On 18 August 2017 at 14:48, Johan S. H. Rosenkilde <maill...@atuin.dk> wrote:
> 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.
I entirely agree. If you had asked me what these methods
('leading_term') etc meant for matrices I would have had absolutely no
idea. But then the same would be true if you had asked me what the
"leading term" was of an element of the free module R^n (for any ring
R). So my recommendation would be to get rid of these at that level.
They may have meaning for some modules which happen to be free
R-modules of finite rank (such as polynomials over R of fixed degree,
where they do of course make sense) but not on __all__ R-modules!
They have been put in the wrong place. [In my opinion!]
>
> 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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