public static int Test_RationalSymbolMatrixOperations()
{
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.Append(@"\begin{aligned}");
sb.AppendFormat(@"&{0}", (A1 * A2).ToLatex("F") + @" \\ \\");
sb.AppendFormat(@"&{0}", (A1 + A2).ToLatex("F") + @" \\ \\");
sb.AppendFormat(@"&{0}", (A1 - A2).ToLatex("F"));
sb.Append(@"\end{aligned}");
HtmlOutputMethods.WriteLatexEqToHtmlAndLaunch(sb.ToString(), "Test_RationalSymbolMatrixOperations.html"); //display Latex via mathjax
return(0);
}
public static int Test_CramersRule()
{
RationalFactory rf = new RationalFactory(); //Create rational factory
RationalSquareMatrix ACopy = rf[3, 3, //Matrix to solve
"1", "2", "-2",
"-1", "1", "3",
"2", "-1", "2"
];
RationalVector rv = new RationalVector {
-7, 3, 8
}; //values to solve for
StringBuilder sb = new StringBuilder(); //Start building latex
sb.Append(@"\begin{aligned}");
//Start system of linear equations
sb.AppendFormat(@"&x_1 + 2x_2 - 2x_3 = -7 \\ \\");
sb.AppendFormat(@"&-x_1 + x_2 + 3x_3 = 3 \\ \\");
sb.AppendFormat(@"&2x_1 - x_2 + 2x_3 = 8 \\ \\");
RationalVector rvSolved = ACopy.CramersRule(rv); //solve system of linear equations
sb.AppendFormat(@"&x_1 = {0}, x_2 = {1}, x_3 = {2}", rvSolved[0].ToLatex(), rvSolved[1].ToLatex(), rvSolved[2].ToLatex()); //output values
sb.Append(@"\end{aligned}");
HtmlOutputMethods.WriteLatexEqToHtmlAndLaunch(sb.ToString(), "Test_CramersRule.html"); //display Latex via mathjax
return(0);
}
public static int Test_KroneckerSum()
{
RealFactory rf = new RealFactory();
SquareRealMatrix A = rf[2, 2,
1, -1,
0, 2
];
SquareRealMatrix B = rf[2, 2,
1, 0,
2, -1
];
StringBuilder sb = new StringBuilder();//Start building latex
sb.Append(@"\begin{aligned}");
sb.AppendFormat(@"&A = {0}\;B = {1}", A.ToLatex(), B.ToLatex() + @" \\ \\");
sb.AppendFormat(@"&C = A\;\oplus\;B = {0}", SquareRealMatrix.KroneckerSum(A, B).ToLatex());
sb.Append(@"\end{aligned}");
HtmlOutputMethods.WriteLatexEqToHtmlAndLaunch(sb.ToString(), "Test_KroneckerSum.html"); //display Latex via mathjax
return(0);
}
public static int Test_UnitVector_Col_Row_Accessors()
{
List <double> initer = new List <double> {
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16
}; //init matrix vector
SquareRealMatrix A = new SquareRealMatrix(4, 4, initer); //create 4X4 matrix
A.Name = "A"; //give it a name
UnitVectorSpace uvs = new UnitVectorSpace(4); //Create unit vector space to use
UnitVector e2 = new UnitVector("e2", 4, RowColumn.Column);
UnitVector e2_p = new UnitVector("e2", 4, RowColumn.Row);
RealVector rv = A * e2;
StringBuilder sb = new StringBuilder();//Start building latex
sb.Append(@"\begin{aligned}");
sb.AppendFormat(@"&A = &{0} \\ \\", A.ToLatex()); //Display Original A matrix
sb.Append(@"&A_{.2} = &" + rv.ToLatex() + @" \\ \\");
