0
votes
1answer
39 views

Formula of signed distance from hyperplane to point

Let $H$ be a hyperplane defined by the points $p_1, p_2, ..., p_n$ and single point $x$ generally out of the hyperplane. Is there any formula to calculate the signed distance between $x$ and $H$? I ...
2
votes
1answer
109 views

How to extract the indeterminates from a set of polynomial?

I am a biologist and I am facing a huge problem. I would like to extract the indeterminates of a set of polynomials, for example, I have: $f_{1} = \{\\x_{3}^{2} + x_{1}*x_{2} + x_{1} + x_{1}*x_{3},\\ ...
0
votes
1answer
394 views

How to find whether the line is inside the polygon or outside.

I have a polygon How can i prove whether the black color line lies outside the polygon or inside the polygon . Given the coordinates of the black line and all the vertices of the polygon.
4
votes
3answers
275 views

Average degree of convex hull vertices in a Delaunay triangulation

Let $P \subset \mathbb{R}^2$. The boundary of $DT(P)$, the Delaunay triangulation of the point set $P$, is $conv(P)$. It is also known that the average degree of the vertices of $DT(P)$ is $\lt 6$. ...
3
votes
3answers
580 views

Studying the envelope of a family of circles.

This is an exercise on page 150 of Cox/Little/O'Shea's Ideal, varieties and algorithms: an introduction to computational algebraic geometry and commutative algebra, 3rd ed. I get lost in this ...
2
votes
2answers
127 views

Did I write the right “expressions”?

$9$. Consider the parametric curve $K\subset R^3$ given by $$x = (2 + \cos(2s)) \cos(3s)$$ $$y = (2 + \cos(2s)) \sin(3s)$$ $$z = \sin(2s)$$ a) Express the equations of K as polynomial ...
3
votes
1answer
123 views

Computing the free-part

I wanted to ask about some existing algorithms for computing points over elliptic curves. Background : We know that the famous theorem of Mordell and Weil says that " Group of rational points on an ...