Questions tagged [mathematical-software]
Mathematical questions related to mathematical software systems such as Sage, Mathematica, Maple, Pari/GP, and GAP. Note that troubleshooting questions are generally considered off-topic.
39
questions with no upvoted or accepted answers
37
votes
0
answers
1k
views
Computer calculations in A_infinity categories?
Is there a good computer program for doing calculations in A-infinity categories?
Explicit calculations in A-infinity categories are an important, useful, yet very tedious task. One has to keep track ...
32
votes
0
answers
2k
views
Is there software to compute the cohomology of an affine variety?
I have some affine varieties whose cohomology (topological, with $\mathbb{C}$ coefficients) I would like to know. They are very nice, they are all of the form $\mathbb{A}^n \setminus \{ f=0 \}$ for ...
16
votes
0
answers
644
views
real algebraic geometry software?
Does anyone have suggestions/experience for any software packages to study real algebraic varieties (for example, counting connected components of hypersurfaces, figuring out the topological type of ...
9
votes
0
answers
654
views
Software for explicit computations in representations of classical Lie algebras
I'm pretty sure many a mathematician has longed for such a tool but I wasn't able to find such a question here, so here we go.
Is there, by any chance, an existing package or program that allows one ...
7
votes
0
answers
118
views
Softwares to determine semi-simple types of Lie algebras generated over $\mathbb{R}$ or $\mathbb{C}$ by a set of matrices
I wish to determine the type of a Lie algebra generated over $\mathbb{R}$ or $\mathbb{C}$ by a set of square matrices with irrational elements. For example,
\begin{align}
n^+ =
\begin{pmatrix}
...
7
votes
0
answers
250
views
How many simultaneous polynomial equations of degree 2 can software solve today?
Consider the following problem:
Input: $n$ polynomial equations of degree $2$ in approximately $n$ variables.
Each equation contains about $\sqrt{n}$ monomials.
We would like to find one simultaneous ...
6
votes
0
answers
264
views
Papers/Programs for computing periodic KL polynomials?
Periodic Kazhdan-Lusztig polynomials (for an affine Weyl group) are polynomials that control Jordan-Holder multiplicities for certain representations ("baby Verma modules") of an algebraic group in ...
6
votes
0
answers
196
views
Software for BMW algebra calculations?
Does software exist for computations in the BMW algebra?
For example, I'd like to be able to express elements in a basis of "totally descending tangles" as in a paper of Morton–Wassermann. At ...
4
votes
0
answers
219
views
Referring to computer software in a paper
I'm performing a calculation of the Smith normal form of an integral matrix based on the SageMath worksheet. Is it sufficient in the paper to say something like ``Using a software package like ...
4
votes
0
answers
129
views
program to compute hurwitz numbers
Is there a computer program available to compute Hurwitz numbers easily? In fact I only care about counting covers $C\to\mathbb{P}^1$ branched over $0,1,\infty$, and am even willing to restrict to the ...
4
votes
0
answers
180
views
Math software / language for analytic / multiplicative number theory
What software/languages are the most used to do computations in analytic / multiplicative number theory?
I use Python, Maple, etc., but each time I want to compute expressions like, for $n$ with an ...
4
votes
0
answers
131
views
Choice of MIP (mixed integer programming) solver
I would start using MIP solver for the research on the tiling.
I know (heard of) the open source solver jump:
https://github.com/JuliaOpt/JuMP.jl
and also the gold standard solver from IBM cplex.
...
3
votes
0
answers
124
views
Geometric construction exercises
Many of you know dynamic geometry exercises in Euclidea; if not, here is one example.
It lets you do a geometric construction and sends a message once you achieve the result.
I am looking for a way to ...
3
votes
0
answers
169
views
(Implemented) algorithm for Hodge numbers
Let $X$ be a smooth projective toric variety. Do any of the math computer algebra systems have an algorithm implemented to compute the Hodge numbers of a generic complete intersection in $X$? Say in ...
3
votes
0
answers
362
views
Intersection Multiplicity
Let $X$ be an hyper-surface in an affine space defined by an equation $F$. We can assume that the ground field is $\mathbb{C}$ and $X$ is normal. Take functions $f_1,\dots, f_n$ on $X$ and let $B$ ...
3
votes
0
answers
3k
views
Mathematica package for Lie algebra computations?
I am interested in performing Lie algebra computations in Mathematica. I did a bit of searching and found several packages (LieART, KILLING, SuperLie, maybe more), and wondered if anyone would ...
3
votes
0
answers
386
views
Software for Combinatorial Algebra sought
I am looking for software which helps me do straightforward tasks in combinatorial algebra. Let me give an example of what I mean by a straightforward task:
I have two graded (generally ...
2
votes
0
answers
74
views
Gröbner implicitization with relationships between the variables
I have the following parametric equations, where cost$=\cos t$, cos2t$=\cos 2t$, and $A^2+B^2=1$:
...
2
votes
0
answers
158
views
Representations in Archimedean quadratic modules
Let $\mathbb R [X] = \mathbb R [X_1,\dots,X_n]$ and $\Sigma[X] = \big\{ \, f \in \mathbb R[X] \mid \exists r \in \mathbb N, \ g_i \in \mathbb R[X] \colon f = g_1^2 + \dots + g_r^2 \,\big\}$ denote ...
2
votes
0
answers
71
views
Software recommendation request: deciding whether a system of polynomial equations is solvable by radicals
The following system of equations comes from a very simple geometric figure I have to deal with a lot at work. Here $r_0,r_1,r_2$ and $L$ are known parameters, and the $x_i$s are the coordinates I'm ...
