public static void Execute()
{
CultureInfo.CurrentCulture = new CultureInfo("en-US");
//Define basis vectors before rotation
var u1 = "1<1>".GaPoTNumParseVector();
var u2 = "1<2>".GaPoTNumParseVector();
var u3 = "1<3>".GaPoTNumParseVector();
var u123 = GaPoTNumUtils.OuterProduct(u1, u2, u3);
Console.WriteLine($@"u1 = {u1.TermsToText()}");
Console.WriteLine($@"u2 = {u2.TermsToText()}");
Console.WriteLine($@"u3 = {u3.TermsToText()}");
Console.WriteLine();
Console.WriteLine($@"u123 = {u123.TermsToText()}");
Console.WriteLine($@"inverse(u1234) = {u123.Inverse().TermsToText()}");
Console.WriteLine();
//Define voltage vector basis e1, e2
var e1 = u2 - u1;
var e2 = u3 - u1;
var e12 = GaPoTNumUtils.OuterProduct(e1, e2);
Console.WriteLine($@"e1 = {e1.TermsToText()}");
Console.WriteLine($@"e2 = {e2.TermsToText()}");
Console.WriteLine($@"e12 = {e12.TermsToText()}");
Console.WriteLine();
//Ortho-normalize e1, e2
var orthoVectors = new[] { e1, e2 }.ApplyGramSchmidt(true).ToArray();
var c1 = orthoVectors[0];
var c2 = orthoVectors[1];
var c3 = -GaPoTNumUtils.OuterProduct(c1, c2).Gp(u123.Inverse()).GetVectorPart();
//Define basis vectors after rotation
var c123 = GaPoTNumUtils.OuterProduct(c1, c2, c3);
Console.WriteLine($@"c1 = {c1.TermsToText()}");
Console.WriteLine($@"c2 = {c2.TermsToText()}");
Console.WriteLine($@"c3 = {c3.TermsToText()}");
Console.WriteLine();
//Make sure c1,c2,c3 are mutually orthonormal
Console.WriteLine($@"c1 . c1 = {c1.DotProduct(c1):G}");
Console.WriteLine($@"c2 . c2 = {c2.DotProduct(c2):G}");
Console.WriteLine($@"c3 . c3 = {c3.DotProduct(c3):G}");
Console.WriteLine($@"c1 . c2 = {c1.DotProduct(c2):G}");
Console.WriteLine($@"c2 . c3 = {c2.DotProduct(c3):G}");
Console.WriteLine($@"c1 . c3 = {c1.DotProduct(c3):G}");
Console.WriteLine();
Console.WriteLine($@"c123 = {c123.TermsToText()}");
Console.WriteLine($@"inverse(c123) = {c123.Inverse().TermsToText()}");
Console.WriteLine();
//Find a simple rotor to get c1 from u1
var rotor1 = u1.GetRotorToVector(c1);
//Make sure this is a rotor
Console.WriteLine($@"rotor1 = {rotor1.TermsToText()}");
Console.WriteLine($@"reverse(rotor1) = {rotor1.Reverse().TermsToText()}");
Console.WriteLine($@"rotor1 gp reverse(rotor1) = {rotor1.Gp(rotor1.Reverse()).TermsToText()}");
Console.WriteLine();
//Rotate all basis vectors using rotor1
var u1_1 = u1.ApplyRotor(rotor1);
var u2_1 = u2.ApplyRotor(rotor1);
var u3_1 = u3.ApplyRotor(rotor1);
Console.WriteLine($@"rotation of u1 under rotor1 = {u1_1.TermsToText()}");
Console.WriteLine($@"rotation of u2 under rotor1 = {u2_1.TermsToText()}");
Console.WriteLine($@"rotation of u3 under rotor1 = {u3_1.TermsToText()}");
Console.WriteLine();
//Find a simple rotor to get c2 from u2_1
var rotor2 = u2_1.GetRotorToVector(c2);
//Make sure this is a rotor
Console.WriteLine($@"rotor2 = {rotor2.TermsToText()}");
Console.WriteLine($@"reverse(rotor2) = {rotor2.Reverse().TermsToText()}");
Console.WriteLine($@"rotor2 gp reverse(rotor2) = {rotor2.Gp(rotor2.Reverse()).TermsToText()}");
Console.WriteLine();
