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+% Copyright The Numerical Algorithms Group Limited 1992-94. All rights reserved.
+% !! DO NOT MODIFY THIS FILE BY HAND !! Created by ht.awk.
+\newcommand{\RadixExpansionXmpTitle}{RadixExpansion}
+\newcommand{\RadixExpansionXmpNumber}{9.65}
+%
+% =====================================================================
+\begin{page}{RadixExpansionXmpPage}{9.65 RadixExpansion}
+% =====================================================================
+\beginscroll
+
+It possible to expand numbers in general bases.
+
+\labelSpace{2pc}
+\xtc{
+Here we expand \spad{111} in base \spad{5}.
+This means
+\texht{$10^2+10^1+10^0 = 4 \cdot 5^2+2 \cdot 5^1 + 5^0.$}{%
+\spad{10**2+10**1+10**0 = 4*5**2+2*5**1+5**0.}}
+}{
+\spadpaste{111::RadixExpansion(5)}
+}
+
+\xtc{
+You can expand fractions to form repeating expansions.
+}{
+\spadpaste{(5/24)::RadixExpansion(2)}
+}
+\xtc{
+}{
+\spadpaste{(5/24)::RadixExpansion(3)}
+}
+\xtc{
+}{
+\spadpaste{(5/24)::RadixExpansion(8)}
+}
+\xtc{
+}{
+\spadpaste{(5/24)::RadixExpansion(10)}
+}
+\xtc{
+For bases from 11 to 36 the letters A through Z are used.
+}{
+\spadpaste{(5/24)::RadixExpansion(12)}
+}
+\xtc{
+}{
+\spadpaste{(5/24)::RadixExpansion(16)}
+}
+\xtc{
+}{
+\spadpaste{(5/24)::RadixExpansion(36)}
+}
+\xtc{
+For bases greater than 36, the ragits are separated by blanks.
+}{
+\spadpaste{(5/24)::RadixExpansion(38)}
+}
+\xtc{
+The \spadtype{RadixExpansion} type provides operations to obtain the
+individual ragits.
+Here is a rational number in base \spad{8}.
+}{
+\spadpaste{a := (76543/210)::RadixExpansion(8) \bound{a}}
+}
+\xtc{
+The operation \spadfunFrom{wholeRagits}{RadixExpansion} returns a list of the
+ragits for the integral part of the number.
+}{
+\spadpaste{w := wholeRagits a \free{a}\bound{w}}
+}
+\xtc{
+The operations \spadfunFrom{prefixRagits}{RadixExpansion} and \spadfunFrom{cycleRagits}{RadixExpansion}
+return lists of the initial and repeating ragits in the
+fractional part of the number.
+}{
+\spadpaste{f0 := prefixRagits a \free{a}\bound{f0}}
+}
+\xtc{
+}{
+\spadpaste{f1 := cycleRagits a \free{a}\bound{f1}}
+}
+\xtc{
+You can construct any radix expansion by giving the
+whole, prefix and cycle parts.
+The declaration is necessary to let \Language{}
+know the base of the ragits.
+}{
+\spadpaste{u:RadixExpansion(8):=wholeRadix(w)+fractRadix(f0,f1) \free{w f0 f1}\bound{u}}
+}
+\xtc{
+If there is no repeating part, then the list \spad{[0]} should be used.
+}{
+\spadpaste{v: RadixExpansion(12) := fractRadix([1,2,3,11], [0]) \bound{v}}
+}
+\xtc{
+If you are not interested in the repeating nature of the expansion,
+an infinite stream of ragits can be obtained using
+\spadfunFrom{fractRagits}{RadixExpansion}.
+}{
+\spadpaste{fractRagits(u) \free{u}}
+}
+\xtc{
+Of course, it's possible to recover the fraction representation:
+}{
+\spadpaste{a :: Fraction(Integer) \free{a}}
+}
+
+\showBlurb{RadixExpansion}
+More examples of expansions are available in
+\downlink{`DecimalExpansion'}{DecimalExpansionXmpPage}\ignore{DecimalExpansion},
+\downlink{`BinaryExpansion'}{BinaryExpansionXmpPage}\ignore{BinaryExpansion}, and
+\downlink{`HexadecimalExpansion'}{HexadecimalExpansionXmpPage}\ignore{HexadecimalExpansion}.
+\endscroll
+\autobuttons
+\end{page}
+%