Hi there,

On Wed, 18 Sep 2002, Tatiana Zolo wrote:

we need to use the function `lsolve()' that appears on page 5 of the tutorial for GiNaC 1.0.10, but not in the Concept Index. We couldn't find it elsewhere, not even in the specifications for the class matrix. We would like to know its specifications, if possible. In particular, we have linear systems whose associated matrix may have some linear dependencies.

That is indeed not very well documented, sorry. `lsolve()' is declared and implemented in inifcns.h and inifcns.cpp, respectively. It basically calls `matrix::solve()' where an appropiate elimination method is chosen heuristically. It also works on underdetermined linear systems, since the elimination tries to find an echelon form as opposed to a pure trinagular form. The solutions will then contain trivial entries like x==x (where `x' is a symbol). For that reason, a vector (or even matrix) of undeterminates needs to be passed to `matrix::solve()'.

You may either directly use `lsolve()' or `matrix::solve()'. The best way to find out how they are used is by looking into the check/ subdirectory and study the files {exam|check}_{matrices|lsolve}.cpp.

A formal specification is not given anywhere since there really isn't anyhting open for discussion -- solving linear systems not trivial but totally unambiguous. Either a solution exists and it is returned or the system is overdetermined and an exception is thrown by `matrix::solve()' in which case the list of solutions of `lsolve()' is empty. The only problematic thing may be the heuristic choice of elimination algorithm when the dimension of the system becomes larger than three, say. For that reason you may force it to use some algorithm of your choice. They may differ greatly in asymptotic runtime. Please refer to ginac/flags.h for an enumeration of such algorithms.

Regards -richy.