Wolfram Mathematica

2:32 AM

@Verde Tell you what: if there are at least ten questions entirely about manipulating derivatives, then we make a derivatives tag; otherwise, they can stay under the calculus-and-analysis tag for now.

@acl The $m_i$ are arbitrary unitary matrices? The thing you're proposing isn't obvious to me at a glance; I'll have to think a bit...

acl

@J.m. Yes, but from my brute force approach this should be true for arbitrary matrices (but I haven't checked numerically now that I think about it). Thanks for thinking about it (nevertheless do not spend much time, I can show it by manipulating indices, I was simply wondering if it can be deduced from some property I don't remember)

Gustavo Bandeira

3:08 AM

I'm trying to do this:
i = RandomInteger[{1, 12}]
If[(p = RandomInteger[{1, 12}]) == i, p, RandomInteger[{1, 12}]]

i generates a random integer, and the function above will generate another integer that must be differente, I want to build a function that will try to re-evaluate it again, in the case of it being equal to i.

J. M.

3:22 AM

@GustavoBandeira Why not use RandomInteger[{1, 12}, 2]? In the off chance that the result has two identical integers, evaluate again.

Gustavo Bandeira

@J.M. Is there a way to re-evaluate one line if I have 2 equal integers?

I'm trying to make a function to generate random chords - the same note can never be repeated again.

R.M

f[] := f[RandomInteger[{1, 12}, 2]]
f[{a_, b_}] := a
f[{a_, a_}] := f[]

Is that simple to follow?

Gustavo Bandeira

@R.M Yes, but there's a chance of this outputing two equal integers, right?

R.M

Well, I'm not really sure what you want to do... :D

How many notes do you need at a time for the chord?

Gustavo Bandeira

@R.M I want to create a function that will generate 2 integers, say, x and y. If x=y, then it will re-evaluate itself again.

R.M

3:35 AM

@GustavoBandeira Well, then just change the second definition in my function above to {a, b}

That's all the change you need.

You'll never get two integers that are the same.

Even simpler would be: RandomSample[Range@12, 2]

Gustavo Bandeira

a = Table[RandomInteger[{1, 12}, 2], {x, 1, 100}];
DeleteDuplicates[
Table[If[a[[x]][[1]] == a[[x]][[2]], {True, x}], {x, 1, Length[a]}]]

It's possible to get repeated integers.

(I used to do this kind of thing with While - It's so much easier to do with tables!)

@R.M Yes, this is the right function!

I could also use the code I generated above to do that, by excluding the "true" ones. =D

Brett Champion

3:54 AM

@GustavoBandeira Use RandomSample[Range[12], 2] which is guaranteed to give you two unique elements from the set.

R.M

4:17 AM

@acl are you certain that they're dependent on $n$ and just trying to prove it or are you trying to find out if they're dependent?

Gustavo Bandeira

3:31 PM

I did a progress bar:
`ProgressIndicator[Dynamic[g], {1, 10001}, ImageSize -> {600, 50}]`

How can I put a percentage on it? I want it to be: [____________50%____________]

F'x

3:47 PM

@GustavoBandeira I would say use an Overlay, but it doesn't work

Overlay[{ProgressIndicator[Dynamic[g], {1, 10001},
   ImageSize -> {600, 50}]},
 Style["50%", 14, Bold], Alignment -> {Center, Center}]

Gustavo Bandeira

@F'x Do you know any other alternative?

F'x

no, wait, I matched my braces wrong

This works:

Overlay[{ProgressIndicator[Dynamic[g], {1, 10001},
   ImageSize -> {600, 30}, BaselinePosition -> Baseline],
  Style[Dynamic[ToString[Round[100*g/10001]] <> "%"], 16, Bold]},
 Alignment -> {Center, Center}]

It's actually pretty cool :)

anyway, gotta go, I hope this helps

please leave me a comment if you find a problem with it (or ask it as a question on the site itself)

see you

Gustavo Bandeira

@F'x Thanks for the help.

Verde

7:29 PM

@GustavoBandeira See my comment at your Range@13 question

Not sure if you are calculating it the hard way for another reason, though

R.M

7:43 PM

¡Hola!

Verde

7:53 PM

@R.M olas!

@R.M You here?

Oleksandr R.

@J.M. way tubular!

@Verde beat me to it there. :) Also: oeis.org/A003418

@Verde if so then compilation gives a reasonable boost (~25×)

Verde

8:10 PM

@OleksandrR. Yeah, but I don't really know if his intention is to calculate the LCM, or if it is a toy problem for understanding something else. That's why I didn't post an answer

Oleksandr R.

Of course, the algorithm runs in exponential time, so compilation doesn't really buy you much for very long...

Verde

@OleksandrR. I think one could design a better algorithm tuned for the Range@x case

Verde

8:49 PM

@OleksandrR. Exp@Total@MangoldtLambda@Range@13

Oleksandr R.

@Verde that's a good one! MangoldtLambda is new to me...

Verde

@OleksandrR. wolframalpha.com/input/?i=chebyshev+functions

I don't believe timmings are much better than those of LCM

In fact they are worse :(

Oleksandr R.

Well, it's still a nice identity. Number theory isn't my strong suit, that's for sure.

Verde

Srinivasa Ramanujan

Srinivasa Ramanujan FRS () (22 December 1887 – 26 April 1920) was an Indian mathematician and autodidact who, with almost no formal training in pure mathematics, made extraordinary contributions to mathematical analysis, number theory, infinite series, and continued fractions. Living in India with no access to the larger mathematical community, which was centered in Europe at the time, Ramanujan developed his own mathematical research in isolation. As a result, he sometimes rediscovered known theorems in addition to producing new work. Ramanujan was said to be a natural genius by t...

Gustavo Bandeira

9:22 PM

@Verde I've read his history.

Some days ago.

I wish I had such achievements.

@Verde Yep,I've seen.

Verde

OK!

@GustavoBandeira Ramanujan was one of a kind.

Gustavo Bandeira

Caps means you're screaming!

Yep.

I'm going to take a nap.

Cya.

Verde

bye!

Oleksandr R.

9:47 PM

Word to the wise... FindFit/NonlinearModelFit/(probably the other fitting functions too) have a parameter localization bug. Parameters of the form f[g, x] are localized correctly, but those like f[g[x]] aren't. I found this quite obscure.

Most bizarrely of all, the bug does not manifest if you use the (undocumented) Method -> "PrincipalAxis" option.

Verde

@OleksandrR. Thanks! Comment flagged as Too Localized :)

Oleksandr R.

@Verde that's precisely the reason I haven't asked any questions so far... everything I find difficulties with is waaay too localized.

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