public static SymbolMatrix C3()
{
List <string> kgL = new List <string>
{
"a", "b", "c",
"c", "a", "b",
"b", "c", "a"
};
SymbolMatrix retVal = new SymbolMatrix(3, 3);
int cnt = 0;
for (int rows = 0; rows < retVal.Rows; rows++)
{
for (int cols = 0; cols < retVal.Columns; cols++)
{
Symbol sym = new Symbol(kgL[cnt++]);
sym.IsExpression = true;
retVal[rows, cols] = sym;
}
}
retVal.FullRep = @"C_3 = " + retVal.ToLatex();
return(retVal);
}
public static SymbolMatrix C3(List <string> variables)
{
List <string> kgL = new List <string>
{
"a", "b", "c",
"c", "a", "b",
"b", "c", "a"
};
List <string> mapper = kgL.Take(3).ToList();
SymbolMatrix retVal = new SymbolMatrix(3, 3);
int cnt = 0;
for (int rowCount = 0; rowCount < retVal.Rows; rowCount++)
{
for (int colCount = 0; colCount < retVal.Columns; colCount++)
{
int ind = mapper.FindIndex(t => t == kgL[cnt]);
Symbol sym = new Symbol(variables[ind]);
cnt++;
sym.IsExpression = true;
retVal[rowCount, colCount] = sym;
}
}
retVal.FullRep = @"C_3 = " + retVal.ToLatex();
return(retVal);
}
public static SymbolMatrix RightChiralQuaternion()
{
List <string> kgL = new List <string>
{
"a", "b", "c", "d",
"-b", "a", "d", "-c",
"-c", "-d", "a", "b",
"-d", "c", "-b", "a"
};
SymbolMatrix retval = new SymbolMatrix(4, 4);
int cnt = 0;
for (int rowCount = 0; rowCount < retval.Rows; rowCount++)
{
for (int colCount = 0; colCount < retval.Columns; colCount++)
{
Symbol sym = new Symbol(kgL[cnt++]);
sym.IsExpression = true;
retval[rowCount, colCount] = sym;
}
}
retval.FullRep = @"\mathbb{H}_{R\chi} = " + retval.ToLatex();
return(retval);
}
public static SymbolMatrix C4RowColumn()
{
List <string> kgL = new List <string>
{
"a", "b", "c", "d",
"e", "f", "g", "h",
"i", "j", "k", "l",
"m", "n", "o", "p",
};
SymbolMatrix retVal = new SymbolMatrix(4, 4);
int cnt = 0;
for (int rowCount = 0; rowCount < retVal.Rows; rowCount++)
{
for (int colCount = 0; colCount < retVal.Columns; colCount++)
{
Symbol sym = new Symbol(kgL[cnt++]);
sym.IsExpression = true;
retVal[rowCount, colCount] = sym;
}
}
retVal.FullRep = @"C_4 = " + retVal.ToLatex();
return(retVal);
}
public static SymbolMatrix KleinGroup()
{
List <string> kgL = new List <string>
{
"a", "b", "c", "d",
"b", "a", "d", "c",
"c", "d", "a", "b",
"d", "c", "b", "a"
};
SymbolMatrix retVal = new SymbolMatrix(4, 4);
int cnt = 0;
for (int rowCount = 0; rowCount < retVal.Rows; rowCount++)
{
for (int colCount = 0; colCount < retVal.Columns; colCount++)
{
Symbol sym = new Symbol(kgL[cnt++]);
sym.IsExpression = true;
retVal[rowCount, colCount] = sym;
}
}
retVal.FullRep = @"C_2\;\times\;C_2 = " + retVal.ToLatex();
return(retVal);
}
public static SymbolMatrix operator /(SymbolMatrix a, SymbolMatrix b)
{
SymbolMatrix retVal = new SymbolMatrix(a.Rows, a.Columns);
for (int rowCount = 0; rowCount < retVal.Rows; rowCount++)
{
for (int colCount = 0; colCount < retVal.Columns; colCount++)
{
for (int retColCount = 0; retColCount < retVal.Columns; retColCount++)
