Compared to Sage 8.0, matrices in Sage 8.1.beta1 now have a host of new
methods:

  - leading_coefficient
  - leading_item
  - leading_monomial
  - leading_support
  - leading_term

These are inherited from the category of finite dimensional modules with
basis of which matrix spaces are now members.

The semantics is that an e.g. 3x3 matrix over R is an R-module over the
basis

   [1 0 0]  [0 1 0]  [0 0 1]
   [0 0 0], [0 0 0], [0 0 0], ...
   [0 0 0]  [0 0 0]  [0 0 0]

and hence, M.leading_coefficient() on such a matrix returns M[2,2] if
this is non-zero, otherwise M[2,1] if this is non-zero, etc.

While it is arguably too rigid to say that this is "senseless" (as I
wrote in the subject), I believe that the use of these functions for
matrices is very narrow. And since matrices are an extremely central
object that beginners immediately start playing around with, it is
unfortunate that they will pollute the tab-completion to such a degree,
and with doc strings which are not very helpful to the algebraically
uninitiated.

My question here is whether it is really intended that all matrices get
stuck with these (almost) senseless methods?

(this came up during #23619 where we are introducing "leading_matrix"
and "leading_position" for matrices over a univariate polynomial ring.)

Best,
Johan

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