**Notation of the exceptional divisors: ** An
element of the list of exceptional divisors consists of the symbolic
name (e.g. **E _{1}**) of the divisor and the list of charts
in which it appears (i.e. in which its restriction is nonempty),
together with the index of the E element of the basic object with
largest dimension which defines it.

**Description of blowing up centers: ** The third
column contains the value of the stratifying function along the center
of the blowing up which created the exceptional divisor (defined on
the same row). Under the function value appears the list of charts in
which the center appears (i.e. in which its restriction is nonempty).
Under that one finds the list of indices of ("global") exceptional
divisors which contain the blowing up center (at the stage of the
resolution when it was computed). The last datum is the dimension of
the center.

**Remark: ** The boldface chart IDs mark the
charts of the final ambient variety (in which the resolution problem
is solved (modulo hypersurface blowing ups)).

**What does the stratifying function value consist
of?: ** We used the definition of the function
which can be found in the paper: *A Course on Constructive
Desingularization and Equivariance*, S. Encinas and
O. Villamayor, in *Resolution of Singularities, A research
textbook in tribute to Oscar Zariski* editors H. Hauser,
J. Lipman, F. Oort, A. Quirós, Progress in
Mathematics 181, Birkhäuser Boston, 2000.

The values of the subfunctions which are computed in different dimensions are separated by parentheses or brackets. The values of the generic (nontrivial) branch of the function appear in brackets, while the values of the monomial and good-point branches in parentheses (please recall that any value in parentheses is smaller than any other in brackets (provided that they measure resolution problems of the same dimension)).

The order components of the values should be understood as rational
orders computed for powered ideals (see, for instance, *Two
computational techniques for singularity resolution*,
G. Bodnár and J. Schicho, *Journal of Symbolic
Computation*, **32**(1-2): 39-54, 2001, or *Algorithmic
Resolution of Singularities*, G. Bodnár, PhD thesis,
Johannes Kepler University, RISC-Linz, 2000), which are just the
**c** components of weighted basic objects. In the same context,
the exponents in the **a** functions can also well be rational
numbers.

The last component of the parenthesized function values stands for the list of exceptional divisors defining the blowing up center in the monomial case. The numbers in these lists index the global exceptional divisor list (therefore they can be different from the numbers that appear in the chart data or in the chart tree).

Asterisks mark the case when the codimension-one part of the maximum stratum is not empty, thus the maximal function value is 'infinity'.

**Notation of the hyperbonds: ** A hyperbond is
defined by the indices of the vertices which it connects. A pair
defines an edge, a triple a face, a quadruple a solid, etc.

The list does not contain those hyperbonds of lower dimension which are implied by higher dimensional ones. That is, if there is a face between three vertices, say [1,2,3], then the edges between all the pairs of the vertices, [1,2],[1,3],[2,3], are implied by the face .