Given two vectors \(p\) and \(q\) of non-negative integer numbers, denote by \(A(p, q)\) the number of matrices with non-negative integer entries whose row sum and column sum respectively are \(p\... [Read more...]

Here is a parameterization of a four-dimensional torus knot: \[ p(\theta, \phi) = \begin{pmatrix} \cos\theta \cdot \cos\phi \\ \cos\theta \cdot \sin\phi \\ \sin\theta \cdot \cos 3\phi/2 \\ \sin\theta ... [Read more...]

Nice achievment: I have been able to implement the Jack polynomials with a symbolic Jack parameter, in Haskell and in R. My Julia package JackPolynomials, a couple of years old, allows to get them as well... [Read more...]

I will soon release an update of qspray on CRAN as well as a new package: resultant. This post shows an application of these two packages. Consider the two algebraic curves \(f(x,y)=... [Read more...]

The ‘RowReorder’ extension of datatables is available in the DT package. This extension allows to reorder the rows of a DT table by dragging and dropping. However, if you enable this extension in a Shiny ... [Read more...]

Sometimes the Shiny reactivity is not desirable. Assume for example the Shiny app renders a plot and the title of this plot is given by the user with a text input. So in the Shiny UI you have ... [Read more...]

Assume you have a Shiny app allowing to upload a data file and to perform various operations on the uploaded data. Now, if the user uploads a new file, the current state of the app is lost, and you want t... [Read more...]

The function below generates a Shiny dropdown list including some icons. library(shiny) library(fontawesome) library(htmltools) selectInputWithIcons [Read more...]

Yesod is a web framework for Haskell. In this post I show how to do a Yesod application allowing to upload some data from a CSV or a XLSX file and to display a R graphic representing two selected columns of the ... [Read more...]

I have a mathematical question for you, because it is a mystery for me. Look at this animation: I get it as follows. Each frame corresponds to a value of \(t \in [0,3[\)... [Read more...]

You can forget my post Mapping a picture on a donut or a Hopf torus. Almost everything I wrote in this post is wrong. I have even been unable to define what is the conformality property of a parameterizat... [Read more...]

In a previous post, I showed how to use the CGAL parameterizations ported to my package cgalMeshes to decorate the Enneper surface of order three with a radial checkerboard. Here I w... [Read more...]

An elliptic Dupin cyclide can be obtained by inversion of a torus with respect to a sphere. In the previous post, I showed a rotoid (an helix) dancing around a cyclide: ... [Read more...]

The most used parameterization of the ordinary torus (the donut) is: \[ \textrm{torus}_{R,r}(u, v) = \begin{pmatrix} (R + r \cos v) \cos u \\ (R + r \cos v) \sin u \\ r \sin v \end{pmatrix}. \] ... [Read more...]

If you didn’t read or if you don’t remember my post Using implicitization to split a ball, take a look at it before reading this one. To sum up, I took a spherical curve, namely a satellite curve, and I derived a... [Read more...]

On my former blog, I wrote a post about the Cantor expansion of a natural integer. This is a generalization of the well-known binary expansion. For example, the Cantor \((3,4,5)\)-expansion of a ... [Read more...]

Here are four representations of the Klein j-invariant function: The Klein j-invariant function is a complex function defined on the upper half-plane of the complex nu... [Read more...]

The github branch of my Github repository cgalMeshes has a vignette explaining how to use parameterizations of surface meshes. A parameterization allows to map a texture on a mesh. Some of them ar... [Read more...]

The visualization of a rgl mesh is rather shiny by default. We’ll see how to make it dull and shadowed. Take for instance the Barth sextic: ## Barth sextic is the isosurface f=0 #### phi [Read more...]

The runcinated tesseract is a 4D polytope. Thanks to the cxhull package, I extracted all the tetrahedral cells from it, I rounded them and I plotted them with a 4D rotation and a stereographic projection.... [Read more...]