Souleiman omar hoche wrote: >
> I had another question.
>
> In my rules for the simplification of my matrix 4*4, there a lot of
> expression of the type y11*y12==-y12*y11, in fact the place of the
> yij (in the first position or in the second position, there are
> commuting
> only if all the indice are different) is important but i remark
> that for
> fricas it is the same.
>
If you just have products of two things there is a little trick
that may help. Namely, you can define new operator, call it
'left' and 'right'. Then instead of y11*y12 use left(y11)*right(y12)
which clearly is different than left(y12)*right(y11). Of course
if you multiply more things this will no longer work. More
precisely, for a fixed number of factors you can modify this
to encode position using appropriate operator (say pos1, pos2, ...).
But again, there is problem if you want to do longer calculations.
In general FriCAS way is to create new algebra which respect
your rules. For example, XDistributedPolynomial is a domain
where coefficients may be noncommutative, variables do not
commute but it is assumend that variables commute with
coefficients. Note: XDistributedPolynomial makes no extra
assumptions so by itself will not porform simplifications
due to specific commutation rules.
> Here are my rules
For me your rules appear mangled. But they look similar to
rules for Grassman algebra. Maybe you can use one of standard
algebras buit into FriCAS. Or do a little Spad coding to
create algebra fitting your problem.
--
Waldek Hebisch
[email protected]
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