//Rotate all basis vectors using rotor2
var u1_2 = u1_1.ApplyRotor(rotor2);
var u2_2 = u2_1.ApplyRotor(rotor2);
var u3_2 = u3_1.ApplyRotor(rotor2);
Console.WriteLine($@"rotation of u1_1 under rotor2 = {u1_2.TermsToText()}");
Console.WriteLine($@"rotation of u2_1 under rotor2 = {u2_2.TermsToText()}");
Console.WriteLine($@"rotation of u3_1 under rotor2 = {u3_2.TermsToText()}");
Console.WriteLine();
//Compute final rotor as rotor3 gp rotor2 gp rotor1
var rotor = rotor2.Gp(rotor1);
//Make sure this is a rotor
Console.WriteLine($@"rotor = {rotor.TermsToText()}");
Console.WriteLine($@"reverse(rotor) = {rotor.Reverse().TermsToText()}");
Console.WriteLine($@"rotor gp reverse(rotor) = {rotor.Gp(rotor.Reverse()).TermsToText()}");
Console.WriteLine();
//Rotate all original basis vectors using final rotor to make sure it's the correct one
var cc1 = u1.ApplyRotor(rotor);
var cc2 = u2.ApplyRotor(rotor);
var cc3 = u3.ApplyRotor(rotor);
Console.WriteLine($@"rotation of u1 under rotor = {cc1.TermsToText()}");
Console.WriteLine($@"rotation of u2 under rotor = {cc2.TermsToText()}");
Console.WriteLine($@"rotation of u3 under rotor = {cc3.TermsToText()}");
Console.WriteLine();
//Find the projections of u1, u2, u3 on e12
var pu1 = u1.GetProjectionOnBlade(e12);
var pu2 = u2.GetProjectionOnBlade(e12);
var pu3 = u3.GetProjectionOnBlade(e12);
Console.WriteLine($@"projection of u1 on e12 = {pu1.TermsToText()}");
Console.WriteLine($@"projection of u2 on e12 = {pu2.TermsToText()}");
Console.WriteLine($@"projection of u3 on e12 = {pu3.TermsToText()}");
Console.WriteLine();
Console.WriteLine($@"angle between projections of u1,u2 on e12 = {pu1.GetAngle(pu2).RadiansToDegrees():G}");
Console.WriteLine($@"angle between projections of u2,u3 on e12 = {pu2.GetAngle(pu3).RadiansToDegrees():G}");
Console.WriteLine($@"angle between projections of u1,u3 on e12 = {pu1.GetAngle(pu3).RadiansToDegrees():G}");
Console.WriteLine();
}
public static void Execute()
{
var n = 3;
var fbdFrame = GaPoTNumFrame.CreateFbdFrame(n);
var m1 = fbdFrame.GetMatrix(n - 1).GetLaTeXArray();
var m2 = fbdFrame.GetInnerProductsMatrix().GetLaTeXArray();
var m3 = fbdFrame.GetInnerAnglesInDegreesMatrix().GetLaTeXArray();
Console.WriteLine("FBD Frame Matrix:");
Console.WriteLine(m1);
Console.WriteLine();
Console.WriteLine("FBD Frame Inner Products Matrix:");
Console.WriteLine(m2);
Console.WriteLine();
Console.WriteLine("FBD Frame Inner Angles Matrix:");
Console.WriteLine(m3);
Console.WriteLine();
//return;
var sourceFrame = GaPoTNumFrame.CreateBasisFrame(n);
var uPseudoScalar = GaPoTNumMultivector
.CreateZero()
.SetTerm((1 << n) - 1, 1.0d);
for (var refVectorIndex = 0; refVectorIndex < n; refVectorIndex++)
{
Console.Write(@"\section{Reference vector: $\mu_" + (refVectorIndex + 1) + "$}");
Console.WriteLine();
var kirchhoffFrameBase = GaPoTNumFrame.CreateEmptyFrame();
var refVector = sourceFrame[refVectorIndex];
for (var i = 0; i < n; i++)
{
if (i == refVectorIndex)
{
continue;
}
kirchhoffFrameBase.AppendVector(sourceFrame[i] - refVector);
}
var kirchhoffFramesList =
