Add documentation what the Q-class abbreviations min.1, max.1 or group.1 refer to?

[kiryph]

For degree = 2 output of Q_catalog:

abbreviation  degree  symbol  order  discriminant  zclasses  affine_classes  torsionfree_space_groups  con_classes_number  idempotent_number

min.2  2  1,1   1  (2)^1  1  1  1  1   1
group.1  2  1,1   2  (2)^1  1  1  0  2   1
min.3  2  1;1   2  (2)^2  2  3  1  2   2
group.2  2  1;1   4  (2)^2  2  4  0  4   2
min.4  2  2-1   4  (2)^2  1  1  0  4   1
max.2  2  2-1   8  (2)^4  1  2  0  5   1
max.3  2  2-2   12  (1)^2(3)^2  1  1  0  6   1
min.5  2  2-2   3  (1)^1(3)^1  1  1  0  3   1
group.3  2  2-2   6  (1)^1(3)^1  1  1  0  6   1
group.4  2  2-2   6  (1)^2(3)^2  2  2  0  3   1

Conditions:   degree = 2
Q_Classes: # 10,   Z_Classes: # 13,   Affine Classes: #17

IMHO, the used abbreviations, e.g. min.2/max.2/group.1 for Q-classes are not self-explanatory.

Apparently the first level sorting is done by the family symbol. I am not sure what the second level is.

Can you add to the documentation of carat and the help of Q_catalog what min/max/group and the integer refer to?

It helps user to make sense of it. I have no idea what group.3 or group.4 mean. What is enumerated (families) ?

I checked the existing documentation, e.g.:

• https://lbfm-rwth.github.io/carat/doc/progs/Name.html
• https://lbfm-rwth.github.io/carat/doc/progs/Reverse_name.html

and also corresponding publications:

• Counting Crystallographic Groups in Low Dimension (2000)
• Crystallographic Algorithms and Tables (1998)

and the source code of CARAT. But could not find any hint.

Only the family symbol f.s. $(d_1-\alpha_1,...,d_1-\alpha_1;d_2-\alpha_2,...,d_2-\alpha_2;...;d_a-\alpha_a,...d_a-\alpha_a)$ is explained.