Sage is a mathematical software system, and this tag is intended for questions involving this software in a substantive way. This tag should hardly ever be the only tag of a question; typically there should be additional tags to indicate the mathematical content of the question. Please note that ...

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10
votes
2answers
372 views

Computing intersection of subrings

Let $R$ be a finitely generated commutative ring over a field, for concreteness. If $S,T \leq R$ are two finitely generated subrings, is their intersection also finitely generated? (Certainly ...
9
votes
3answers
640 views

What CASes say about the analytic rank of rank 8 elliptic curve '457532830151317a1'

For the rank $8$ elliptic curve with a-invariants $(0, 0, 1, -23737, 960366)$ sage 5.3 reports analytic rank $4$ in about 2.4 hours. Almost sure this a bug, so I am interested what other CAS say on ...
7
votes
3answers
552 views

Multiprecision numerical evaluation of integral: Sage vs. PARI/GP vs. mpmath

I am trying to compute thousands of integrals of the below type, that comes up in a conformal mapping problem, to as many accurate digits as possible (preferably 50+): $$ \int_{-1}^1\textrm{d}t \frac{...
7
votes
0answers
186 views

Genus of the graph $K_{4,2,2,2}$

I have ask this question in math.stackexchange, here. Since, there is no answer and apart from that i feel that the problem is difficult, i would like to ask it here. The problem is to find the genus ...
6
votes
3answers
384 views

Torsion group of the following elliptic curve

Let $p_1=2, p_2 = 3,\ldots,$ be the prime numbers, and define $n_i = \prod_{j=1}^i p_j$. Moreover, let $E_i $ be the elliptic curve defined by $y^2 = x^3 + n_i$. Can one compute the torsion group $...
4
votes
2answers
204 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 ...
4
votes
1answer
223 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 ...
4
votes
0answers
135 views

Is there an integral simple fusion ring rank<6, FPdim>60 and Frobenius type?

A fusion ring is a finite dimensional complex space $\mathbb{C}\mathcal{B}$ together with a distinguished basis $\mathcal{B} = \{ h_1,...,h_r\}$ and fusion rules $ h_i \cdot h_j = \sum_k n_{ij}^kh_k $...
2
votes
2answers
113 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 ...
2
votes
0answers
167 views

Is there an integral simple fusion ring of multiplicity one and Frobenius type? (obvious excepted)

To avoid any confusion, we rewrite the basic definitions for a fusion ring (already written in this post). A fusion ring is a finite dimensional complex space $\mathbb{C}\mathcal{B}$ together ...
1
vote
2answers
250 views

Ihara zeta function (graph theory) coefficients using a line graph [closed]

I'VE COMPLETELY REVISED MY QUESTION I wish to take a simple undirected graph (i.e. the complete graph K_4) Arbitrarily direct said graph, and then create a line graph from the directed version of ...
1
vote
1answer
59 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 ...
1
vote
0answers
41 views

Basis for a set of polynomials in Sage? [closed]

I have a large set of polynomials in the coordinates $x,y,z$ in Sage, (e.g. $x^5y-3x^2y^2+2xy^3+x^2yz-y^2z$). I want to know, for example, if $x^5y$ is in the span of my set. Is there a Sage command ...
-2
votes
1answer
177 views

reducing an n-order differential equation to a first order system of equations using either sagemath or sympy [closed]

I want to reduce a n-order ordinary differential equation into a first order system of equations. This is in preparation for numerical analysis. I use both Sympy and Sagemath for Computer Algebra, but ...