Constraint Hierarchies as Triangular Systems

Constraint hierarchies where each constraint is an equation, are considered in this report. Each of the equations is labelled with a preference so that one is able to allow inconsistent equations to be included in such a hierarchy. Such constraint hierarchies are treated as triangular systems, whereby one can easily see the relationship between triangular matrices and local propagation for acyclic constraint hierarchies and the relationship between block triangular matrices and cyclic constraint hierarchies. A constraint solver, Triangular Solver, has been designed based on the triangularization of equation systems. This solver is able to solve simultaneous linear equations which correspond to cycles in a constraint network. Constraint hierarchies are solved using locally-predicate-better comparator. The solver can be invoked via three procedures, solveAll for solving an entire constraint hierarchy, addOne for adding a new constraint to a solved system and removeOne for removing a co..