldOpts in list)
{
bool isLast = fieldOpts == list[list.Count - 1];
// PROCESSING SOME `WHERE` AND `FOR` TOKENS
foreach (var expressionSegment in expressionSegments)
{
for (int i = 1; i < fieldOpts.Count; i++)
{
if (fieldOpts[i] is EqKeyword &&
((fieldOpts[i] as EqKeyword).Type == Keyword.Type.WHERE ||
(fieldOpts[i] as EqKeyword).Type == Keyword.Type.FOR) &&
CustomData.GetType((fieldOpts[i] as EqKeyword).GetAfterEq()) == CustomData.Type.FIXED &&
CustomData.GetType((fieldOpts[i] as EqKeyword).GetBeforeEq()) == CustomData.Type.FIXED &&
FixedKeyword.IsVariable((fieldOpts[i] as EqKeyword).GetBeforeEq()))
{
expressionSegment.Substitute((fieldOpts[i] as EqKeyword).GetBeforeEq(), (fieldOpts[i] as EqKeyword).GetAfterEq());
}
}
res.InterpretedAs.Add(fieldOpts.Build() + " " + expressionSegment.Build());
}
var fieldType = FindField(fieldOpts[0].Keyname);
List <string> newExprs = new List <string>();
List <string> newLatexExprs = new List <string>();
bool quickExit = false;
foreach (var expressionSegment in expressionSegments)
{
if (fieldType == FieldType.BOOL)
{
var vars = expressionSegment.tokens.ExtractVariables();
vars = Functions.MakeUnique(vars);
foreach (var v in vars)
{
if (v.Length > 1)
{
throw new ParsingException("Multi-symbol vars are forbidden in boolean mode");
}
}
var be = new BoolEng(expressionSegment.Build());
string newExpr;
newExpr = be.CompileTable();
string line = "{";
foreach (var onevar in vars)
{
line += ": " + onevar + " %";
}
line += ": F %}\n";
newExpr = line + newExpr;
newExprs.Add(newExpr);
{
newExpr = newExpr.Replace(":", "<th>");
newExpr = newExpr.Replace("%", "</th>");
newExpr = newExpr.Replace("{", "<tr>");
newExpr = newExpr.Replace("}", "</tr>");
newExpr = newExpr.Replace("[", "<td class=\"cellbool-res\">");
newExpr = newExpr.Replace("]", "</td>");
newExpr = newExpr.Replace("\n", "");
newExpr = "<table id=\"bool-res\">" + newExpr + "</table>";
}
newLatexExprs.Add(newExpr);
quickExit = true;
break;
}
else if (AscCalc.MathAnalysis.Contains(fieldType))
{
expressionSegment.tokens.AddOmittedOps();
var vars = expressionSegment.tokens.ExtractVariables();
string diffVar;
vars = Functions.MakeUnique(vars);
if (fieldOpts.Select(Names.FOR).Count == 0)
{
if (vars.Contains("x") || vars.Count == 0)
{
diffVar = "x";
}
else if (vars.Contains("y"))
{
diffVar = "y";
}
else
{
diffVar = vars[0];
}
res.InterpretedAs.Add("Interpreted as `" + Names.FOR + " " + diffVar + "`");
}
else if (fieldOpts.Select(Names.FOR).Count == 1)
{
diffVar = (fieldOpts.Select(Names.FOR).Item() as FixedKeyword).GetVariable();
}
else
{
diffVar = (fieldOpts.Select(Names.FOR)[0] as FixedKeyword).GetVariable();
}
vars.Add(diffVar);
vars = Functions.MakeUnique(vars);
string req = expressionSegment.Build();
if (fieldType == FieldType.DERIVATIVE)
{
newExprs.Add(MathS.FromString(req).Derive(MathS.Var(diffVar)).ToString());
if (isLast && latex)
{
newLatexExprs.Add("$$" + MathS.FromString(req).Derive(MathS.Var(diffVar)).Latexise().ToString() + "$$");
}
}
else if (fieldType == FieldType.SOLVE)
{
expressionSegment.tokens.AddOmittedOps();
if (vars.Count > 1)
{
throw new InvalidRequestException();
}
var roots = MathS.FromString(req).SolveNt(MathS.Var(diffVar), precision: 400);
foreach (var root in roots)
{
newExprs.Add(root.ToString());
}
if (isLast && latex)
{
foreach (var root in roots)
{
newExprs.Add("$$" + root.ToString() + "$$");
}
}
}
}
else if (fieldType == FieldType.SIMPLIFICATION)
{
expressionSegment.tokens.AddOmittedOps();
var vars = expressionSegment.tokens.ExtractVariables();
vars = Functions.MakeUnique(vars);
