Vector spaces of IsVectorObj objects

[ThomasBreuer]

This discussion is intended to collect comments on implications of the problems mentioned in issue #5347.

• The first question is whether vector spaces of IsVectorObj objects are desirable at all.
• If the answer is no then we should remove the partial support that is available, and we can close this discussion. (Looks like the easiest solution.)
• If the answer is yes then the next question is which type these vector spaces shall have:
  Currently they try to be row spaces in the sense of IsRowSpace; however, IsVectorObj does not imply IsRowVector --note that IsRowVector implies IsList, which we do not want to force for IsVectorObj objects.
  Thus the question is whether we want to generalize IsRowSpace to spaces that contain IsVectorObj objects or whether we introduce a new filter IsVectorObjSpace in parallel to IsRowSpace.
  In the former case, the existing code for IsRowSpace must be changed such that it works in the more general setup;
  note that it was written under the assumption that the vectors are lists, thus the code uses Concatenation, for x in v do ... and constructors which return [ 1 .. len ] * Zero(F), etc.
  In the latter case, new code must be written for IsVectorObjSpace.
• If we want to support vector spaces of IsVectorObj objects then the next question is how general they shall be.
  For row spaces, the domain of scalars (the LeftActingDomain attribute) need not be equal to the base domain of the vectors.
  (To be precise, there is no concept of a strict base domain of a set of row vectors.)
  Due to the fact that each IsVectorObj object stores its base domain, we could argue that a vector space of such objects should always have their common base domain as LeftActingDomain value.
  For example, if a GF(4)-vector space shall be created from objects with base domain GF(2) then the generators do not support the multiplication with Z(4); the only way out seems to be to replace the given generators by vector objects with base domain GF(4) and to store these new vector objects as generators; this may cause trouble later on.
  (Creating a GF(4)-vector space of vectors with base domain GF(8) causes even more complications, and seems to be beyond the area of applications for which vector and matrix objects have been designed. Nevertheless, supporting this in the same way as in the case of row spaces would not be a problem.)