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, 06 Jul 2016 09:11:55 +0200Checking if Quotient Rings are Isomorphichttps://ask.sagemath.org/question/34037/checking-if-quotient-rings-are-isomorphic/ Hey all!
I was wondering if there was a way to check if two quotient polynomial rings were isomorphic to each other in SAGE. In particular I tried this
R.<x,y,z> = PolynomialRing(QQ)
I = R.ideal(x+y+z,x^2,y^2,z^2,x^3,y^3,z^3,x^2*y,y^2*x,x*y*z,y^2*z,y*z^2,x*z^2,z*x^2)
S = R.quotient_ring(I)
T.<w> = PolynomialRing(QQ)
J = T.ideal(w^3)
P = T.quotient_ring(J)
S.is_isomorphic(P)
But there is no is_isomorphic for Quotient Rings that I could find
Thanks!Tue, 05 Jul 2016 23:08:19 +0200https://ask.sagemath.org/question/34037/checking-if-quotient-rings-are-isomorphic/Answer by tmonteil for <p>Hey all!</p>
<p>I was wondering if there was a way to check if two quotient polynomial rings were isomorphic to each other in SAGE. In particular I tried this</p>
<p>R.<x,y,z> = PolynomialRing(QQ)</p>
<p>I = R.ideal(x+y+z,x^2,y^2,z^2,x^3,y^3,z^3,x^2<em>y,y^2</em>x,x<em>y</em>z,y^2<em>z,y</em>z^2,x<em>z^2,z</em>x^2)</p>
<p>S = R.quotient_ring(I)</p>
<p>T.<w> = PolynomialRing(QQ)</p>
<p>J = T.ideal(w^3)</p>
<p>P = T.quotient_ring(J)</p>
<p>S.is_isomorphic(P)</p>
<p>But there is no is_isomorphic for Quotient Rings that I could find</p>
<p>Thanks!</p>
https://ask.sagemath.org/question/34037/checking-if-quotient-rings-are-isomorphic/?answer=34038#post-id-34038It seems indeed that this is not implemented in Sage. If you know some algorithm that do that, it would make a great improvement to Sage !
Wed, 06 Jul 2016 09:11:55 +0200https://ask.sagemath.org/question/34037/checking-if-quotient-rings-are-isomorphic/?answer=34038#post-id-34038