kirchhoffFrameBase.GetFramePermutations();
var j = 1;
foreach (var kirchhoffFrame in kirchhoffFramesList)
{
Console.Write(@"\subsection{Kirchhoff Frame Permutation " + j + "}");
Console.WriteLine();
var targetFrame = kirchhoffFrame.GetOrthogonalFrame(true);
targetFrame.AppendVector(
-GaPoTNumUtils
.OuterProduct(targetFrame)
.Gp(uPseudoScalar.CliffordConjugate())
.GetVectorPart()
);
Debug.Assert(
targetFrame.IsOrthonormal()
);
Debug.Assert(
sourceFrame.HasSameHandedness(targetFrame)
);
DisplayFrames(
sourceFrame,
kirchhoffFrame,
targetFrame
);
j++;
}
}
}
public static void Execute()
{
CultureInfo.CurrentCulture = new CultureInfo("en-US");
//Define basis vectors before rotation
var u1 = "1<1>".GaPoTNumParseVector();
var u2 = "1<2>".GaPoTNumParseVector();
var u3 = "1<3>".GaPoTNumParseVector();
var u4 = "1<4>".GaPoTNumParseVector();
var u1234 = GaPoTNumUtils.OuterProduct(u1, u2, u3, u4);
Console.WriteLine($@"u1 = {u1.TermsToText()}");
Console.WriteLine($@"u2 = {u2.TermsToText()}");
Console.WriteLine($@"u3 = {u3.TermsToText()}");
Console.WriteLine($@"u4 = {u4.TermsToText()}");
Console.WriteLine();
Console.WriteLine($@"u1234 = {u1234.TermsToText()}");
Console.WriteLine($@"inverse(u1234) = {u1234.Inverse().TermsToText()}");
Console.WriteLine();
//Define basis vectors after rotation
var c1 = "1<1>, -1<4>".GaPoTNumParseVector() / Math.Sqrt(2);
var c2 = "-1<1>, 2<2>, -1<4>".GaPoTNumParseVector() / Math.Sqrt(6);
var c3 = "-1<1>, -1<2>, 3<3>, -1<4>".GaPoTNumParseVector() / Math.Sqrt(12);
var c4 = -GaPoTNumUtils.OuterProduct(c1, c2, c3).Gp(u1234.Inverse()).GetVectorPart();
var c1234 = GaPoTNumUtils.OuterProduct(c1, c2, c3, c4);
Console.WriteLine($@"c1 = {c1.TermsToText()}");
Console.WriteLine($@"c2 = {c2.TermsToText()}");
Console.WriteLine($@"c3 = {c3.TermsToText()}");
Console.WriteLine($@"c4 = {c4.TermsToText()}");
Console.WriteLine();
//Make sure c1,c2,c3,c4 are mutually orthonormal
Console.WriteLine($@"c1 . c1 = {c1.DotProduct(c1):G}");
Console.WriteLine($@"c2 . c2 = {c2.DotProduct(c2):G}");
Console.WriteLine($@"c3 . c3 = {c3.DotProduct(c3):G}");
Console.WriteLine($@"c4 . c4 = {c4.DotProduct(c4):G}");
Console.WriteLine($@"c1 . c2 = {c1.DotProduct(c2):G}");
Console.WriteLine($@"c2 . c3 = {c2.DotProduct(c3):G}");
Console.WriteLine($@"c3 . c4 = {c3.DotProduct(c4):G}");
Console.WriteLine($@"c4 . c1 = {c4.DotProduct(c1):G}");
Console.WriteLine($@"c1 . c3 = {c1.DotProduct(c3):G}");
Console.WriteLine($@"c2 . c4 = {c2.DotProduct(c4):G}");
Console.WriteLine();
Console.WriteLine($@"c1234 = {c1234.TermsToText()}");
Console.WriteLine($@"inverse(c1234) = {c1234.Inverse().TermsToText()}");
Console.WriteLine();
//Find angles between basis vectors
var ang1 = u1.GetAngle(c1);
var ang2 = u2.GetAngle(c2);
var ang3 = u3.GetAngle(c3);
var ang4 = u4.GetAngle(c4);
Console.WriteLine($@"Angle1 = {ang1.RadiansToDegrees():G}");
Console.WriteLine($@"Angle2 = {ang2.RadiansToDegrees():G}");
Console.WriteLine($@"Angle3 = {ang3.RadiansToDegrees():G}");
Console.WriteLine($@"Angle4 = {ang4.RadiansToDegrees():G}");
