ASKSAGE: Sage Q&A Forum - Latest question feedhttps://ask.sagemath.org/questions/Q&A Forum for SageenCopyright Sage, 2010. Some rights reserved under creative commons license.Tue, 17 Sep 2019 18:19:57 -0500How sage checks the irreducibility of a polynomial?https://ask.sagemath.org/question/47951/how-sage-checks-the-irreducibility-of-a-polynomial/ Hi, given a polynomial we can check whether its irreducibility via `.is_irreducible()` command. I wonder how sage checks it so fast even though the polynomial has large degree with large coefficients?captainTue, 17 Sep 2019 18:19:57 -0500https://ask.sagemath.org/question/47951/Irreducibility of Polynomialshttps://ask.sagemath.org/question/37240/irreducibility-of-polynomials/ g(n,u,x)=gen_laguerre(n,u+1/2,x); I am finding it difficult to see whether g(n,-10,x) is irreducible or not for a certain range of n say (2,10). I have used .factor() to factor the polynomial which solves my problem in a way but it is not economical and very difficult to check. I just want to see whether the function is irreducible? Please help me urgently if you can. I am doing all the computations in sage.
PranabeshSun, 09 Apr 2017 07:37:19 -0500https://ask.sagemath.org/question/37240/Elliptic Curve over finite fields - Irreducibility proofhttps://ask.sagemath.org/question/36115/elliptic-curve-over-finite-fields-irreducibility-proof/ Hello,
I am new to Sage and I want to prove an elliptic curve is irreducible.
How can I prove that?
Example:
- E = EllipticCurve(GF(256),[8,4,3,2,0])
Thank youemrealparslanWed, 28 Dec 2016 14:30:26 -0600https://ask.sagemath.org/question/36115/number fields and irreducible polynomialshttps://ask.sagemath.org/question/35028/number-fields-and-irreducible-polynomials/Hello gentle people. Let's see an example.
f=x^2+4
g=x^4+16
F=NumberField(f,'a')
The extension field of `F` by `g` cannot obtained by `F.extension(g(s),'s')` although we input `s=var('s')` before.
Because `g` is reducible in `F`. ( g=(x^2-4I)(x^2+4I) )
Can I check irreducibility of a polynomial in a number field?
Is there any method which makes a number field by given polynomial?
Thanks in advance.SeminSun, 02 Oct 2016 00:26:00 -0500https://ask.sagemath.org/question/35028/irreducibility of a polynomialhttps://ask.sagemath.org/question/34244/irreducibility-of-a-polynomial/If f $f(x)$ is a polynomial, i know that the command $f.factor()$ gives the factorization of f. But I am interested in knowing whether the polynomial is irreducible or not, not its factors. Is there any command for that ? nebuckandazzerTue, 26 Jul 2016 15:54:08 -0500https://ask.sagemath.org/question/34244/