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#11751 2013-07-13 05:17:57

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 84,597

Re: Linear Interpolation FP1 Formula

Is it possible you are using the wrong poles? That might make the answer change sign.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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#11752 2013-07-13 05:24:05

zetafunc.
Guest

Re: Linear Interpolation FP1 Formula

I don't think so... type this into Wolfram Alpha:

"residues of the function sqrt(z)/(1+z^3)"

It gives i/3, i/3 and -i/3, the sum of which is i/3.

2iπ(i/3) = -2π/3... but I don't know why.....

#11753 2013-07-13 05:33:31

zetafunc.
Guest

Re: Linear Interpolation FP1 Formula

Never mind, I figured it out. It's not me that's wrong, it's Wolfram. The arguments of the poles should all be positive, but for some reason Mathematica doesn't do that.

#11754 2013-07-13 05:36:36

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 84,597

Re: Linear Interpolation FP1 Formula

Those are the correct residues.

I have a worked example using a keyhole contour. It is slightly different than your problem but it might help to clear up what you are doing wrong.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

Offline

#11755 2013-07-13 05:38:19

zetafunc.
Guest

Re: Linear Interpolation FP1 Formula

I think those residues I gave are wrong. If you use positive arguments/angles for the poles (i.e. 5pi/6 instead of -pi/3) you will get the correct residue. The reason for this discrepancy is that Mathematica defines the negative real axis as the branch cut, when it is actually the positive axis.

#11756 2013-07-13 05:53:54

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 84,597

Re: Linear Interpolation FP1 Formula

Okay, glad it worked out.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

Offline

#11757 2013-07-13 05:54:36

zetafunc.
Guest

Re: Linear Interpolation FP1 Formula

The lesson here is that you should never be 100% certain about a CAS's answer... right?

#11758 2013-07-13 05:57:11

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 84,597

Re: Linear Interpolation FP1 Formula

The way I understand it and not too well at that is that M has to make a decision about the branch cuts from a number of choices. They set it up to pick the most useful one. But that may not always be the one you want.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

Offline

#11759 2013-07-13 06:23:10

zetafunc.
Guest

Re: Linear Interpolation FP1 Formula

So it is clearly best to compute the residues for these types of problems by hand, then.

#11760 2013-07-13 06:32:13

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 84,597

Re: Linear Interpolation FP1 Formula

When possible, you should always be checking their results...

For simple poles the residues will not be difficult.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

Offline

#11761 2013-07-13 06:35:12

zetafunc.
Guest

Re: Linear Interpolation FP1 Formula

What I mean is that it is probably best not to tell a CAS to find the residues of f(z). Instead, input the calculation for the residues, so there is no ambiguity. (Or at least, far less.)

#11762 2013-07-13 06:38:37

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 84,597

Re: Linear Interpolation FP1 Formula

That is how I get mine.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

Offline

#11763 2013-07-13 21:41:40

zetafunc.
Guest

Re: Linear Interpolation FP1 Formula

So what did you need help understanding in my keyhole contour of that problem? I did skip over some steps, I can explain them if it would help.

#11764 2013-07-13 21:46:59

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 84,597

Re: Linear Interpolation FP1 Formula

Hi;

Anything that you would like to add to the original post would be fine for me as well as anyone else.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

Offline

#11765 2013-07-14 00:21:35

zetafunc.
Guest

Re: Linear Interpolation FP1 Formula

I cannot edit posts but I can post it again. What should be added?

#11766 2013-07-14 04:25:07

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 84,597

Re: Linear Interpolation FP1 Formula

HI;

you do not see this at the bottom of your posts?

View Image: 2013-07-14_091949.gif

In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

Offline

#11767 2013-07-14 04:57:50

zetafunc.
Guest

Re: Linear Interpolation FP1 Formula

No, I only see the Quote button.

#11768 2013-07-14 04:59:50

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 84,597

Re: Linear Interpolation FP1 Formula

Do you see my avatar?


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

Offline

#11769 2013-07-14 05:03:43

zetafunc.
Guest

Re: Linear Interpolation FP1 Formula

Yes.

#11770 2013-07-14 05:09:36

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 84,597

Re: Linear Interpolation FP1 Formula

I see, it is because you are a guest.

For the keyhole contour you do not have to add anything. It is fine. But if you want to post more about it you can of course.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

Offline

#11771 2013-07-14 06:04:28

zetafunc.
Guest

Re: Linear Interpolation FP1 Formula

I think there might be some keyhole contour problems in the Schaum's book. There is definitely an example in there that uses exactly the same method that I used in that post.

#11772 2013-07-14 08:49:39

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 84,597

Re: Linear Interpolation FP1 Formula

Sorry, I was having back problems and had to get on the floor for a couple of hours.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

Offline

#11773 2013-07-15 11:41:01

zetafunc.
Guest

Re: Linear Interpolation FP1 Formula

What happened?

#11774 2013-07-15 14:37:33

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 84,597

Re: Linear Interpolation FP1 Formula

Nothing yet, I feel pretty bad but I am hungry so I have to get up and sit like a human being.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

Offline

#11775 2013-07-16 02:11:41

zetafunc.
Guest

Re: Linear Interpolation FP1 Formula

You were on the floor for hours? That sounds pretty serious.

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