Compute the multiplicative inverse of in

where .

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- April 5th 2013, 04:51 PMBernhardPolynomial Rings - Z5[X]/<p(x)>
Compute the multiplicative inverse of in

where . - April 5th 2013, 07:35 PMGusbobRe: Polynomial Rings - Z5[X]/<p(x)>
Because , we have . It is easy to see that , so is the inverse.

However, it is not always so easy to solve for inverses by inspection. The surefire way to do this is to use linear algebra, as I will demonstrate.

You want (we only go up to the second degree since )

Expanding the left hand side gives

So we want to find such that . Although it is obvious what the solution is in this case, I'll write down the general way to do it:

With respect to the basis , this is equivalent to solving the linear system

Which has solutions . Hence the inverse is , which is the same answer as we got from inspection. - April 6th 2013, 09:06 PMHowDoIMathRe: Polynomial Rings - Z5[X]/<p(x)>
How do you guys post equations so neatly?

By copying and pasting the original post, this is what I get:

"Compute the multiplicative inverse of a(x) = \overline{x^2 + x + 1} in \mathbb{Z}_5/<p(x)>

where p(x) = x^3 + x^2 + x + 1 = (x^2 + 1)(x +1) . " - April 7th 2013, 12:37 AMBernhardRe: Polynomial Rings - Z5[X]/<p(x)>
Hi HowDoIMath,

You need to use the Latex language for Maths expressions - see Latex Help and download the very helpful tutorials or help sheets.

Note that you need [TEX] and then the same with a / before the T around the math expressions to get Latex to work

Peter - April 7th 2013, 02:16 PMHowDoIMathRe: Polynomial Rings - Z5[X]/<p(x)>
Ok thanks