2.18 Thursday, August 6, 2020

2.18.1 Top new questions this week
2.18.2 Greatest hits from previous weeks
2.18.3 Can you answer these questions?

2.18.1 Top new questions this week

How can I find a functional square root in Mathematica?
The numerics of FresnelS[]
How to enter a nuclear reaction?
How to find a numerical antiderivative with NIntegrate methods?
How to draw one-line Venn diagram?
How to express permutation as the least number of exchanges
Remove mesh triangles in contour plot

How can I find a functional square root in Mathematica?

https://mathematica.stackexchange.com/landing/r/digest?cta=question&id=227863

A functional square root of a function \(g\) is another function \(f\) such that \(g=f\circ f\). According to that article, there is a systematic approach to finding a functional square root that involves ...

asked by flinty https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=72682 10 votes

answered by flinty https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=72682 2 votes

The numerics of FresnelS[]

https://mathematica.stackexchange.com/landing/r/digest?cta=question&id=227893

Bug introduced in 12.1 or earlier and persisting through 12.1.1 or later [CASE:4615361]

Note: A worse problem existed in 12.0 for inputs greater than 8 and of precisions less than 43.66; 12.1 fixed ...

asked by Michael E2 https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=4999 9 votes

answered by J. M.’s technical difficulties https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=50 6 votes

How to enter a nuclear reaction?

https://mathematica.stackexchange.com/landing/r/digest?cta=question&id=227846

Sometimes the simplest things are the most difficult, I need to make a presentation, and I thought to do it in Mathematica, I wanted to do a demonstration too, well...this is the Rutherford’s equation

asked by Chris Schwenke https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=65367 9 votes

answered by Bob Hanlon https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=9362 14 votes

How to find a numerical antiderivative with NIntegrate methods?

https://mathematica.stackexchange.com/landing/r/digest?cta=question&id=227869

@JimBelk asked in Interpolating an Antiderivative how to find a numerical antiderivative. I gave an answer that uses NDSolve with the default method for integrating \(y'=f(x,y)\). However for ...

asked by Michael E2 https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=4999 8 votes

answered by Michael E2 https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=4999 9 votes

How to draw one-line Venn diagram?

https://mathematica.stackexchange.com/landing/r/digest?cta=question&id=227990

This is the a list of set.

data = {{"A"}, {"J"}, {"Q"}, {"G", "H"}, {"I", "O"}, 
  {"B", "C", "E",  ...

asked by partida https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=15961 6 votes

answered by kglr https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=125 10 votes

How to express permutation as the least number of exchanges

https://mathematica.stackexchange.com/landing/r/digest?cta=question&id=227996

If there are grammatical or terminological errors in the following description, please help correct:

In some problems, it is necessary to find out what minimum number of exchanges can change a list ...

asked by Ordinary users68 https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=42417 5 votes

answered by Hausdorff https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=73380 5 votes

Remove mesh triangles in contour plot

https://mathematica.stackexchange.com/landing/r/digest?cta=question&id=227837

How do I get rid of the mesh in this contour plot?

 ContourPlot[x^2 + y^2, {x, -10, 10}, {y, -10, 10}, 
    Contours -> {1.0, 4.0, 10.5}, ContourStyle -> None, 
    ContourShading ->  ...

asked by QuantumDot https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=2048 5 votes

answered by Michael E2 https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=4999 6 votes

2.18.2 Greatest hits from previous weeks

How to create animated snowfall?
What does # mean in Mathematica?
Elegant operations on matrix rows and columns
Help find a bright object on Mars!
Plot, extract data to a file
Labeling individual curves in Mathematica
How to add a vertical line to a plot

How to create animated snowfall?

https://mathematica.stackexchange.com/landing/r/digest?cta=question&id=16881

Well, the title is self-explanatory. What sorts of snowfall can we generate using Mathematica? There are two options I suggest to consider:

1) Continuous GIF animations with smallest possible number ...

asked by faleichik https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=219 39 votes

answered by Simon Woods https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=862 53 votes

What does # mean in Mathematica?

