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Quotient of free algebra on 2 generators (x, y) over rational field by a non-homogenous ideal

asked 2013-10-09 04:50:37 -0500

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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

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answered 2013-10-09 14:19:24 -0500

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It doesn't look like general quotients of free algebras are implemented. See Sage's reference manual for one way to do this: implement a reduce method for your ideal, as in the PowerIdeal class defined in the example. See also the documentation for QuotientRing, although the examples there don't look as helpful.

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Asked: 2013-10-09 04:50:37 -0500

Seen: 44 times

Last updated: Oct 09 '13