/// <inheritdoc/>
public override ExpNode Execute(MultiplicationOperNode node)
{
// TODO: Sinusoidal u substitutions
// TODO: Constants recognitions for v
Differentiator differentiator = new(_variable);
// \int{u'vwx} = uvwx - \int{uv'wx} - \int{uvw'x} - \int{uvwx'}
int partCount = node.ChildCount - 1;
// Get u and du
ExpNode du = node.GetChild(partCount);
ExpNode u = du.Clone().Execute(this);
// Get dvs and vs
ExpNode[] dvs = new ExpNode[partCount];
ExpNode[] vs = new ExpNode[partCount];
for (int i = 0; i < partCount; i++)
{
vs[i] = node.GetChild(i);
dvs[i] = vs[i].Clone().Execute(differentiator);
}
AdditionOperNode aNode = new();
// u*vs
MultiplicationOperNode mNode = new();
mNode.AddChild(u.Clone());
for (int i = 0; i < partCount; i++)
{
mNode.AddChild(vs[i].Clone());
}
aNode.AddChild(mNode);
// Combinatoric integrals
for (int i = 0; i < partCount; i++)
{
IntegralOperNode intNode = new();
mNode = new MultiplicationOperNode();
intNode.Variable = new VarValueNode(_variable);
mNode.AddChild(u.Clone());
for (int j = 0; j < partCount; j++)
{
if (i == j)
{
mNode.AddChild(dvs[j].Clone());
}
else
{
mNode.AddChild(vs[j].Clone());
}
}
intNode.AddChild(mNode);
aNode.AddChild(QuickOpers.Negative(intNode));
}
return(aNode);
}
private static ExpNode SineTable(SineOperNode node)
{
return(node.SineFunction switch
{
SineFunction.SINE => new SineOperNode(SineFunction.COSINE)
{
Child = node.Child
},
SineFunction.COSINE => QuickOpers.Negative(new SineOperNode(SineFunction.SINE)
{
Child = node.Child
}),
_ => node,
});
/// <inheritdoc/>
public override ExpNode Execute(RowElimOperNode node)
{
// Ensure matrix.
if (node.Child is TensorNode tensorNode && tensorNode.TensorType == TensorType.Matrix)
{
MatrixByRow matrix = new MatrixByRow(tensorNode);
int[] leadingPositions = RefHelpers.GetLeadingColumns(matrix);
// Put in row-echelon form
for (int i = 0; i < matrix.Height; i++)
{
int leftMostCol = RefHelpers.GetLeftMostColumn(leadingPositions, i);
matrix.SwapRows(i, leftMostCol);
Common.Swap(ref leadingPositions[i], ref leadingPositions[leftMostCol]);
if (leadingPositions[i] == -1)
{
continue;
}
matrix[i].MultiplyRow(QuickOpers.Reciprical(matrix[i][leadingPositions[i]]));
for (int j = i + 1; j < matrix.Height; j++)
{
matrix[j].AddRowToRow(matrix[i], QuickOpers.Negative(matrix[j][leadingPositions[i]]));
leadingPositions[j] = RefHelpers.GetLeadingColumn(matrix[j]);
}
}
if (node.EliminationMethod == RowElimMethod.GaussJordan)
{
// Put in reduced row-echelon form
for (int i = matrix.Height - 1; i > 0; i--)
{
for (int j = i - 1; j >= 0; j--)
{
matrix[j].AddRowToRow(matrix[i], QuickOpers.Negative(matrix[j][leadingPositions[i]]));
leadingPositions[j] = RefHelpers.GetLeadingColumn(matrix[j]);
}
}
}
return(matrix.AsExpNode());
}
return(HandleError(new CannotReduceNonMatrix(this, node.Child)));
}