ASKSAGE: Sage Q&A Forum - Individual question feedhttp://ask.sagemath.org/questions/Q&A Forum for SageenCopyright Sage, 2010. Some rights reserved under creative commons license.Fri, 23 Sep 2011 01:25:01 -0500Quotient of ideals in powerseries ringhttp://ask.sagemath.org/question/8333/quotient-of-ideals-in-powerseries-ring/Is it possible to take quotient (colon) of two ideals in a multivariable powerseries ring over a field?
e.g. the following code gives me error(s):
sage: R.<x,y,z> = PolynomialRing(QQ,3)
sage: I = Ideal([x^2+x*y*z,y^2-z^3*y,z^3+y^5*x*z])
sage: J = Ideal([x])
sage: Q = I.quotient(J)
Thanks and regards
--VInay
Mon, 19 Sep 2011 21:17:26 -0500http://ask.sagemath.org/question/8333/quotient-of-ideals-in-powerseries-ring/Answer by niles for <p>Is it possible to take quotient (colon) of two ideals in a multivariable powerseries ring over a field?</p>
<p>e.g. the following code gives me error(s):</p>
<pre><code>sage: R.<x,y,z> = PolynomialRing(QQ,3)
sage: I = Ideal([x^2+x*y*z,y^2-z^3*y,z^3+y^5*x*z])
sage: J = Ideal([x])
sage: Q = I.quotient(J)
</code></pre>
<p>Thanks and regards</p>
<p>--VInay</p>
http://ask.sagemath.org/question/8333/quotient-of-ideals-in-powerseries-ring/?answer=12664#post-id-12664The code you posted gives me no errors (in version 4.7.1). Did you mean to make R a power series ring? If you did, that would certainly give you errors as ideal quotients have not been implemented for power series rings.Tue, 20 Sep 2011 01:58:08 -0500http://ask.sagemath.org/question/8333/quotient-of-ideals-in-powerseries-ring/?answer=12664#post-id-12664Comment by VInay Wagh for <p>The code you posted gives me no errors (in version 4.7.1). Did you mean to make R a power series ring? If you did, that would certainly give you errors as ideal quotients have not been implemented for power series rings.</p>
http://ask.sagemath.org/question/8333/quotient-of-ideals-in-powerseries-ring/?comment=12672#post-id-12672I precisely mean to take R as a Power Series Ring. Is it that the same algorithm (as that for Polynomials) does not work for Power Series? In that case where is the problem?
-- VInayTue, 20 Sep 2011 19:38:17 -0500http://ask.sagemath.org/question/8333/quotient-of-ideals-in-powerseries-ring/?comment=12672#post-id-12672Comment by niles for <p>The code you posted gives me no errors (in version 4.7.1). Did you mean to make R a power series ring? If you did, that would certainly give you errors as ideal quotients have not been implemented for power series rings.</p>
http://ask.sagemath.org/question/8333/quotient-of-ideals-in-powerseries-ring/?comment=21213#post-id-21213The problem is that no one has implemented the algorithm! If you're interested, you should do it :)Fri, 23 Sep 2011 01:25:01 -0500http://ask.sagemath.org/question/8333/quotient-of-ideals-in-powerseries-ring/?comment=21213#post-id-21213