03/04/83 I wrote MUMATRIX.FIX to improve the performance of the mumath package MATRIX.ARR (version 2.10). After you have loaded MATRIX.ARR together with its prerequisite files, enter the musimp command "RDS (MUMATRIX,FIX);". This produces the following changes: 1) The function IDMAT is redefined so that IDMAT now generates a square identity matrix instead of a truncated lower triangular matrix. This alteration fixes a serious bug in the "\" function. The bug causes an incorrect calculation of EX1\EX2 when EX1 and EX2 do not commute. 2) The transpose function is redefined so that now the transpose of a column matrix (column of rows) is also a column matrix. As a result the symmetric and antisymmetric parts of a square column matrix can be extracted in the usual way. The original transpose function converts a column matrix to a row matrix (row of columns), a result which unfortunately does not add correctly with a column matrix. The documented procedure for converting a row matrix to a column matrix, multiplication by the appropriate identity matrix, is extremely slow. The new transpose function is extremely fast. 3) A new recognizer function NULL is defined. This function returns TRUE if its argument is zero or an array whose elements are all zero (a condition not recognized by ZERO); otherwise NULL returns FALSE. ------------------------------------------------------------- NOTE: I have recently completed a major extension of mumath for advanced applications. The extension supports total differentiation with respect to an arbitrary function, floating point approximation to arbitrary order, and abstract non- commutative multiplication. If you might be interested in beta testing any or all of these extensions, leave a message for me on this RBBS. Karl Kornacker Columbus, Ohio --------------------------------------------------------------  .