**7**

votes

**0**answers

241 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**

votes

**0**answers

427 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**

votes

**0**answers

135 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**

votes

**0**answers

231 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**

votes

**0**answers

109 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**

votes

**0**answers

168 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**

votes

**0**answers

290 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. ...

**4**

votes

**0**answers

197 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**

votes

**0**answers

151 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**

votes

**0**answers

223 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**

votes

**0**answers

284 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**

votes

**0**answers

136 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 ...

**2**

votes

**0**answers

222 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 ...

**1**

vote

**0**answers

133 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**

vote

**0**answers

120 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} ...

**1**

vote

**0**answers

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 ...

**1**

vote

**0**answers

250 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 ...

**1**

vote

**0**answers

104 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 ...

**1**

vote

**0**answers

140 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 ...

**1**

vote

**0**answers

209 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 ...

**0**

votes

**0**answers

66 views

### Computer software for manipulating loop groups or matrices with polynomial entries

I need to deal with loop groups $LG$ over the complex numbers $\mathbb{C}$, as well as related spaces like the affine Grassmannian and affine flag variety a lot.
In type A, the loop group consists ...

**0**

votes

**0**answers

170 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**

votes

**0**answers

167 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?

**0**

votes

**0**answers

103 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 ...

**0**

votes

**0**answers

747 views

### Efficient quadratic residue mod 2^32

I want to determine if a value is a quadratic residue mod $2^{32}$.
I've developed a very fast pre-screening method based on a Bloom Filter that identifies quadratic residues for mod $2^7=128$ in ...