{
retVal.InternalRep[rowCount, colCount] += a.InternalRep[rowCount, retColCount] / b.InternalRep[retColCount, colCount];
}
}
}
StringBuilder sb = new StringBuilder();
sb.Append(a.ToLatex());
sb.Append(b.ToLatex());
sb.Append(" = ");
sb.Append(retVal.ToLatex());
retVal.FullRep = sb.ToString();
return(retVal);
}
/***************************Operators**********************************/
private static SymbolMatrix MultiplyRational(SymbolMatrix a, SymbolMatrix b)
{
SymbolMatrix retVal = new SymbolMatrix(a.Rows, a.Columns);
retVal.SymbolMatrixSymbolType = SymbolType.Rational;
for (int rowCount = 0; rowCount < retVal.Rows; rowCount++)
{
for (int colCount = 0; colCount < retVal.Columns; colCount++)
{
for (int retColCount = 0; retColCount < retVal.Columns; retColCount++)
{
Rational inter = Rational.Parse(retVal.InternalRep[rowCount, colCount].Expression);
inter += Rational.Parse(a.InternalRep[rowCount, retColCount].Expression) * Rational.Parse(b.InternalRep[retColCount, colCount].Expression);
Symbol sym = new Symbol(inter.ToString());
sym.LatexString = inter.ToLatex();
retVal.InternalRep[rowCount, colCount] = sym;
}
}
}
StringBuilder sb = new StringBuilder();
sb.Append(a.ToLatex());
sb.Append(b.ToLatex());
sb.Append(" = ");
sb.Append(retVal.ToLatex());
retVal.FullRep = sb.ToString();
return(retVal);
}
public static int Test_D3()
{
SymbolMatrix D3 = SymbolMatrixUtilities.D3();
StringBuilder sb = new StringBuilder();//Start building latex
sb.AppendFormat(@"{0}", D3.ToLatex());
HtmlOutputMethods.WriteLatexEqToHtmlAndLaunch(sb.ToString(), "Test_D3.html"); //display Latex via mathjax
return(0);
}
public static int Test_Flip()
{
SymbolMatrix C3Flip = SymbolMatrixUtilities.C3().Flip().ReName(new List <string> {
"d", "e", "f"
});
StringBuilder sb = new StringBuilder();//Start building latex
sb.Append(@"\begin{aligned}");
sb.AppendFormat(@"&{0} \\ \\", SymbolMatrixUtilities.C3().ToLatex());
sb.AppendFormat(@"&{0}", C3Flip.ToLatex());
sb.Append(@"\end{aligned}");
HtmlOutputMethods.WriteLatexEqToHtmlAndLaunch(sb.ToString(), "Test_Flip.html"); //display Latex via mathjax
return(0);
}
public static int Test_Symbol_Groups()
{
SymbolMatrix smK = SymbolMatrixUtilities.KleinGroup(); //Get kleingroup cayle table
SymbolMatrix smQL = SymbolMatrixUtilities.LeftChiralQuaternion();
SymbolMatrix smQR = SymbolMatrixUtilities.RightChiralQuaternion();
StringBuilder sb = new StringBuilder();//Start building latex
sb.Append(@"\begin{aligned}");
sb.AppendFormat(@"&{0} \\ \\", smK.ToLatex("F"));
sb.AppendFormat(@"&{0} \\ \\", smQL.ToLatex("F"));
sb.AppendFormat(@"&{0}", smQR.ToLatex("F"));
sb.Append(@"\end{aligned}");
HtmlOutputMethods.WriteLatexEqToHtmlAndLaunch(sb.ToString(), "Test_KleinGroup.html"); //display Latex via mathjax
return(0);
}
public static SymbolMatrix KroneckerProduct(SymbolMatrix a, SymbolMatrix b)
{
int Rows = a.Rows * b.Rows; // calculate number of rows.
