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 ricsi046 April 12th, 2014 12:27 AM

Multiplicative inverse in factor ring?

Hello,
can someone tell me how to find the multiplicative inverse of an element in a factor ring?
Let the element be f and the factor ring T[x]/(m).
The basic idea is to solve a diophantine equation like f*u-m*v=1,right?and we need to find u

 Olinguito April 12th, 2014 04:03 AM

You have the right idea – except that an element of \$T[x]/(m)\$ is of the form \$f+(m)\$ where \$f\$ is a polynomial of degree at most \$\deg(m)-1\$. When you have found a polynomial \$u\$ such that \$fu=1+mv\$ for some polynomial \$v\$, the multiplicative inverse of \$f+(m)\$ will be \$u+(m)\$.

 ricsi046 April 12th, 2014 04:05 AM

i see,thanks

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