Reciprocal Sextic

[R.D. Silverman]

Would someone with access to a CA package please find
the coefficients of the reciprocal sextic for 2,1694M?

The 2^1694M/2^242M is

2^726 - 2^666 + 2^605 - 2^484 + 2^424 - 2^363 + 2^303 - 2^242 +
2^121 - 2^61 + 1

This should be expressible as a sextic polynomial in (2x + 1/x) with x = 2^61.

Doing it by hand is a mess.

[fivemack]

Don't you mean x=2^60 here?

% gp
a = factor(2^14*x^28+1)[3,1]
u = 2*x + 1/x
(x^6 * (u^6-2*u^5-10*u^4+20*u^3+16*u^2-32*u+8)) - a

so I reckon the sextic is
u^6-2*u^5-10*u^4+20*u^3+16*u^2-32*u+8

with u = 2x+1/x, x=2^60

Tom

[R. Gerbicz]

Originally Posted by fivemack

Don't you mean x=2^60 here?

so I reckon the sextic is
u^6-2*u^5-10*u^4+20*u^3+16*u^2-32*u+8

with u = 2x+1/x, x=2^60

Tom

You're right. I've checked your polynom, it's good with u=2x+1/x, x=2^60.

[fivemack]

Originally Posted by R.D. Silverman

Would someone with access to a CA package please find
the coefficients of the reciprocal sextic for 2,1694M?

For calculations that take less than 20 seconds, magma, which is the superpower of number-theoretical computer algebra packages, is available at http://magma.maths.usyd.edu.au/calc/

[R.D. Silverman]

Originally Posted by fivemack

For calculations that take less than 20 seconds, magma, which is the superpower of number-theoretical computer algebra packages, is available at http://magma.maths.usyd.edu.au/calc/

I am not allowed to download any software over the net owing to
security considerations.

[Wacky]

Originally Posted by R.D. Silverman

I am not allowed to download any software over the net owing to security considerations.

Bob,

AFAICT, this is a website address that allows you to run a "simple" magma calculation on THEIR server and returns the result to you.

Nothing is "downloaded". It is a simple submit/response system.

[R.D. Silverman]

Originally Posted by Wacky

Bob,

AFAICT, this is a website address that allows you to run a "simple" magma calculation on THEIR server and returns the result to you.

Nothing is "downloaded". It is a simple submit/response system.

Thanks for the heads up.

[xilman]

Originally Posted by R.D. Silverman

Thanks for the heads up.

Originally Posted by A very handsome gentleman

re: bob's post about getting some weird thing done but he cannot download programs at work, and that he doesn't want to do it by hand because it is too messy:

Wouldn't it be more satisfying to write the program yourself? If we make things too easy then there is no sense of accomplishment.



or something to that effect

who takes the challenge?

OK, I'm game.



Paul

[R.D. Silverman]

Originally Posted by xilman

OK, I'm game.



re: bob's post about getting some weird thing done but he cannot download programs at work, and that he doesn't want to do it by hand because it is too messy:

Wouldn't it be more satisfying to write the program yourself? If we make things too easy then there is no sense of accomplishment.


Paul

I already know how to solve the problem. I know how to write the code.
Writing such code would not give me a sense of accomplishment. I
would learn nothing in the process.

It is an easy, but *tedious* exercize in junior high school algebra.
I just don't have the time to write such a program. My time is better
spent on developing new ideas.

I don't ask others to solve any of my problems unless I already know how
to do it myself.