this is for holding javascript data
Massimiliano Sala edited bits2.tex
over 7 years ago
Commit id: 080b25568f7161b818c5f9c003997d66ce026701
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In order to complete our study on polynomial operations, we have
to define one more operation: \emph{the division of polynomials}.
\\
Thanks to a theoretical algebraic property A consequence of
polynomial, we know that, if more advanced theory for polynomials with coefficients in a field is the
following. If we consider two polynomials
$f(x), g(x)$, $f(x)$ and $g(x)$ in $\Fb[x]$,
we can find two other polynomials, say $q(x), r(x)$, such that $f(x)=g(x)\cdot q(x) +r(x)$ and $\deg(r(x))< \deg(g(x))$. \\
The polynomial $q(x)$ is called \emph{quotient}, whereas $r(x)$ is the
remainder. \textbf{remainder}. If $r(x)=0$ then we say that $g(x)$ \emph{divides} $f(x)$, or that
we have performed an \emph{exact division} between $f(x)$ and $g(x)$.\\
This is a general property and, in particular, it holds for polynomials in bits.
\begin{Example}\label{QuotRem}