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author | dos-reis <gdr@axiomatics.org> | 2007-08-14 05:14:52 +0000 |
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committer | dos-reis <gdr@axiomatics.org> | 2007-08-14 05:14:52 +0000 |
commit | ab8cc85adde879fb963c94d15675783f2cf4b183 (patch) | |
tree | c202482327f474583b750b2c45dedfc4e4312b1d /src/hyper/pages/BINARY.ht | |
download | open-axiom-ab8cc85adde879fb963c94d15675783f2cf4b183.tar.gz |
Initial population.
Diffstat (limited to 'src/hyper/pages/BINARY.ht')
-rw-r--r-- | src/hyper/pages/BINARY.ht | 56 |
1 files changed, 56 insertions, 0 deletions
diff --git a/src/hyper/pages/BINARY.ht b/src/hyper/pages/BINARY.ht new file mode 100644 index 00000000..e43dce27 --- /dev/null +++ b/src/hyper/pages/BINARY.ht @@ -0,0 +1,56 @@ +% Copyright The Numerical Algorithms Group Limited 1992-94. All rights reserved. +% !! DO NOT MODIFY THIS FILE BY HAND !! Created by ht.awk. +\newcommand{\BinaryExpansionXmpTitle}{BinaryExpansion} +\newcommand{\BinaryExpansionXmpNumber}{9.4} +% +% ===================================================================== +\begin{page}{BinaryExpansionXmpPage}{9.4 BinaryExpansion} +% ===================================================================== +\beginscroll + +All rational numbers have repeating binary expansions. +Operations to access the individual bits of a binary expansion can +be obtained by converting the value to \spadtype{RadixExpansion(2)}. +More examples of expansions are available in +\downlink{`DecimalExpansion'}{DecimalExpansionXmpPage}\ignore{DecimalExpansion}, +\downlink{`HexadecimalExpansion'}{HexadecimalExpansionXmpPage}\ignore{HexadecimalExpansion}, and +\downlink{`RadixExpansion'}{RadixExpansionXmpPage}\ignore{RadixExpansion}. + +\xtc{ +The expansion (of type \spadtype{BinaryExpansion}) of a rational number +is returned by the \spadfunFrom{binary}{BinaryExpansion} operation. +}{ +\spadpaste{r := binary(22/7) \bound{r}} +} +\xtc{ +Arithmetic is exact. +}{ +\spadpaste{r + binary(6/7) \free{r}} +} +\xtc{ +The period of the expansion can be short or long \ldots +}{ +\spadpaste{[binary(1/i) for i in 102..106] } +} +\xtc{ +or very long. +}{ +\spadpaste{binary(1/1007) } +} +\xtc{ +These numbers are bona fide algebraic objects. +}{ +\spadpaste{p := binary(1/4)*x**2 + binary(2/3)*x + binary(4/9) \bound{p}} +} +\xtc{ +}{ +\spadpaste{q := D(p, x) \free{p}\bound{q}} +} +\xtc{ +}{ +\spadpaste{g := gcd(p, q) \free{p q}\bound{g}} +} +\endscroll +\autobuttons +\end{page} +% |