RealVector rvRow = e2_p * A;
sb.Append(@"&A_{2.}' = &" + rvRow.ToLatex());
sb.Append(@"\end{aligned}");
HtmlOutputMethods.WriteLatexEqToHtmlAndLaunch(sb.ToString(), "Test_UnitVector_Col_Row_Accessors.html"); //display Latex via mathjax
return(0);
}
public static int Test_EMatrix()
{
RationalFactory rf = new RationalFactory();
RationalSquareMatrix I = RationalSquareMatrix.IdentityMatrix(3);
RationalSquareMatrix ACopy = rf[3, 3,
"1", "2", "-2",
"-1", "1", "3",
"2", "-1", "2"
];
RationalSquareMatrix ACopy2 = rf[3, 3,
"-7", "2", "-2",
"-3", "1", "3",
"8", "-1", "2"
];
RationalSquareMatrix ACopy3 = rf[4, 4,
"4", "7", "2", "3",
"1", "3", "1", "2",
"2", "5", "3", "4",
"1", "4", "2", "3"
];
string ll = RationalSquareMatrix.DetFullRep(ACopy);
HtmlOutputMethods.WriteLatexEqToHtmlAndLaunch(ll, "Test_EMatrix.html"); //display Latex via mathjax
return(0);
}
public static int Test_Partioned_Matrix()
{
List <double> initer = new List <double> {
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16
}; //init matrix vector
SquareRealMatrix A = new SquareRealMatrix(4, 4, initer); //create 4X4 matrix
A.Name = "A"; //give it a name
SquareRealMatrix AColumns = new SquareRealMatrix(new List <RealVector> {
A[".1"], A[".2"], A[".3"], A[".4"]
}); //Create partioned matrix from columns
SquareRealMatrix ARows = new SquareRealMatrix(new List <RealVector> {
A["1."], A["2."], A["3."], A["4."]
}); //Create partioned matrix from rows
StringBuilder sb = new StringBuilder(); //Start building latex
sb.Append(@"\begin{aligned}");
sb.AppendFormat(@"&A = &{0} \\ \\", A.ToLatex()); //Display Original A matrix
sb.Append(@"&A = \left[ A_{.1}\;A_{.2}\;A_{.3}\;A_{.4} \right] = \;\;" + "&" + AColumns.ToLatex() + @" \\ \\"); //partioned matrix via columns of A
sb.Append(@"&\left[ A_{1.}\;A_{2.}\;A_{3.}\;A_{4.} \right] = \;\;" + "&" + ARows.ToLatex() + @" \\ \\"); //partioned matrix via rows of A
sb.Append(@"&A = \left[ A_{1.}\;A_{2.}\;A_{3.}\;A_{4.} \right]' = \;\;" + "&" + ARows.Transpose().ToLatex() + @" \\ \\"); //transpose to get A
sb.Append(@"\end{aligned}");
HtmlOutputMethods.WriteLatexEqToHtmlAndLaunch(sb.ToString(), "Test_Partioned_Matrix.html"); //display Latex via mathjax
return(0);
}
public static int Test_SRM_To_Elem()
{
SquareRealMatrix elem = SquareRealMatrix.ElementaryMatrix(4, 4, "E22"); //E22 elementary matrix
HtmlOutputMethods.WriteLatexEqToHtmlAndLaunch(elem.ToString("F"), "Test_SRM_To_Elem.html"); //display Latex via mathjax
return(0);
}
//From now on, our comments will use latex syntax
public static int Test_ElementaryMatrix_Multiply_ElementaryMatrix()
{
/*
* E_{ij}E_{rs} = e_ie'_je_re'_s = \delta_{r j}e'_ie'_s = \delta_{j r}E_{is} \\
* if\;r = j \\
* E_{ij}E_{rs} = \delta_{j j}E_{is} = E_{is}
*
*/
