ASKSAGE: Sage Q&A Forum - RSS feedhttps://ask.sagemath.org/questions/Q&A Forum for SageenCopyright Sage, 2010. Some rights reserved under creative commons license.Wed, 09 Oct 2013 21:19:24 +0200Quotient of free algebra on 2 generators (x, y) over rational field by a non-homogenous idealhttps://ask.sagemath.org/question/10602/quotient-of-free-algebra-on-2-generators-x-y-over-rational-field-by-a-non-homogenous-ideal/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
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TypeError: quotient() takes exactly 4 arguments (3 given)
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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
Wed, 09 Oct 2013 11:50:37 +0200https://ask.sagemath.org/question/10602/quotient-of-free-algebra-on-2-generators-x-y-over-rational-field-by-a-non-homogenous-ideal/Answer by John Palmieri for <p>Hi all,</p>
<p>Here I asked a question in sage but there is an error which I can not solve it:</p>
<pre><code>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
</code></pre>
<hr/>
<p>TypeError: quotient() takes exactly 4 arguments (3 given)</p>
<hr/>
<p>Please help me to find the forth argument should I put.</p>
<p>Actually I want to construct a quotient of infinite dimensional non-commutative free algebra F by a non-homogenous ideal.</p>
<p>Thanks</p>
https://ask.sagemath.org/question/10602/quotient-of-free-algebra-on-2-generators-x-y-over-rational-field-by-a-non-homogenous-ideal/?answer=15534#post-id-15534It doesn't look like general quotients of free algebras are implemented. See [Sage's reference manual](http://www.sagemath.org/doc/reference/rings/sage/rings/quotient_ring.html) 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](http://www.sagemath.org/doc/reference/rings/sage/rings/quotient_ring.html#sage.rings.quotient_ring.QuotientRing), although the examples there don't look as helpful.Wed, 09 Oct 2013 21:19:24 +0200https://ask.sagemath.org/question/10602/quotient-of-free-algebra-on-2-generators-x-y-over-rational-field-by-a-non-homogenous-ideal/?answer=15534#post-id-15534