2
votes
0
answers
66
views
Is there a software to solve functional inequalities?
Suppose I have some inequalities that my function (say $\mathbb R\to \mathbb R$) needs to satisfy, like $\forall x,y\; f(x)+f(y)\le f(x+y)$ and $f(1)=0$. Is there some software that can find solutions/...
2
votes
0
answers
349
views
Reducing a System of Polynomial Equations
I am currently writing a program in SAGE which computes Nilpotent Orbit Varieties for an Algebraic Geometry research project and I have reduced my problem to the following:
Consider a system of ...
2
votes
0
answers
103
views
Tools for "bound guessing"
I have a somewhat complicated symbolic expression of the form $\frac{J-a+\frac{q}{a}}{J(J-a)+q}$, where $J,a$ and $q$ are themselves affine functions of four other variables $d,r,c,s$, and I want to ...
1
vote
0
answers
138
views
Properties of pointless projective curves over finite fields?
Probably not research level, feel free to downvote.
We got construction of bounded degree projective curves
with no points over finite fields. This construction generalizes to higher dimension.
One of ...
1
vote
0
answers
176
views
Using Bertini software to determine whether or not a variety is empty
I have a system of polynomials $f_1,\dots, f_n \in \mathbb{C}[x_1,\dots, x_m]$, and I would like to determine whether the set of solutions to the system $f_1(x)=\dots=f_n(x)=0$ is empty or not. Since ...
1
vote
0
answers
141
views
pari/gp "bnfisintnorm" as poor man (quadratic) Thue equations solver?
For simplicity explaining only the quadratic case.
Given integers $n,m$, pari/gp "bnfisintnorm" finds $X,Y$
such that $X^2+n Y^2=m$ working in the number field
with defining polynomial $x^2+...
1
vote
0
answers
622
views
Generate all connected non-isomorphic graphs of n vertices modulo local complementation?
I'd like to generate a list of all simple, connected, undirected graphs of $n$ vertices, modulo standard graph isomorphism, and modulo local complementation, which is the following operation: for a ...
1
vote
0
answers
110
views
Lie Algebra Module Decomposition in GAP
Let $\mathfrak{g}$ be a complex finite-dimensional Lie algebra and let $V$ be a finite-dimensional $\mathfrak{g}$-module. Is there a way for me to check in GAP or some other software package whether $...
1
vote
0
answers
825
views
Proof of the ABC conjecture - how feasible would it be to automate some of the deciphering of Shinichi Mochizuki’s proof?
This is a question I will come back to. I am very interested in Shinichi Mochizuki’s proof, and in particular, the idiosyncrasies of his notation, which I understand to be at the root of why it is ...
1
vote
0
answers
53
views
Software for matching theorems to inputted conditions/hypotheses
Many times I find myself going through analysis books, wikipedia and papers, looking for what is known for my functions/objects at hand.
So is there any software that at least tries to move in that ...
1
vote
0
answers
218
views
How to check that an ideal of $\mathbb{C}[GL_n]$ is a coideal or not?
Let $I$ be an ideal of $\mathbb{C}[GL_n]$. Are there effective methods or software to check whether $I$ is a coideal or not? Thank you very much.
For example, let I be the ideal of $\mathbb{C}[GL_3]$ ...
1
vote
1
answer
199
views
Finding generators of symmetric cones
I have a bunch of vectors $\mathbf v_i$ in $\mathbb R^n$. I would like to consider the cone $C$ spanned by these vectors, together with all the other vectors that can be obtained by permuting the ...
1
vote
0
answers
126
views
How to check with a CAS if a surface is of general type?
The main question is:
How to check with a CAS if a surface is of general type?
Magma's function KodairaEnriquesType is close to this,
but doesn't always work.
...
1
vote
0
answers
118
views
Programmatically computing dual Hopf algebras: state of the art
Given a graded Hopf algebra of finite type, we know the (graded) linear dual is also a graded Hopf algebra. For instance the dual Hopf algebra to the polynomial algebra on an even degree generator, $R[...
0
votes
0
answers
102
views
Non-isomorphic cubic fields with a given discriminant
For a cubic field $K$ with defining polynomial $P(x)=x^3 + \frac{39}{25}x^2 + \frac{22}{25}x +\frac{4}{25}$ Magma calculates the discriminant $D=-3340$.
...
0
votes
0
answers
98
views
Software for Intersection of Ideals in Noncommutative Polynomial algebra
I am looking for software which can compute an intersection of ideals (in particular right ideals) in a noncommutative polynomial algebra and then find its Gröbner Basis.
Most software somehow does ...
0
votes
2
answers
260
views
Simplification of hypergeometric Function
First of all I am not at all a math expert, but I have some working knowledge.
That said, please excuse "dumb" questions.
I am looking at the following process: Assume you are on the 2-...
0
votes
0
answers
108
views
Common integer roots of polynomials
I have two polynomials of form
$$f_1(w,x)=M_1$$
$$f_2(y,z)=M_2$$
and I have two polynomials of form
$$g_1(w,x,y,z)=M_3$$
$$g_2(w,x,y,z)=M_4$$
where $f_1,f_2,g_1,g_2\in\mathbb Z[w,x,y,z]$ and $M_1,M_2,...
0
votes
0
answers
150
views
Series expansion with remaining $log n$
Hi,
I'm studying the asymptotic behavior $(n \rightarrow \infty)$ of the following formula, where $k$ is a given constant.
$$ \frac{1}{n^{k(k+1)/(2n)}(2kn−k(1+k) \ln n)^2}$$
I'm trying to do a ...