string req = expressionSegment.Build();
string newExpr;
newExpr = MathS.FromString(req).SimplifyIntelli().ToString();
newExprs.Add(newExpr);
if (isLast && latex)
{
newExpr = MathS.FromString(req).SimplifyIntelli().Latexise();
newLatexExprs.Add("$$" + newExpr + "$$");
}
}
}
if (newExprs.Count == 0)
{
res.Result = "No answer";
break;
}
if (!isLast && !quickExit)
{
expressionSegments = new List <ExpressionSegment>();
foreach (var nexp in newExprs)
{
expressionSegments.Add(new ExpressionSegment("expression", nexp));
}
}
else
{
res.Result = "";
foreach (var segm in newExprs)
{
res.Result += segm + " ";
}
res.LatexResult = "";
foreach (var segm in newLatexExprs)
{
res.LatexResult += segm + " ";
}
break; // For quickExit case
}
}
}
catch (Exception e)
{
throw e;
}
return(res);
}
public void TestDM()
{
Assert.IsTrue(MathS.FromString("1 + -1").Eval() == 0);
}
public void TestSqrt()
{
var expr = MathS.FromString("sqrt(x)");
Assert.IsTrue(expr == MathS.Sqrt(x));
}
public void AssertErrorWhenMultiplyingNumberAccordingToSetting(string expr)
{
using var _ = ExplicitParsingOnly.Set(true);
Assert.Throws <InvalidArgumentParseException>(() => MathS.FromString(expr));
}
public void Test2()
{
const string expr = "2 ^ 3 + sin(3)";
Assert.AreEqual(expr, MathS.FromString(expr).ToString());
}
public void Test4()
{
MathS.FromString((MathS.Sin(x) / MathS.Cos(x)).Derive(x).ToString());
}
public void Test1()
{
const string expr = "1 + 2 * log(2, 3)";
Assert.AreEqual(expr, MathS.FromString(expr).ToString());
}
/// <summary>
/// A dirty way to convert to an AngouriMath string without actually parsing LaTeX.
/// </summary>
/// <remarks>
/// This converter is much more picky than <see cref="ConvertToMathString(string)"/>,
/// but in most cases it will be faster.
/// </remarks>
public static string DirtyConvertToMathString(string latexIn)
{
string output = "";
var matches = Regex.Matches(latexIn.Replace(@"\ ", " "), @"\\?(\{.*\}|[^\\\s])*");
foreach (Match m in matches)
{
string lPart = m.Value;
if (lPart.Length == 0)
{
continue;
}
if (Char.IsDigit(lPart[0]) && Char.IsLetter(lPart.Last()) && lPart.All(c => Char.IsLetterOrDigit(c)))
{
int startOfVar = 1;
while (Char.IsDigit(lPart[startOfVar]))
{
if (startOfVar + 1 < lPart.Length)
{
startOfVar++;
}
}
lPart = lPart.Insert(startOfVar, "*");
}
else if (Char.IsLetter(lPart[0]) && Char.IsDigit(lPart.Last()) && lPart.All(c => Char.IsLetterOrDigit(c)))
{
int startOfNum = 1;
while (Char.IsLetter(lPart[startOfNum]))
{
if (startOfNum + 1 < lPart.Length)
{
startOfNum++;
}
}
lPart = lPart.Insert(startOfNum, "*");
}
else if (!lPart.StartsWith("\\"))
{
// Do nothing, but skip the branches that check for LaTeX commands
}
else if (lPart.StartsWith(@"\,") || lPart.StartsWith(@"\:") || lPart.StartsWith(@"\;") ||
lPart.StartsWith(@"\,") || lPart.StartsWith(@"\ "))
{
// Replace the LaTeX command with a space
lPart = " " + lPart.Remove(0, 2);
}
else if (lPart.StartsWith(@"\quad"))
{
lPart = " " + lPart.Remove(0, @"\quad".Length);
}
else if (lPart.StartsWith(@"\qquad"))
{
lPart = " " + lPart.Remove(0, @"\qquad".Length);
}
else if (lPart.StartsWith(@"\cdot"))
{
lPart = lPart.Replace(@"\cdot", "*");
}
else if (lPart.StartsWith(@"\sin") || lPart.StartsWith(@"\cos") || lPart.StartsWith(@"\tan") ||
lPart.StartsWith(@"\arcsin") || lPart.StartsWith(@"\arccos") || lPart.StartsWith(@"\arctan") ||
lPart.StartsWith(@"\csc") || lPart.StartsWith(@"\sec") || lPart.StartsWith(@"\cot"))
{
lPart = lPart.Remove(0, 1); // Just remove the slash
}
else if (lPart.StartsWith(@"\left"))
{