StringBuilder sb = new StringBuilder();
ElementaryMatrix E12 = new ElementaryMatrix(4, 4, "E13"); // 4 x 4 ElementaryMatrix
ElementaryMatrix E13 = new ElementaryMatrix(4, 4, "E32"); // 4 x 4 ElementaryMatrix
sb.Append(@"E_{ij}E_{rs} = e_ie'_je_re'_s = \delta_{r j}e'_ie'_s = \delta_{j r}E_{is} \\");
sb.Append(@"if\;r = j \\");
sb.Append(@"E_{ij}E_{rs} = \delta_{j j}E_{is} = E_{is} \\");
sb.Append(@"Output\;is: \\");
//Test Elementary Matrix * Elementary Matrix
ElementaryMatrix em = E12 * E13;
sb.Append(em.ToLatex("F"));
HtmlOutputMethods.WriteLatexEqToHtmlAndLaunch(sb.ToString(), "Test_ElementaryMatrix_Multiply_ElementaryMatrix.html"); //display Latex via mathjax
return(0);
}
public static int Test_RationalSquareMatrix()
{
RationalFactory rf = new RationalFactory();
RealFactory rff = new RealFactory();
RationalSquareMatrix A = rf[3, 3,
"1", "2", "-2",
"-1", "1", "3",
"2", "-1", "2"
];
SquareRealMatrix SA = rff[3, 3,
7, 2, -2,
3, 1, 3,
8, -1, 2
];
RationalVector rv = rf["7", "3", "8"];
StringBuilder sb = new StringBuilder();//Start building latex
sb.Append(@"\begin{aligned}");
sb.AppendFormat(@"&A = {0}", A.ToLatex() + @" \\ \\"); //display A matrix
A[0] = rv;
sb.AppendFormat(@"&Ab = {0}", A.ToLatex()); //display Vec A
sb.AppendFormat(@"&Det = {0}", SA.Determinant()); //display Vec A
sb.Append(@"\end{aligned}");
HtmlOutputMethods.WriteLatexEqToHtmlAndLaunch(sb.ToString(), "Test_VecOperator.html"); //display Latex via mathjax
return(0);
}
public static int Test_ElementaryMatrix_ElementaryMatrix()
{
ElementaryMatrix em = new ElementaryMatrix(4, 4, "E11");
HtmlOutputMethods.WriteLatexEqToHtmlAndLaunch(em.ToLatex("F"), "Test_ElementaryMatrix_ElementaryMatrix.html");
return(0);
}
public static int Test_UnitVector_UnitVector()
{
UnitVector uv = new UnitVector("e1", 3);
HtmlOutputMethods.WriteLatexEqToHtmlAndLaunch(uv.ToLatex("F"), "Test_UnitVector_UnitVector.html");
return(0);
}
public static int Test_UnitVectorSpace_UnitVectorSpace()
{
UnitVectorSpace uvs = new UnitVectorSpace(3);
HtmlOutputMethods.WriteLatexEqToHtmlAndLaunch(uvs.ToLatex(), "Test_UnitVectorSpace_UnitVectorSpace.html");
return(0);
}
public static int Test_OneVector_OneVector()
{
UnitVectorSpace uvs = new UnitVectorSpace(3);
HtmlOutputMethods.WriteLatexEqToHtmlAndLaunch(uvs.OneVector().ToLatex("F"), "Test_OneVector_OneVector.html");
return(0);
}
public static void Write2DVectorToHtmlAndLaunch(RealVector rv, string FileName)
{
string path = Directory.GetCurrentDirectory();
string fil = Path.Combine(path, FileName);
string text = HtmlOutputMethods.ToHtmlVectorGraph2D(rv);
File.WriteAllText(fil, text);
OpenBrowser(fil);
}
public static void WriteLatexEqToHtmlAndLaunch(string Latex, string FileName)
{
string path = Directory.GetCurrentDirectory() + "/html/";
