## 145 Reputation

15 years, 263 days

Thank you.

## Ah, I should have known that...

Ah, I should have known that what I want is called a histogram, but I would have never come up with that bincount trick which enables it to be plotted the way I want in the first place.

Thank you again, this is very helpful.

## Eliminating the values that...

Eliminating the values that have a 0 in the 2nd column actually helps but I want them to be plotted, too.

The last approach looks good but it's not quite what I wanted (I want to count how often each possible difference occurs and plot this). But since the plot works here I guess it can be done in a similar way to this.

## Of course the...

Of course the two-dimensional thing was nonsense. It's an one-dimensional array containing two-dimensional vectors ;)

After initialization I want the array to contain the vectors <0,0>, <1,0>, <2,0> , ... <t,0>. I tried something like your example but it doesn't work: Array(0 .. t, 1 .. 2, (a) -> <a,0>)

Thanks, I already had figured it out but my code turned out way longer:

```> g := PositionVector([s, s^3]);
> with(plots); display([PlotPositionVector(g, s = -2 .. 2, curveoptions = [color = red, thickness = 2, numpoints = 1000]), seq(PlotPositionVector(eval(V, [s = i]), t = 0 .. 2*Pi, curveoptions = [color = blue, thickness = 1, numpoints = 1000]), i = {-1, 1, -1/2, -1/24, 1/2, 1/24})], scaling = constrained);

```
```

```

## Whoops, of course there...

Whoops, of course there should be a different variable :

> g := PositionVector([s, s^3]);
> V := VectorCalculus[`+`](VectorCalculus[`+`](g, VectorCalculus[`*`](PrincipalNormal(g, s, normalized), RadiusOfCurvature(g))), PositionVector([VectorCalculus[`*`](RadiusOfCurvature(g), cos(t)), VectorCalculus[`*`](RadiusOfCurvature(g), sin(t))]));

## Hooray, I think I understood...

Hooray, I think I understood the whole thing now. :)

Turns out, the only thing I "forgot" was to use map(rationalize,...) which is why the result looked terrible.

The matrix I posted above actually is extended, because there where terms in x^1*y^0 and x^0*y^1 and x^0*y^0 in the original equation. (Is there a command to get this extended matrix automatically?)

Thanks a lot.

## I tried it but I only get a...

I tried it but I only get a terrible matrix that isn't even diagonalized. :(

The matrix should be A := [[-1,3/2,-5/2],[3/2,3,0],[-5/2,0,-1]].

So I computed the following:

Lambda, X := Eigenvectors(A);
x := Column(X, 1);
y := Column(X, 2);
z := Column(X, 3);
S := Matrix([x,y,z])
D := Multiply(MatrixInverse(S),Multiply(A,S))

I also don't really see the point of doing so.

## This seems to be another...

This seems to be another useful command to know, so thanks to both of you.

Thank you.

Thanks!

## Thank you, andmap was just...

Thank you, andmap was just what I was looking for.

## ^ That sounds good. I'm...

^ That sounds good, I'm going to try it. But why do I only need to check the property for all the coprimes smaller than n? I mean, there is most likely an infinite number of coprimes greater than n, too.

EDIT: I came up with the following code. I bet it's a mess:

## Thank you, now I just need...

Thank you, now I just need to understand how I could've found this myself.

 Page 1 of 1
﻿