1Would like to thartk At Barr for his support and encouragement of the publication

of this research. Al Barr and Ronen Bat-d have provided many

helpful comments md suggestions. This work was funded, in part, by IBM,

Hewlett-Packard, and the National Science Foundation.

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Appendix - A Robust Test for Global Parameterizability

Consider an rdimcnsicmsl manifold defined as he solution [o a systim of n - r cquxtiOnsin

npamnWem(r E{ O,l,.. ,,n- l)):

fl(~l!~2,..., %) = o

Jkr(xl, q,...,%) = o

~lvenamtofrpmt=iAka,A= {kl, k2, . ..lk,), andmintavat XE 1“,

we detioss subimewufof X overA ass set dependiion rpammelm fY17Y2). ..?Yrk

yj E Xk,. ~fi~ by

Thus, a subint~sl is m intervat subset of X, r of whose com-diitez area specikt

C02kSW2t. and the rest of whose CO02dinStCSu= tbc karrx3as in X.

The sokution to a system of n - r equations in n pamwrem is Cstkedgk2k47lfypammstsn”

oz61e inrherparametas indexsdby A overanintavat Xifrhemisatrnmt

one soJution to he system in my subintenak of X overA. Put - sizqrly, the system

of equations is globally parameteriz.skdeif r parameters can be fuund -h that dzsre is

at most ane sotution to the systcm for my paAculsr vahze of ths r pmametm in ths