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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 :- Now since b $in $ F1 . Therefore 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 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 : But |
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 It returns How to I access this Echelon basis matrix directly? I have tried this but it says |
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 it said |
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2016-06-22 02:51:52 -0500 | commented answer | Evaluating discriminant of a polynomial in Z_n[x]/<x^r-1> Thanks a lot ! Can you kindly help me with this question also. |
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2016-06-22 01:10:18 -0500 | asked a question | Evaluating discriminant of a polynomial in Z_n[x]/<x^r-1> Consider the following code 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 ? |
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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 |
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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 $q = p^r$ |
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2016-06-07 03:01:44 -0500 | asked a question | Coefficient of polynomial in a Finite field Consider the following code :- 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. 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. |