Using computers to solve algebraic problems. Questions with this tag should typically include at least one other tag indicating what sort of algebraic problem is involved, such as ac.commutative-algebra or rt.representation-theory.

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246 views

Computer Algebra solution for simplicial resolutions for André-Quillen cohomology

Hello, I would like to experiment with André-Quillen (co)homology. Especially for singular rings. A key problem is that the construction of a simplicial resolution of a ring seems to require a rather ...
6
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0answers
77 views

Constructing the normal sheaf for the plucker embedding in MAGMA (or a similar programming language)

How would one construct the normal sheaf $N_{G(2,6)/\mathbb P^{14}}$ to the plucker embedding of the grassmannian $G(2,6) \rightarrow \mathbb P^{14}$ as a sheaf in MAGMA (or another programming ...
6
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0answers
432 views

Where can I find tables of dual canonical basis vectors?

Leclerc (arXiv:math/0209133) has given us an algorithm for computing the dual canonical basis of the upper part of a quantised enveloping algebra. Now presumably this algorithm has been implemented ...
5
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142 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 ...
5
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0answers
233 views

What became of PoSSo and FRISCO

I know PoSSo and FRISCO were pretty big projects involving many European universities. Interestingly, I couldn't find much information about these projects (the the top of the PoSSo homepage says ...
4
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115 views

Computing Tamagawa numbers for jacobians of hyperelliptic curves

Do exist some computational approach to calculation of Tamagawa number for the jacobian of hyperelliptic curve at prime $p$? As followed from this question one can compute $\Phi(\overline{\mathbb ...
4
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0answers
177 views

Dimension of a commuting nilpotent variety

Fix $k$ an algebraically closed field, $n$ a natural number, and $\lambda=(\lambda_1,\ldots,\lambda_m)$ a partition of $n$. Let $A$ be any $n\times n$ nilpotent matrix with entries in $k$ whose ...
4
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302 views

On finding A-polynomials

I have two questions to obtain the explicit forms of A-polynomials. Takata used the mathematica pacage qMultisum.m to obtain the recursion relation of the colored Jones polynomials for twist knots. ...
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199 views

Algorithm/denominators of elements of a rational affine space

I hope it's not a trivial question... Suppose I have a finite dimensional vector space $V$ over $\mathbb{Q}$ with a distinguished basis (in my case it's the $k$th graded piece of the free associative ...
3
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0answers
161 views

What is the function like when its Mobius inversion is $\sum_{w|r, (w,t)=1}\mu(w)q^{r/w}$?

Everyone, I am now reading a paper named The Irreducible Factors of $(cx+d)x^{q^m}-(ax+b)$ over $GF(q)$, http://qjmath.oxfordjournals.org/content/14/1/61.extract. And I’m confused with one of its ...
3
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241 views

Using the Affine Maxima Package

The Maxima computer algebra system has a package called Affine for doing the calculations implicit in Bergman's diamond lemma for rings. It can be viewed as a kind of noncommutative analogue of ...
3
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299 views

Rank of Subgroup of Elliptic Curve

I'm currently looking at two rational points $ p, q $ on an elliptic curve $E$ over $ \mathbb{Q} $. SAGE tells me that $E$ has rank 5 and no torsion, and that $p$ and $q$ both have infinite order. ...
2
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80 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 ...
2
votes
0answers
142 views

Randomized alternative to Buchberger's algorithm

Richard Lipton's blog describes a A New Way To Solve Linear Equations by Prasad Raghavendra. Can the ideas in this algorithm be generalized to systems of polynomial equations to provide a randomized ...
2
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0answers
228 views

Efficient computing critical points of algebraic function involved radical expression

I am interested in finding local optima of an algebraic function $f(X,Y)$. Suppose, that this expression involves radicals, for example $f(X,Y)= \frac{1}{2}(X+Y)-\sqrt{XY}$. The approach in which i am ...
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0answers
146 views

How do I check if a sequence of R-modules is exact?

Let R be a ring. For example, take $R=k[x_1,\ldots,x_n]$ or, if possible, $R = \Bbb{Z}[x_1,\ldots,x_n]$. Consider a sequence of free R-modules $$R^a \stackrel{f}\to R^b \stackrel{g}\to R^c$$ where ...
1
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0answers
121 views

Calogero-Moser eigenfunction

The folllowing function \begin{equation} J(t_1,t_2,t_3,m,h)=[(1-e^{t_1-t_2})(1-e^{t_2-t_3})(1-e^{t_1-t_3})]^{-m/h} ...
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96 views

Benchmark problems for computing rational points on varieties

Are there standard benchmark problem sets used for empirically evaluating algorithms designed for computing rational points on (various classes of) algebraic varieties? If so, could you please point ...
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0answers
281 views

Finding a generator of an ideal in an algebraic function field

I have an algebraic function field $\mathbb{Q}(x,y)$, where $y$ satisfies $$ (y^2-1)^2 = x^2(1+x^2), $$ and I need to find a rational function that has a first order root at $x=0,y=1$ a first order ...
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0answers
115 views

Testing functional equivalence

We are looking for the most efficient (most recent, or best) techniques to check if two algebraic expressions (elementary, Calculus-type functions) are equivalent (or if an expression is equivalent to ...
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0answers
173 views

Computer package to compute HOMFLY polynomial?

I apologize of already asked by someone else, but what (in your opinion) is the best package for computing HOMFLY polynomials?
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211 views

How to ask Magma to compute the induced morphisim on divisor group

Suppose Magma has computed homomorphism $h$ between function fields $F1 \to F2$. Then we have an induced homomorphism $h$ on the divisor group. Now my question is that if there's a better way to ...
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0answers
65 views

Grobner basis for a general algebra

Let $R$ be a quotient of the polynomial ring $\mathbb{C}[x_1,\dots , x_n]$. We fix a $\mathbb{C}^*$ action on $R$ which preserve homogenous components and the multiplication. (The geometric analogue ...
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0answers
75 views

Systems of linear modular equations with unknowns in the moduli

I am interested in systems of linear modular equations, where the unknowns also appear in the moduli. The general form would be: $A \vec{x}= \vec{b} \;\textrm{mod} \; (C \vec{x}+\vec{d})$ where A ...
0
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0answers
186 views

Understanding a program for computing Khovanov homology

I would like to understand how a computer program for computing Khovanov homology works. The particular program I have in mind is by John Baldwin: https://web.math.princeton.edu/~baldwinj/Kh.cpp The ...
0
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105 views

What is the largest computed summatory liouville interval ?

I am interested to know the largest computed summatory liouville interval, an implementation of which is detailed in Section 4.1 of [1]. The wikipedia page [2] for the function charts summatory ...