Console.WriteLine();
var rotor = c1.ToMultivector().Gp(u1.ToMultivector()) + c2.ToMultivector().Gp(u2.ToMultivector()) + c3.ToMultivector().Gp(u3.ToMultivector()) + c4.ToMultivector().Gp(u4.ToMultivector());
rotor = rotor / rotor.Norm();
//Make sure this is actually a versor
Console.WriteLine($@"rotor = {rotor.TermsToText()}");
Console.WriteLine($@"rotor gp inverse(rotor) = {rotor.Gp(rotor.Inverse()).TermsToText()}");
Console.WriteLine();
var cc1 = u1.ApplyRotor(rotor);
var cc2 = u2.ApplyRotor(rotor);
var cc3 = u3.ApplyRotor(rotor);
var cc4 = u4.ApplyRotor(rotor);
Console.WriteLine($@"cc1 = {cc1.TermsToText()}");
Console.WriteLine($@"cc2 = {cc2.TermsToText()}");
Console.WriteLine($@"cc3 = {cc3.TermsToText()}");
Console.WriteLine($@"cc4 = {cc4.TermsToText()}");
Console.WriteLine();
Console.WriteLine($@"c1 - cc1 = {(c1 - cc1).TermsToText()}");
Console.WriteLine($@"c2 - cc2 = {(c2 - cc2).TermsToText()}");
Console.WriteLine($@"c3 - cc3 = {(c3 - cc3).TermsToText()}");
Console.WriteLine($@"c4 - cc4 = {(c4 - cc4).TermsToText()}");
Console.WriteLine();
}
public static void Execute()
{
CultureInfo.CurrentCulture = new CultureInfo("en-US");
//Define basis vectors before rotation
var u1 = "1<1>".GaPoTNumParseVector();
var u2 = "1<2>".GaPoTNumParseVector();
var u3 = "1<3>".GaPoTNumParseVector();
var u4 = "1<4>".GaPoTNumParseVector();
var u1234 = GaPoTNumUtils.OuterProduct(u1, u2, u3, u4);
Console.WriteLine($@"u1 = {u1.TermsToText()}");
Console.WriteLine($@"u2 = {u2.TermsToText()}");
Console.WriteLine($@"u3 = {u3.TermsToText()}");
Console.WriteLine($@"u4 = {u4.TermsToText()}");
Console.WriteLine();
Console.WriteLine($@"u1234 = {u1234.TermsToText()}");
Console.WriteLine($@"inverse(u1234) = {u1234.Inverse().TermsToText()}");
Console.WriteLine();
//Define voltage vector basis e1, e2, e3
var e1 = u2 - u1;
var e2 = u3 - u1;
var e3 = u4 - u1;
var e123 = GaPoTNumUtils.OuterProduct(e1, e2, e3);
Console.WriteLine($@"e1 = {e1.TermsToText()}");
Console.WriteLine($@"e2 = {e2.TermsToText()}");
Console.WriteLine($@"e3 = {e3.TermsToText()}");
Console.WriteLine($@"e123 = {e123.TermsToText()}");
Console.WriteLine();
//Ortho-normalize e1, e2, e3
var orthoVectors = new[] { e1, e2, e3 }.ApplyGramSchmidt(true).ToArray();
var c1 = orthoVectors[0];
var c2 = orthoVectors[1];
var c3 = orthoVectors[2];
var c4 = -GaPoTNumUtils.OuterProduct(c1, c2, c3).Gp(u1234.Inverse()).GetVectorPart();
var c1234 = GaPoTNumUtils.OuterProduct(c1, c2, c3, c4);
Console.WriteLine($@"c1 = {c1.TermsToText()}");
Console.WriteLine($@"c2 = {c2.TermsToText()}");
Console.WriteLine($@"c3 = {c3.TermsToText()}");
Console.WriteLine($@"c4 = {c4.TermsToText()}");
Console.WriteLine();
//Make sure c1,c2,c3,c4 are mutually orthonormal
Console.WriteLine($@"c1 . c1 = {c1.DotProduct(c1):G}");
Console.WriteLine($@"c2 . c2 = {c2.DotProduct(c2):G}");
Console.WriteLine($@"c3 . c3 = {c3.DotProduct(c3):G}");
Console.WriteLine($@"c4 . c4 = {c4.DotProduct(c4):G}");
Console.WriteLine($@"c1 . c2 = {c1.DotProduct(c2):G}");
Console.WriteLine($@"c2 . c3 = {c2.DotProduct(c3):G}");
