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Old 2007-01-12, 22:48   #1
roger
 
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Default Meaning and format of Phi, GF

I've been using Proth's program, and unfortunately do not understand the format of both GF(n, m) and Phi(an, m).

I know that F29 or whatever number in place of 29 is the nth Fermat, but not how GF(n, m) corresponds to an expression, eg F29 = 22[sup]29[/sup]+1.

For Phi, I know that it is an irregular decimal number, like pi, but not how it can be expressed either.

I tried looking for definitions of the two, but didn't get too much of the basics.

Thanks for your help, and sorry for my ignorance,

Roger
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Old 2007-01-14, 16:36   #2
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Quote:
Originally Posted by roger View Post

For Phi, I know that it is an irregular decimal number, like pi, but not how it can be expressed either.

I tried looking for definitions of the two, but didn't get too much of the basics.

Roger
The natural golden mean constant is known as Phi.

It can be expressed as (1 + sq.rt. 5) /2 = 1.618033989.....

Mally
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Old 2007-01-15, 03:53   #3
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I think GF(n,m) = n^(2^m)+1, so GF(2,m) = Fm.
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Old 2007-01-15, 06:06   #4
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I think Phi here refers to Cylotomic Polynomials
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Old 2007-01-15, 17:12   #5
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Quote:
Originally Posted by axn1 View Post
I think Phi here refers to Cylotomic Polynomials


Quote:
Originally Posted by Roger
For Phi, I know that it is an irregular decimal number, like pi, but not how it can be expressed either.
Mally
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Old 2007-01-17, 23:36   #6
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Quote:
Originally Posted by axn1 View Post
I think Phi here refers to Cylotomic Polynomials
But where does the abbreviation "Phi" come from?
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Old 2007-01-18, 12:12   #7
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Quote:
Originally Posted by Unregistered View Post
But where does the abbreviation "Phi" come from?
It is not an abbreviation, it is a Greek letter.
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Old 2007-01-18, 12:29   #8
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"cyclotomic" means "circle cutting", because the complex roots of x^n-1 cut the unit circle into regular sections, and the divisors of x^n-1 are the cyclotomic polynomials Φk(x) with k|n. The Greek letter Φ (Phi) looks like a circle with a line cutting it into two pieces, so I suppose that's why this letter was chosen for cyclotomic polynomials. (Specifically, the line going through the two primitive roots i, -i of x^4-1 cuts the unit circle vertically in the complex plane, so that would look just like the Φ)

Alex

Last fiddled with by akruppa on 2007-01-19 at 12:44 Reason: the *primitive* roots don't cut into *regular* sections
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Old 2007-01-20, 15:46   #9
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Quote:
Originally Posted by rogue View Post
It is not an abbreviation, it is a Greek letter.

Yes its a letter of the Greek alphabet. It was suggested in the early days of the last century that the Greek letter phi- the initial letter of Phidias's name should be adopted to designate the golden ratio. The ubiquity of phi in mathematics aroused the interest of many math'cians in the Middle ages and during the Renaissance. So first and foremost it denotes the golden ratio = (sq.rt.5 +1)/2 =1.618033989.....though it is also used in other calculations as the one cited above/below.

Mally
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Old 2007-01-21, 06:33   #10
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Originally Posted by mfgoode View Post

Yes its a letter of the Greek alphabet. It was suggested in the early days of the last century that the Greek letter phi- the initial letter of Phidias's name should be adopted to designate the golden ratio.

Mally

For more on this Greek Character refer to

http://en.wikipedia.org/wiki/Phidias

Mally
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