I had to have been trying to re-invent the STRIDER (steerable transport replaceable in-situ device employing rotation) earlier --- I just needed to locate under what denotational stone the outside world had ingeniously concealed it. Now that a colleague of longstanding has gently brought to my attention that such a gizmo is customarily referred to as the "wheel", permit me to share with the list my welcome enlightenment concerning systems of simultaneous algebraic inequalities. [A good deal of this material -- eg. Hilbert's 17-th problem -- I had previously encountered many years before, but still could not make the connection.] Buzzwords: the topic comes under headings "semialgebraic sets" or "real algebraic geometry"; basic notions include constructible sets, cylindrical decomposition (historical), triangular decomposition, CTD. There is an handy potted survey with plenty of citations at http://en.wikipedia.org/wiki/Real_algebraic_geometry MAPLE (version 17) has a package documented at http://www.maplesoft.com/support/help/Maple/view.aspx?path=SolveTools/SemiAl... together with a detailed discussion of the implementation at http://www.cecm.sfu.ca/~mmonagan/MITACS/papers/ConsSets.pdf This software proved inadequate to cope with `real-life' parametric problems, doubtless becoming bogged down in Gröbner bases; however it crunched happily (though leisurely) enough on non-parametric systems, inspection of relevant function plots having suggested suitable values to substitute for parameters. MAGMA also documents relevant tools in sect. 107 of the handbook, though it's not immediately clear how to utilise these to solve a given system. I have no information on MATHEMATICA: anybody else know? The current algorithm appears sufficiently practical and the implementation reliable to be usable for applications; and its utility to a mathematician is at least on a par with linear programming. More people should know about it! Fred Lunnon