This directory contains benchmark examples to decompose a pure dimensional solution set into irreducible components. The systems are given in their extrinsic embedded format, the last number in the file name is the dimension.

We have three families of problems:

1. Adjacent Minors of a 2-by-(n+1) matrix, n = 2,3,..,7
2. Cyclic n-roots problems, n = 4,8,9
3. Mechanical design

Description of the test problems:

```+----+------------+----------------------------------------------------+
|    | file name  |         description of the polynomial system       |
+----+------------+----------------------------------------------------+
|  1 | adjmin22e4 | adjacent 2-by-2 minors of a general 2-by-3 matrix  |
|  2 | adjmin23e5 | adjacent 2-by-2 minors of a general 2-by-4 matrix  |
|  3 | adjmin24e6 | adjacent 2-by-2 minors of a general 2-by-5 matrix  |
|  4 | adjmin25e7 | adjacent 2-by-2 minors of a general 2-by-6 matrix  |
|  5 | adjmin26e8 | adjacent 2-by-2 minors of a general 2-by-7 matrix  |
|  6 | adjmin27e9 | adjacent 2-by-2 minors of a general 2-by-8 matrix  |
|  7 | adjmin28eA | adjacent 2-by-2 minors of a general 2-by-9 matrix  |
|  8 | adjmin29eB | adjacent 2-by-2 minors of a general 2-by-10 matrix |
|  9 | adjmin2AeC | adjacent 2-by-2 minors of a general 2-by-11 matrix |
| 10 | adjmin2BeD | adjacent 2-by-2 minors of a general 2-by-12 matrix |
+----+------------+----------------------------------------------------+
| 11 | cyclic4e1  | cyclic 4-roots problem, defines two quadrics       |
| 12 | cyclic8e1  | cyclic 8-roots, 8 quadrics + 8 16-degree curves    |
| 13 | cyclic9e2  | cyclic 9-roots, defines six cubic 2-dim surfaces   |
+----+------------+----------------------------------------------------+
| 14 | sevenbare1 | seven bar mechanism which permits motion           |
| 15 | spatburme1 | spatial Burmester problem, body guidance           |
| 16 | grifdufAe1 | Griffis-Duffy platform, one large degree component |
| 17 | grifdufBe1 | Griffis-Duffy platform, components of low degree   |
+----+------------+----------------------------------------------------+
```

Characteristics of the test problems:

```+----+------------+------+------+------+------+
|    | file name  |   n  |  dim |  deg | #fac |
+----+------------+------+------+------+------+
|  1 | adjmin22e4 |   6  |   4  |    4 |   2  |
|  2 | adjmin23e5 |   8  |   5  |    8 |   3  |
|  3 | adjmin24e6 |  10  |   6  |   16 |   5  |
|  4 | adjmin25e7 |  12  |   7  |   32 |   8  |
|  5 | adjmin26e8 |  14  |   8  |   64 |  13  |
|  6 | adjmin27e9 |  16  |   9  |  128 |  21  |
|  7 | adjmin28eA |  18  |  10  |  256 |  34  |
|  8 | adjmin29eB |  20  |  11  |  512 |  55  |
|  9 | adjmin2AeC |  22  |  12  | 1024 |  89  |
| 10 | adjmin2BeD |  24  |  13  | 2048 | 144  |
+----+------------+------+------+------+------+
| 11 | cyclic4e1  |   4  |   1  |    4 |   2  |
| 12 | cyclic8e1  |   8  |   1  |  144 |  16  |
| 13 | cyclic9e2  |   9  |   2  |   18 |   6  |
+----+------------+------+------+------+------+
| 14 | sevenbare1 |  12  |   1  |    6 |   1  |
| 15 | spatburme1 |   6  |   1  |   20 |   1  |
| 16 | grifdufAe1 |   8  |   1  |   40 |  13  |
| 17 | grifdufBe1 |   8  |   1  |   40 |  17  |
+----+------------+------+------+------+------+

legend:
n     #variables = dimension of ambient space
dim   top dimension of solution set
deg   sum of degrees of all irreducible components
#fac  number of irreducible components
```