Re: sine and modulus ?

On Mon, 20 Oct 2008 15:23:07 EDT, amy666 <tommy1729@xxxxxxxxxxx>
wrote:

quasi :

On Sun, 19 Oct 2008 15:54:30 EDT, amy666
<tommy1729@xxxxxxxxxxx>
wrote:

quasi wrote :

On Sun, 19 Oct 2008 07:17:44 EDT, amy666
<tommy1729@xxxxxxxxxxx>
wrote:

im thinking about a sine defined for modulus
algebra.

Sounds like fun.

sin(a) mod p = b mod p

cos(a) mod p = c mod p

b^2 + c^2 = 1 mod p

where the sine and cosine can be computed by
their
taylor series expanded at 0 and mod p.

But regardless of the modulus, the coefficients of
the
Taylor series are eventually all undefined
(division by 0).

huh ?

mod p is chosen such that all elements have
multiplicative inverses ...

All _nonzero_ elements have multiplicative inverses.

What is the Taylor series for sin(x)? (over the
reals)

Now try it (mod 2). Next try (mod 3).

Do you see a problem?

x - x^3/3! + x^5/5! - ...

computing divisions and powers is no problem in modulus.

So let's see you compute sin(1) (mod p) for a few selected values of
p, for example, p = 2 and p = 3.

Don't worry about limits -- just compute the first few terms.

quasi
.

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