lPart = lPart.Remove(0, @"\left".Length);
}
else if (lPart.StartsWith(@"\right"))
{
lPart = lPart.Remove(0, @"\right".Length);
}
else if (lPart.StartsWith(@"\over"))
{
lPart = lPart.Replace(@"\over", "/");
}
else if (lPart.StartsWith(@"\frac"))
{
var parameters = ParseParameters(lPart);
// Handle derivatives
if (parameters.Count >= 3 && parameters[0].StartsWith("d") && parameters[1].StartsWith("d"))
{
// Get the variable to derive with respect to
string varName = Regex.Match(parameters[1], @"d(\S)$").Value.Substring(1);
var varWRT = MathS.Var(varName);
// Derive the function with respect to varWRT
var derFunc = MathS.FromString(parameters[2], true).Differentiate(varWRT);
lPart = derFunc.Simplify().ToString();
}
else
{
lPart = $"({parameters[0]})/({parameters[1]})";
}
}
else if (lPart.StartsWith(@"\sqrt"))
{
var parameters = ParseParameters(lPart);
lPart = $"sqrt({parameters[0]})";
}
else if (lPart.StartsWith(@"\int"))
{
// User must put paratheses around the expression to integrate
var parameters = ParseParameters(lPart);
if (parameters.Count == 3)
{
string expression = parameters[2];
// Get the variable to integrate with respect to
string varName = Regex.Match(expression, @"d(\S)$").Value;
if (!String.IsNullOrEmpty(varName))
{
expression = expression.Replace(varName, String.Empty);
varName = varName.Substring(1);
}
else
{
varName = "x";
}
var varWRT = MathS.Var(varName);
// TODO: Support expressions for start and end
// Get start and end of interval
double start = Double.Parse(parameters[0]);
double end = Double.Parse(parameters[1]);
var intFunc = MathS.FromString(expression).Integrate(varWRT);
lPart = (intFunc.Substitute(varWRT, end) - intFunc.Substitute(varWRT, start)).Simplify().ToString();
}
else if (parameters.Count == 1)
{
string expression = parameters[0];
// Get the variable to integrate with respect to
string varName = Regex.Match(expression, @"d(\S)$").Value;
if (!String.IsNullOrEmpty(varName))
{
expression = expression.Replace(varName, String.Empty);
varName = varName.Substring(1);
}
else
{
varName = "x";
}
var varWRT = MathS.Var(varName);
lPart = MathS.FromString(expression).Integrate(varWRT).Simplify().ToString();
}
}
output += lPart;
}
return(output);
}
public static string ConvertToMathString(IList <MathAtom> atoms)
{
string output = "";
for (int i = 0; i < atoms.Count; i++)
{
var atom = atoms[i];
if (atom is Variable variable)
{
output += atom.Nucleus;
if (i + 1 < atoms.Count && atoms[i + 1] is Variable)
{
output += "*";
}
}
else if (atom is Fraction fraction)
{
output += $"({ConvertToMathString(fraction.Numerator)})/({ConvertToMathString(fraction.Denominator)})";
}
else if (atom is Inner inner)
{
output += $"({ConvertToMathString(inner.InnerList)})";
}
else if (atom is BinaryOperator binaryOperator)
{
if (binaryOperator.Nucleus == "·")
{
output += "*";
}
}
else if (atom is LargeOperator largeOperator)
{
if (largeOperator.Nucleus == "∫")
{
// Figure out which kind of intergral we're dealing with
if (largeOperator.Subscript.Count > 0 || largeOperator.Superscript.Count > 0)
{
// Definite integral
// Find the variable to integrate with respect to
bool foundWRT = false;
int idxOfWRT = i + 1;
while (!foundWRT && idxOfWRT + 1 < atoms.Count)
{
foundWRT = atoms[idxOfWRT] is Variable intWRTMarker && intWRTMarker.Nucleus == "d" &&
atoms[idxOfWRT + 1] is Variable;
idxOfWRT++;
}
// Get the bounds of integration
LaTeXParser.MathListFromLaTeX(@"\infty").Deconstruct(out MathList defaultUpperBound, out _);
LaTeXParser.MathListFromLaTeX(@"-\infty").Deconstruct(out MathList defaultLowerBound, out _);
