I don't follow... how will curve fitting help you factorise a^6 + 8b^6 for example?

bobbym

2012-07-03 07:08:39

Hi;

If you know the form you want you can curve fit.

zetafunc.

2012-07-03 06:36:46

What is that method?

bobbym

2012-07-03 06:34:57

There is a general method for all types of problems like this one.

zetafunc.

2012-07-03 05:57:59

I read the Wolfram article again and looked at (21), (22) and (23), I can see where you got the factors from now. So cyclotomic polynomials cannot be used for this particular problem because of the two variables?

bobbym

2012-07-03 05:54:46

Hi;

It may not be generated from them. I do not know how to do one with two variables.

zetafunc.

2012-07-03 05:53:12

But how is the Sophie Germain identity generated from cyclotomic polynomials? I can sort of see where you are getting your x^18 - 1 from (the factors are all cyclotomic polynomials) but how do I then get that into a useful form, such as your a^6 + 8b^6 example?

bobbym

2012-07-03 05:46:32

Me neither but you try to get yours into one of the forms.

zetafunc.

2012-07-03 05:41:59

I am able to generate them, but I'm not sure how I can use them here?

bobbym

2012-07-03 05:41:18

Hi anonimnystefy;

Firstly I did it on a TI-92.

Hi zetafunc.;

You can use that table to generate lots of them.

zetafunc.

2012-07-03 05:22:59

Looks like the absence of the comma is indicating that it's not restricted to the primitive roots of unity. Not sure how they differ to ordinary roots of unity, so will check the other article out.

anonimnystefy

2012-07-03 05:21:21

What did you develop the software in?

zetafunc.

2012-07-03 05:20:44

Never mind, I understand it now! Was just confused what to do for the value of n in my roots of unity, then just realised you're using it in (1).

zetafunc.

2012-07-03 05:17:39

The very first line (1), what does the apostrophe/comma on top of the product symbol mean? Is that an error or does it mean something different?

bobbym

2012-07-03 05:07:57

Hi anonimnystefy;

Did not see your post, sorry. Long ago I developed the software to do these things. Sorry, I forgot most of it.