resolution of singularity not working

[jxs2628@…]

I tried to resolve the singularity below:

LIB "resolve.lib"; LIB "reszeta.lib"; LIB "resgraph.lib"; ring R=0,(x,y,z,w),dp; ideal I=x3+y3-zw,z3+w3-xy; complete intersection surface cusp singularity list L=resolve(I,1); debug mode

The computations always gets stuck at:

Overview of Current Chart +++++++++++++++++++++++ Current number of final charts: 8 Total number of charts currently in chart-tree: 37 Index of the current chart in chart-tree: 26 +++++++++++++++++++++++++++++++++++++++++++++++++

and does not produce a solution.

[hannes]

Inside resolve there are many Groebner basis computations both for determining the center (including computations with coefficient ideals and coefficient ideals of coefficient ideals, which are of high degrees) and for doing the blow-ups. One of these Groebner basis computations grows and grows without getting to an end in your example. It is this unpredictable behaviour of groebner bases which also makes the practical behaviour of the implementation of the resolution algorithm not very predictable. Even for hypersurface singularities, a resolution of something like x5 + y7 + z11 (prime and mutually coprime exponents) leads to a behaviour as you observed - here the computations become huge because of the need to either handle roots of unity or blow up at several points simultaneously.

Anne Fruehbis-Krueger