string fil = Path.Combine(path, FileName);
string text = HtmlOutputMethods.ToHtmlWithMathJaxEquation(Latex);
File.WriteAllText(fil, text);
OpenBrowser(fil);
}
public static int Test_RealVector_ColumnVector()
{
RealVector rv = new RealVector {
1, 2, 3, 4
};
HtmlOutputMethods.WriteLatexEqToHtmlAndLaunch(rv.ToLatex(), "Test_RealVector_ColumnVector.html");
return(0);
}
public static int Test_Rational_Determinant()
{
RationalFactory rf = new RationalFactory();
RationalSquareMatrix A = rf[3, 3,
"1", "2", "-2",
"-1", "1", "3",
"2", "-1", "2"
];
RationalSquareMatrix ACopy3 = rf[4, 4,
"4", "7", "2", "3",
"1", "3", "1", "2",
"2", "5", "3", "4",
"1", "4", "2", "3"
];
RationalSquareMatrix ACopy3_2 = rf[3, 3,
1, 2, 3,
4, 1, 6,
7, 8, 1
];
List <RationalCoFactorInfo> cfList = RationalSquareMatrix.GetAllMatrixCoFactors(ACopy3);
StringBuilder sb = new StringBuilder();//Start building latex
sb.Append(@"\begin{aligned}");
sb.AppendFormat(@"&{0} \\ \\", ACopy3.ToLatex());
//foreach(IGrouping<string, RationalCoFactorInfo> funk in q.ToList())
foreach (RationalCoFactorInfo ci in cfList)
{
sb.AppendFormat(@"&{0} \\ \\", ci.Minor.MinorName + " = " + ((ci.Sign < 0) ? "-" : "") + ci.CoFactor.ToLatex() + ci.Minor.ToLatex());
foreach (List <RationalCoFactorInfo> lstChild in ci.ListOfLists)
{
foreach (RationalCoFactorInfo ci2 in lstChild)
{
//if (ci2.Minor.Rows == 4)
{
sb.AppendFormat(@"&{0} \\ \\", ci.Minor.MinorName + " = " + ((ci.Sign < 0) ? "-" : "") + ci.CoFactor.ToLatex() + ci2.CoFactor.ToLatex() + ci2.Minor.ToLatex());
}
}
}
}
sb.Append(@"&Det = " + RationalSquareMatrix.Det(ACopy3_2));
sb.Append(@"\end{aligned}");
HtmlOutputMethods.WriteLatexEqToHtmlAndLaunch(sb.ToString(), "Test_Rational_Determinant.html"); //display Latex via mathjax
return(0);
}
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_UnitVectorProductTo_ElementaryMatrix()
{
UnitVectorSpace uvs = new UnitVectorSpace(4); //Order four Unit Vector Space
UnitVector e2 = uvs["e2"]; // order 4 e2 unit vector
UnitVector e1 = uvs["e1"]; //order 4 e1 unit operator
ElementaryMatrix em = e2 * e1; //product of Unit Vectors
HtmlOutputMethods.WriteLatexEqToHtmlAndLaunch(em.ToLatex("F"), "Test_UnitVectorProductTo_ElementaryMatrix.html"); //display Latex via mathjax
return(0);
}
public static int Test_Rows_Of_Matrix()
{
List <double> initer = new List <double> {
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16
}; //init matrix vector
SquareRealMatrix A = new SquareRealMatrix(4, 4, initer); //create 4X4 matrix
A.Name = "A"; //give it a name
RealVector rvRow = A["2."]; //use accessor to get row 2 of matrix
string outR = @"\begin{aligned}&A = " + A.ToLatex() + @" \\ \\" + "&" + rvRow.ToLatex("F") + @"\end{aligned}"; //use row accessor A2. which returns row 2.
