How to create a list of pairs from 1d list(s)?

Say I've got two 1-dimensional lists

A = {1,2,3}
B = {a,b,c}

How do I

create a list of all pairs from list A such that the result looks like {{1,2},{1,3},{2,3}}?

create a list of all pairs from lists A and B such that the result looks like {{1,a},{1,b},{1,c},{2,a},{2,b},{2,c},{3,a},{3,b},{3,c}}?

I would also need both options, one with no duplicates as above and one with duplicates, e.g. one where the result from case 1 also includes {{2,1},{3,1},{3,2}}.

Answer

Ad. 1

ordering not valid:

Subsets[A, {2}]

{{1, 2}, {1, 3}, {2, 3}}

or with ordering

Permutations[A, {2}]

Ad. 2

Outer[List, A, B]

{{{1, a}, {1, b}, {1, c}}, {{2, a}, {2, b}, {2, c}}, {{3, a}, {3, b}, {3, c}}}

or exactly

Outer[List, A, B] // Flatten[#, 1] &

 {{1, a}, {1, b}, {1, c}, {2, a}, {2, b}, {2, c}, {3, a}, {3, b}, {3, c}}

Comments

plotting - Filling between two spheres in SphericalPlot3D

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plotting - Plot 4D data with color as 4th dimension

I have a list of 4D data (x position, y position, amplitude, wavelength). I want to plot x, y, and amplitude on a 3D plot and have the color of the points correspond to the wavelength. I have seen many examples using functions to define color but my wavelength cannot be expressed by an analytic function. Is there a simple way to do this? Answer Here a another possible way to visualize 4D data: data = Flatten[Table[{x, y, x^2 + y^2, Sin[x - y]}, {x, -Pi, Pi,Pi/10}, {y,-Pi,Pi, Pi/10}], 1]; You can use the function Point along with VertexColors . Now the points are places using the first three elements and the color is determined by the fourth. In this case I used Hue, but you can use whatever you prefer. Graphics3D[ Point[data[[All, 1 ;; 3]], VertexColors -> Hue /@ data[[All, 4]]], Axes -> True, BoxRatios -> {1, 1, 1/GoldenRatio}]

plotting - Adding a thick curve to a regionplot

Suppose we have the following simple RegionPlot: f[x_] := 1 - x^2 g[x_] := 1 - 0.5 x^2 RegionPlot[{y < f[x], f[x] < y < g[x], y > g[x]}, {x, 0, 2}, {y, 0, 2}] Now I'm trying to change the curve defined by $y=g[x]$ into a thick black curve, while leaving all other boundaries in the plot unchanged. I've tried adding the region $y=g[x]$ and playing with the plotstyle, which didn't work, and I've tried BoundaryStyle, which changed all the boundaries in the plot. Now I'm kinda out of ideas... Any help would be appreciated! Answer With f[x_] := 1 - x^2 g[x_] := 1 - 0.5 x^2 You can use Epilog to add the thick line: RegionPlot[{y < f[x], f[x] < y < g[x], y > g[x]}, {x, 0, 2}, {y, 0, 2}, PlotPoints -> 50, Epilog -> (Plot[g[x], {x, 0, 2}, PlotStyle -> {Black, Thick}][[1]]), PlotStyle -> {Directive[Yellow, Opacity[0.4]], Directive[Pink, Opacity[0.4]],

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