Tagged Questions

0
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0answers
33 views

Approximating a spheroid using spheres

I seek a way to approximate a spheroid using spheres. I guess this is a classic sphere packing problem? I am dealing mostly with prolate spheroids. I use the definition given here ...
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0answers
28 views

weighted initial ideal versus lex or graded reverse lex initial ideal

$$ $$ By imposing certain weights $\mathbf{w}$ on the variables, say, of a polynomial ring $k[x_1,\ldots, x_n]$, I read that we may obtain the initial ideal $In_{\mathbf{w}}(I)$ of an ideal $I$ with ...
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0answers
40 views

using weight vector in M2

Let $R = k[x_1,\ldots, x_n]$ be a polynomial ring and assume $f_i$ and $g_i$ are homogeneous of degree 2, and $h_j$'s are linear forms. I would like to show that assuming $A = \{f_i + t g_i, h_j\}$ ...
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votes
3answers
374 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
112 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
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1answer
117 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 ...