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_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_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_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_FaddevasMethod()
{
RationalFactory rf = new RationalFactory();
RationalSquareMatrix A = rf[3, 3,
"1", "0", "-2",
"4", "1", "0",
"0", "2", "1"
];
RationalVector rv = new RationalVector();
RationalSquareMatrix AInv = RationalSquareMatrix.FaddevasMethod(A, out rv);
StringBuilder sb = new StringBuilder();//Start building latex
sb.Append(@"A^{-1} = " + AInv.ToLatex());
HtmlOutputMethods.WriteLatexEqToHtmlAndLaunch(AInv.ToString("F"), "Test_FaddevasMethod_Determinant.html"); //display Latex via mathjax
/*
* RationalSquareMatrix A1 = A.Clone();
* StringBuilder sb = new StringBuilder();//Start building latex
* sb.Append(@"\begin{aligned}");
* sb.AppendFormat(@"&A1 = {0} \\ \\", A1.ToLatex());
*
* Rational b1 = -A1.Trace();
* sb.AppendFormat(@"&b1 = {0} \\ \\", b1.ToLatex());
* RationalSquareMatrix I = RationalSquareMatrix.IdentityMatrix(A.Rows);
*
* RationalSquareMatrix B1 = A1 + (b1 * I);
* sb.AppendFormat(@"&B1 = {0} \\ \\", B1.ToLatex());
*
* RationalSquareMatrix A2 = A * B1;
* sb.AppendFormat(@"&A2 = {0} \\ \\", A2.ToLatex());
*
* Rational b2 = A2.Trace() / -2;
* sb.AppendFormat(@"&b2 = {0} \\ \\", b2.ToLatex());
*
* I = RationalSquareMatrix.IdentityMatrix(A.Rows);
* RationalSquareMatrix B2 = A2 + b2 * I;
* sb.AppendFormat(@"&B2 = {0} \\ \\", B2.ToLatex());
*
* RationalSquareMatrix A3 = A * B2;
* sb.AppendFormat(@"&A3 = {0} \\ \\", A3.ToLatex());
*
* Rational b3 = A3.Trace() / -3;
* sb.AppendFormat(@"&b3 = {0} \\ \\", b3.ToLatex());
*
* RationalSquareMatrix AInv = 1/b3 * B2;
* sb.Append(@"&A^{-1} = " + AInv.ToLatex() + @" \\ \\");
*
*
* RationalSquareMatrix A_n = A;
* Rational b_n = 1;
* RationalSquareMatrix B_n = null;
* int i = 0;
* for(i = 0; i < A.Rows - 1; i++)
* {
* b_n = -A_n.Trace() / (i + 1);
* I = RationalSquareMatrix.IdentityMatrix(A.Rows);
*
* B_n = A_n + b_n * I;
* sb.Append(@"&Bn = " + B_n.ToLatex() + @" \\ \\");
*
* A_n = A * B_n;
* sb.Append(@"&An = " + A_n.ToLatex() + @" \\ \\");
* }
*
* b_n = -A_n.Trace() / (i + 1);
* sb.Append(@"&bn = " + b_n.ToLatex() + @" \\ \\");
*
* AInv = 1/b_n * B_n;
* sb.Append(@"&A^{-1} = " + AInv.ToLatex() + @" \\ \\");
*
* sb.Append(@"\end{aligned}");
* HtmlOutputMethods.WriteLatexEqToHtmlAndLaunch(sb.ToString(), "Test_FaddevasMethod_Determinant.html"); //display Latex via mathjax
*/
return(0);
}
