since version 1.0.0. This is the only allowed root element. The potential children are linearProgram, sparseVector, sparseMatrix, and linearProgramSolution. None of these children are requried and there is no limit on how many are present. A sparseVector is composed of two vectors. They are idx which is an index vector and nonz which is the vector of nonzero elements. This is a sparse matrix stored either by columns or rows. The vector pntANonz points to the end of a column (row) of nonzero elements. The nonzero elements are stored in the matrix aNonz. The vector numNonz, if present, stores the number of nonzero elements in the column (row). If numNonz is not present, then nonz stores the columns (rows) in matrix order. If the matrix is stored by column (row) rowIdx (colIdx) is the vector of row (colulmn) indices. The primary construct, it is made up of columns section, rows section, sparseMatrix section, and lpDescription section. The result of solving the linear program. At present it is composed of sparseVectors for the primal and dual solution. Plus a status element and a non-required solver message. A dense vector of integers or base64 binary data. A dense vector of doubles or base64. Since XML is so verbose, we may wish to store sparseMatrix as base64Binary data. Especially the pntANonz vector. We can store any of the sparseMatrix vectors as simply base64BinaryData instead of as a MathML vector. There is also an attribute on this element sizeOf which is the number of bytes in the attribute numericType. The basic properities of the linear program, such as the source number of rows and columns This is for the future -- allow our sparseMatrix of nonzero elements, nonz, to contain nonlinear expressions. For exmaple, if it is a Jacobian. A primal or dual solution vector This is an attribute in the column element. It can take on the values of rhs, continuous, binary, or integer. This goes in the lpDescription and tells us if we have a max or min to solve If we are storing data as base64BinaryData we need to know what we are storing. Current values are double, float, decimal, int, long, and string. The result of solving the linear program. The possibilities are optimalSolutionFound, unbounded, infeasible, or alternativeOptima