Console.WriteLine($@"c3 . c4 = {c3.DotProduct(c4):G}");
Console.WriteLine($@"c4 . c1 = {c4.DotProduct(c1):G}");
Console.WriteLine($@"c1 . c3 = {c1.DotProduct(c3):G}");
Console.WriteLine($@"c2 . c4 = {c2.DotProduct(c4):G}");
Console.WriteLine();
Console.WriteLine($@"c1234 = {c1234.TermsToText()}");
Console.WriteLine($@"inverse(c1234) = {c1234.Inverse().TermsToText()}");
Console.WriteLine();
//Find a simple rotor to get c1 from u1
var rotor1 = u1.GetRotorToVector(c1);
//Make sure this is a rotor
Console.WriteLine($@"rotor1 = {rotor1.TermsToText()}");
Console.WriteLine($@"reverse(rotor1) = {rotor1.Reverse().TermsToText()}");
Console.WriteLine($@"rotor1 gp reverse(rotor1) = {rotor1.Gp(rotor1.Reverse()).TermsToText()}");
Console.WriteLine();
//Rotate all basis vectors using rotor1
var u1_1 = u1.ApplyRotor(rotor1);
var u2_1 = u2.ApplyRotor(rotor1);
var u3_1 = u3.ApplyRotor(rotor1);
var u4_1 = u4.ApplyRotor(rotor1);
Console.WriteLine($@"rotation of u1 under rotor1 = {u1_1.TermsToText()}");
Console.WriteLine($@"rotation of u2 under rotor1 = {u2_1.TermsToText()}");
Console.WriteLine($@"rotation of u3 under rotor1 = {u3_1.TermsToText()}");
Console.WriteLine($@"rotation of u4 under rotor1 = {u4_1.TermsToText()}");
Console.WriteLine();
//Find a simple rotor to get c2 from u2_1
var rotor2 = u2_1.GetRotorToVector(c2);
//Make sure this is a rotor
Console.WriteLine($@"rotor2 = {rotor2.TermsToText()}");
Console.WriteLine($@"reverse(rotor2) = {rotor2.Reverse().TermsToText()}");
Console.WriteLine($@"rotor2 gp reverse(rotor2) = {rotor2.Gp(rotor2.Reverse()).TermsToText()}");
Console.WriteLine();
//We can combine the two simple rotors to get <c1, c2> from <u1, u2> directly
var rotor21 = rotor2.Gp(rotor1);
Console.WriteLine($@"rotor21 = {rotor21.TermsToText()}");
Console.WriteLine($@"reverse(rotor21) = {rotor21.Reverse().TermsToText()}");
Console.WriteLine($@"rotor21 gp reverse(rotor21) = {rotor21.Gp(rotor21.Reverse()).TermsToText()}");
Console.WriteLine();
Console.WriteLine($@"rotation of u1 under rotor21 = {u1.ApplyRotor(rotor21).TermsToText()}");
Console.WriteLine($@"rotation of u2 under rotor21 = {u2.ApplyRotor(rotor21).TermsToText()}");
Console.WriteLine($@"rotation of u3 under rotor21 = {u3.ApplyRotor(rotor21).TermsToText()}");
Console.WriteLine($@"rotation of u4 under rotor21 = {u4.ApplyRotor(rotor21).TermsToText()}");
Console.WriteLine();
//Rotate all basis vectors using rotor2
var u1_2 = u1_1.ApplyRotor(rotor2);
var u2_2 = u2_1.ApplyRotor(rotor2);
var u3_2 = u3_1.ApplyRotor(rotor2);
var u4_2 = u4_1.ApplyRotor(rotor2);
Console.WriteLine($@"rotation of u1_1 under rotor2 = {u1_2.TermsToText()}");
Console.WriteLine($@"rotation of u2_1 under rotor2 = {u2_2.TermsToText()}");
Console.WriteLine($@"rotation of u3_1 under rotor2 = {u3_2.TermsToText()}");
Console.WriteLine($@"rotation of u4_1 under rotor2 = {u4_2.TermsToText()}");
Console.WriteLine();
//Find a simple rotor to get c3 from u3_2
var rotor3 = u3_2.GetRotorToVector(c3);
//Make sure this is a rotor
