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% decimal.htex

All rationals have repeating decimal expansions.
Operations to access the individual digits of a decimal expansion can
be obtained by converting the value to \spadtype{RadixExpansion(10)}.
More examples of expansions are available in
\xmpref{BinaryExpansion},
\xmpref{HexadecimalExpansion}, and
\xmpref{RadixExpansion}.
\showBlurb{DecimalExpansion}

\xtc{
The operation \spadfunFrom{decimal}{DecimalExpansion} is used to create
this expansion of type \spadtype{DecimalExpansion}.
}{
\spadcommand{r := decimal(22/7) \bound{r}}
}
\xtc{
Arithmetic is exact.
}{
\spadcommand{r + decimal(6/7) \free{r}}
}
\xtc{
The period of the expansion can be short or long \ldots
}{
\spadcommand{[decimal(1/i) for i in 350..354] }
}
\xtc{
or very long.
}{
\spadcommand{decimal(1/2049) }
}
\xtc{
These numbers are bona fide algebraic objects.
}{
\spadcommand{p := decimal(1/4)*x^2 + decimal(2/3)*x + decimal(4/9)  \bound{p}}
}
\xtc{
}{
\spadcommand{q := differentiate(p, x) \free{p}\bound{q}}
}
\xtc{
}{
\spadcommand{g := gcd(p, q)            \free{p q} \bound{g}}
}
