Abdolrasoul Baharifard's profile - activity

Maybe I miss understood the definition of free algebra. When I put F.<x,y>=FreeAlgebra(QQ) "Sage" write me "Free Algebra en two generators x,y"" and when I write F.<x,y>=FreeAlgebra(QQ, implementation='letterplace') it gives me "Unital associative free algebra with two generators", but I think the both is the same, yes? Now, my problem is to construct a quotient of this algebra ba a non-homogenous ideal. Do you know, how can I do that?

Hi all,

Here I asked a question in sage but there is an error which I can not solve it:

F.<x,y>=FreeAlgebra(QQ)
I=F*[x*y*x*y-y*x, y*x*y*x-x*y]*F
G.<a,b>=F.quo(I)
G

TypeError: quotient() takes exactly 4 arguments (3 given)

Please help me to find the forth argument should I put.

Actually I want to construct a quotient of infinite dimensional non-commutative free algebra F by a non-homogenous ideal.

Thanks

But I need an unital associative free algebra and if I drop the "implementation= 'letterplace", it just give me free algebra.

I want to define a two-sided ideal I = [x*y*x*y - x*y] in a unital associative free algebra K.<x,y>.

But I get:

ArithmeticError: Can only subtract elements of the same degree.

Is there any way to define such an ideal in Sage?

Actually the problem is here:

F.<x,y> = FreeAlgebra(QQ, implementation='letterplace') I=F[xyx-2xy]*F J=F.quo(I)

And the eroor is :

ArithmaticError : can only subtract the elements of the same degree"

Hi every one,

I have a problem for subtracting two non-homogenous monomial "xyyx-xyx" in a unital associative free algebra with two generators x&y.

The error which is appeared is "ArithmaticError : can only subtract the elements of the same degree".

I will apreciate some one who tell me what is the soloution.

Thanks

Abdolrasoul