**35**

votes

**0**answers

505 views

### Reasons to prefer one large prime over another to approximate characteristic zero

Background:
In running algebraic geometry computations using software such as Macaulay2, it is often easier and faster to work over $\mathbb F_p = \mathbb Z / p\mathbb Z$ for a large prime $p$, rather ...

**7**

votes

**0**answers

139 views

### Fractional Helly for more than one piercing

Fractional Helly Theorem says the following:
For every $0<\alpha\leq 1$ there exists $\beta = \beta(d, \alpha)$ with the following property. Let $C_1 , C_2 , ..., C_n$ be convex sets in $R^d$, $n ...

**6**

votes

**0**answers

61 views

### Constructing a polyhedron of maximal possible volume from given bounds on areas of its faces

Consider $n$ variables $a_1,...,a_n$ ranging over $\mathbb{R}^+$. Suppose we are given $n$ pairs of positive rational numbers $(p_1,q_1),...,(p_n,q_n)$ where each pair imposes bounds on the ...

**4**

votes

**0**answers

154 views

### Intuition behind minimizing the Dirichlet energy of a mapping

What does minimizing the Dirichlet energy of a mapping $\Phi$ achieve intuitively?
Roughly it is the integral (or sum, if discrete) of $|\nabla \Phi(\;)|^2 dV$, with $V$ the volume.
So is it, in some ...

**4**

votes

**0**answers

143 views

### Upper bounds on art gallery problems using independent witnesses

Given a polygon $P$, the art gallery problem looks to find a smallest set of points that sees all of $P$. One way of bounding the number of guards necessary (from below) is to find a largest set of ...

**4**

votes

**0**answers

387 views

### Generating random polygons from a given triangulation of points

Given a triangulation $T$ of a planar set point $S$, we would like to randomly generate a polygon (hamiltonian cycle) $P$.
However, it has been proved that Hamiltonian Circuit Problem on maximal ...

**3**

votes

**0**answers

62 views

### Computing with Graphs in Surfaces

I asked this question yesterday on math.stackexchange, but the only response so far hasn't really addressed the question, so I thought I'd cross-post it.
I am currently working on a research project ...

**2**

votes

**0**answers

257 views

### Solving 3D equation system (inverse-projecting a triangle)

Please, how is the equation system below named exactly (to search further literature)?
Does it have an analytical solution? If it doesn't, then what could be the fastest numerical method for it ...

**1**

vote

**0**answers

88 views

### Combinatorial design for minimization problem over binary strings

Suppose the cost of a binary string $B$ of length $k$ is the number of $1$s that occur before the last $0$. For example, $1110$ has cost 3 while $0111$ has cost 0. Now suppose you can choose $k$ ...

**1**

vote

**0**answers

41 views

### Covering a set of points by bounded geometric object/objects

1) Let $S$ be a set of $n$ points in $R^d$. Now, given a bounded geometric object $G$, the problem is to check whether $S$ can be contained in $G$.
2) Also, in general setting, the problem is to ...

**1**

vote

**0**answers

88 views

### Boundary surfaces in a 3d Voronoi tessellation with obstacles

Let $x_1,\dots,x_n$ be a set of points in $\mathbb{R}^3$ and let $\mathcal{O}_1 ,\dots, \mathcal{O}_m$ denote a set of polyhedral obstacles. What is the name for the surfaces that describe the ...

**1**

vote

**0**answers

88 views

### minimizing the sum of euclidean norms

minimizing the sum of euclidean norms with box constraints
I am a graduate student in computer science, making a thesis on uncertainty geometry. During my thesis I came across the following ...

**1**

vote

**0**answers

139 views

### Compute generalized pentagram map

Hi,
(This is my first question on MathOverflow! :-)
Imagine you have a set of points $S = \{p_1, \ldots, p_n\}$ in $\mathbb{R}^d$, of which $t$ are "bad". I want to compute a "safe convex hull", ...

**1**

vote

**0**answers

134 views

### Techniques for refining or constraining a Voronoi diagram?

I have a dataset coming from weather stations where each vertex used to generate the Voronoi diagram is the lat/long of the station. As such, each cell represents the area whose weather is being ...

**1**

vote

**0**answers

188 views

### Which rational subfields are corresponding to the two dimensional subspaces of holomorphic differentials

I implemented the algorithm that Felipe Voloch's suggested in his reply to the question:
Subfields of a function field
the algorithm is here:
Subfields of a function field
I considered the ...

**1**

vote

**0**answers

171 views

### Finding equations for projective bundles associated to vector bundles over explicitly given varieties

Suppose I have a projective variety V over a field k. It is given explicitly in terms of homogeneous equations. Moreover, say I have an explicitly given vector bundle E (in terms of a module ...

**0**

votes

**0**answers

46 views

### plotting parametrized algebraic curves near singularities

I have a parametrized algebraic curve:
x(t)=A(t)/D(t);
y(t)=B(t)/D(t);
with A(t) and B(t) being polynomials in t. The curve is solution of a linear system in two unknowns x and y with Cramer's ...

**0**

votes

**0**answers

67 views

### minimizing the sum of euclidean norms with box constraints

minimizing the sum of euclidean norms with box constraints
I am a graduate student in computer science, making a thesis on uncertainty geometry. During my thesis I came across the following ...

**0**

votes

**0**answers

36 views

### Covering the annulus of symmetric convex body

Consider a symmetric convex body $A$ in $R^d$. Now, we draw another object, $A'$, concentric and translated with respect to A and having radius slightly greater than twice to the radius of $A$.
Now ...

**0**

votes

**0**answers

173 views

### Determining the simplices in freudenthal triangulation

HI,
I have a doubt on Freudenthal Triangulation. I want to partition a simplex into finer simplices.
The FT gives me the vertices of the simplices which partition my original simplex into ...

**0**

votes

**0**answers

118 views

### Orientation predicate CG

Shewchuk 97 gives me the orientation of 4 points, by finding the sign of a determinant, where the matrix is composed of the coordinates of the points. So, the signed volume of a tetrahedron, or which ...

**0**

votes

**0**answers

100 views

### Queries On PH Quintic Splines

This is with respect to the Pythagorean Hodograph Splines of degree 5, developed here: link text.
I'm trying to code these up and can't really get clear about a couple of points:
(1) Are these ...