ASKSAGE: Sage Q&A Forum - Latest question feedhttp://ask.sagemath.org/questions/Q&A Forum for SageenCopyright Sage, 2010. Some rights reserved under creative commons license.Thu, 21 Jun 2018 08:54:57 -0500Killed Process Meaning?http://ask.sagemath.org/question/42708/killed-process-meaning/ I tried computing this -
sage : K = CyclotomicField(37^5)
But after almost a minute, the process just popped up "Killed" and automatically exited sage session.
Why does that happen and what is the meaning?
Is there any alternative way to do this? mathjainThu, 21 Jun 2018 08:54:57 -0500http://ask.sagemath.org/question/42708/how to find minimal polynomialhttp://ask.sagemath.org/question/34412/how-to-find-minimal-polynomial/How to find the minimal polynomial of an element ? Let $\zeta_n$ be a primitive $n$-th root of unity. I want to find the minimal polynomial of $\zeta_n$ over $\mathbb{Q}(\zeta_n+\zeta_{n}^{-1})$. How do I do that ?nebuckandazzerWed, 10 Aug 2016 12:45:47 -0500http://ask.sagemath.org/question/34412/Evaluating discriminant of a polynomial in Z_n[x]/<x^r-1>http://ask.sagemath.org/question/33879/evaluating-discriminant-of-a-polynomial-in-z_nxxr-1/Consider the following code
Zn=Zmod(n)
R = PolynomialRing(Zn,'x')
F = R.quotient((x**r)-1)
y=F((x+1))
f=F(y**n)
Clearly **f** will be a polynomial in xbar , I want to consider this polynomial as a polynomial in $ \mathbb{Z}[x] $ and evaluate its discriminant.
I tried **"f.polynomial()"** but it is not working. Any suggestions ? vishbWed, 22 Jun 2016 01:10:18 -0500http://ask.sagemath.org/question/33879/Taking gcd with respect to one variablehttp://ask.sagemath.org/question/33734/taking-gcd-with-respect-to-one-variable/ I want to compute $$ gcd_{X}((X-y)^2 -a , X^{\frac{q-1}{2}}-1)$$ with respect to X(taking y as a field constant).
I can't see any direct implementation of this in sage. Can any one suggest how to implement it.
Here Arithmetic is over $GF(p)$ and y is root of cyclotomic polynomial of degree r over $GF(p)$ and $q = p^r$vishbFri, 10 Jun 2016 07:17:30 -0500http://ask.sagemath.org/question/33734/How make Kummer extensionshttp://ask.sagemath.org/question/33553/how-make-kummer-extensions/ I want to calculate the relative discriminant of field extensions of this kind:
$$\mathbb{Q}(\zeta_5)(\sqrt[5]{a})$$
Where $a \in \mathbb{Q}(\zeta_5)$. So I use SAGE and make this calculations:
K.<b>=CyclotomicField(5); //my field base
alpha=1+3*b^2; //an element of my field base
f=(1+3*b^2).minpoly(); //its minimal polynomial
f.is_irreducible() //is it irreducible?
R.<a>=K.extension(f) //the field extension of my field base
R.relative_discriminant() //the calculation of the relative discriminant
But when I execute it, appears this error
defining polynomial (x^4 - x^3 + 6*x^2 + 14*x + 61) must be irreducible
But it is irreducible, what am I doing wrong? Or how can I solve this?belvedereThu, 26 May 2016 08:10:12 -0500http://ask.sagemath.org/question/33553/variable assumptionhttp://ask.sagemath.org/question/33126/variable-assumption/I have an expression in term of an independent variable $q$. Now, I would like to assume that $q$ is an arbitrary $14$-th root of unity (i.e. $q^{14}=1$).
It is not allow to evaluate in any primitive root of unity, say $\eta$, since the coefficients of my expression are in the $7$-th cyclotomic field (i.e. the field is generated by $\xi=e^{2\pi i/7}$), so $\eta$ is in the field.
I also tried with "assume(q^14==1)", but it didn't work.
How can I do?
**Added after Bruno's comment**: Here is an example. I have the expression
exp=q^16*xi^5 + (q^325-12*q^235)*xi^2.
where q is an independent variable and xi is the 7th-root of unity with least argument. In other words, I have an expression in terms of an independent variable q with coefficients in the 7-th cyclotomic field
K.<xi> = CyclotomicField(7)
Now, I want to assume that $q^{14}=1$, thus the resultant expression should be
q^2*xi^5 + (q^3-12*q^11)*xi^2
since $16\equiv 2\pmod {14}$, $325 \equiv 3\pmod {14}$ and $235\equiv 11\pmod {14}$.
How can I do that? Note that it is not sufficient to evaluate the expression in $q=$some primitive $14$-th root of unity, since $q$ can be $+1$ or $-1$.
Please, think that the expression have thousands of terms, so I cannot do it by hand as above.
emiliocbaFri, 15 Apr 2016 18:49:39 -0500http://ask.sagemath.org/question/33126/is the class field a kind of field(group,ring,feild)?http://ask.sagemath.org/question/8068/is-the-class-field-a-kind-of-fieldgroupringfeild/is the class field a kind of field(group,ring,feild)?
if it is,finite field or unfinite field?cjshWed, 25 Dec 2013 17:01:36 -0600http://ask.sagemath.org/question/8068/how to run CyclotomicField([zeta7+zeta7^-1]?http://ask.sagemath.org/question/10813/how-to-run-cyclotomicfieldzeta7zeta7-1/ - LL.<x>=CyclotomicField(7);LL
Cyclotomic Field of order 7 and
degree 6
x.conjugate()
-x^5 - x^4 - x^3 - x^2 - x - 1
LL.<c>=CyclotomicField(-x^5 - x^4 - x^3 - x^2 - 1);LL
Traceback (click to the left of this block for traceback)
...
TypeError: Unable to
coerce -x^5 - x^4 - x^3 - x^2 - 1 to
an integer
s=LL.gen() + (LL.gen()).conjugate();s
LL.<y>=CyclotomicField(s);LL
Traceback (click to the left of this
block for traceback) ... TypeError:
Unable to coerce -x^5 - x^4 - x^3 -
x^2 - 1 to an integer
KK.<s> = NumberField(-x^5 - x^4 - x^3 - x^2 - 1); KK
Traceback (click to the left of this block for traceback)
... NotImplementedError: number
fields for non-monic polynomials not
yet implemented.
KKK.<s> = NumberField(x^5 + x^4 + x^3 + x^2 + 1); KKK
Number Field in s with defining polynomial x^5 + x^4 +
x^3 + x^2 + 1
KKK is same with Q[zeta7+zeta7^-1]?cjshFri, 06 Dec 2013 19:34:12 -0600http://ask.sagemath.org/question/10813/