Console.WriteLine($@"rotor3 = {rotor3.TermsToText()}");
Console.WriteLine($@"reverse(rotor3) = {rotor3.Reverse().TermsToText()}");
Console.WriteLine($@"rotor3 gp reverse(rotor3) = {rotor3.Gp(rotor3.Reverse()).TermsToText()}");
Console.WriteLine();
//Rotate all basis vectors using rotor2
var u1_3 = u1_2.ApplyRotor(rotor3);
var u2_3 = u2_2.ApplyRotor(rotor3);
var u3_3 = u3_2.ApplyRotor(rotor3);
var u4_3 = u4_2.ApplyRotor(rotor3);
Console.WriteLine($@"rotation of u1_2 under rotor3 = {u1_3.TermsToText()}");
Console.WriteLine($@"rotation of u2_2 under rotor3 = {u2_3.TermsToText()}");
Console.WriteLine($@"rotation of u3_2 under rotor3 = {u3_3.TermsToText()}");
Console.WriteLine($@"rotation of u4_2 under rotor3 = {u4_3.TermsToText()}");
Console.WriteLine();
//Compute final rotor as rotor3 gp rotor2 gp rotor1
var rotor = rotor3.Gp(rotor2).Gp(rotor1);
//Make sure this is a rotor
Console.WriteLine($@"rotor = {rotor.TermsToText()}");
Console.WriteLine($@"reverse(rotor) = {rotor.Reverse().TermsToText()}");
Console.WriteLine($@"rotor gp reverse(rotor) = {rotor.Gp(rotor.Reverse()).TermsToText()}");
Console.WriteLine();
//Are the two rotors are orthogonal? No.
//var diffRotors = rotor21.Gp(rotor3) - rotor3.Gp(rotor21);
//Console.WriteLine($@"Are the two rotors are orthogonal (0 means Yes)? {diffRotors.TermsToText()}");
//Console.WriteLine();
//Rotate all original basis vectors using final rotor
var cc1 = u1.ApplyRotor(rotor);
var cc2 = u2.ApplyRotor(rotor);
var cc3 = u3.ApplyRotor(rotor);
var cc4 = u4.ApplyRotor(rotor);
Console.WriteLine($@"rotation of u1 under rotor = {cc1.TermsToText()}");
Console.WriteLine($@"rotation of u2 under rotor = {cc2.TermsToText()}");
Console.WriteLine($@"rotation of u3 under rotor = {cc3.TermsToText()}");
Console.WriteLine($@"rotation of u4 under rotor = {cc4.TermsToText()}");
Console.WriteLine();
//Find the projections of u1, u2, u3, u4 on e234
var pu1 = u1.GetProjectionOnBlade(e123);
var pu2 = u2.GetProjectionOnBlade(e123);
var pu3 = u3.GetProjectionOnBlade(e123);
var pu4 = u4.GetProjectionOnBlade(e123);
Console.WriteLine($@"projection of u1 on e123 = {pu1.TermsToText()}");
Console.WriteLine($@"projection of u2 on e123 = {pu2.TermsToText()}");
Console.WriteLine($@"projection of u3 on e123 = {pu3.TermsToText()}");
Console.WriteLine($@"projection of u4 on e123 = {pu4.TermsToText()}");
Console.WriteLine();
Console.WriteLine($@"angle between projections of u1,u2 on e123 = {pu1.GetAngle(pu2).RadiansToDegrees():G}");
Console.WriteLine($@"angle between projections of u2,u3 on e123 = {pu2.GetAngle(pu3).RadiansToDegrees():G}");
Console.WriteLine($@"angle between projections of u1,u3 on e123 = {pu1.GetAngle(pu3).RadiansToDegrees():G}");
Console.WriteLine($@"angle between projections of u1,u4 on e123 = {pu1.GetAngle(pu4).RadiansToDegrees():G}");
Console.WriteLine($@"angle between projections of u2,u4 on e123 = {pu2.GetAngle(pu4).RadiansToDegrees():G}");
Console.WriteLine($@"angle between projections of u3,u4 on e123 = {pu3.GetAngle(pu4).RadiansToDegrees():G}");
Console.WriteLine();
}