6.3.1 Top new questions this week

6.3.1.1 Raytracing; why so slow?

https://mathematica.stackexchange.com/landing/r/digest?cta=question&id=219629

I'm trying to get some rays to bounce in a circle. But I want to be able to control the reflections, i.e. the direction the rays bounce in the circle. I have a MWE below, and it is severely limited by  ... 
[performance-tuning] [regions]
 

asked by Tomi https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=36939 10 votes

answered by MassDefect https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=42264 18 votes

6.3.1.2 How use the black mode permanently

https://mathematica.stackexchange.com/landing/r/digest?cta=question&id=219317

Now I can use this functionResourceFunction["DarkMode"][] to use the dark mode, but when I turn on Mathematica again, the black mode will not work. How can I set to use the black mode permanently. 
 
... 
[stylesheet] [system]
 

asked by  https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=71882 9 votes

answered by M.R. https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=403 5 votes

6.3.1.3 DeleteCases depending on all elements

https://mathematica.stackexchange.com/landing/r/digest?cta=question&id=219412

I have a listed of Tupels 
 
list = {{10, 5}, {20, 4}, {20, 3}, {10, 6}}; 
 
 
If there are two elements a and b for which 
 
a[[1]] <= b[[1]] && a[[2]] <= b[[2]] 
 
 
then I would like to delete  ... 
[list-manipulation]
 

asked by fravity https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=22275 8 votes

answered by kglr https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=125 7 votes

6.3.1.4 Mathematica is unable to compute the derivative of the function $\frac \sin^2(x) x$

https://mathematica.stackexchange.com/landing/r/digest?cta=question&id=219273

Consider the function 
$$f: \mathbb R\to\mathbb R, x\mapsto\begin{cases}\frac{\sin^2(x)}x, & x\neq 0, \\ 0, & x=0.\end{cases}$$ 
 
It is clear that $f\in\mathcal C^1(\mathbb R)$ and that 
... 
[calculus-and-analysis] [discontinuity]
 

asked by Maximilian Janisch https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=68670 8 votes

answered by Bob Hanlon https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=9362 12 votes

6.3.1.5 How to download "Epidemic Data for Novel Coronavirus COVID-19"

https://mathematica.stackexchange.com/landing/r/digest?cta=question&id=219282

I am using Mathematica and I would like to download the dataset "Epidemic Data for Novel Coronavirus COVID-19" for basic investigation from Wolfram homepage. Can anyone give me some instructions or  ... 
[data] [download]
 

asked by Johann Riedler https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=71867 7 votes

answered by morbo https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=48686 6 votes

6.3.1.6 NIntegrate vs quadGK in Julia

https://mathematica.stackexchange.com/landing/r/digest?cta=question&id=219198

I am trying to understand the numerical integration routine by using as a benchmark the function 
 
f[x_] := -x^2 + x^4 
 
 
used to define the following function 
 
g[z_] := NIntegrate[1/Sqrt[-f[x]], {x, z,  ... 
[numerical-integration]
 

asked by Smerdjakov https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=55615 7 votes

answered by MassDefect https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=42264 7 votes

6.3.1.7 Overflow with NDSolve

https://mathematica.stackexchange.com/landing/r/digest?cta=question&id=219593

Backslide introduced in 10.0, persisting through 12.1. 
 
 
 
I am trying to solve the following differential equation and plot the result: 
 
ClearAll["Global`*"] 
rin = 10^-30; 
sol = NDSolve[{Sqrt[x]  ... 
[differential-equations] [error] [finite-element-method] [backslide]
 

asked by mattiav27 https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=8822 6 votes

answered by xzczd https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=1871 2 votes