Am 11.11.19 um 22:53 schrieb Ralf Hemmecke:
> On 11/4/19 11:24 PM, Prof. Dr. Johannes Grabmeier privat wrote:
>> Hi all,
>> I have enhanved TwoDimensionalArray to include arithmetic for block
>> matrices and have an operation array2 (similar to matrix for Matrix) for
>> easy creation of two-dimensional array and would suggest to include this
>> into the next version:
> I guess the background of this is relatively clear. FriCAS currently
> forbids the creation of Matrix(Matrix Integer).
>
> (15) -> A := matrix([[A11, A12],[A21, A22]])$Matrix(Matrix Integer)
>
> Matrix(Matrix(Integer)) is not a valid type.
>
> You basically suggest to get around this problem, but extending
> TwoDimensionalArray.
>
> What application do you have in mind?
block matrices as in the example I gave. I am really using them, when I
have to split a matrix in subblocks according to orbits of group operations.
>
> Why I would be against this extension is that TwoDimensionaArray is a
> data structure domain, i.e., no algebraic operations.
>
> Your operations should live in an "algebraic" domain. But even then I
> see problems, because + and * will be partial functions (much as in
> Matrix(Matrix Integer) if it were possible).
that is very subtle distinction, what should be an arithmetic domain, if
it has a + and/or a *. Is /\ etc. also an arithmetic operation? Do you
propagate a meta classification of domains, which - right now - only can
be in the peoples mind, not in a valid FriCAS definition?
Is the domain Matrix an algebraic domain with all its partial functions
+ and *? Your argument would had been valid against the creation of a
domain Matrix as well.
I do not care, if someone, rewrites/enhances Matrix to allow Matrix
Matrix Integer e.g., I would be content, from the practical point, one
simply should be able to use block matrices and sophisticated meta
discussions should not hinder practical implementations.
>
> A good motivation for your extensions would help to consider them for
> FriCAS.
>
> Ralf
>
--
Mit freundlichen Grüßen
Johannes Grabmeier
Fraktionsvorsitzender
FREIE WÄHLER, Stadtrat Deggendorf
Prof. Dr. Johannes Grabmeier
Köckstraße 1, D-94469 Deggendorf
Tel. +49-(0)-991-2979584, Tel. +49-(0)-151-681-70756
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