HtmlOutputMethods.WriteLatexEqToHtmlAndLaunch(outR, "TestRows_Of_Matrix.html"); //display Latex via mathjax
return(0);
}
public static int Test_ES()
{
EinsteinSummation es = new EinsteinSummation(3);
//Symbol s = es["a{ij}x_ix_j"];
List <ITensor> lstT = es.ExpandToList("a_{ij}x_ix_j");
string s = es.FormatQuadratic(lstT);
//HtmlOutputMethods.WriteLatexEqToHtmlAndLaunch(s.NakedTokenString, "Test_ES.html"); //display Latex via mathjax
//Console.WriteLine(s);
HtmlOutputMethods.WriteLatexEqToHtmlAndLaunch(s, "Test_ES.html"); //display Latex via mathjax
//Console.WriteLine(p.Tensor.Expand());
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 string ToLatex()
{
string ret = @"
\left(
\begin{array}{REPLACE_THECC}
REPLACE_MY_TOP_ROW\\
REPLACE_MY_BOTTOM_ROW\\
\end{array}
\right)
";
string cc = HtmlOutputMethods.RepeatCharacter('c', this.TopRow.Length);
return(ret.Replace("REPLACE_THECC", cc)
.Replace("REPLACE_MY_TOP_ROW", string.Join("&", this.TopRow))
.Replace("REPLACE_MY_BOTTOM_ROW", string.Join("&", this.BottomRow)));
}
public static int Test_UnitVectorProduct_ToInt()
{
UnitVectorSpace uvs = new UnitVectorSpace(4); //Order four Unit Vector Space
UnitVector e1 = uvs["e1"]; //order 4 e1 unit operator
e1.IsRowOrColumn = RowColumn.Row;
UnitVector e2 = uvs["e2"]; // order 4 e2 unit vector
int dp = e1 * e2; //product of Unit Vectors
UnitVector e2prime = new UnitVector("e2", 4, RowColumn.Row);
int dp2 = e2prime * e2;
string latex = "e'_{1}e_{2} = " + dp.ToString() + @"\;,e'_{2}e_{2} = " + dp2.ToString();
HtmlOutputMethods.WriteLatexEqToHtmlAndLaunch(latex, "Test_UnitVectorProduct_ToInt.html"); //display Latex via mathjax
return(0);
}
public static int Test_TraceFunction()
{
RealFactory rf = new RealFactory(); //create a real factory
SquareRealMatrix A = rf[3, 3, //create a 3 X 3 real matrix
1, 2, 3,
7, 8, 9,
6, 5, 4
];
StringBuilder sb = new StringBuilder();//Start building latex
sb.Append(@"\begin{aligned}");
sb.AppendFormat(@"&A = {0}", A.ToLatex() + @" \\ \\"); //display A matrix
sb.AppendFormat(@"&tr A = {0}", A.Trace() + @" \\ \\"); //display trace
sb.Append(@"\end{aligned}");
HtmlOutputMethods.WriteLatexEqToHtmlAndLaunch(sb.ToString(), "Test_TraceFunction.html"); //display Latex via mathjax
return(0);
}
public static int Test_KroneckerProduct()
{
SymbolMatrix A1 = new SymbolMatrix(2, 2, //create a 2 X 2 symbol matrix with symbols a,b,c,d
new List <Symbol>
{
new Symbol("a"), new Symbol("b"),
new Symbol("c"), new Symbol("d")
});
SymbolMatrix A2 = new SymbolMatrix(2, 2, //create a 2 X 2 symbol matrix with symbols e,f,g,h
new List <Symbol>
{
new Symbol("e"), new Symbol("f"),
new Symbol("g"), new Symbol("h")
});
StringBuilder sb = new StringBuilder();//Start building latex
sb.AppendFormat(@"{0}", SymbolMatrixUtilities.KroneckerProduct(A1, A2).ToLatex("F"));
HtmlOutputMethods.WriteLatexEqToHtmlAndLaunch(sb.ToString(), "Test_KroneckerProduct.html"); //display Latex via mathjax
