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/polynomial evaluationhttps://ask.sagemath.org/question/9769/polynomial-evaluation/If I have a polynomial p in variables $x_0,...,x_n$, how do I specialize the algebra appropriately to substitute values for $x_i$'s? For example, how do I compute $p(1,1,...,1)$? Or replace $x_i$ by $q^i$ ($q$ a parameter) so to compute $p(1,q,...,q^n)$? In Mathematica, if the variables were x[[i]], one could do "./x[[i]] -> q^i //Simplify" and it is the equivalent of this replace and simplify that I am looking for.
This is coming from symmetric polynomials/functions theory and I know some of the specializations are built in, but at the end of the day I want to try small examples with different specializations than what is already built in.dbTue, 05 Feb 2013 10:27:47 +0100https://ask.sagemath.org/question/9769/