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seen Dec 9 at 0:51

May
22
comment N points in a circle around a point on a sphere.
Can you detail the second part ? (Then, use a 3D rotation...)
May
9
comment Definite integral $\int_{R_0}^{R}\frac{dr}{r^2\sqrt{\frac{R_0-R_S}{R_0^3}-\frac{1}{r^2}\left(1-\frac{R_{s}}{r}\right)}}$
Redoing all the calculations, I have one last question : why $\wp^{-1}\left(\beta\right) = w_{1}+w_{2}$ ?
May
5
comment Definite integral $\int_{R_0}^{R}\frac{dr}{r^2\sqrt{\frac{R_0-R_S}{R_0^3}-\frac{1}{r^2}\left(1-\frac{R_{s}}{r}\right)}}$
See the related question: physics.stackexchange.com/questions/111272/… if you have any idea..
May
5
comment Definite integral $\int_{R_0}^{R}\frac{dr}{r^2\sqrt{\frac{R_0-R_S}{R_0^3}-\frac{1}{r^2}\left(1-\frac{R_{s}}{r}\right)}}$
I've finally implemented it in C++ and it works well ! Thanks !
May
4
comment Fundamental period of the WeierstrassP elliptic function?
@achillehui Is it the complete or half period ?
May
4
comment Fundamental period of the WeierstrassP elliptic function?
But in that case $\lambda$ is negative as $e_1 > e_2 > e_3$ so I cannot compute the $K(k)$...
May
4
comment Fundamental period of the WeierstrassP elliptic function?
So it is simply $K(\sqrt{\frac{e_3-e_2}{e_1-e_2}})$ ?
May
4
comment Definite integral $\int_{R_0}^{R}\frac{dr}{r^2\sqrt{\frac{R_0-R_S}{R_0^3}-\frac{1}{r^2}\left(1-\frac{R_{s}}{r}\right)}}$
Thanks ! One last question : what would be the final expression in terms of inverse Jacobi elliptic functions ?
Mar
11
comment Name of the generalization of quadtree and octree?
No, K-d tree obeys a different logic, and I am speaking of the generalization of quadtree/octree...
Mar
3
comment Is it true to say that every tensor is an element of a monoid?
Ok so, 1. what is a tensor, 2. what is the relation between monoids and tensor product ?
Mar
3
comment Is it true to say that every tensor is an element of a monoid?
So what is the most general algebraic structure on which the tensor product is defined ?
Mar
2
comment What is the most generic algebraic structure for which we can define a tensor product?
@ZevChonoles And in set theory (not category theory), what is the most generic mathematical object where we can form a product ?
Mar
2
comment What is the most generic algebraic structure for which we can define a tensor product?
@ZevChonoles I am not very fluent in category theory, but is it correct to say that we can always define a tensor product of two monoids?
Mar
2
comment Point as an element of an affine space vs point as an element of a topological space?
Thanks. Last question if you have time: what are the extra properties I bring to point if I define them as members of a topological space (in the most general sense).
Mar
2
comment Point as an element of an affine space vs point as an element of a topological space?
From the programming point of view, to declare an element (for runtime execution) one of the best option is to define the set it comes from at compile-time: when you declare a vector you can say "I take an element of this vector space". If you have the knowledge on affine space/topological space, could you elaborate on question 1./2. so I can upvote your explanation ?
Mar
2
comment Point as an element of an affine space vs point as an element of a topological space?
See the edit...
Mar
1
comment Relations between an affine space and a topological space
See the edited question.
Feb
28
comment Origin in vector space?
Ok, so here origin means the null vector, not a "point" (my problem was that a point is not an element of a vector space, but an element of an affine space). Do you agree with that ?
Feb
27
comment Rigorous definition and relations between point/vector/affine space/vector space/basis/frame/coordinate system
I have good notions of set theory and linear algebra and I do not have big problem on these concepts taken separetely. But I do not have a clear picture of how to assemble and construct a coherent landscape with these concepts.
Dec
31
comment Square vs non-square tensors?
Are you sure of what you are saying because in some documents, authors seem to say that the second fundamental form is a tensor of type (2, 0) (see section 17.3 of this document: maths-people.anu.edu.au/~andrews/DG/DG_chap17.pdf, or page 171 of this document : win.tue.nl/~rvhassel/Onderwijs/Tensor-ConTeX-Bib/…)