Dear Mariano, dear Forum,

>> (The naming scheme for functions is sometimes surprising, going from verbs 
>> to adjectives to nouns... I hope in some parallel universe GAP has a better 
>> naming convention :) )

This may be of an interest - the manual for next version of GAP will have a 
section on naming conventions, 
shown below. In particular, it explains that a verb normally modify its 
argument(s) but does not return anything. 
Of course, there may be exceptions…

Best wishes,
Alexander


5.5 Naming Conventions

The way functions are named in GAP might help to memorize or even guess names 
of library functions.

If a variable name consists of several words then the first letter of each word 
is capitalized.

If the first part of the name of a function is a verb then the function may 
modify its argument(s) but does not return anything, for example Append 
(21.4-5) appends the list given as second argument to the list given as first 
argument. Otherwise the function returns an object without changing the 
arguments, for example Concatenation (21.20-1) returns the concatenation of the 
lists given as arguments.

If the name of a function contains the word "Of" then the return value is 
thought of as information deduced from the arguments. Usually such functions 
are attributes (see 13.5). Examples are GeneratorsOfGroup (39.2-3), which 
returns a list of generators for the group entered as argument, or 
DiagonalOfMat (24.12-1).

For the setter and tester functions of an attribute Attr the names SetAttr 
resp. HasAttr are available (see 13.5).

If the name of a function contains the word "By" then the return value is 
thought of as built in a certain way from the parts given as arguments. For 
example, creating a group as a factor group of a given group by a normal 
subgroup can be done by taking the image ofNaturalHomomorphismByNormalSubgroup 
(39.18-1). Other examples of "By" functions areGroupHomomorphismByImages 
(40.1-1) and LaurentPolynomialByCoefficients (66.13-1).

Often such functions construct an algebraic structure given by its generators 
(for example, RingByGenerators (56.1-4)). In some cases, "By" may be replaced 
by "With" (like e.g. GroupWithGenerators (39.2-2)) or even both versions of the 
name may be used. The difference between StructByGenerators and 
StructWithGenerators is that the latter guarantees that the GeneratorsOfStruct 
value of the result is equal to the given set of generators (see 31.3).

If the name of a function has the form "AsSomething" then the return value is 
an object (usually a collection which has the same family of elements), which 
may, for example:

• know more about its own structure (and so support more operations) than its 
input (e.g. if the elements of the collection form a group, then this group can 
be constructed using AsGroup (39.2-4));

• discard its additional structure (e.g. AsList (30.3-8) applied to a group 
will return a list of its elements);

• contain all elements of the original object without duplicates (like e.g. 
AsSet (30.3-10) does if its argument is a list of elements from the same 
family);

• remain unchanged (like e.g. AsSemigroup (51.1-5) does if its argument is a 
group).

If Something and the argument of AsSomething are domains, some further rules 
apply as explained in Tutorial: Changing the Structure.

If the name of a function fun1 ends with "NC" then there is another function 
fun2 with the same name except that the NC is missing. NCstands for "no check". 
When fun2 is called then it checks whether its arguments are valid, and if so 
then it calls fun1. The functionsSubgroupNC (39.3-1) and Subgroup (39.3-1) are 
a typical example.

The idea is that the possibly time consuming check of the arguments can be 
omitted if one is sure that they are unnecessary. For example, if an algorithm 
produces generators of the derived subgroup of a group then it is guaranteed 
that they lie in the original group; Subgroup(39.3-1) would check this, and 
SubgroupNC (39.3-1) omits the check.

Needless to say, all these rules are not followed slavishly, for example there 
is one operation Zero (31.10-3) instead of two operationsZeroOfElement and 
ZeroOfAdditiveGroup.

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