return(0);
}
public static int Test_VecOperator()
{
RealFactory rf = new RealFactory(); //create a real factory
SquareRealMatrix A = rf[2, 2, //create a 2 X 2 real matrix
1, 2,
3, 4
];
RealVector VecA = A.Vec("A"); //use Vec operator giving the matrix a name
StringBuilder sb = new StringBuilder(); //Start building latex
sb.Append(@"\begin{aligned}");
sb.AppendFormat(@"&A = {0}", A.ToLatex() + @" \\ \\"); //display A matrix
sb.AppendFormat(@"&{0}", VecA.ToLatex("F")); //display Vec A
sb.Append(@"\end{aligned}");
HtmlOutputMethods.WriteLatexEqToHtmlAndLaunch(sb.ToString(), "Test_VecOperator.html"); //display Latex via mathjax
return(0);
}
public static int Test_UnitVector_Multiply_ElementaryMatrix()
{
/*
* e'r * Eij = e'r * ei * e'j = &ri *e'j where & = Kronecker delta
*
*/
StringBuilder sb = new StringBuilder();
ElementaryMatrix E12 = new ElementaryMatrix(4, 4, "E12"); // 4 x 4 ElementaryMatrix
UnitVector e1 = new UnitVector("e1", 4); //Order four unit vector e1
UnitVector e2 = new UnitVector("e2", 4, RowColumn.Row); //Order four row unit vector e2
UnitVector er = new UnitVector("e3", 4, RowColumn.Row); //Order four unit row vector e3 our er above
/*
* i = 1, j = 2, r = 3
*/
sb.Append(@"e'_rE_{ij} = e'_re_ie'_j = \delta_{r j}e'j \\");
//Test matrix unit vector * Elementary Matrix, er * Eij
UnitVector uvE1 = er * E12;
sb.Append(@"e'_3E_{12} = " + uvE1.ToLatex() + @"\;");
//Test e'r * ei * e'j
UnitVector uvE2 = er * e1 * e2;
sb.Append(@"e'_3e_1e'_2 = " + uvE2.ToLatex() + @"\;");
//Test &ri * e'j
UnitVector uvE3 = UnitVector.KroneckerDelta(3, 1) * e2;
sb.Append(@" \delta_{3 1}e_2 = " + uvE3.ToLatex() + @" \tag{1}");
HtmlOutputMethods.WriteLatexEqToHtmlAndLaunch(sb.ToString(), "Test_UnitVector_Multiply_ElementaryMatrix.html"); //display Latex via mathjax
return(0);
}
public static int Test_ElementaryMatrix_Multiply_UnitVector()
{
/*
* Eij * er = ei*e'j*er = &jr *ei where & = Kronecker delta
*
*/
StringBuilder sb = new StringBuilder();
ElementaryMatrix E12 = new ElementaryMatrix(4, 4, "E12"); // 4 x 4 ElementaryMatrix
UnitVector e1 = new UnitVector("e1", 4); //Order four unit vector e1
UnitVector e2 = new UnitVector("e2", 4, RowColumn.Row); //Order four row unit vector e2
UnitVector er = new UnitVector("e3", 4); //Order four unit vector e3 our er above
/*
* i = 1, j = 2, r = 3
*/
//Test matrix * unit vector, Eij * er
UnitVector uvE1 = E12 * er;
sb.Append(@"E_{12}e_3 = " + uvE1.ToLatex() + @"\;");
//Test e1* e'j * er
UnitVector uvE2 = e1 * e2 * er;
sb.Append(@"e_1e'_2e_3 = " + uvE2.ToLatex() + @"\;");
//Test &jr * ei
UnitVector uvE3 = UnitVector.KroneckerDelta(2, 3) * e1;
sb.Append(@" \delta_{2 3}e_1 = " + uvE3.ToLatex());
HtmlOutputMethods.WriteLatexEqToHtmlAndLaunch(sb.ToString(), "Test_ElementaryMatrix_Multiply_UnitVector.html"); //display Latex via mathjax
return(0);
}