var upperBound = MathS.FromString(
ConvertToMathString(largeOperator.Superscript.Count == 0 ? defaultUpperBound : largeOperator.Superscript)
);
var lowerBound = MathS.FromString(
ConvertToMathString(largeOperator.Subscript.Count == 0 ? defaultLowerBound : largeOperator.Subscript)
);
// Get the list of atoms that we need to integrate
// i+1 to skip the integral symbol, and idxOfWRT-i-2 to remove the dx
var intAtoms = atoms.Skip(i + 1).Take(idxOfWRT - i - 2).ToList();
// Calculate the integral of the expression
var varWRT = MathS.Var(foundWRT ? atoms[idxOfWRT].Nucleus : "x");
var antiderivative = MathS.FromString(ConvertToMathString(intAtoms)).Integrate(varWRT).Simplify();
output += (antiderivative.Substitute(varWRT, upperBound) - antiderivative.Substitute(varWRT, lowerBound)).Simplify().ToString();
// Make sure the atoms involved in the integration aren't parsed again
i = idxOfWRT;
continue;
}
else
{
// Indefinite integral
// Find the variable to integrate with respect to
bool foundWRT = false;
int idxOfWRT = i + 1;
while (!foundWRT && idxOfWRT + 1 < atoms.Count)
{
foundWRT = atoms[idxOfWRT] is Variable intWRTMarker && intWRTMarker.Nucleus == "d" &&
atoms[idxOfWRT + 1] is Variable;
idxOfWRT++;
}
// Get the list of atoms that we need to integrate
// i+1 to skip the integral symbol, and idxOfWRT-i-2 to remove the dx
var intAtoms = atoms.Skip(i + 1).Take(idxOfWRT - i - 2).ToList();
// Calculate the integral of the expression
var varWRT = MathS.Var(foundWRT ? atoms[idxOfWRT].Nucleus : "x");
output += MathS.FromString(ConvertToMathString(intAtoms)).Integrate(varWRT).Simplify().ToString();
// Make sure the atoms involved in the integration aren't parsed again
i = idxOfWRT;
continue;
}
}
else
{
output += atom.Nucleus;
}
}
else
{
output += atom.Nucleus;
}
if (atom.Superscript.Count > 0)
{
output += $"^({ConvertToMathString(atom.Superscript)})";
}
}
return(output);
}
public void VarsExpanded(string expr, int rootCount)
{
var eq = MathS.FromString(expr);
TestSolver(eq.Expand(), rootCount);
}
// Testing parsing
[Benchmark] public void ParseEasy() => MathS.FromString("1 + 2 / x + 2 / (y + x)", useCache: false);
public void Vars(string expr, int rootCount)
{
var eq = MathS.FromString(expr);
TestSolver(eq, rootCount);
}
[Benchmark] public void ParseHard() => MathS.FromString("x ^ (x + y ^ 2 ^ sin(3 / z + i)) - log(-i, 3) ^ (x + x * y) - sqrt(y) / (i + sqrt(-1))", useCache: false);
public void TestDP()
{
Assert.IsTrue(MathS.FromString("-23").Eval() == -23);
}
[Fact] public void TestDP() => Assert.Equal(-23, MathS.FromString("-23").EvalNumerical());
public void TestB()
{
Assert.IsTrue(MathS.FromString("1 + (-1)").Eval() == 0);
}
[Fact] public void TestB() => Assert.Equal(0, MathS.FromString("1 + (-1)").EvalNumerical());
public void TestMm()
{
Assert.IsTrue(MathS.FromString("-1 * -1 * -1").Eval() == -1);
}
[Fact] public void TestMi() => Assert.Equal(1, MathS.FromString("-i^2").EvalNumerical());
public void Test1() => Assert.IsTrue(Measure(() => MathS.FromString("x + x^2 + x^3")) < 4);
[Fact] public void TestMm() => Assert.Equal(-1, MathS.FromString("-1 * -1 * -1").EvalNumerical());
public void Circle(string inputIsOutput) => Assert.Equal(inputIsOutput, MathS.FromString(inputIsOutput).Stringize());
public static Entity ToEntity(this String expr) => MathS.FromString(expr);
public void TestDiscrete(string inputIsOutput) => Assert.Equal(inputIsOutput, MathS.FromString(inputIsOutput).Stringize());
public void Test15()
{
Assert.IsTrue(MathS.FromString("x(2 + 3)").Simplify() == 5 * x);
}