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2019-02-27 03:50:26 -0500 commented answer Quotient of non-commutative ring

This was helpful, thanks !!

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2019-02-16 18:33:41 -0500 asked a question Quotient of non-commutative ring

I'm trying to make a non-commutative ring, where X^2 = -1 ; XY = -YX and Y^2 = 0, something like this ;

                               R[X,Y] / (X^2 + 1 , XY + YX , Y^2)

To get the non-commutative part, I did :

A.<x,y> = FreeAlgebra(QQ,2)

P.<x,y> = A.g_algebra(relations={yx:-xy})

What is the next command to have the quotient by (X^2+1 , Y^2) ? Or maybe an other way to build the entire ring, if there exists a simpler method :) thanks !