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.Tue, 15 Dec 2020 11:44:22 +0100Inconsistentency in parent of specialization of a polynomial?https://ask.sagemath.org/question/54684/inconsistentency-in-parent-of-specialization-of-a-polynomial/I have a family of polynomials and I want to consider special members of this family. In other words I'm considering polynomials in a ring $R = K[x]$ where $K = \mathbb{Q}[t]$. In sage I do the following:
K = PolynomialRing(QQ, ["t"])
R = PolynomialRing(K, ["x"])
t = K.gen(0)
x = R.gen(0)
f = (t**2 - QQ(1/10)*t + 1)*x**2 + (QQ(3/4)*t + QQ(7/2))*x - t + 8
f1 = f.specialization({t: 1})
This works fine and as expected $f_1$ is a polynomial only in $x$:
f1.parent() == QQ["x"] # True
Now I want to do exactly the same but over $\overline{\mathbb{Q}}$ instead:
L = PolynomialRing(QQbar, ["t"])
S = PolynomialRing(L, ["x"])
t = L.gen(0)
x = S.gen(0)
g = (t**2 - QQ(1/10)*t + 1)*x**2 + (QQ(3/4)*t + QQ(7/2))*x - t + 8
g1 = g.specialization({t: 1})
I would expect $g_1$ to be a polynomial only in $x$ as above, i.e. I would expect $g_1 \in \overline{\mathbb{Q}}[x]$. However, I get:
g1.parent() == QQbar["x"] # False
g1.parent() == S # True
Is this a bug? Or am I misunderstanding something?mvkTue, 15 Dec 2020 11:44:22 +0100https://ask.sagemath.org/question/54684/Enumerating points in 0-dimensional ideals over Qbarhttps://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?Mathieu Dutour SikiricSun, 23 Sep 2018 12:24:34 +0200https://ask.sagemath.org/question/43728/