https://mathematica.stackexchange.com/landing/r/digest?cta=question&id=19035

I asked Mathematica to compute the following

Solve[c (1-x)^2-x^(1/4) == 0, x] 
 
and it returned this: 
 
  x = Root[#1^8 c^4 - 8 #1^7 c^4 + 28 #1^6 c^4 - 56 #1^5 c^4 + 70 #1^4 c^4 - 56 #1^3 c^4 + 28  ...

asked by ronanymous https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=5730 37 votes

answered by Dr. belisarius https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=193 63 votes

Elegant operations on matrix rows and columns

https://mathematica.stackexchange.com/landing/r/digest?cta=question&id=3069

Question

The Mathematica tutorial has a section ’Basic Matrix Operations’, describing operations like transpose, inverse and determinant. These operations all work on entire matrices. I am missing a ...

asked by sjdh https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=515 179 votes

answered by Mr.Wizard https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=121 60 votes

Help find a bright object on Mars!

https://mathematica.stackexchange.com/landing/r/digest?cta=question&id=11819

In today’s news, scientists found a bright object on one of Curiosity’s photos (it’s near the bottom of the picture below). It’s a bit tricky to find - I actually spent quite some time staring at the ...

asked by Victor K. https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=1351 198 votes answered by Niki Estner https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=242 257 votes

Plot, extract data to a file

https://mathematica.stackexchange.com/landing/r/digest?cta=question&id=19859

I need to save data that Mathematica uses inside the Plot command. The format that I would like to have is:

x1 y1 
x2 y2

i.e. basically, two columns, x and y (sorted, if possible) so that I ...

asked by molkee https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=5097 29 votes

answered by Mr.Wizard https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=121 46 votes

Labeling individual curves in Mathematica

https://mathematica.stackexchange.com/landing/r/digest?cta=question&id=4444

I need to create a plot for export and inclusion in a report. Is there a better way to label curves than PlotLegends? From what I’ve read and my personal experience, PlotLegends is pretty bad.

Is ...

asked by Tianxiang Xiong https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=1041 62 votes

answered by Artes https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=184 46 votes

How to add a vertical line to a plot

https://mathematica.stackexchange.com/landing/r/digest?cta=question&id=3561

In the plot below I would like to add two vertical lines at \(x = \frac {\pi }{15} \pm \frac {1}{20}\). How can I do that?

f[x_] := (x^2 z)/((x^2 - y^2)^2 + 4 q^2 x^2) /. {y -> /15, z -> 1, q ->  ...

asked by sjdh https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=515 56 votes

answered by Ajasja https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=745 76 votes

2.18.3 Can you answer these questions?

Does MMA have a built-in function or a user-defined function to judge whether the two matrices are congruent
Symbolic solution to periodic boundary conditions
Collecting terms in NCAlgebra

Does MMA have a built-in function or a user-defined function to judge whether the two matrices are congruent

https://mathematica.stackexchange.com/landing/r/digest?cta=question&id=227756

It can be seen from the following relationship that matrix A and matrix B must be congruent matrices with each other:

A = {{1, 4, 4}, {5, 2, 2}, {3, 1, 3}}; 
B = EulerMatrix[{/4, 0,  ...

asked by Ordinary users68 https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=42417 3 votes

Symbolic solution to periodic boundary conditions

https://mathematica.stackexchange.com/landing/r/digest?cta=question&id=228028

Is it possible to get an analytical solution to the following problem? If so, how? \[a w^{(1,0)}(x,t)+b w^{(0,1)}(x,t)=p(x)+g w(x,t)\]

asked by Scott G https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=74062 1 vote

answered by Michael Seifert https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=27813 0 votes

Collecting terms in NCAlgebra

https://mathematica.stackexchange.com/landing/r/digest?cta=question&id=227812

Let's say we have GP[v],GM[v]: two noncommutative objects depending on the commutative variable v. 
<< NC`; 
<< NCAlgebra`; 
SetCommutative[v]; 
SetNonCommutative[GP, GM] 
NCCollect[ 
 GM[v] **  ...

asked by Kawette https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=60529 1 vote