All Questions
Tagged with computer-algebra sage
17 questions
3
votes
1
answer
228
views
Compute generators for group of totally positive units of a number field?
Given a number field $K$, I would like to compute (in Sage) generators for the group of totally positive units of $K$.
Update: I've tried some code (details below), which I've received some help on in ...
- 111
1
vote
0
answers
90
views
Can computer algebra system compute Galois group/splitting field of a polynomial over $p$-adic number field of higher degree?
I am looking for a computer algebra system that checks if the splitting fields of two polynomials over a $p$-number field are the same or not. At least, knowing their splitting fields are isomorphic ...
- 195
1
vote
1
answer
141
views
Factorial series $j(D)=\sum_{n=1}^\infty \frac{1}{(n^D)!}$ and hypergeometric functions
For positive integer $D$, define $j(D)=\sum_{n=1}^\infty \frac{1}{(n^D)!}$.
For $D \le 6$, sage finds closed form in terms of hypergeometric functions
at algrebraic arguments and fails to find closed ...
- 25.4k
1
vote
0
answers
133
views
Hall-Littlewood polynomials with sage
I need to make some computations with Sage involving Hall-Littlewood polynomials. I couldn't find any satisfying information in the Sage manuals/tutorials that I found on the internet. What I found is ...
- 6,349
4
votes
0
answers
193
views
Is it possible to compute Lie bialgebra structures with SageMath?
Is it possible to use SageMath (or some Linux open source program) to compute the bialgebra structures on a given finite dimensional Lie algebra? I wonder if such program can compute all the ...
- 523
1
vote
0
answers
136
views
Can PARI compute class numbers without factoring the discriminant?
When calculating properties of algebraic number fields, one of the hardest steps is factorizing the discriminant of a defining polynomial. This is necessary in the Pohst-Zassenhaus algorithm for ...
- 125
2
votes
1
answer
196
views
Software for $S$-unit equation
Is there any implementation available of an algorithm which solves in full generality the $S$-unit equation $x+y=1$ in a number field? It seems that Magma solves $ax+by=c$ but only in the algebraic ...
- 509
4
votes
1
answer
486
views
All rational periodic points
I am trying to find all rational periodic points of a polynomial. To specify: a periodic point is the point that satisfy $f^n(x)=x$. It is related to dynamical systems in fact. So the current codes ...
- 41
3
votes
2
answers
380
views
How to find a solution of a large system of linear diophantine inequalities?
I need to find a solution (all solutions, or at least upper and lower bounds) in positive integer numbers to the system $Ax \ge f$, where $A$ is an integer matrix.
With SageMath, I solved it with the ...
4
votes
1
answer
202
views
Branching to Levi subgroups in SAGE and the circle action
In the SAGE computer package, there useful exist tools for branching representations of a simple Lie group to a Levi subgroup:
http://doc.sagemath.org/html/en/reference/combinat/sage/combinat/...
- 835
11
votes
1
answer
635
views
How do computer algebra packages like Sagemath implement rank of a matrix
I am not sure if this is the right place to ask this question, but I believe there will be people here who do computations on computer algebra packages like Sage in their work.
I have been using ...
- 263
2
votes
1
answer
286
views
Memory usage of Gröbner basis computation
I've been calculating some Gröbner bases in preparation for finding non-commutative Hilbert series (and, once I recreate that, characters of group actions). Specifically, I've been using the ...
9
votes
6
answers
4k
views
Computation of a minimal polynomial
It is relatively easy (but sometimes quite cumbersome) to compute the minimal polynomial of an algebraic number $\alpha$ when $\alpha$ is expressible in radicals. For example, the simple query
"...
- 1,625
1
vote
1
answer
820
views
magma generators for unit group/ sage totally positive
Does anyone know how to find explicit generators for the unit group of a number field on magma?
For example, in sage one could do
K. = NumberField(x^3+x^2-2*x-1)
UnitGroup(K).gens()
and it ...
2
votes
2
answers
411
views
Computer algebra system that test zero divisors in a quotient algebra
I have an algebra $A$ over a Noetherian ring and an ideal $I=(x,y)$, where $x,y \in A$. I need to examine whether a polynomial $h \in A$ is a zero divisor in $A/I$ or not.
Is there a computer algebra ...
- 21
5
votes
2
answers
640
views
Matroids relaxations of a given matroid
Let $\mathcal{M}$ be a rank-$d$ matroid on $[n]$. Say a matroid $\mathcal{N}$ is a relaxation of $\mathcal{M}$ if $\mathrm{rank}(\mathcal{N})=d$, $\mathrm{groundset}(\mathcal{N})=[n]$, and every ...
- 902
4
votes
2
answers
754
views
Finding relations between invariant polynomials
Suppose I have an action of a linear reductive group ($GL(2,\mathbb{C})^2$ in this case) on a complex vector space (of dimension $16$) and I want to compute explicitly the ring of invariants of this ...
- 305