2020-07-18 16:16:06 -0500 received badge ● Popular Question (source) 2018-11-13 08:52:18 -0500 received badge ● Popular Question (source) 2018-05-02 00:34:35 -0500 received badge ● Famous Question (source) 2018-03-06 15:35:08 -0500 received badge ● Famous Question (source) 2018-03-06 15:35:08 -0500 received badge ● Notable Question (source) 2018-02-20 12:53:53 -0500 received badge ● Notable Question (source) 2017-03-24 19:57:55 -0500 received badge ● Popular Question (source) 2016-12-06 07:59:02 -0500 received badge ● Nice Question (source) 2016-09-30 00:39:14 -0500 asked a question symbolic calculation for resultant I want to find Resultant of trinomials of this form $x^i-x^j-1$. Is it possible to do symbolic calculation for this in sage ? 2016-09-14 09:06:29 -0500 asked a question residocity of elements in an extension of $\mathbb{F}_p$ Consider the following code :- p=10010113 F=GF(p) R=PolynomialRing(F,'x') f=x^5 + 3212480*x^4 + 5943978*x^3 + 1041193*x^2 + 3212605*x + 4505026 F1.=F.extension(f) R1=PolynomialRing(F1,'x') f1=derivative(f(x),x) b=R1(f1(a)) b=F1(b)  Now since b $in$ F1 . Therefore F1(b**p^5-1) should output 1, but I am getting this output sage: F1(b**(((p^5)-1))) /usr/lib/sagemath/local/bin/sage-ipython:1: RuntimeWarning: invalid value encountered in power #!/usr/bin/env python 9745575*a^4 + 8100949*a^3 + 6855548*a^2 + 351457*a + 548263  Which is absurd ! 2016-09-11 01:25:52 -0500 commented question Division polynomials just a function of x ! Are we replacing $y$ by $x^2+ax+b$ everywhere ? 2016-09-11 01:13:41 -0500 asked a question Division polynomials just a function of x ! I evaluated Divison polynomials using R.=PolynomialRing(ZZ) E = EllipticCurve([A,B]) g = E.division_polynomial(k)  The results i noticed were just function of $x$ , In theory i saw that division polynomials for k even depends on y. In there something I am unable to notice. For example : E.division_polynomial(k) returned 4*x^3 + 4*A*x + 4*B but theory says it is 2y. From this one can get a intuition that may be we are squaring them. But E.division_polynomial(8) returned a degree $33$ polynomial which means that clearly we are not squaring things. 2016-08-27 01:06:49 -0500 asked a question Finding order of a polynomial over finite field order of a polynomial $f(x)$ in $\mathbb{F}_p [x]$ is defined as minimum $e$ such that $f(x) | x^e -1$ . Do we have an inbuilt function in sage to find the same ? 2016-06-23 09:15:06 -0500 asked a question Accessing the "Echelon basis matrix" of kernel of a Matrix For any matrix A when we type A.kernel()  It returns  A.kernel() Free module of degree 45 and rank 12 over Integer Ring Echelon basis matrix:[ 1 0 -1][ 0 1 2][ 0 0 0]  How to I access this Echelon basis matrix directly? I have tried this A.kernel.echelon_form()  but it says TypeError: echelon_form() takes at least 2 arguments (1 given)  2016-06-23 01:16:00 -0500 asked a question How to find Kernel of a Matrix in $\mathbb{Z}/n$ When I tried to find it directly using A.kernel()  it said  Cannot compute a matrix kernel over Ring of integers modulo 11053185041  2016-06-22 03:08:36 -0500 received badge ● Nice Question (source) 2016-06-22 02:51:52 -0500 commented answer Evaluating discriminant of a polynomial in Z_n[x]/ Thanks a lot ! Can you kindly help me with this question also. 2016-06-22 02:33:22 -0500 received badge ● Supporter (source) 2016-06-22 01:10:18 -0500 asked a question Evaluating discriminant of a polynomial in Z_n[x]/ 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 ? 2016-06-22 00:51:33 -0500 received badge ● Popular Question (source) 2016-06-10 10:34:48 -0500 commented answer Taking gcd with respect to one variable @tmonteil In your example Cyclotomic polynomial factors (here it splits that is has roots in GF(p) ), but what if it is irreducible (which it would be when ord_r(p)=r-1, take r=5 in your example). In that case your algorithms gives "No roots". I am interested in the cases when y doesn't lie in GF(p) but in some extension of it. 2016-06-10 10:17:16 -0500 commented question Taking gcd with respect to one variable One can choose 'a' to be any quadratic residue modulo p 2016-06-10 09:32:11 -0500 received badge ● Student (source) 2016-06-10 07:18:09 -0500 received badge ● Editor (source) 2016-06-10 07:17:30 -0500 asked a question 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 $q = p^r$ 2016-06-10 07:07:22 -0500 received badge ● Scholar (source) 2016-06-07 03:01:44 -0500 asked a question Coefficient of polynomial in a Finite field Consider the following code :- p=104711 r=101 K=GF(p) L.=K.extension(cyclotomic_polynomial(r)) for a in range(10000,10000000): f=(y+1)^(a) L=f.list() if L.count(0)>1: print "special low support %d" %a for i in range(100): if L[i]==0: print i  I want the list of coefficient of f(y) but when L is a field (which it for the above stated parameters ) it is giving this error. AttributeError: 'sage.rings.finite_rings.element_pari_ffelt.FiniteFieldElement_pari_ffel\ t' object has no attribute 'list'  when L is a ring it is working perfectly. Also when I try to use f.coeff() it basically consider f(y) as a constant.