Support consistency checks for Vector, Matrix

[ThomasBreuer]

The idea is to admit/force consistency checks in the constructions of vector and matrix objects, via Vector, NewVector, Matrix, NewMatrix:
One either may want to make sure that the given arguments are consistent (e.g., the entries are really in the given ring, the intended shape of a matrix fits to the given number of columns, and the entries also fit to the intended representation) or one wants to omit such checks if possible.

Some problems have been described in #4884, #5133, #5135.
(Consistency checks will also be needed in operations that change existing vector and matrix objects, such as assignments via :=.)

I propose to use a global option Check that is supported by Vector, NewVector, Matrix, and NewMatrix, as follows:
If Check is false then the code for methods of these operations is allowed to omit consistency checks, otherwise consistency checks are recommended for methods of NewVector and NewMatrix.

(Before that, I had tried the idea to introduce new operations VectorNC and NewVectorNC (likewise for matrices) such that

• Vector computes the necessary data for calling NewVector,
• VectorNC computes the necessary data for calling NewVectorNC,
• NewVector first checks for consistency and then calls NewVectorNC.
  Up to now, each implementation of a new type of vector objects must provide a NewVector method. After the change, a NewVectorNC method would be needed for each type of vector objects.
  Due to the fact that NewVector and NewVectorNC must be constructors (in the sense of GAP, i. e., they get created with DeclareConstructor), we cannot have one default method for NewVector with the above behaviour.
  Thus each implementation of a new type of vector objects would have to provide also a NewVector method.
  This idea does not look sensible.)

[fingolfin]

I note that the majority of our existing global options are all-lowercase. I wonder if we have established any rules on this anywhere?

[fingolfin]

Wasn't the idea to insert (optional) checks into these Matrix functions, to validate things like that nrCols and Length(list) are compatible, that the given lists don't have holes, that entries are contained in the given basedomain etc ?

[ThomasBreuer]

My point of view is as follows:

The documentation says that implementing new types of matrix objects requires the installation of a NewMatrix method,
whereas there are default Matrix methods which compute the missing arguments for NewMatrix.
The question whether the arguments of Matrix (and hence the arguments that are then passed to NewMatrix) are consistent depends on the type of the matrix objects in question; it may be required that all matrix entries lie in the base domain, or more general situations are possible. The documentation is (deliberately?) vague in this respect, and adding the concrete consistency conditions to the NewMatrix method in question will make precise what is allowed for the given type of matrix objects.

I think that consistency checks in Matrix methods can be either only partial checks (which need more checks in the NewMatrix methods) or default checks (which need individual Matrix methods with modified checks if the default does not fit). Wouldn't that be more complicated in the end?

[fingolfin]

@ThomasBreuer so should I merge this, or do you plan to make changes based on our discussion from last week? (I am not sure if / which changes are needed right now, if any; but e.g. perhaps Check renamed to check?)

[ThomasBreuer]

Yes, I am going to push an update.