Ok thanks for your answer. I tried with left and right operators but it doesn't works unfortunately. Can you help me to create my own algebra with the rules (completed): *relationrules:= rule(y11*y11+y21*y21==1;y11*y11+y12*y12==1;y12*y12+y22*y22==1;y21*y21+y22*y22==1;y11*y12+y21*y22==0;y11*y21+y12*y22==0;y12*y11+y22*y21==0;y21*y11+y22*y12==0;y11*y22+y12*y21==sigma;y11*y22==y22*y11;y12*y21==y21*y12;y11*y12==-y12*y11;y21*y22==-y22*y21;y11*y21==-y21*y11;y22*y12==-y12*y22)*. I have the fricas documentation but i dont really understand how to use it for this.Now, i just need to make some matrix multiplication using yij and simplify the result with this relations. Thanks for all. Sorry, if my post is again in HTML to be honest, i dont know what is the correct form for posting. Le mardi 9 juin 2015 14:56:01 UTC+2, Waldek Hebisch a écrit : > > 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] <javascript:> >
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