int Columns = a.Columns * b.Rows; // calculate number of columns
int incC = 0; // increment variable for column of b matrix
int incR = 0; // increment variable for row of b matrix
int incAMC = 0; // increment variable for column of a matrix
int incAMR = 0; // increment variable for row of a matrix
SymbolMatrix retVal = new SymbolMatrix(Rows, Columns);
int rowCount;
int colCount;
string exp = string.Empty;
for (rowCount = 0; rowCount < retVal.Rows; rowCount++)
{
if (incR > b.Rows - 1) // reached end of rows of b matrix
{
incR = 0;
incAMR++;
}
incAMC = 0;
for (colCount = 0; colCount < retVal.Columns; colCount++)
{
exp = a[incAMR, incAMC].Expression + b[incR, incC].Expression;
incC++;
if (incC > b.Columns - 1) // reached end of columns of b matrix
{
incC = 0;
incAMC++;
}
retVal[rowCount, colCount] = new Symbol(exp);
}
incR++;
}
retVal.FullRep = a.ToLatex() + @"\;\otimes\;" + b.ToLatex() + " = " + retVal.ToLatex(); //produce latex string
return(retVal);
}
public static int Test_MultiplyRationalSymbolMatrix()
{
SymbolFactory sf = new SymbolFactory(SymbolType.Rational);
SymbolMatrix A1 = sf[2, 2, //create a 2 X 2 symbol matrix with rationals
"1/2", "1/5",
"2/3", "7/8"
];
SymbolMatrix A2 = sf[2, 2, //create a 2 X 2 symbol with rationals
"1/4", "7/9",
"3/10", "4/7"
];
SymbolMatrix symMul = A1 * A2; //multiply the matrices
StringBuilder sb = new StringBuilder(); //Start building latex
sb.AppendFormat(@"{0}", symMul.ToLatex("F"));
HtmlOutputMethods.WriteLatexEqToHtmlAndLaunch(sb.ToString(), "Test_Multiply_Rational_Symbol_Matrix.html"); //display Latex via mathjax
return(0);
}
public static int Test_Symbol_Determinant()
{
//SymbolMatrix C3 = SymbolMatrixUtilities.C3RowColumn();
//Symbol det = C3.Determinant();
//Symbol det = SymbolMatrixUtilities.C4RowColumn().Determinant();
//SymbolMatrix smK = SymbolMatrixUtilities.KleinGroup(); //Get kleingroup cayle table
//Symbol det = smK.Determinant();
SymbolMatrix smK = SymbolMatrixUtilities.C3RowColumn();
List <CoFactorInfo> cfList = SymbolMatrix.GetAllMatrixCoFactors(smK);
StringBuilder sb = new StringBuilder();//Start building latex
sb.Append(@"\begin{aligned}");
sb.AppendFormat(@"&{0} \\ \\", smK.ToLatex());
/*
* int inc = 0;
* CoFactorInfo cfi = null;
*
* while(inc < cfList.Count)
* {
* if(cfi == null)
* {
* cfi = cfList[inc];
* }
* else if(cfi != null && cfi.ListOfLists.Count == 0) //init value
* {
* List<CoFactorInfo> cfListChild = SymbolMatrix.GetCoFactors(cfi.Minor);
* cfi.ListOfLists.Add(cfListChild);
*
* if(cfListChild[0].Minor.Rows == 2) //end of line
* {
* cfList[inc] = cfi;
* cfi = null;
* inc++;
* }
* }
* else if(cfi != null && cfi.ListOfLists.Count > 0) //have values
* {
* List<CoFactorInfo> cfListChild = SymbolMatrix.GetCoFactors(cfi.Minor);
* cfi.ListOfLists.Add(cfListChild);
*
* if(cfListChild[0].Minor.Rows == 2) //end of line
* {
* cfList[inc] = cfi;
* cfi = null;
* inc++;
* }
*
* }
* }
*
*/
foreach (CoFactorInfo ci in cfList)
{
sb.AppendFormat(@"&{0} \\ \\", ci.CoFactor.Tokens[0].Value + ci.Minor.ToLatex());
/*
* if (ci.Minor.Rows > 2)
* {
* List<CoFactorInfo> cfList2 = SymbolMatrix.GetCoFactors(ci.Minor);
*
* foreach (CoFactorInfo ci2 in cfList2)
* {
* sb.AppendFormat(@"&{0} \\ \\", ci.CoFactor.Tokens[0].Value + ci2.CoFactor.Tokens[0].Value + ci2.Minor.ToLatex());
* }
* }
*/
foreach (List <CoFactorInfo> lstChild in ci.ListOfLists)
{
foreach (CoFactorInfo ci2 in lstChild)
{
//if (ci2.Minor.Rows == 4)
{
sb.AppendFormat(@"&{0} \\ \\", ci.CoFactor.Tokens[0].Value + ci2.CoFactor.Tokens[0].Value + ci2.Minor.ToLatex());
/*
* string det = string.Format("({0} - {1})",
* ci2.Minor[0, 0].Tokens[0]. Value + ci2.Minor[1, 1].Tokens[0]. Value,
* ci2.Minor[1, 0].Tokens[0]. Value + ci2.Minor[0, 1].Tokens[0]. Value);
*
* sb.AppendFormat(@"&{0} \\ \\", ci.CoFactor.Tokens[0].Value + ci2.CoFactor.Tokens[0].Value + det);
*/
}
}
}
}
sb.Append(@"\end{aligned}");
HtmlOutputMethods.WriteLatexEqToHtmlAndLaunch(sb.ToString(), "Test_Symbol_Determinant.html"); //display Latex via mathjax
return(0);
}