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.Sun, 23 Sep 2018 11:02:38 -0500Enumerating points in 0-dimensional ideals over Qbarhttp://ask.sagemath.org/question/43728/enumerating-points-in-0-dimensional-ideals-over-qbar/I would like to find the points of a 0-dimensional ideal over Qbar. That is I do not want just the rational points,
The problem is that I found multiple problem while doing that.
1) While the code
R.<t1,t2,t3,e1,e2,e3> = PolynomialRing(QQbar,6, order="degrevlex(3),lex(3)")
is legal, the code
R.<t1,t2,t3> = PolynomialRing(QQbar,6, order="degrevlex(3)")
is not for reasons that esapes me.
2) The code
R.<t1,t2,t3,e1,e2,e3> = PolynomialRing(QQbar,6, order="degrevlex(3),lex(3)")
tvars = [t1,t2,t3]
eltsyms = [R((SymmetricFunctions(QQbar).elementary())[i].expand(3,alphabet=tvars)) for i in range(4)]
is not legal, it is if we replace QQbar by QQ. Why?Sun, 23 Sep 2018 05:24:34 -0500http://ask.sagemath.org/question/43728/enumerating-points-in-0-dimensional-ideals-over-qbar/Answer by tmonteil for <p>I would like to find the points of a 0-dimensional ideal over Qbar. That is I do not want just the rational points,</p>
<p>The problem is that I found multiple problem while doing that.</p>
<p>1) While the code </p>
<pre><code>R.<t1,t2,t3,e1,e2,e3> = PolynomialRing(QQbar,6, order="degrevlex(3),lex(3)")
</code></pre>
<p>is legal, the code </p>
<pre><code>R.<t1,t2,t3> = PolynomialRing(QQbar,6, order="degrevlex(3)")
</code></pre>
<p>is not for reasons that esapes me.</p>
<p>2) The code</p>
<pre><code>R.<t1,t2,t3,e1,e2,e3> = PolynomialRing(QQbar,6, order="degrevlex(3),lex(3)")
tvars = [t1,t2,t3]
eltsyms = [R((SymmetricFunctions(QQbar).elementary())[i].expand(3,alphabet=tvars)) for i in range(4)]
</code></pre>
<p>is not legal, it is if we replace QQbar by QQ. Why?</p>
http://ask.sagemath.org/question/43728/enumerating-points-in-0-dimensional-ideals-over-qbar/?answer=43730#post-id-43730There is clearly an issue. Actully, your first example istelf has an issue:
sage: R.<t1,t2,t3,e1,e2,e3> = PolynomialRing(QQbar,6, order="degrevlex(3),lex(3)")
sage: t1
<repr(<sage.rings.polynomial.multi_polynomial_element.MPolynomial_polydict at 0x7f6cf1fb5500>) failed: TypeError: Argument 'self' has incorrect type (expected sage.rings.polynomial.polydict.ETuple, got tuple)>
As for the second example, on the left side of the equality you put 3 indeterminates, while on the right side, you require 6 indeterminates.
I have no idea where it comes from, it requires some more exploration. Thanks for reporting.Sun, 23 Sep 2018 11:02:38 -0500http://ask.sagemath.org/question/43728/enumerating-points-in-0-dimensional-ideals-over-qbar/?answer=43730#post-id-43730