spacegrp -- detects the symmetry group of points in n-dimensional
space.
Usage: spacegrp [-p prec] [-e epsilon] [-acdgorlstv] vfile
The first two integers of vfile are number of vertices and dimension,
respectively. After these two numbers, the vertices are listed.
Whitespace, newlines are irrelevant. Can deal with "#" comments.
If no vfile specified, input becomes standard in.
"prec" is an integer specifying the precision of the symbolic
adjacency matrix.
"epsilon" is a small floating-point number used in determining
independance of vectors when giving the space group. The abstract
group is found before any linear algebra is done, so this number won't
effect the group size, only possibly the numerical accuracy of the
transformation matrices, eigenvalues, and eigenvectors printed.
-a print the permutation representation the group elements.
-c print a summary of the orders of the group elements.
-d print edge classes.
-g print group order.
-o print the order of each group element.
-r print the raw permutation matrix.
-s print the space representation of each group element
(the transformation matrix).
-t print the transpose of -s and -v
-u print the eigenvalues of each group element.
-v print the eigenvectors of each group element
(in rows if -t, columns otherwise).