At https://github.com/sagemath/sage/pull/40875, Frédéric is harmonizing the 
prefix of the names of methods returning the number of facets (points, 
vertices, parts, etc.) of polytopes to `n_facets`, before it was `nfacets`.

While I think this is very good, I would rather go one tiny step further, 
and harmonize both to `number_of_facets`, or, in fact, just make 
`number_of_facets` an alias.

My question here is: is anybody strictly against this?  More precisely:

Any method returning the number of some components of a structure should be 
named `number_of_xxx`, other aliases are OK.

I did a quick grep, the current situation is as follows:

grep -r --include=*.{py,pyx} --color=auto -nH --null -e "def[^(]* 
number_of_.*(" *
125 matches

grep -r --include=*.{py,pyx} --color=auto -nH --null -e "def[^(]* num_.*(" *
22 matches
most important example: graph.num_verts

grep -r --include=*.{py,pyx} --color=auto -nH --null -e "def[^(]* n_.*(" *
97 matches
mostly geometry/polyhedron

most important example for nxxx is of course ngens, and I'm afraid we 
shouldn't rename that one.  But there is also `nvars` (in sat/solvers), 
`ncols` and `nrows` for matrices, `ncusps` in `arithgroup`, and the 
polytope methods.

Finally, there are a few really odd ones, which I stumble across every 
other month (and hate): 

combinat/binary_tree.py:1752:    def left_children_node_number(self, 
direction='left'):
combinat/binary_tree.py:2600:    def hook_number(self):
combinat/abstract_tree.py:1159:    def node_number(self):
combinat/permutation.py:2442:    def 
longest_increasing_subsequences_number(self):
combinat/posets/posets.py:2714:    def relations_number(self):

Martin

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